This script contains the analyses conducted on data related to participants who took part in our study “Toward a Social Rubber Hand”.
First, we load packages we need for analyses #PACKAGES
library (tidyverse) #for data handling## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
## ✔ ggplot2 3.4.0 ✔ purrr 0.3.5
## ✔ tibble 3.1.8 ✔ dplyr 1.0.10
## ✔ tidyr 1.2.1 ✔ stringr 1.4.1
## ✔ readr 2.1.3 ✔ forcats 0.5.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()library(readxl) #to read excel files
library(writexl) #to export data as excel file ## Warning: il pacchetto 'writexl' è stato creato con R versione 4.2.3library(lme4) ## Caricamento del pacchetto richiesto: Matrix
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## Caricamento pacchetto: 'Matrix'
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## I seguenti oggetti sono mascherati da 'package:tidyr':
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## expand, pack, unpacklibrary(lmerTest)##
## Caricamento pacchetto: 'lmerTest'
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## Il seguente oggetto è mascherato da 'package:lme4':
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## lmer
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## Il seguente oggetto è mascherato da 'package:stats':
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## steplibrary(emmeans) ## Welcome to emmeans.
## Caution: You lose important information if you filter this package's results.
## See '? untidy'library(ggplot2)Then, we proceed with by importing the row data matrix
#import file
SRHI <- read_excel("LMM_Matrix.xlsx") #import file
#SRH_TraitQuestionnaires <- SRH_TraitQuestionnaires[-1,]
SRHI## # A tibble: 2,340 × 37
## Block Session Subject VisuoSp…¹ RTNoO…² Basel…³ Drift1 Drift2 Owner…⁴ Locat…⁵
## <chr> <dbl> <dbl> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 A 2 1 cong 219 17.8 17.6 18.7 -3 -3
## 2 A 2 1 cong 246 17.8 17.6 18.7 -3 -3
## 3 A 2 1 cong 253 17.8 17.6 18.7 -3 -3
## 4 A 2 1 cong 254 17.8 17.6 18.7 -3 -3
## 5 A 2 1 cong 267 17.8 17.6 18.7 -3 -3
## 6 A 2 1 cong 279 17.8 17.6 18.7 -3 -3
## 7 A 2 1 cong 279 17.8 17.6 18.7 -3 -3
## 8 A 2 1 cong 297 17.8 17.6 18.7 -3 -3
## 9 A 2 1 cong 298 17.8 17.6 18.7 -3 -3
## 10 A 2 1 cong 300 17.8 17.6 18.7 -3 -3
## # … with 2,330 more rows, 27 more variables: HandLoss <dbl>, RT1_I <dbl>,
## # RT2_F <dbl>, RT3_P <dbl>, DT1_I <dbl>, DT2_F <dbl>, DT3_P <dbl>,
## # SI_1 <dbl>, SI_2 <dbl>, SI_3 <dbl>, Noticing <dbl>, NotDistracting <dbl>,
## # NotWorrying <dbl>, AttentionRegulation <dbl>, EmotionalAwareness <dbl>,
## # SelfRegulation <dbl>, BodyListening <dbl>, Trusting <dbl>,
## # PerspectiveTaking <dbl>, Fantasy <dbl>, EmpaticConcern <dbl>,
## # PersonalDistress <dbl>, Means_STQ <dbl>, TouchComfortability <dbl>, …Then we declare our factors, that are: the Subject number, the Session order (if participants performed first the a/synchronous block), the block (a/synchronous) and the VisuoSpatialCongruency (in/congruent).
factor_decl = c("Subject", "Session", "Block","VisuoSpatialCongruency")
SRHI[factor_decl] <- lapply(SRHI[factor_decl], factor) #LMM We first test the effect of “Block” (stroking type, Synchronous or Asynchronous) and “VisuoSpatialCongruency” (visuo-tactile Congruence or Incongruence) on pre-processed Reaction Times “RTNoOutlier”, considering “Subject” as random effect.
#LMM
lmm_model <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
#verifysingularity
isSingular(lmm_model)## [1] FALSE#lookattheresult
summary(lmm_model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## RTNoOutlier ~ Block * VisuoSpatialCongruency + (1 + Block * VisuoSpatialCongruency |
## Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28753
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0684 -0.5747 -0.1239 0.3773 5.9497
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8691 93.22
## BlockS 1939 44.03 0.01
## VisuoSpatialCongruencyinc 3298 57.43 0.10 -0.45
## BlockS:VisuoSpatialCongruencyinc 2101 45.84 -0.27 0.36 -0.55
## Residual 11569 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 322.741 16.790 31.952 19.222 < 2e-16
## BlockS 9.770 9.783 31.901 0.999 0.325
## VisuoSpatialCongruencyinc 123.264 11.890 32.860 10.367 6.85e-12
## BlockS:VisuoSpatialCongruencyinc -12.761 12.033 33.426 -1.060 0.297
##
## (Intercept) ***
## BlockS
## VisuoSpatialCongruencyinc ***
## BlockS:VisuoSpatialCongruencyinc
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC
## BlockS -0.109
## VsSptlCngrn -0.008 -0.138
## BlckS:VsSpC -0.078 -0.129 -0.596Since the model is not singular, we continue to explore the data through post-hoc comparisons.
# Means of Block e VisuoSpatialCongruency
emmeans_interaction <- emmeans(lmm_model, ~ Block * VisuoSpatialCongruency)
emmeans_block <- emmeans(lmm_model, ~ Block)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo <- emmeans(lmm_model, ~ VisuoSpatialCongruency)## NOTE: Results may be misleading due to involvement in interactions# Post hoc comparisons
posthoc_block <- contrast(emmeans_block, adjust = "bonferroni")
posthoc_visuo <- contrast(emmeans_visuo, adjust = "bonferroni")
posthoc_interaction <- pairs(emmeans_interaction, adjust = "bonferroni")
#post hoc summary
summary(posthoc_block)## contrast estimate SE df t.ratio p.value
## A effect -1.69 5.4 32 -0.314 1.0000
## S effect 1.69 5.4 32 0.314 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo)## contrast estimate SE df t.ratio p.value
## cong effect -58.4 4.81 32 -12.158 <.0001
## inc effect 58.4 4.81 32 12.158 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_interaction)## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.77 9.78 32.0 -0.999 1.0000
## A cong - A inc -123.26 11.90 31.9 -10.361 <.0001
## A cong - S inc -120.27 12.21 32.0 -9.851 <.0001
## S cong - A inc -113.49 16.41 32.0 -6.915 <.0001
## S cong - S inc -110.50 10.76 31.9 -10.267 <.0001
## A inc - S inc 2.99 14.50 31.9 0.206 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 tests#STQ The social touch questionnaire (STQ; Wilhelm et al., 2001) comprises 20 items. Participants were asked to ‘Indicate to what extent each of the following statements is characteristic or true for you’ on a 0–4 scale (0=not at all, 1=slightly, 2=moderately, 3=very, 4=extremely).
Items were chosen to provide a broad sample of affects and attitudes towards social touch. The scoring were preprocessed in a different script. Here we considered the mean scores as covariate for our LMM.
#LMM + STQ covariate
lmm_model_STQ <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * Means_STQ + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
#verifysingularity
isSingular(lmm_model_STQ)## [1] FALSE#summary
summary(lmm_model_STQ)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * Means_STQ + (1 +
## Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28721
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0788 -0.5756 -0.1252 0.3865 5.9393
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8950 94.60
## BlockS 2009 44.83 0.01
## VisuoSpatialCongruencyinc 3375 58.10 0.11 -0.46
## BlockS:VisuoSpatialCongruencyinc 2224 47.16 -0.26 0.34 -0.54
## Residual 11570 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 302.838 56.622 30.986 5.348
## BlockS 27.662 32.944 31.146 0.840
## VisuoSpatialCongruencyinc 148.489 39.713 31.427 3.739
## Means_STQ 10.355 28.126 30.965 0.368
## BlockS:VisuoSpatialCongruencyinc -27.745 40.364 32.017 -0.687
## BlockS:Means_STQ -9.320 16.374 31.207 -0.569
## VisuoSpatialCongruencyinc:Means_STQ -13.118 19.700 31.251 -0.666
## BlockS:VisuoSpatialCongruencyinc:Means_STQ 7.799 20.066 32.056 0.389
## Pr(>|t|)
## (Intercept) 7.92e-06 ***
## BlockS 0.407481
## VisuoSpatialCongruencyinc 0.000739 ***
## Means_STQ 0.715245
## BlockS:VisuoSpatialCongruencyinc 0.496796
## BlockS:Means_STQ 0.573320
## VisuoSpatialCongruencyinc:Means_STQ 0.510379
## BlockS:VisuoSpatialCongruencyinc:Means_STQ 0.700097
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC Mn_STQ BlS:VSC BS:M_S VSC:M_
## BlockS -0.104
## VsSptlCngrn -0.002 -0.150
## Means_STQ -0.954 0.099 0.002
## BlckS:VsSpC -0.082 -0.126 -0.590 0.078
## BlckS:M_STQ 0.099 -0.954 0.143 -0.104 0.121
## VsSpC:M_STQ 0.002 0.143 -0.953 -0.001 0.561 -0.151
## BS:VSC:M_ST 0.078 0.121 0.560 -0.082 -0.953 -0.127 -0.587Since the model is not singular, we can continue to explore the data through post-hoc comparisons.
# Means of Block e VisuoSpatialCongruency
emmeans_interaction_STQ <- emmeans(lmm_model_STQ, ~ Block * VisuoSpatialCongruency| Means_STQ)
emmeans_block_STQ <- emmeans(lmm_model_STQ, ~ Block| Means_STQ)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_STQ <- emmeans(lmm_model_STQ, ~ VisuoSpatialCongruency| Means_STQ)## NOTE: Results may be misleading due to involvement in interactionsemmeans_interaction2_STQ <- emmeans(lmm_model_STQ, ~ Block * Means_STQ| VisuoSpatialCongruency)
emmeans_interaction3_STQ <- emmeans(lmm_model_STQ, ~ VisuoSpatialCongruency * Means_STQ| Block)
# Post hoc comparisons
posthoc_block_STQ <- contrast(emmeans_block_STQ, adjust = "bonferroni")
posthoc_visuo_STQ <- contrast(emmeans_visuo_STQ, adjust = "bonferroni")
posthoc_interaction_STQ <- pairs(emmeans_interaction_STQ, adjust = "bonferroni")
posthoc_interaction2_STQ <- pairs(emmeans_interaction2_STQ, adjust = "bonferroni")
posthoc_interaction3_STQ <- pairs(emmeans_interaction3_STQ, adjust = "bonferroni")
#post hoc summary
summary(posthoc_block_STQ)## Means_STQ = 1.92:
## contrast estimate SE df t.ratio p.value
## A effect -1.7 5.48 31 -0.309 1.0000
## S effect 1.7 5.48 31 0.309 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_STQ)## Means_STQ = 1.92:
## contrast estimate SE df t.ratio p.value
## cong effect -58.5 4.86 31 -12.039 <.0001
## inc effect 58.5 4.86 31 12.039 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_interaction_STQ)## Means_STQ = 1.92:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.78 9.89 31.0 -0.989 1.0000
## A cong - A inc -123.32 12.00 30.9 -10.280 <.0001
## A cong - S inc -120.32 12.31 31.0 -9.776 <.0001
## S cong - A inc -113.54 16.66 31.0 -6.816 <.0001
## S cong - S inc -110.54 10.92 31.0 -10.126 <.0001
## A inc - S inc 3.00 14.72 30.9 0.204 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction2_STQ)## VisuoSpatialCongruency = cong:
## contrast estimate SE df
## A Means_STQ1.91865384615385 - S Means_STQ1.91865384615385 -9.78 9.89 31.0
## t.ratio p.value
## -0.989 0.3305
##
## VisuoSpatialCongruency = inc:
## contrast estimate SE df
## A Means_STQ1.91865384615385 - S Means_STQ1.91865384615385 3.00 14.72 30.9
## t.ratio p.value
## 0.204 0.8398
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction3_STQ)## Block = A:
## contrast estimate SE
## cong Means_STQ1.91865384615385 - inc Means_STQ1.91865384615385 -123 12.0
## df t.ratio p.value
## 30.9 -10.280 <.0001
##
## Block = S:
## contrast estimate SE
## cong Means_STQ1.91865384615385 - inc Means_STQ1.91865384615385 -111 10.9
## df t.ratio p.value
## 31.0 -10.126 <.0001
##
## Degrees-of-freedom method: kenward-roger#MAIA We used the French validate version of the Multidimensional Assessment of Interoceptive Awareness (Willem et al., 2022). It is a 32-item rating scale that measures Interoceptive Awareness, which refers to the features of interoception that are accessible to consciousness. The MAIA is a 6-point Likert format, ranging from 0 (never) to 5 (always), which evaluates 8 dimensions of interoceptive awareness: NOTICING; NOT DISTRACTING and NOT WORRYING; ATTENTION REGULATION; EMOTIONAL AWARENESS; SELF-REGULATION; BODY LISTENING and TRUSTING.
The scoring were preprocessed in a different script. Here we considered the mean scores as covariate for our LMM.
#LMM + MAIA dimensions as covariate
lmm_model_N <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * Noticing + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
lmm_model_ND <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * NotDistracting + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
lmm_model_NW <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * NotWorrying + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
lmm_model_AR <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * AttentionRegulation + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
lmm_model_EA <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * EmotionalAwareness + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
lmm_model_SR <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * SelfRegulation + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
lmm_model_BL <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * BodyListening + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
lmm_model_T <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * Trusting + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
#verifysingularity
isSingular(lmm_model_N)## [1] FALSEisSingular(lmm_model_ND)## [1] FALSEisSingular(lmm_model_NW)## [1] FALSEisSingular(lmm_model_AR)## [1] FALSEisSingular(lmm_model_EA)## [1] FALSEisSingular(lmm_model_SR)## [1] FALSEisSingular(lmm_model_BL)## [1] FALSEisSingular(lmm_model_T)## [1] FALSE#summary
summary(lmm_model_N)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * Noticing + (1 +
## Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28722.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0757 -0.5735 -0.1260 0.3810 5.9423
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8991 94.82
## BlockS 1910 43.70 0.00
## VisuoSpatialCongruencyinc 3425 58.52 0.10 -0.44
## BlockS:VisuoSpatialCongruencyinc 2242 47.35 -0.26 0.35 -0.55
## Residual 11570 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 315.432 80.844 30.911 3.902
## BlockS 61.389 46.162 30.910 1.330
## VisuoSpatialCongruencyinc 105.463 58.276 34.009 1.810
## Noticing 2.171 23.493 30.907 0.092
## BlockS:VisuoSpatialCongruencyinc -19.564 58.913 34.243 -0.332
## BlockS:Noticing -15.344 13.414 30.905 -1.144
## VisuoSpatialCongruencyinc:Noticing 5.286 16.875 33.623 0.313
## BlockS:VisuoSpatialCongruencyinc:Noticing 2.034 17.059 33.871 0.119
## Pr(>|t|)
## (Intercept) 0.000481 ***
## BlockS 0.193288
## VisuoSpatialCongruencyinc 0.079186 .
## Noticing 0.926973
## BlockS:VisuoSpatialCongruencyinc 0.741853
## BlockS:Noticing 0.261469
## VisuoSpatialCongruencyinc:Noticing 0.756009
## BlockS:VisuoSpatialCongruencyinc:Noticing 0.905805
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC Notcng BlS:VSC BlcS:N VsSC:N
## BlockS -0.107
## VsSptlCngrn -0.008 -0.128
## Noticing -0.977 0.105 0.008
## BlckS:VsSpC -0.078 -0.125 -0.613 0.076
## BlckS:Ntcng 0.105 -0.977 0.126 -0.107 0.123
## VsSptlCng:N 0.008 0.126 -0.978 -0.008 0.599 -0.129
## BlckS:VSC:N 0.076 0.123 0.599 -0.078 -0.978 -0.126 -0.610summary(lmm_model_ND)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * NotDistracting +
## (1 + Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28715.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0665 -0.5769 -0.1248 0.3804 5.9518
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8983 94.78
## BlockS 2018 44.92 0.00
## VisuoSpatialCongruencyinc 3447 58.71 0.10 -0.44
## BlockS:VisuoSpatialCongruencyinc 1598 39.98 -0.32 0.34 -0.64
## Residual 11569 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 330.316 47.603 31.050
## BlockS 20.764 27.694 31.217
## VisuoSpatialCongruencyinc 119.698 33.799 32.219
## NotDistracting -3.766 22.097 30.987
## BlockS:VisuoSpatialCongruencyinc 52.888 31.958 33.688
## BlockS:NotDistracting -5.487 12.835 30.966
## VisuoSpatialCongruencyinc:NotDistracting 1.799 15.707 32.282
## BlockS:VisuoSpatialCongruencyinc:NotDistracting -32.708 14.844 33.684
## t value Pr(>|t|)
## (Intercept) 6.939 8.69e-08 ***
## BlockS 0.750 0.45900
## VisuoSpatialCongruencyinc 3.541 0.00124 **
## NotDistracting -0.170 0.86577
## BlockS:VisuoSpatialCongruencyinc 1.655 0.10723
## BlockS:NotDistracting -0.428 0.67197
## VisuoSpatialCongruencyinc:NotDistracting 0.115 0.90952
## BlockS:VisuoSpatialCongruencyinc:NotDistracting -2.203 0.03451 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC NtDstr BlS:VSC BlS:ND VSC:ND
## BlockS -0.115
## VsSptlCngrn -0.011 -0.135
## NotDstrctng -0.934 0.106 0.010
## BlckS:VsSpC -0.092 -0.168 -0.634 0.086
## BlckS:NtDst 0.106 -0.934 0.127 -0.113 0.155
## VsSptlCn:ND 0.010 0.126 -0.934 -0.010 0.592 -0.137
## BlcS:VSC:ND 0.086 0.155 0.593 -0.093 -0.934 -0.164 -0.635summary(lmm_model_NW)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * NotWorrying +
## (1 + Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28724
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0761 -0.5741 -0.1281 0.3746 5.9421
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8974 94.73
## BlockS 2042 45.18 0.00
## VisuoSpatialCongruencyinc 3405 58.35 0.10 -0.44
## BlockS:VisuoSpatialCongruencyinc 2171 46.59 -0.25 0.33 -0.54
## Residual 11569 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 312.9309 43.6057 30.9163
## BlockS 11.1986 25.4444 30.9245
## VisuoSpatialCongruencyinc 110.0922 30.6132 31.1755
## NotWorrying 5.0054 20.4790 30.8905
## BlockS:VisuoSpatialCongruencyinc 7.6747 30.9050 31.9594
## BlockS:NotWorrying -0.7404 11.9307 30.7044
## VisuoSpatialCongruencyinc:NotWorrying 6.7077 14.3363 30.8330
## BlockS:VisuoSpatialCongruencyinc:NotWorrying -10.3835 14.4537 31.4774
## t value Pr(>|t|)
## (Intercept) 7.176 4.63e-08 ***
## BlockS 0.440 0.6629
## VisuoSpatialCongruencyinc 3.596 0.0011 **
## NotWorrying 0.244 0.8085
## BlockS:VisuoSpatialCongruencyinc 0.248 0.8055
## BlockS:NotWorrying -0.062 0.9509
## VisuoSpatialCongruencyinc:NotWorrying 0.468 0.6432
## BlockS:VisuoSpatialCongruencyinc:NotWorrying -0.718 0.4778
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC NtWrry BlS:VSC BlS:NW VSC:NW
## BlockS -0.108
## VsSptlCngrn -0.011 -0.140
## NotWorrying -0.920 0.099 0.009
## BlckS:VsSpC -0.075 -0.132 -0.584 0.069
## BlckS:NtWrr 0.099 -0.921 0.130 -0.107 0.121
## VsSptlCn:NW 0.010 0.130 -0.920 -0.010 0.536 -0.142
## BlcS:VSC:NW 0.070 0.121 0.537 -0.076 -0.920 -0.130 -0.583summary(lmm_model_AR)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * AttentionRegulation +
## (1 + Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28722.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0758 -0.5729 -0.1267 0.3780 5.9422
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8991 94.82
## BlockS 2038 45.15 0.00
## VisuoSpatialCongruencyinc 3419 58.48 0.10 -0.44
## BlockS:VisuoSpatialCongruencyinc 2243 47.36 -0.26 0.33 -0.55
## Residual 11570 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error
## (Intercept) 324.0907 79.0096
## BlockS 14.5727 46.0858
## VisuoSpatialCongruencyinc 100.7414 55.6754
## AttentionRegulation -0.4592 26.1313
## BlockS:VisuoSpatialCongruencyinc -16.9415 56.6434
## BlockS:AttentionRegulation -1.6260 15.2411
## VisuoSpatialCongruencyinc:AttentionRegulation 7.6263 18.3886
## BlockS:VisuoSpatialCongruencyinc:AttentionRegulation 1.4107 18.6849
## df t value Pr(>|t|)
## (Intercept) 31.0020 4.102 0.000275
## BlockS 31.1369 0.316 0.753955
## VisuoSpatialCongruencyinc 31.7277 1.809 0.079866
## AttentionRegulation 31.0080 -0.018 0.986092
## BlockS:VisuoSpatialCongruencyinc 32.6196 -0.299 0.766769
## BlockS:AttentionRegulation 31.1315 -0.107 0.915721
## VisuoSpatialCongruencyinc:AttentionRegulation 31.5867 0.415 0.681144
## BlockS:VisuoSpatialCongruencyinc:AttentionRegulation 32.3348 0.076 0.940281
##
## (Intercept) ***
## BlockS
## VisuoSpatialCongruencyinc .
## AttentionRegulation
## BlockS:VisuoSpatialCongruencyinc
## BlockS:AttentionRegulation
## VisuoSpatialCongruencyinc:AttentionRegulation
## BlockS:VisuoSpatialCongruencyinc:AttentionRegulation
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC AttntR BlS:VSC BlS:AR VSC:AR
## BlockS -0.109
## VsSptlCngrn -0.008 -0.137
## AttntnRgltn -0.976 0.107 0.008
## BlckS:VsSpC -0.078 -0.130 -0.594 0.076
## BlckS:AttnR 0.107 -0.976 0.133 -0.110 0.127
## VsSptlCn:AR 0.008 0.133 -0.976 -0.008 0.580 -0.137
## BlcS:VSC:AR 0.076 0.127 0.580 -0.078 -0.976 -0.130 -0.594summary(lmm_model_EA)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * EmotionalAwareness +
## (1 + Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28722.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0732 -0.5708 -0.1271 0.3781 5.9450
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8943 94.57
## BlockS 2042 45.19 0.00
## VisuoSpatialCongruencyinc 3434 58.60 0.10 -0.44
## BlockS:VisuoSpatialCongruencyinc 2230 47.22 -0.25 0.33 -0.55
## Residual 11569 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error
## (Intercept) 360.2162 95.2747
## BlockS 8.1817 55.5623
## VisuoSpatialCongruencyinc 138.2942 66.9204
## EmotionalAwareness -10.4112 26.0393
## BlockS:VisuoSpatialCongruencyinc -36.3767 67.4827
## BlockS:EmotionalAwareness 0.4393 15.1876
## VisuoSpatialCongruencyinc:EmotionalAwareness -4.1813 18.3125
## BlockS:VisuoSpatialCongruencyinc:EmotionalAwareness 6.5785 18.4754
## df t value Pr(>|t|)
## (Intercept) 30.8980 3.781 0.000672
## BlockS 30.6435 0.147 0.883897
## VisuoSpatialCongruencyinc 30.7128 2.067 0.047297
## EmotionalAwareness 30.8946 -0.400 0.692037
## BlockS:VisuoSpatialCongruencyinc 30.9490 -0.539 0.593707
## BlockS:EmotionalAwareness 30.6577 0.029 0.977112
## VisuoSpatialCongruencyinc:EmotionalAwareness 30.8438 -0.228 0.820899
## BlockS:VisuoSpatialCongruencyinc:EmotionalAwareness 31.1241 0.356 0.724191
##
## (Intercept) ***
## BlockS
## VisuoSpatialCongruencyinc *
## EmotionalAwareness
## BlockS:VisuoSpatialCongruencyinc
## BlockS:EmotionalAwareness
## VisuoSpatialCongruencyinc:EmotionalAwareness
## BlockS:VisuoSpatialCongruencyinc:EmotionalAwareness
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC EmtnlA BlS:VSC BlS:EA VSC:EA
## BlockS -0.108
## VsSptlCngrn -0.010 -0.142
## EmtnlAwrnss -0.984 0.106 0.010
## BlckS:VsSpC -0.076 -0.128 -0.587 0.075
## BlckS:EmtnA 0.106 -0.984 0.139 -0.108 0.126
## VsSptlCn:EA 0.010 0.139 -0.984 -0.010 0.578 -0.142
## BlcS:VSC:EA 0.075 0.126 0.577 -0.076 -0.984 -0.128 -0.588summary(lmm_model_SR)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * SelfRegulation +
## (1 + Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28723.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0721 -0.5718 -0.1304 0.3798 5.9456
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8889 94.28
## BlockS 1849 42.99 -0.03
## VisuoSpatialCongruencyinc 3434 58.60 0.10 -0.47
## BlockS:VisuoSpatialCongruencyinc 2127 46.12 -0.24 0.43 -0.56
## Residual 11570 107.57
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 352.367 53.754 30.860
## BlockS 49.700 30.507 30.561
## VisuoSpatialCongruencyinc 128.275 38.522 32.637
## SelfRegulation -10.078 17.353 30.857
## BlockS:VisuoSpatialCongruencyinc -43.771 38.653 33.453
## BlockS:SelfRegulation -13.573 9.843 30.496
## VisuoSpatialCongruencyinc:SelfRegulation -1.661 12.389 32.232
## BlockS:VisuoSpatialCongruencyinc:SelfRegulation 10.486 12.423 32.996
## t value Pr(>|t|)
## (Intercept) 6.555 2.61e-07 ***
## BlockS 1.629 0.11355
## VisuoSpatialCongruencyinc 3.330 0.00216 **
## SelfRegulation -0.581 0.56563
## BlockS:VisuoSpatialCongruencyinc -1.132 0.26551
## BlockS:SelfRegulation -1.379 0.17794
## VisuoSpatialCongruencyinc:SelfRegulation -0.134 0.89418
## BlockS:VisuoSpatialCongruencyinc:SelfRegulation 0.844 0.40473
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC SlfRgl BlS:VSC BlS:SR VSC:SR
## BlockS -0.137
## VsSptlCngrn -0.010 -0.153
## SelfRegultn -0.949 0.129 0.009
## BlckS:VsSpC -0.064 -0.090 -0.602 0.061
## BlckS:SlfRg 0.129 -0.949 0.145 -0.137 0.085
## VsSptlCn:SR 0.009 0.146 -0.950 -0.010 0.571 -0.154
## BlcS:VSC:SR 0.061 0.086 0.571 -0.065 -0.950 -0.090 -0.600summary(lmm_model_BL)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * BodyListening +
## (1 + Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28723.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0764 -0.5725 -0.1299 0.3819 5.9418
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8991 94.82
## BlockS 2013 44.87 0.00
## VisuoSpatialCongruencyinc 3202 56.58 0.11 -0.49
## BlockS:VisuoSpatialCongruencyinc 2227 47.19 -0.26 0.34 -0.54
## Residual 11569 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 320.0419 48.2560 30.9346
## BlockS 23.8403 27.9816 30.8506
## VisuoSpatialCongruencyinc 162.7383 33.2503 31.7091
## BodyListening 0.9758 16.4257 30.9020
## BlockS:VisuoSpatialCongruencyinc -22.9312 34.6160 32.6602
## BlockS:BodyListening -5.1181 9.5203 30.7649
## VisuoSpatialCongruencyinc:BodyListening -14.3621 11.3166 31.6655
## BlockS:VisuoSpatialCongruencyinc:BodyListening 3.7301 11.7696 32.5292
## t value Pr(>|t|)
## (Intercept) 6.632 2.08e-07 ***
## BlockS 0.852 0.401
## VisuoSpatialCongruencyinc 4.894 2.76e-05 ***
## BodyListening 0.059 0.953
## BlockS:VisuoSpatialCongruencyinc -0.662 0.512
## BlockS:BodyListening -0.538 0.595
## VisuoSpatialCongruencyinc:BodyListening -1.269 0.214
## BlockS:VisuoSpatialCongruencyinc:BodyListening 0.317 0.753
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC BdyLst BlS:VSC BlS:BL VSC:BL
## BlockS -0.108
## VsSptlCngrn -0.006 -0.167
## BodyListnng -0.935 0.101 0.005
## BlckS:VsSpC -0.079 -0.123 -0.591 0.074
## BlckS:BdyLs 0.101 -0.935 0.157 -0.108 0.114
## VsSptlCn:BL 0.005 0.157 -0.935 -0.005 0.553 -0.168
## BlcS:VSC:BL 0.074 0.114 0.553 -0.080 -0.936 -0.122 -0.592summary(lmm_model_T)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * Trusting + (1 +
## Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28717.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0830 -0.5731 -0.1202 0.3654 5.9352
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 7098 84.25
## BlockS 1971 44.40 0.09
## VisuoSpatialCongruencyinc 3378 58.12 0.19 -0.48
## BlockS:VisuoSpatialCongruencyinc 2239 47.32 -0.33 0.35 -0.55
## Residual 11569 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 492.204 63.129 31.054 7.797
## BlockS -22.500 40.749 31.485 -0.552
## VisuoSpatialCongruencyinc 89.515 49.317 31.524 1.815
## Trusting -47.250 17.080 31.048 -2.766
## BlockS:VisuoSpatialCongruencyinc 2.468 50.327 32.413 0.049
## BlockS:Trusting 8.984 11.018 31.403 0.815
## VisuoSpatialCongruencyinc:Trusting 9.409 13.360 31.636 0.704
## BlockS:VisuoSpatialCongruencyinc:Trusting -4.233 13.614 32.371 -0.311
## Pr(>|t|)
## (Intercept) 8.38e-09 ***
## BlockS 0.58474
## VisuoSpatialCongruencyinc 0.07904 .
## Trusting 0.00946 **
## BlockS:VisuoSpatialCongruencyinc 0.96118
## BlockS:Trusting 0.42098
## VisuoSpatialCongruencyinc:Trusting 0.48643
## BlockS:VisuoSpatialCongruencyinc:Trusting 0.75784
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC Trstng BlS:VSC BlcS:T VsSC:T
## BlockS -0.053
## VsSptlCngrn 0.050 -0.156
## Trusting -0.970 0.051 -0.049
## BlckS:VsSpC -0.112 -0.129 -0.590 0.108
## BlckS:Trstn 0.051 -0.970 0.152 -0.053 0.125
## VsSptlCng:T -0.049 0.151 -0.970 0.050 0.572 -0.156
## BlckS:VSC:T 0.108 0.125 0.573 -0.112 -0.970 -0.128 -0.592Since the models are not singular, we can continue to explore the data through post-hoc comparisons.
# Means of Block * VisuoSpatialCongruency interaction
emmeans_interaction_N <- emmeans(lmm_model_N, ~ Block * VisuoSpatialCongruency| Noticing)
emmeans_interaction_N2 <- emmeans(lmm_model_N, ~ Block * Noticing| VisuoSpatialCongruency)
emmeans_interaction_N3 <- emmeans(lmm_model_N, ~ VisuoSpatialCongruency * Noticing| Block)
emmeans_interaction_ND <- emmeans(lmm_model_ND, ~ Block * VisuoSpatialCongruency| NotDistracting)
emmeans_interaction_ND2 <- emmeans(lmm_model_ND, ~ Block * NotDistracting| VisuoSpatialCongruency)
emmeans_interaction_ND3 <- emmeans(lmm_model_ND, ~ VisuoSpatialCongruency * NotDistracting| Block)
emmeans_interaction_NW <- emmeans(lmm_model_NW, ~ Block * VisuoSpatialCongruency| NotWorrying)
emmeans_interaction_NW2 <- emmeans(lmm_model_NW, ~ Block * NotWorrying| VisuoSpatialCongruency)
emmeans_interaction_NW3 <- emmeans(lmm_model_NW, ~ VisuoSpatialCongruency * NotWorrying| Block)
emmeans_interaction_AR <- emmeans(lmm_model_AR, ~ Block * VisuoSpatialCongruency| AttentionRegulation)
emmeans_interaction_AR2 <- emmeans(lmm_model_AR, ~ Block * AttentionRegulation| VisuoSpatialCongruency)
emmeans_interaction_AR3 <- emmeans(lmm_model_AR, ~ VisuoSpatialCongruency * AttentionRegulation| Block)
emmeans_interaction_EA <- emmeans(lmm_model_EA, ~ Block * VisuoSpatialCongruency| EmotionalAwareness)
emmeans_interaction_EA2 <- emmeans(lmm_model_EA, ~ Block * EmotionalAwareness| VisuoSpatialCongruency)
emmeans_interaction_EA3 <- emmeans(lmm_model_EA, ~ VisuoSpatialCongruency * EmotionalAwareness| Block)
emmeans_interaction_SR <- emmeans(lmm_model_SR, ~ Block * VisuoSpatialCongruency| SelfRegulation)
emmeans_interaction_SR2 <- emmeans(lmm_model_SR, ~ Block * SelfRegulation| VisuoSpatialCongruency)
emmeans_interaction_SR3 <- emmeans(lmm_model_SR, ~ VisuoSpatialCongruency * SelfRegulation| Block)
emmeans_interaction_BL <- emmeans(lmm_model_BL, ~ Block * VisuoSpatialCongruency| BodyListening)
emmeans_interaction_BL2 <- emmeans(lmm_model_BL, ~ Block * BodyListening| VisuoSpatialCongruency)
emmeans_interaction_BL3 <- emmeans(lmm_model_BL, ~ VisuoSpatialCongruency * BodyListening| Block)
emmeans_interaction_T <- emmeans(lmm_model_T, ~ Block * VisuoSpatialCongruency| Trusting)
emmeans_interaction_T2 <- emmeans(lmm_model_T, ~ Block * Trusting| VisuoSpatialCongruency)
emmeans_interaction_T3 <- emmeans(lmm_model_T, ~ VisuoSpatialCongruency * Trusting| Block)
# Means of Block
emmeans_block_N <- emmeans(lmm_model_N, ~ Block| Noticing)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_ND <- emmeans(lmm_model_ND, ~ Block| NotDistracting)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_NW <- emmeans(lmm_model_NW, ~ Block| NotWorrying)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_AR <- emmeans(lmm_model_AR, ~ Block| AttentionRegulation)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_EA <- emmeans(lmm_model_EA, ~ Block| EmotionalAwareness)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_SR <- emmeans(lmm_model_SR, ~ Block| SelfRegulation)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_BL <- emmeans(lmm_model_BL, ~ Block| BodyListening)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_T <- emmeans(lmm_model_T, ~ Block| Trusting)## NOTE: Results may be misleading due to involvement in interactions# Means of VisuoSpatialCongruency
emmeans_visuo_N <- emmeans(lmm_model_N, ~ VisuoSpatialCongruency| Noticing)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_ND <- emmeans(lmm_model_ND, ~ VisuoSpatialCongruency| NotDistracting)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_NW <- emmeans(lmm_model_NW, ~ VisuoSpatialCongruency| NotWorrying)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_AR <- emmeans(lmm_model_AR, ~ VisuoSpatialCongruency| AttentionRegulation)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_EA <- emmeans(lmm_model_EA, ~ VisuoSpatialCongruency| EmotionalAwareness)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_SR <- emmeans(lmm_model_SR, ~ VisuoSpatialCongruency| SelfRegulation)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_BL <- emmeans(lmm_model_BL, ~ VisuoSpatialCongruency| BodyListening)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_T <- emmeans(lmm_model_T, ~ VisuoSpatialCongruency| Trusting)## NOTE: Results may be misleading due to involvement in interactions#
# Post hoc comparisons of Block * VisuoSpatialCongruency
posthoc_interaction_N <- pairs(emmeans_interaction_N, adjust = "bonferroni")
posthoc_interaction_N2 <- pairs(emmeans_interaction_N2, adjust = "bonferroni")
posthoc_interaction_N3 <- pairs(emmeans_interaction_N3, adjust = "bonferroni")
posthoc_interaction_ND <- pairs(emmeans_interaction_ND, adjust = "bonferroni")
posthoc_interaction_ND2 <- pairs(emmeans_interaction_ND2, adjust = "bonferroni")
posthoc_interaction_ND3 <- pairs(emmeans_interaction_ND3, adjust = "bonferroni")
posthoc_interaction_NW <- pairs(emmeans_interaction_NW, adjust = "bonferroni")
posthoc_interaction_NW2 <- pairs(emmeans_interaction_NW2, adjust = "bonferroni")
posthoc_interaction_NW3 <- pairs(emmeans_interaction_NW3, adjust = "bonferroni")
posthoc_interaction_AR <- pairs(emmeans_interaction_AR, adjust = "bonferroni")
posthoc_interaction_AR2 <- pairs(emmeans_interaction_AR2, adjust = "bonferroni")
posthoc_interaction_AR3 <- pairs(emmeans_interaction_AR3, adjust = "bonferroni")
posthoc_interaction_EA <- pairs(emmeans_interaction_EA, adjust = "bonferroni")
posthoc_interaction_EA2 <- pairs(emmeans_interaction_EA2, adjust = "bonferroni")
posthoc_interaction_EA3 <- pairs(emmeans_interaction_EA3, adjust = "bonferroni")
posthoc_interaction_SR <- pairs(emmeans_interaction_SR, adjust = "bonferroni")
posthoc_interaction_SR2 <- pairs(emmeans_interaction_SR2, adjust = "bonferroni")
posthoc_interaction_SR3 <- pairs(emmeans_interaction_SR3, adjust = "bonferroni")
posthoc_interaction_BL <- pairs(emmeans_interaction_BL, adjust = "bonferroni")
posthoc_interaction_BL2 <- pairs(emmeans_interaction_BL2, adjust = "bonferroni")
posthoc_interaction_BL3 <- pairs(emmeans_interaction_BL3, adjust = "bonferroni")
posthoc_interaction_T <- pairs(emmeans_interaction_T, adjust = "bonferroni")
posthoc_interaction_T2 <- pairs(emmeans_interaction_T2, adjust = "bonferroni")
posthoc_interaction_T3 <- pairs(emmeans_interaction_T3, adjust = "bonferroni")
# Post hoc comparisons of Block
posthoc_block_N <- contrast(emmeans_block_N, adjust = "bonferroni")
posthoc_block_ND <- contrast(emmeans_block_ND, adjust = "bonferroni")
posthoc_block_NW <- contrast(emmeans_block_NW, adjust = "bonferroni")
posthoc_block_AR <- contrast(emmeans_block_AR, adjust = "bonferroni")
posthoc_block_EA <- contrast(emmeans_block_EA, adjust = "bonferroni")
posthoc_block_SR <- contrast(emmeans_block_SR, adjust = "bonferroni")
posthoc_block_BL <- contrast(emmeans_block_BL, adjust = "bonferroni")
posthoc_block_T <- contrast(emmeans_block_T, adjust = "bonferroni")
# Post hoc comparisons of VisuoSpatialCongruency
posthoc_visuo_N <- contrast(emmeans_visuo_N, adjust = "bonferroni")
posthoc_visuo_ND <- contrast(emmeans_visuo_ND, adjust = "bonferroni")
posthoc_visuo_NW <- contrast(emmeans_visuo_NW, adjust = "bonferroni")
posthoc_visuo_AR <- contrast(emmeans_visuo_AR, adjust = "bonferroni")
posthoc_visuo_EA <- contrast(emmeans_visuo_EA, adjust = "bonferroni")
posthoc_visuo_SR <- contrast(emmeans_visuo_SR, adjust = "bonferroni")
posthoc_visuo_BL <- contrast(emmeans_visuo_BL, adjust = "bonferroni")
posthoc_visuo_T <- contrast(emmeans_visuo_T, adjust = "bonferroni")
#
#post hoc summary of Block * VisuoSpatialCongruency
summary(posthoc_interaction_N)## Noticing = 3.37:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.66 9.74 31.0 -0.991 1.0000
## A cong - A inc -123.29 12.06 30.9 -10.224 <.0001
## A cong - S inc -120.23 12.37 31.0 -9.722 <.0001
## S cong - A inc -113.63 16.45 31.0 -6.907 <.0001
## S cong - S inc -110.58 10.90 30.9 -10.144 <.0001
## A inc - S inc 3.05 14.62 31.0 0.209 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_N2)## VisuoSpatialCongruency = cong:
## contrast estimate SE df
## A Noticing3.3715811965812 - S Noticing3.3715811965812 -9.66 9.74 31
## t.ratio p.value
## -0.991 0.3292
##
## VisuoSpatialCongruency = inc:
## contrast estimate SE df
## A Noticing3.3715811965812 - S Noticing3.3715811965812 3.05 14.62 31
## t.ratio p.value
## 0.209 0.8361
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_N3)## Block = A:
## contrast estimate SE df
## cong Noticing3.3715811965812 - inc Noticing3.3715811965812 -123 12.1 30.9
## t.ratio p.value
## -10.224 <.0001
##
## Block = S:
## contrast estimate SE df
## cong Noticing3.3715811965812 - inc Noticing3.3715811965812 -111 10.9 30.9
## t.ratio p.value
## -10.144 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_ND)## NotDistracting = 2.02:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.71 9.91 31.0 -0.980 1.0000
## A cong - A inc -123.32 12.09 30.9 -10.204 <.0001
## A cong - S inc -120.01 11.36 31.0 -10.567 <.0001
## S cong - A inc -113.62 16.66 31.0 -6.821 <.0001
## S cong - S inc -110.30 10.07 30.9 -10.955 <.0001
## A inc - S inc 3.31 13.81 30.9 0.240 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_ND2)## VisuoSpatialCongruency = cong:
## contrast estimate
## A NotDistracting2.01509971509972 - S NotDistracting2.01509971509972 -9.71
## SE df t.ratio p.value
## 9.91 31.0 -0.980 0.3347
##
## VisuoSpatialCongruency = inc:
## contrast estimate
## A NotDistracting2.01509971509972 - S NotDistracting2.01509971509972 3.31
## SE df t.ratio p.value
## 13.81 30.9 0.240 0.8119
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_ND3)## Block = A:
## contrast
## cong NotDistracting2.01509971509972 - inc NotDistracting2.01509971509972
## estimate SE df t.ratio p.value
## -123 12.1 30.9 -10.204 <.0001
##
## Block = S:
## contrast
## cong NotDistracting2.01509971509972 - inc NotDistracting2.01509971509972
## estimate SE df t.ratio p.value
## -110 10.1 30.9 -10.955 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_NW)## NotWorrying = 1.97:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.74 9.94 31.0 -0.980 1.0000
## A cong - A inc -123.30 12.03 30.9 -10.246 <.0001
## A cong - S inc -120.27 12.40 31.0 -9.696 <.0001
## S cong - A inc -113.56 16.63 30.9 -6.829 <.0001
## S cong - S inc -110.53 10.94 30.9 -10.102 <.0001
## A inc - S inc 3.04 14.64 30.9 0.208 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_NW2)## VisuoSpatialCongruency = cong:
## contrast estimate SE
## A NotWorrying1.96980056980057 - S NotWorrying1.96980056980057 -9.74 9.94
## df t.ratio p.value
## 31.0 -0.980 0.3348
##
## VisuoSpatialCongruency = inc:
## contrast estimate SE
## A NotWorrying1.96980056980057 - S NotWorrying1.96980056980057 3.04 14.64
## df t.ratio p.value
## 30.9 0.208 0.8369
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_NW3)## Block = A:
## contrast estimate
## cong NotWorrying1.96980056980057 - inc NotWorrying1.96980056980057 -123
## SE df t.ratio p.value
## 12.0 30.9 -10.246 <.0001
##
## Block = S:
## contrast estimate
## cong NotWorrying1.96980056980057 - inc NotWorrying1.96980056980057 -111
## SE df t.ratio p.value
## 10.9 30.9 -10.102 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_AR)## AttentionRegulation = 2.96:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.76 9.94 31.0 -0.982 1.0000
## A cong - A inc -123.33 12.05 30.9 -10.232 <.0001
## A cong - S inc -120.32 12.38 31.0 -9.718 <.0001
## S cong - A inc -113.57 16.64 31.0 -6.826 <.0001
## S cong - S inc -110.56 10.88 30.9 -10.160 <.0001
## A inc - S inc 3.01 14.73 30.9 0.204 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_AR2)## VisuoSpatialCongruency = cong:
## contrast
## A AttentionRegulation2.96129426129426 - S AttentionRegulation2.96129426129426
## estimate SE df t.ratio p.value
## -9.76 9.94 31.0 -0.982 0.3338
##
## VisuoSpatialCongruency = inc:
## contrast
## A AttentionRegulation2.96129426129426 - S AttentionRegulation2.96129426129426
## estimate SE df t.ratio p.value
## 3.01 14.73 30.9 0.204 0.8396
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_AR3)## Block = A:
## contrast
## cong AttentionRegulation2.96129426129426 - inc AttentionRegulation2.96129426129426
## estimate SE df t.ratio p.value
## -123 12.1 30.9 -10.232 <.0001
##
## Block = S:
## contrast
## cong AttentionRegulation2.96129426129426 - inc AttentionRegulation2.96129426129426
## estimate SE df t.ratio p.value
## -111 10.9 30.9 -10.160 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_EA)## EmotionalAwareness = 3.59:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.76 9.94 31.0 -0.982 1.0000
## A cong - A inc -123.28 12.07 30.9 -10.213 <.0001
## A cong - S inc -120.29 12.41 31.0 -9.692 <.0001
## S cong - A inc -113.52 16.66 30.9 -6.813 <.0001
## S cong - S inc -110.53 10.95 30.9 -10.098 <.0001
## A inc - S inc 2.99 14.71 30.9 0.203 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_EA2)## VisuoSpatialCongruency = cong:
## contrast
## A EmotionalAwareness3.59196581196581 - S EmotionalAwareness3.59196581196581
## estimate SE df t.ratio p.value
## -9.76 9.94 31.0 -0.982 0.3339
##
## VisuoSpatialCongruency = inc:
## contrast
## A EmotionalAwareness3.59196581196581 - S EmotionalAwareness3.59196581196581
## estimate SE df t.ratio p.value
## 2.99 14.71 30.9 0.203 0.8404
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_EA3)## Block = A:
## contrast
## cong EmotionalAwareness3.59196581196581 - inc EmotionalAwareness3.59196581196581
## estimate SE df t.ratio p.value
## -123 12.1 30.9 -10.213 <.0001
##
## Block = S:
## contrast
## cong EmotionalAwareness3.59196581196581 - inc EmotionalAwareness3.59196581196581
## estimate SE df t.ratio p.value
## -111 10.9 30.9 -10.098 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_SR)## SelfRegulation = 2.95:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.63 9.64 31.0 -0.998 1.0000
## A cong - A inc -123.37 12.07 30.9 -10.221 <.0001
## A cong - S inc -120.18 12.38 31.0 -9.711 <.0001
## S cong - A inc -113.74 16.54 31.0 -6.877 <.0001
## S cong - S inc -110.56 10.82 31.0 -10.220 <.0001
## A inc - S inc 3.19 14.73 30.9 0.216 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_SR2)## VisuoSpatialCongruency = cong:
## contrast estimate
## A SelfRegulation2.95235042735043 - S SelfRegulation2.95235042735043 -9.63
## SE df t.ratio p.value
## 9.64 31.0 -0.998 0.3259
##
## VisuoSpatialCongruency = inc:
## contrast estimate
## A SelfRegulation2.95235042735043 - S SelfRegulation2.95235042735043 3.19
## SE df t.ratio p.value
## 14.73 30.9 0.216 0.8301
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_SR3)## Block = A:
## contrast
## cong SelfRegulation2.95235042735043 - inc SelfRegulation2.95235042735043
## estimate SE df t.ratio p.value
## -123 12.1 30.9 -10.221 <.0001
##
## Block = S:
## contrast
## cong SelfRegulation2.95235042735043 - inc SelfRegulation2.95235042735043
## estimate SE df t.ratio p.value
## -111 10.8 31.0 -10.220 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_BL)## BodyListening = 2.75:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.75 9.9 31.0 -0.985 1.0000
## A cong - A inc -123.19 11.8 30.9 -10.462 <.0001
## A cong - S inc -120.28 12.1 31.0 -9.966 <.0001
## S cong - A inc -113.44 16.6 31.0 -6.839 <.0001
## S cong - S inc -110.53 10.8 31.0 -10.250 <.0001
## A inc - S inc 2.91 14.7 30.9 0.198 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_BL2)## VisuoSpatialCongruency = cong:
## contrast estimate SE
## A BodyListening2.7537037037037 - S BodyListening2.7537037037037 -9.75 9.9
## df t.ratio p.value
## 31.0 -0.985 0.3324
##
## VisuoSpatialCongruency = inc:
## contrast estimate SE
## A BodyListening2.7537037037037 - S BodyListening2.7537037037037 2.91 14.7
## df t.ratio p.value
## 30.9 0.198 0.8445
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_BL3)## Block = A:
## contrast estimate
## cong BodyListening2.7537037037037 - inc BodyListening2.7537037037037 -123
## SE df t.ratio p.value
## 11.8 30.9 -10.462 <.0001
##
## Block = S:
## contrast estimate
## cong BodyListening2.7537037037037 - inc BodyListening2.7537037037037 -111
## SE df t.ratio p.value
## 10.8 31.0 -10.250 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_T)## Trusting = 3.59:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.77 9.83 31.0 -0.993 1.0000
## A cong - A inc -123.31 12.00 30.9 -10.276 <.0001
## A cong - S inc -120.34 12.20 31.0 -9.863 <.0001
## S cong - A inc -113.54 16.67 31.0 -6.810 <.0001
## S cong - S inc -110.57 10.91 31.0 -10.139 <.0001
## A inc - S inc 2.97 14.71 30.9 0.202 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_T2)## VisuoSpatialCongruency = cong:
## contrast estimate SE df
## A Trusting3.59173789173789 - S Trusting3.59173789173789 -9.77 9.83 31.0
## t.ratio p.value
## -0.993 0.3282
##
## VisuoSpatialCongruency = inc:
## contrast estimate SE df
## A Trusting3.59173789173789 - S Trusting3.59173789173789 2.97 14.71 30.9
## t.ratio p.value
## 0.202 0.8415
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_T3)## Block = A:
## contrast estimate SE
## cong Trusting3.59173789173789 - inc Trusting3.59173789173789 -123 12.0
## df t.ratio p.value
## 30.9 -10.276 <.0001
##
## Block = S:
## contrast estimate SE
## cong Trusting3.59173789173789 - inc Trusting3.59173789173789 -111 10.9
## df t.ratio p.value
## 31.0 -10.139 <.0001
##
## Degrees-of-freedom method: kenward-roger#post hoc summary of Block
summary(posthoc_block_N)## Noticing = 3.37:
## contrast estimate SE df t.ratio p.value
## A effect -1.65 5.41 31 -0.305 1.0000
## S effect 1.65 5.41 31 0.305 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_ND)## NotDistracting = 2.02:
## contrast estimate SE df t.ratio p.value
## A effect -1.6 5.29 31 -0.302 1.0000
## S effect 1.6 5.29 31 0.302 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_NW)## NotWorrying = 1.97:
## contrast estimate SE df t.ratio p.value
## A effect -1.68 5.47 31 -0.306 1.0000
## S effect 1.68 5.47 31 0.306 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_AR)## AttentionRegulation = 2.96:
## contrast estimate SE df t.ratio p.value
## A effect -1.69 5.49 31 -0.307 1.0000
## S effect 1.69 5.49 31 0.307 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_EA)## EmotionalAwareness = 3.59:
## contrast estimate SE df t.ratio p.value
## A effect -1.69 5.48 31 -0.309 1.0000
## S effect 1.69 5.48 31 0.309 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_SR)## SelfRegulation = 2.95:
## contrast estimate SE df t.ratio p.value
## A effect -1.61 5.44 31 -0.296 1.0000
## S effect 1.61 5.44 31 0.296 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_BL)## BodyListening = 2.75:
## contrast estimate SE df t.ratio p.value
## A effect -1.71 5.48 31 -0.312 1.0000
## S effect 1.71 5.48 31 0.312 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_T)## Trusting = 3.59:
## contrast estimate SE df t.ratio p.value
## A effect -1.7 5.46 31 -0.311 1.0000
## S effect 1.7 5.46 31 0.311 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 tests#post hoc summary of VisuoSpatialCongruency
summary(posthoc_visuo_N)## Noticing = 3.37:
## contrast estimate SE df t.ratio p.value
## cong effect -58.5 4.87 31 -12.011 <.0001
## inc effect 58.5 4.87 31 12.011 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_ND)## NotDistracting = 2.02:
## contrast estimate SE df t.ratio p.value
## cong effect -58.4 4.78 31 -12.227 <.0001
## inc effect 58.4 4.78 31 12.227 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_NW)## NotWorrying = 1.97:
## contrast estimate SE df t.ratio p.value
## cong effect -58.5 4.89 31 -11.966 <.0001
## inc effect 58.5 4.89 31 11.966 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_AR)## AttentionRegulation = 2.96:
## contrast estimate SE df t.ratio p.value
## cong effect -58.5 4.86 31 -12.031 <.0001
## inc effect 58.5 4.86 31 12.031 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_EA)## EmotionalAwareness = 3.59:
## contrast estimate SE df t.ratio p.value
## cong effect -58.5 4.89 30.9 -11.963 <.0001
## inc effect 58.5 4.89 30.9 11.963 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_SR)## SelfRegulation = 2.95:
## contrast estimate SE df t.ratio p.value
## cong effect -58.5 4.87 31 -12.007 <.0001
## inc effect 58.5 4.87 31 12.007 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_BL)## BodyListening = 2.75:
## contrast estimate SE df t.ratio p.value
## cong effect -58.4 4.75 31 -12.301 <.0001
## inc effect 58.4 4.75 31 12.301 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_T)## Trusting = 3.59:
## contrast estimate SE df t.ratio p.value
## cong effect -58.5 4.85 31 -12.052 <.0001
## inc effect 58.5 4.85 31 12.052 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 tests#IRI The LInterpersonal Reactivity Index (Davis, 1980; Gilet et al., 2013) is a self-report questionnaire about empathic tendencies. The IRI consists of 28 items on a 5-point Likert scale ranging from 0 (does not describe me well) to 4 (describes me very well). It is divided in 4 dimensions: Perspective Taking, Fantasy, Empatic Concern, and Personal Distress scores, computed by summing the scores every seven items, so that the minimum (0) and maximum (28) score of each dimension is the same. The scoring were preprocessed in a different script. Here we considered the mean scores as covariate for our LMM.
#LMM + IRI dimensions as covariate
lmm_model_PT <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * PerspectiveTaking + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
lmm_model_F <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * Fantasy + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
lmm_model_EC <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * EmpaticConcern + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
lmm_model_PD <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * PersonalDistress + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
#verifysingularity
isSingular(lmm_model_PT)## [1] FALSEisSingular(lmm_model_F)## [1] FALSEisSingular(lmm_model_EC)## [1] FALSEisSingular(lmm_model_PD)## [1] FALSE#summary
summary(lmm_model_PT)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * PerspectiveTaking +
## (1 + Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28730.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0852 -0.5724 -0.1232 0.3829 5.9329
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8669 93.11
## BlockS 1844 42.94 -0.06
## VisuoSpatialCongruencyinc 3373 58.08 0.08 -0.51
## BlockS:VisuoSpatialCongruencyinc 2116 46.00 -0.22 0.44 -0.53
## Residual 11570 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 417.625 93.033 30.947
## BlockS 83.961 53.308 30.548
## VisuoSpatialCongruencyinc 166.198 65.848 30.711
## PerspectiveTaking -5.789 5.581 30.932
## BlockS:VisuoSpatialCongruencyinc -71.917 65.997 30.742
## BlockS:PerspectiveTaking -4.525 3.198 30.520
## VisuoSpatialCongruencyinc:PerspectiveTaking -2.621 3.955 30.816
## BlockS:VisuoSpatialCongruencyinc:PerspectiveTaking 3.613 3.964 30.867
## t value Pr(>|t|)
## (Intercept) 4.489 9.27e-05 ***
## BlockS 1.575 0.126
## VisuoSpatialCongruencyinc 2.524 0.017 *
## PerspectiveTaking -1.037 0.308
## BlockS:VisuoSpatialCongruencyinc -1.090 0.284
## BlockS:PerspectiveTaking -1.415 0.167
## VisuoSpatialCongruencyinc:PerspectiveTaking -0.663 0.512
## BlockS:VisuoSpatialCongruencyinc:PerspectiveTaking 0.912 0.369
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC PrspcT BlS:VSC BlS:PT VSC:PT
## BlockS -0.162
## VsSptlCngrn -0.030 -0.177
## PrspctvTkng -0.984 0.159 0.030
## BlckS:VsSpC -0.051 -0.091 -0.580 0.050
## BlckS:PrspT 0.159 -0.984 0.174 -0.162 0.089
## VsSptlCn:PT 0.030 0.174 -0.983 -0.030 0.571 -0.177
## BlcS:VSC:PT 0.050 0.089 0.571 -0.051 -0.983 -0.091 -0.581summary(lmm_model_F)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * Fantasy + (1 +
## Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28733
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0754 -0.5753 -0.1341 0.3822 5.9424
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8845 94.05
## BlockS 1777 42.16 0.05
## VisuoSpatialCongruencyinc 3426 58.53 0.09 -0.45
## BlockS:VisuoSpatialCongruencyinc 2153 46.40 -0.29 0.44 -0.57
## Residual 11570 107.57
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 274.7914 70.6189 30.8954 3.891
## BlockS 73.6650 39.6965 30.7257 1.856
## VisuoSpatialCongruencyinc 110.1295 50.7239 32.6419 2.171
## Fantasy 3.1706 4.5341 30.8947 0.699
## BlockS:VisuoSpatialCongruencyinc -48.3825 50.8618 33.0587 -0.951
## BlockS:Fantasy -4.2235 2.5487 30.7250 -1.657
## VisuoSpatialCongruencyinc:Fantasy 0.8708 3.2544 32.5810 0.268
## BlockS:VisuoSpatialCongruencyinc:Fantasy 2.3489 3.2622 32.9503 0.720
## Pr(>|t|)
## (Intercept) 0.000496 ***
## BlockS 0.073111 .
## VisuoSpatialCongruencyinc 0.037293 *
## Fantasy 0.489611
## BlockS:VisuoSpatialCongruencyinc 0.348379
## BlockS:Fantasy 0.107673
## VisuoSpatialCongruencyinc:Fantasy 0.790721
## BlockS:VisuoSpatialCongruencyinc:Fantasy 0.476581
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC Fantsy BlS:VSC BlcS:F VsSC:F
## BlockS -0.076
## VsSptlCngrn -0.013 -0.132
## Fantasy -0.971 0.074 0.012
## BlckS:VsSpC -0.097 -0.093 -0.615 0.095
## BlckS:Fntsy 0.074 -0.971 0.128 -0.076 0.090
## VsSptlCng:F 0.012 0.128 -0.971 -0.013 0.597 -0.132
## BlckS:VSC:F 0.095 0.090 0.597 -0.097 -0.971 -0.093 -0.614summary(lmm_model_EC)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * EmpaticConcern +
## (1 + Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28726.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0749 -0.5678 -0.1321 0.3763 5.9429
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8255 90.85
## BlockS 1743 41.75 -0.12
## VisuoSpatialCongruencyinc 3429 58.56 0.13 -0.45
## BlockS:VisuoSpatialCongruencyinc 2219 47.11 -0.29 0.33 -0.55
## Residual 11570 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 191.644 83.178 30.867
## BlockS -74.065 48.044 30.656
## VisuoSpatialCongruencyinc 142.083 60.781 31.015
## EmpaticConcern 9.528 5.928 30.876
## BlockS:VisuoSpatialCongruencyinc -28.356 61.517 31.727
## BlockS:EmpaticConcern 6.091 3.423 30.613
## VisuoSpatialCongruencyinc:EmpaticConcern -1.370 4.332 31.042
## BlockS:VisuoSpatialCongruencyinc:EmpaticConcern 1.136 4.378 31.592
## t value Pr(>|t|)
## (Intercept) 2.304 0.0281 *
## BlockS -1.542 0.1334
## VisuoSpatialCongruencyinc 2.338 0.0260 *
## EmpaticConcern 1.607 0.1182
## BlockS:VisuoSpatialCongruencyinc -0.461 0.6480
## BlockS:EmpaticConcern 1.780 0.0850 .
## VisuoSpatialCongruencyinc:EmpaticConcern -0.316 0.7540
## BlockS:VisuoSpatialCongruencyinc:EmpaticConcern 0.259 0.7970
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC EmptcC BlS:VSC BlS:EC VSC:EC
## BlockS -0.210
## VsSptlCngrn 0.010 -0.132
## EmpatcCncrn -0.980 0.206 -0.010
## BlckS:VsSpC -0.098 -0.148 -0.588 0.096
## BlckS:EmptC 0.206 -0.980 0.129 -0.211 0.144
## VsSptlCn:EC -0.010 0.129 -0.980 0.010 0.576 -0.131
## BlcS:VSC:EC 0.096 0.145 0.577 -0.098 -0.980 -0.147 -0.589summary(lmm_model_PD)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * PersonalDistress +
## (1 + Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28730.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0657 -0.5757 -0.1222 0.3779 5.9523
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8969 94.70
## BlockS 1720 41.47 0.02
## VisuoSpatialCongruencyinc 3417 58.45 0.10 -0.51
## BlockS:VisuoSpatialCongruencyinc 2040 45.17 -0.29 0.51 -0.55
## Residual 11570 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 341.921 81.413 30.874
## BlockS -71.210 45.023 30.665
## VisuoSpatialCongruencyinc 104.066 57.525 31.764
## PersonalDistress -1.427 5.930 30.863
## BlockS:VisuoSpatialCongruencyinc 52.678 57.148 32.586
## BlockS:PersonalDistress 6.034 3.279 30.653
## VisuoSpatialCongruencyinc:PersonalDistress 1.439 4.198 31.952
## BlockS:VisuoSpatialCongruencyinc:PersonalDistress -4.883 4.167 32.670
## t value Pr(>|t|)
## (Intercept) 4.200 0.00021 ***
## BlockS -1.582 0.12400
## VisuoSpatialCongruencyinc 1.809 0.07992 .
## PersonalDistress -0.241 0.81139
## BlockS:VisuoSpatialCongruencyinc 0.922 0.36342
## BlockS:PersonalDistress 1.840 0.07545 .
## VisuoSpatialCongruencyinc:PersonalDistress 0.343 0.73406
## BlockS:VisuoSpatialCongruencyinc:PersonalDistress -1.172 0.24966
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC PrsnlD BlS:VSC BlS:PD VSC:PD
## BlockS -0.098
## VsSptlCngrn -0.003 -0.171
## PrsnlDstrss -0.978 0.095 0.003
## BlckS:VsSpC -0.093 -0.066 -0.595 0.091
## BlckS:PrsnD 0.095 -0.978 0.167 -0.097 0.065
## VsSptlCn:PD 0.003 0.167 -0.978 -0.003 0.582 -0.171
## BlcS:VSC:PD 0.091 0.064 0.583 -0.093 -0.978 -0.066 -0.597Since the models are not singular, we can continue to explore the data through post-hoc comparisons.
# Means of Block * VisuoSpatialCongruency interaction
emmeans_interaction_PT <- emmeans(lmm_model_PT, ~ Block * VisuoSpatialCongruency| PerspectiveTaking)
emmeans_interaction_PT2 <- emmeans(lmm_model_PT, ~ Block * PerspectiveTaking| VisuoSpatialCongruency)
emmeans_interaction_PT3 <- emmeans(lmm_model_PT, ~ VisuoSpatialCongruency * PerspectiveTaking| Block)
emmeans_interaction_F <- emmeans(lmm_model_F, ~ Block * VisuoSpatialCongruency| Fantasy)
emmeans_interaction_F2 <- emmeans(lmm_model_F, ~ Block * Fantasy| VisuoSpatialCongruency)
emmeans_interaction_F3 <- emmeans(lmm_model_F, ~ VisuoSpatialCongruency * Fantasy| Block)
emmeans_interaction_EC <- emmeans(lmm_model_EC, ~ Block * VisuoSpatialCongruency| EmpaticConcern)
emmeans_interaction_EC2 <- emmeans(lmm_model_EC, ~ Block * EmpaticConcern| VisuoSpatialCongruency)
emmeans_interaction_EC3 <- emmeans(lmm_model_EC, ~ VisuoSpatialCongruency * EmpaticConcern| Block)
emmeans_interaction_PD <- emmeans(lmm_model_PD, ~ Block * VisuoSpatialCongruency| PersonalDistress)
emmeans_interaction_PD2 <- emmeans(lmm_model_PD, ~ Block * PersonalDistress| VisuoSpatialCongruency)
emmeans_interaction_PD3 <- emmeans(lmm_model_PD, ~ VisuoSpatialCongruency * PersonalDistress| Block)
# Means of Block
emmeans_block_PT <- emmeans(lmm_model_PT, ~ Block| PerspectiveTaking)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_F <- emmeans(lmm_model_F, ~ Block| Fantasy)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_EC <- emmeans(lmm_model_EC, ~ Block| EmpaticConcern)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_PD <- emmeans(lmm_model_PD, ~ Block| PersonalDistress)## NOTE: Results may be misleading due to involvement in interactions# Means of VisuoSpatialCongruency
emmeans_visuo_PT <- emmeans(lmm_model_PT, ~ VisuoSpatialCongruency| PerspectiveTaking)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_F <- emmeans(lmm_model_F, ~ VisuoSpatialCongruency| Fantasy)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_EC <- emmeans(lmm_model_EC, ~ VisuoSpatialCongruency| EmpaticConcern)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_PD <- emmeans(lmm_model_PD, ~ VisuoSpatialCongruency| PersonalDistress)## NOTE: Results may be misleading due to involvement in interactions#
# Post hoc comparisons of Block * VisuoSpatialCongruency
posthoc_interaction_PT <- pairs(emmeans_interaction_PT, adjust = "bonferroni")
posthoc_interaction_PT2 <- pairs(emmeans_interaction_PT2, adjust = "bonferroni")
posthoc_interaction_PT3 <- pairs(emmeans_interaction_PT3, adjust = "bonferroni")
posthoc_interaction_F <- pairs(emmeans_interaction_F, adjust = "bonferroni")
posthoc_interaction_F2 <- pairs(emmeans_interaction_F2, adjust = "bonferroni")
posthoc_interaction_F3 <- pairs(emmeans_interaction_F3, adjust = "bonferroni")
posthoc_interaction_EC <- pairs(emmeans_interaction_EC, adjust = "bonferroni")
posthoc_interaction_EC2 <- pairs(emmeans_interaction_EC2, adjust = "bonferroni")
posthoc_interaction_EC3 <- pairs(emmeans_interaction_EC3, adjust = "bonferroni")
posthoc_interaction_PD <- pairs(emmeans_interaction_PD, adjust = "bonferroni")
posthoc_interaction_PD2 <- pairs(emmeans_interaction_PD2, adjust = "bonferroni")
posthoc_interaction_PD3 <- pairs(emmeans_interaction_PD3, adjust = "bonferroni")
# Post hoc comparisons of Block
posthoc_block_PT <- contrast(emmeans_block_PT, adjust = "bonferroni")
posthoc_block_F <- contrast(emmeans_block_F, adjust = "bonferroni")
posthoc_block_EC <- contrast(emmeans_block_EC, adjust = "bonferroni")
posthoc_block_PD <- contrast(emmeans_block_PD, adjust = "bonferroni")
# Post hoc comparisons of VisuoSpatialCongruency
posthoc_visuo_PT <- contrast(emmeans_visuo_PT, adjust = "bonferroni")
posthoc_visuo_F <- contrast(emmeans_visuo_F, adjust = "bonferroni")
posthoc_visuo_EC <- contrast(emmeans_visuo_EC, adjust = "bonferroni")
posthoc_visuo_PD <- contrast(emmeans_visuo_PD, adjust = "bonferroni")
#
#post hoc summary of Block * VisuoSpatialCongruency
summary(posthoc_interaction_PT)## PerspectiveTaking = 16.4:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.91 9.64 31.0 -1.028 1.0000
## A cong - A inc -123.31 11.99 30.9 -10.281 <.0001
## A cong - S inc -120.43 12.26 31.0 -9.823 <.0001
## S cong - A inc -113.40 16.64 30.9 -6.813 <.0001
## S cong - S inc -110.52 10.94 30.9 -10.106 <.0001
## A inc - S inc 2.88 14.72 30.9 0.196 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_PT2)## VisuoSpatialCongruency = cong:
## contrast
## A PerspectiveTaking16.3649572649573 - S PerspectiveTaking16.3649572649573
## estimate SE df t.ratio p.value
## -9.91 9.64 31.0 -1.028 0.3119
##
## VisuoSpatialCongruency = inc:
## contrast
## A PerspectiveTaking16.3649572649573 - S PerspectiveTaking16.3649572649573
## estimate SE df t.ratio p.value
## 2.88 14.72 30.9 0.196 0.8462
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_PT3)## Block = A:
## contrast
## cong PerspectiveTaking16.3649572649573 - inc PerspectiveTaking16.3649572649573
## estimate SE df t.ratio p.value
## -123 12.0 30.9 -10.281 <.0001
##
## Block = S:
## contrast
## cong PerspectiveTaking16.3649572649573 - inc PerspectiveTaking16.3649572649573
## estimate SE df t.ratio p.value
## -111 10.9 30.9 -10.106 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_F)## Fantasy = 15.1:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.76 9.53 31.0 -1.024 1.0000
## A cong - A inc -123.31 12.06 30.9 -10.224 <.0001
## A cong - S inc -120.22 12.38 31.0 -9.711 <.0001
## S cong - A inc -113.55 16.31 31.0 -6.960 <.0001
## S cong - S inc -110.47 10.70 30.9 -10.322 <.0001
## A inc - S inc 3.08 14.67 30.9 0.210 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_F2)## VisuoSpatialCongruency = cong:
## contrast estimate SE df
## A Fantasy15.1311965811966 - S Fantasy15.1311965811966 -9.76 9.53 31.0
## t.ratio p.value
## -1.024 0.3138
##
## VisuoSpatialCongruency = inc:
## contrast estimate SE df
## A Fantasy15.1311965811966 - S Fantasy15.1311965811966 3.08 14.67 30.9
## t.ratio p.value
## 0.210 0.8350
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_F3)## Block = A:
## contrast estimate SE df
## cong Fantasy15.1311965811966 - inc Fantasy15.1311965811966 -123 12.1 30.9
## t.ratio p.value
## -10.224 <.0001
##
## Block = S:
## contrast estimate SE df
## cong Fantasy15.1311965811966 - inc Fantasy15.1311965811966 -110 10.7 30.9
## t.ratio p.value
## -10.322 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_EC)## EmpaticConcern = 13.8:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.85 9.48 31.0 -1.039 1.0000
## A cong - A inc -123.21 12.06 30.9 -10.212 <.0001
## A cong - S inc -120.35 12.06 31.0 -9.979 <.0001
## S cong - A inc -113.36 16.26 30.9 -6.971 <.0001
## S cong - S inc -110.50 10.91 30.9 -10.124 <.0001
## A inc - S inc 2.86 14.28 30.9 0.201 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_EC2)## VisuoSpatialCongruency = cong:
## contrast estimate
## A EmpaticConcern13.775641025641 - S EmpaticConcern13.775641025641 -9.85
## SE df t.ratio p.value
## 9.48 31.0 -1.039 0.3068
##
## VisuoSpatialCongruency = inc:
## contrast estimate
## A EmpaticConcern13.775641025641 - S EmpaticConcern13.775641025641 2.86
## SE df t.ratio p.value
## 14.28 30.9 0.201 0.8424
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_EC3)## Block = A:
## contrast
## cong EmpaticConcern13.775641025641 - inc EmpaticConcern13.775641025641
## estimate SE df t.ratio p.value
## -123 12.1 30.9 -10.212 <.0001
##
## Block = S:
## contrast
## cong EmpaticConcern13.775641025641 - inc EmpaticConcern13.775641025641
## estimate SE df t.ratio p.value
## -111 10.9 30.9 -10.124 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_PD)## PersonalDistress = 13.4:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.81 9.44 31.0 -1.039 1.0000
## A cong - A inc -123.38 12.05 30.9 -10.240 <.0001
## A cong - S inc -120.30 12.33 31.0 -9.757 <.0001
## S cong - A inc -113.57 16.50 31.0 -6.884 <.0001
## S cong - S inc -110.49 10.80 30.9 -10.234 <.0001
## A inc - S inc 3.08 14.72 30.9 0.209 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_PD2)## VisuoSpatialCongruency = cong:
## contrast
## A PersonalDistress13.4260683760684 - S PersonalDistress13.4260683760684
## estimate SE df t.ratio p.value
## -9.81 9.44 31.0 -1.039 0.3068
##
## VisuoSpatialCongruency = inc:
## contrast
## A PersonalDistress13.4260683760684 - S PersonalDistress13.4260683760684
## estimate SE df t.ratio p.value
## 3.08 14.72 30.9 0.209 0.8355
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_PD3)## Block = A:
## contrast
## cong PersonalDistress13.4260683760684 - inc PersonalDistress13.4260683760684
## estimate SE df t.ratio p.value
## -123 12.0 30.9 -10.240 <.0001
##
## Block = S:
## contrast
## cong PersonalDistress13.4260683760684 - inc PersonalDistress13.4260683760684
## estimate SE df t.ratio p.value
## -110 10.8 30.9 -10.234 <.0001
##
## Degrees-of-freedom method: kenward-roger#post hoc summary of Block
summary(posthoc_block_PT)## PerspectiveTaking = 16.4:
## contrast estimate SE df t.ratio p.value
## A effect -1.76 5.44 31 -0.323 1.0000
## S effect 1.76 5.44 31 0.323 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_F)## Fantasy = 15.1:
## contrast estimate SE df t.ratio p.value
## A effect -1.67 5.39 31 -0.309 1.0000
## S effect 1.67 5.39 31 0.309 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_EC)## EmpaticConcern = 13.8:
## contrast estimate SE df t.ratio p.value
## A effect -1.75 5.24 31 -0.333 1.0000
## S effect 1.75 5.24 31 0.333 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_PD)## PersonalDistress = 13.4:
## contrast estimate SE df t.ratio p.value
## A effect -1.68 5.41 31 -0.311 1.0000
## S effect 1.68 5.41 31 0.311 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 tests#post hoc summary of VisuoSpatialCongruency
summary(posthoc_visuo_PT)## PerspectiveTaking = 16.4:
## contrast estimate SE df t.ratio p.value
## cong effect -58.5 4.88 30.9 -11.974 <.0001
## inc effect 58.5 4.88 30.9 11.974 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_F)## Fantasy = 15.1:
## contrast estimate SE df t.ratio p.value
## cong effect -58.4 4.83 31 -12.099 <.0001
## inc effect 58.4 4.83 31 12.099 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_EC)## EmpaticConcern = 13.8:
## contrast estimate SE df t.ratio p.value
## cong effect -58.4 4.88 31 -11.977 <.0001
## inc effect 58.4 4.88 31 11.977 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_PD)## PersonalDistress = 13.4:
## contrast estimate SE df t.ratio p.value
## cong effect -58.5 4.88 31 -11.993 <.0001
## inc effect 58.5 4.88 31 11.993 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 tests##Received Touch Participants were asked to self-report about their socio-tactile interactions levels. The question stated “In the last week, how many tactile interactions have you received?” and three possible tactile interactions were presented on a VAS scale from 0 to 100, stating: (1) Intimate Touch (e.g. kissing, cuddling, caressing by partner or close family); (2) Friendly Touch (e.g. hugs from friends or acceptance); (3) Professional Touch (e.g. shaking hands, touching colleagues’ shoulders, touching carers).
Here we considered the scores to each received touch as covariate for our LMM.
#LMM + Received Touch dimensions as covariate
lmm_model_RT1_I <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * RT1_I + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
lmm_model_RT2_F <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * RT2_F + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)## boundary (singular) fit: see help('isSingular')lmm_model_RT3_P <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * RT3_P + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
#verifysingularity
isSingular(lmm_model_RT1_I)## [1] FALSEisSingular(lmm_model_RT2_F)## [1] TRUEisSingular(lmm_model_RT3_P)## [1] FALSE#summary
summary(lmm_model_RT1_I)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * RT1_I + (1 + Block *
## VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28747.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0790 -0.5700 -0.1267 0.3830 5.9386
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8757 93.58
## BlockS 2030 45.05 0.01
## VisuoSpatialCongruencyinc 3114 55.80 0.16 -0.48
## BlockS:VisuoSpatialCongruencyinc 1632 40.40 -0.40 0.42 -0.48
## Residual 11571 107.57
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 342.33373 27.86308 30.93872 12.286
## BlockS 6.99834 16.39339 30.77716 0.427
## VisuoSpatialCongruencyinc 100.80768 19.17937 31.06641 5.256
## RT1_I -0.49687 0.56173 30.96480 -0.885
## BlockS:VisuoSpatialCongruencyinc 18.20180 18.75098 31.37149 0.971
## BlockS:RT1_I 0.07122 0.33054 30.82602 0.215
## VisuoSpatialCongruencyinc:RT1_I 0.57376 0.38826 31.59169 1.478
## BlockS:VisuoSpatialCongruencyinc:RT1_I -0.79138 0.38001 32.01504 -2.083
## Pr(>|t|)
## (Intercept) 1.95e-13 ***
## BlockS 0.6724
## VisuoSpatialCongruencyinc 1.02e-05 ***
## RT1_I 0.3832
## BlockS:VisuoSpatialCongruencyinc 0.3391
## BlockS:RT1_I 0.8308
## VisuoSpatialCongruencyinc:RT1_I 0.1494
## BlockS:VisuoSpatialCongruencyinc:RT1_I 0.0454 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC RT1_I BlS:VSC BS:RT1 VSC:RT
## BlockS -0.104
## VsSptlCngrn 0.032 -0.157
## RT1_I -0.796 0.083 -0.025
## BlckS:VsSpC -0.144 -0.119 -0.555 0.114
## BlckS:RT1_I 0.083 -0.796 0.125 -0.104 0.095
## VsSpC:RT1_I -0.025 0.124 -0.794 0.031 0.441 -0.155
## BS:VSC:RT1_ 0.114 0.094 0.441 -0.142 -0.793 -0.119 -0.558summary(lmm_model_RT2_F)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * RT2_F + (1 + Block *
## VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28735.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1116 -0.5739 -0.1245 0.3899 5.9076
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8905.2 94.37
## BlockS 971.3 31.17 -0.10
## VisuoSpatialCongruencyinc 3430.1 58.57 0.09 -0.72
## BlockS:VisuoSpatialCongruencyinc 1902.7 43.62 -0.23 0.97 -0.57
## Residual 11566.6 107.55
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 312.6929 25.8338 31.0091 12.104
## BlockS -26.8852 12.4107 39.6803 -2.166
## VisuoSpatialCongruencyinc 117.4639 18.4802 33.2036 6.356
## RT2_F 0.3869 0.7506 31.0510 0.515
## BlockS:VisuoSpatialCongruencyinc 9.8432 18.1068 43.7517 0.544
## BlockS:RT2_F 1.4128 0.3603 39.5987 3.921
## VisuoSpatialCongruencyinc:RT2_F 0.2118 0.5319 32.1515 0.398
## BlockS:VisuoSpatialCongruencyinc:RT2_F -0.8573 0.5183 41.5728 -1.654
## Pr(>|t|)
## (Intercept) 2.77e-13 ***
## BlockS 0.03635 *
## VisuoSpatialCongruencyinc 3.30e-07 ***
## RT2_F 0.60992
## BlockS:VisuoSpatialCongruencyinc 0.58946
## BlockS:RT2_F 0.00034 ***
## VisuoSpatialCongruencyinc:RT2_F 0.69307
## BlockS:VisuoSpatialCongruencyinc:RT2_F 0.10567
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC RT2_F BlS:VSC BS:RT2 VSC:RT
## BlockS -0.201
## VsSptlCngrn -0.014 -0.211
## RT2_F -0.754 0.152 0.011
## BlckS:VsSpC -0.051 0.031 -0.606 0.038
## BlckS:RT2_F 0.152 -0.754 0.158 -0.203 -0.023
## VsSpC:RT2_F 0.011 0.159 -0.758 -0.015 0.458 -0.211
## BS:VSC:RT2_ 0.039 -0.023 0.461 -0.051 -0.760 0.032 -0.602
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')summary(lmm_model_RT3_P)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * RT3_P + (1 + Block *
## VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28742.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0862 -0.5720 -0.1265 0.3833 5.9314
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8863 94.14
## BlockS 1944 44.09 0.03
## VisuoSpatialCongruencyinc 3278 57.25 0.13 -0.51
## BlockS:VisuoSpatialCongruencyinc 2239 47.32 -0.26 0.35 -0.55
## Residual 11571 107.57
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 329.9241 20.3708 30.9558 16.196
## BlockS 3.3736 11.7782 31.0258 0.286
## VisuoSpatialCongruencyinc 115.2004 14.2528 31.5857 8.083
## RT3_P -0.8811 1.3833 31.0955 -0.637
## BlockS:VisuoSpatialCongruencyinc -11.1553 14.6604 32.2233 -0.761
## BlockS:RT3_P 0.7832 0.8009 31.3478 0.978
## VisuoSpatialCongruencyinc:RT3_P 0.9825 0.9608 30.9677 1.023
## BlockS:VisuoSpatialCongruencyinc:RT3_P -0.1954 0.9821 30.8858 -0.199
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## BlockS 0.776
## VisuoSpatialCongruencyinc 3.46e-09 ***
## RT3_P 0.529
## BlockS:VisuoSpatialCongruencyinc 0.452
## BlockS:RT3_P 0.336
## VisuoSpatialCongruencyinc:RT3_P 0.314
## BlockS:VisuoSpatialCongruencyinc:RT3_P 0.844
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC RT3_P BlS:VSC BS:RT3 VSC:RT
## BlockS -0.091
## VsSptlCngrn 0.013 -0.175
## RT3_P -0.555 0.052 -0.006
## BlckS:VsSpC -0.083 -0.127 -0.599 0.045
## BlckS:RT3_P 0.052 -0.556 0.095 -0.095 0.072
## VsSpC:RT3_P -0.006 0.096 -0.554 0.010 0.330 -0.170
## BS:VSC:RT3_ 0.045 0.073 0.332 -0.080 -0.554 -0.132 -0.598Since one model is singular, hence too complex, we create another model in which we do not consider the “Block * VSC” interaction as random factor, but only the two factors separately.
#LMM revised for Received Frendly Touch
lmm_model_RT2_F2 <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * RT2_F + (1 + Block + VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
#singularity and summary
isSingular(lmm_model_RT2_F2)## [1] FALSEsummary(lmm_model_RT2_F2)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * RT2_F + (1 + Block +
## VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28754.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.9268 -0.5722 -0.1273 0.3840 6.1467
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 9505 97.49
## BlockS 2677 51.74 -0.26
## VisuoSpatialCongruencyinc 2462 49.61 0.04 -0.35
## Residual 11681 108.08
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 312.3760 26.6444 31.8957 11.724
## BlockS -26.8401 16.5688 42.8200 -1.620
## VisuoSpatialCongruencyinc 117.4682 16.5288 47.2924 7.107
## RT2_F 0.3973 0.7742 31.9347 0.513
## BlockS:VisuoSpatialCongruencyinc 10.2459 13.9406 2258.2133 0.735
## BlockS:RT2_F 1.4073 0.4811 42.7591 2.925
## VisuoSpatialCongruencyinc:RT2_F 0.2137 0.4752 45.4723 0.450
## BlockS:VisuoSpatialCongruencyinc:RT2_F -0.8702 0.3959 2250.1712 -2.198
## Pr(>|t|)
## (Intercept) 4.23e-13 ***
## BlockS 0.11259
## VisuoSpatialCongruencyinc 5.45e-09 ***
## RT2_F 0.61135
## BlockS:VisuoSpatialCongruencyinc 0.46243
## BlockS:RT2_F 0.00549 **
## VisuoSpatialCongruencyinc:RT2_F 0.65510
## BlockS:VisuoSpatialCongruencyinc:RT2_F 0.02807 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC RT2_F BlS:VSC BS:RT2 VSC:RT
## BlockS -0.311
## VsSptlCngrn -0.070 -0.070
## RT2_F -0.754 0.235 0.053
## BlckS:VsSpC 0.118 -0.376 -0.435 -0.089
## BlckS:RT2_F 0.235 -0.754 0.052 -0.312 0.284
## VsSpC:RT2_F 0.054 0.052 -0.758 -0.071 0.328 -0.069
## BS:VSC:RT2_ -0.091 0.290 0.332 0.121 -0.763 -0.384 -0.426Since the models are now all not singular, we can continue to explore the data through post-hoc comparisons.
# Means of Block * VisuoSpatialCongruency interaction
emmeans_interaction_RT1_I <- emmeans(lmm_model_RT1_I, ~ Block * VisuoSpatialCongruency| RT1_I)
emmeans_interaction_RT1_I2 <- emmeans(lmm_model_RT1_I, ~ Block * RT1_I| VisuoSpatialCongruency)
emmeans_interaction_RT1_I3 <- emmeans(lmm_model_RT1_I, ~ VisuoSpatialCongruency * RT1_I| Block)
emmeans_interaction_RT2_F <- emmeans(lmm_model_RT2_F2, ~ Block * VisuoSpatialCongruency| RT2_F)
emmeans_interaction_RT2_F2 <- emmeans(lmm_model_RT2_F2, ~ Block * RT2_F| VisuoSpatialCongruency)
emmeans_interaction_RT2_F3 <- emmeans(lmm_model_RT2_F2, ~ VisuoSpatialCongruency * RT2_F| Block)
emmeans_interaction_RT3_P <- emmeans(lmm_model_RT3_P, ~ Block * VisuoSpatialCongruency| RT3_P)
emmeans_interaction_RT3_P2 <- emmeans(lmm_model_RT3_P, ~ Block * RT3_P| VisuoSpatialCongruency)
emmeans_interaction_RT3_P3 <- emmeans(lmm_model_RT3_P, ~ VisuoSpatialCongruency * RT3_P| Block)
# Means of Block
emmeans_block_RT1_I <- emmeans(lmm_model_RT1_I, ~ Block| RT1_I)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_RT2_F <- emmeans(lmm_model_RT2_F2, ~ Block| RT2_F)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_RT3_P <- emmeans(lmm_model_RT3_P, ~ Block| RT3_P)## NOTE: Results may be misleading due to involvement in interactions# Means of VisuoSpatialCongruency
emmeans_visuo_RT1_I <- emmeans(lmm_model_RT1_I, ~ VisuoSpatialCongruency| RT1_I)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_RT2_F <- emmeans(lmm_model_RT2_F2, ~ VisuoSpatialCongruency| RT2_F)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_RT3_P <- emmeans(lmm_model_RT3_P, ~ VisuoSpatialCongruency| RT3_P)## NOTE: Results may be misleading due to involvement in interactions#
# Post hoc comparisons of Block * VisuoSpatialCongruency
posthoc_interaction_RT1_I <- pairs(emmeans_interaction_RT1_I, adjust = "bonferroni")
posthoc_interaction_RT1_I2 <- pairs(emmeans_interaction_RT1_I2, adjust = "bonferroni")
posthoc_interaction_RT1_I3 <- pairs(emmeans_interaction_RT1_I3, adjust = "bonferroni")
posthoc_interaction_RT2_F <- pairs(emmeans_interaction_RT2_F, adjust = "bonferroni")
posthoc_interaction_RT2_F2 <- pairs(emmeans_interaction_RT2_F2, adjust = "bonferroni")
posthoc_interaction_RT2_F3 <- pairs(emmeans_interaction_RT2_F3, adjust = "bonferroni")
posthoc_interaction_RT3_P <- pairs(emmeans_interaction_RT3_P, adjust = "bonferroni")
posthoc_interaction_RT3_P2 <- pairs(emmeans_interaction_RT3_P2, adjust = "bonferroni")
posthoc_interaction_RT3_P3 <- pairs(emmeans_interaction_RT3_P3, adjust = "bonferroni")
# Post hoc comparisons of Block
posthoc_block_RT1_I <- contrast(emmeans_block_RT1_I, adjust = "bonferroni")
posthoc_block_RT2_F <- contrast(emmeans_block_RT2_F, adjust = "bonferroni")
posthoc_block_RT3_P <- contrast(emmeans_block_RT3_P, adjust = "bonferroni")
# Post hoc comparisons of VisuoSpatialCongruency
posthoc_visuo_RT1_I <- contrast(emmeans_visuo_RT1_I, adjust = "bonferroni")
posthoc_visuo_RT2_F <- contrast(emmeans_visuo_RT2_F, adjust = "bonferroni")
posthoc_visuo_RT3_P <- contrast(emmeans_visuo_RT3_P, adjust = "bonferroni")
#
#post hoc summary of Block * VisuoSpatialCongruency
summary(posthoc_interaction_RT1_I)## RT1_I = 39.1:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.78 9.92 31.0 -0.986 1.0000
## A cong - A inc -123.24 11.66 30.9 -10.570 <.0001
## A cong - S inc -120.28 12.38 31.0 -9.714 <.0001
## S cong - A inc -113.45 16.44 31.0 -6.899 <.0001
## S cong - S inc -110.50 10.86 30.9 -10.171 <.0001
## A inc - S inc 2.95 14.21 30.9 0.208 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_RT1_I2)## VisuoSpatialCongruency = cong:
## contrast estimate SE df t.ratio
## A RT1_I39.0910256410256 - S RT1_I39.0910256410256 -9.78 9.92 31.0 -0.986
## p.value
## 0.3319
##
## VisuoSpatialCongruency = inc:
## contrast estimate SE df t.ratio
## A RT1_I39.0910256410256 - S RT1_I39.0910256410256 2.95 14.21 30.9 0.208
## p.value
## 0.8369
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_RT1_I3)## Block = A:
## contrast estimate SE df
## cong RT1_I39.0910256410256 - inc RT1_I39.0910256410256 -123 11.7 30.9
## t.ratio p.value
## -10.570 <.0001
##
## Block = S:
## contrast estimate SE df
## cong RT1_I39.0910256410256 - inc RT1_I39.0910256410256 -111 10.9 30.9
## t.ratio p.value
## -10.171 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_RT2_F)## RT2_F = 26.6:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -10.55 10.9 42.3 -0.969 1.0000
## A cong - A inc -123.15 10.8 46.1 -11.426 <.0001
## A cong - S inc -120.82 11.9 31.0 -10.145 <.0001
## S cong - A inc -112.59 15.9 31.0 -7.100 <.0001
## S cong - S inc -110.27 10.7 45.0 -10.296 <.0001
## A inc - S inc 2.32 11.2 47.1 0.208 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_RT2_F2)## VisuoSpatialCongruency = cong:
## contrast estimate SE df t.ratio
## A RT2_F26.5709401709402 - S RT2_F26.5709401709402 -10.55 10.9 42.3 -0.969
## p.value
## 0.3379
##
## VisuoSpatialCongruency = inc:
## contrast estimate SE df t.ratio
## A RT2_F26.5709401709402 - S RT2_F26.5709401709402 2.32 11.2 47.1 0.208
## p.value
## 0.8365
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_RT2_F3)## Block = A:
## contrast estimate SE df
## cong RT2_F26.5709401709402 - inc RT2_F26.5709401709402 -123 10.8 46.1
## t.ratio p.value
## -11.426 <.0001
##
## Block = S:
## contrast estimate SE df
## cong RT2_F26.5709401709402 - inc RT2_F26.5709401709402 -110 10.7 45.0
## t.ratio p.value
## -10.296 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_RT3_P)## RT3_P = 8.26:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.85 9.79 31.0 -1.005 1.0000
## A cong - A inc -123.32 11.87 30.9 -10.387 <.0001
## A cong - S inc -120.40 11.89 30.9 -10.123 <.0001
## S cong - A inc -113.47 16.65 30.9 -6.813 <.0001
## S cong - S inc -110.55 10.78 30.9 -10.258 <.0001
## A inc - S inc 2.92 14.67 30.9 0.199 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_RT3_P2)## VisuoSpatialCongruency = cong:
## contrast estimate SE df t.ratio
## A RT3_P8.26367521367521 - S RT3_P8.26367521367521 -9.85 9.79 31.0 -1.005
## p.value
## 0.3225
##
## VisuoSpatialCongruency = inc:
## contrast estimate SE df t.ratio
## A RT3_P8.26367521367521 - S RT3_P8.26367521367521 2.92 14.67 30.9 0.199
## p.value
## 0.8433
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_RT3_P3)## Block = A:
## contrast estimate SE df
## cong RT3_P8.26367521367521 - inc RT3_P8.26367521367521 -123 11.9 30.9
## t.ratio p.value
## -10.387 <.0001
##
## Block = S:
## contrast estimate SE df
## cong RT3_P8.26367521367521 - inc RT3_P8.26367521367521 -111 10.8 30.9
## t.ratio p.value
## -10.258 <.0001
##
## Degrees-of-freedom method: kenward-roger#post hoc summary of Block
summary(posthoc_block_RT1_I)## RT1_I = 39.1:
## contrast estimate SE df t.ratio p.value
## A effect -1.71 5.42 31 -0.315 1.0000
## S effect 1.71 5.42 31 0.315 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_RT2_F)## RT2_F = 26.6:
## contrast estimate SE df t.ratio p.value
## A effect -2.06 5.04 31.1 -0.408 1.0000
## S effect 2.06 5.04 31.1 0.408 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_RT3_P)## RT3_P = 8.26:
## contrast estimate SE df t.ratio p.value
## A effect -1.73 5.44 31 -0.318 1.0000
## S effect 1.73 5.44 31 0.318 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 tests#post hoc summary of VisuoSpatialCongruency
summary(posthoc_visuo_RT1_I)## RT1_I = 39.1:
## contrast estimate SE df t.ratio p.value
## cong effect -58.4 4.86 31 -12.036 <.0001
## inc effect 58.4 4.86 31 12.036 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_RT2_F)## RT2_F = 26.6:
## contrast estimate SE df t.ratio p.value
## cong effect -58.4 4.88 30.9 -11.969 <.0001
## inc effect 58.4 4.88 30.9 11.969 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_RT3_P)## RT3_P = 8.26:
## contrast estimate SE df t.ratio p.value
## cong effect -58.5 4.78 30.9 -12.242 <.0001
## inc effect 58.5 4.78 30.9 12.242 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 tests##Desired Touch Participants were asked to self-report about their socio-tactile interactions levels. The question stated “In the last week, how many tactile interactions have you desired?” and three possible tactile interactions were presented on a VAS scale from 0 to 100, stating: (1) Intimate Touch (e.g. kissing, cuddling, caressing by partner or close family); (2) Friendly Touch (e.g. hugs from friends or acceptance); (3) Professional Touch (e.g. shaking hands, touching colleagues’ shoulders, touching carers).
Here we considered the scores to each desired touch as covariate for our LMM.
#LMM + Desired Touch scores as covariate
lmm_model_DT1_I <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * DT1_I + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
lmm_model_DT2_F <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * DT2_F + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
lmm_model_DT3_P <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * DT3_P + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
#verifysingularity
isSingular(lmm_model_DT1_I)## [1] FALSEisSingular(lmm_model_DT2_F)## [1] FALSEisSingular(lmm_model_DT3_P)## [1] FALSE#summary
summary(lmm_model_DT1_I)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * DT1_I + (1 + Block *
## VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28745.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0657 -0.5777 -0.1261 0.3785 5.9525
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8926 94.48
## BlockS 1470 38.34 0.05
## VisuoSpatialCongruencyinc 3409 58.39 0.11 -0.57
## BlockS:VisuoSpatialCongruencyinc 1856 43.08 -0.33 0.71 -0.57
## Residual 11569 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 336.5984 34.2130 30.9613 9.838
## BlockS -30.8931 18.1981 31.2358 -1.698
## VisuoSpatialCongruencyinc 114.8018 24.3768 32.6021 4.709
## DT1_I -0.2442 0.5244 30.9403 -0.466
## BlockS:VisuoSpatialCongruencyinc 21.6835 23.9303 34.4370 0.906
## BlockS:DT1_I 0.7168 0.2784 30.9945 2.575
## VisuoSpatialCongruencyinc:DT1_I 0.1456 0.3721 32.1273 0.391
## BlockS:VisuoSpatialCongruencyinc:DT1_I -0.6019 0.3640 33.5330 -1.654
## Pr(>|t|)
## (Intercept) 4.79e-11 ***
## BlockS 0.0995 .
## VisuoSpatialCongruencyinc 4.44e-05 ***
## DT1_I 0.6447
## BlockS:VisuoSpatialCongruencyinc 0.3712
## BlockS:DT1_I 0.0150 *
## VisuoSpatialCongruencyinc:DT1_I 0.6982
## BlockS:VisuoSpatialCongruencyinc:DT1_I 0.1075
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC DT1_I BlS:VSC BS:DT1 VSC:DT
## BlockS -0.082
## VsSptlCngrn 0.000 -0.182
## DT1_I -0.868 0.071 0.000
## BlckS:VsSpC -0.108 -0.017 -0.601 0.094
## BlckS:DT1_I 0.071 -0.868 0.158 -0.081 0.014
## VsSpC:DT1_I 0.000 0.159 -0.870 0.000 0.522 -0.184
## BS:VSC:DT1_ 0.094 0.014 0.524 -0.109 -0.872 -0.015 -0.599summary(lmm_model_DT2_F)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * DT2_F + (1 + Block *
## VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28742.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0974 -0.5749 -0.1241 0.3855 5.9206
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8976 94.74
## BlockS 1259 35.48 -0.01
## VisuoSpatialCongruencyinc 3434 58.60 0.10 -0.60
## BlockS:VisuoSpatialCongruencyinc 1978 44.47 -0.27 0.73 -0.57
## Residual 11570 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 321.41456 27.34017 30.98744 11.756
## BlockS -24.35838 13.92782 31.19601 -1.749
## VisuoSpatialCongruencyinc 119.45849 19.54055 32.93284 6.113
## DT2_F 0.03925 0.63212 31.01554 0.062
## BlockS:VisuoSpatialCongruencyinc 7.86364 19.31808 34.05042 0.407
## BlockS:DT2_F 1.00875 0.32185 31.17250 3.134
## VisuoSpatialCongruencyinc:DT2_F 0.10487 0.44783 31.96951 0.234
## BlockS:VisuoSpatialCongruencyinc:DT2_F -0.60008 0.44060 32.50824 -1.362
## Pr(>|t|)
## (Intercept) 5.91e-13 ***
## BlockS 0.09014 .
## VisuoSpatialCongruencyinc 6.97e-07 ***
## DT2_F 0.95089
## BlockS:VisuoSpatialCongruencyinc 0.68651
## BlockS:DT2_F 0.00374 **
## VisuoSpatialCongruencyinc:DT2_F 0.81635
## BlockS:VisuoSpatialCongruencyinc:DT2_F 0.18257
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC DT2_F BlS:VSC BS:DT2 VSC:DT
## BlockS -0.131
## VsSptlCngrn -0.006 -0.177
## DT2_F -0.782 0.103 0.005
## BlckS:VsSpC -0.078 -0.022 -0.608 0.061
## BlckS:DT2_F 0.103 -0.783 0.138 -0.132 0.018
## VsSpC:DT2_F 0.005 0.139 -0.787 -0.007 0.478 -0.178
## BS:VSC:DT2_ 0.061 0.018 0.480 -0.078 -0.789 -0.022 -0.604summary(lmm_model_DT3_P)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * DT3_P + (1 + Block *
## VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28744.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0833 -0.5762 -0.1240 0.3798 5.9341
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8848 94.06
## BlockS 1957 44.23 0.03
## VisuoSpatialCongruencyinc 3277 57.24 0.13 -0.50
## BlockS:VisuoSpatialCongruencyinc 2237 47.30 -0.25 0.33 -0.58
## Residual 11571 107.57
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 328.4902 18.9814 30.9478 17.306
## BlockS 5.2445 11.0022 30.9790 0.477
## VisuoSpatialCongruencyinc 117.1436 13.2709 31.4472 8.827
## DT3_P -0.7200 1.0737 31.0844 -0.671
## BlockS:VisuoSpatialCongruencyinc -13.7237 13.6502 32.0714 -1.005
## BlockS:DT3_P 0.5660 0.6235 31.3630 0.908
## VisuoSpatialCongruencyinc:DT3_P 0.7708 0.7519 31.7947 1.025
## BlockS:VisuoSpatialCongruencyinc:DT3_P 0.1106 0.7692 31.7465 0.144
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## BlockS 0.637
## VisuoSpatialCongruencyinc 5.09e-10 ***
## DT3_P 0.507
## BlockS:VisuoSpatialCongruencyinc 0.322
## BlockS:DT3_P 0.371
## VisuoSpatialCongruencyinc:DT3_P 0.313
## BlockS:VisuoSpatialCongruencyinc:DT3_P 0.887
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC DT3_P BlS:VSC BS:DT3 VSC:DT
## BlockS -0.091
## VsSptlCngrn 0.013 -0.173
## DT3_P -0.452 0.042 -0.005
## BlckS:VsSpC -0.075 -0.136 -0.611 0.033
## BlckS:DT3_P 0.042 -0.453 0.077 -0.095 0.063
## VsSpC:DT3_P -0.005 0.077 -0.448 0.010 0.273 -0.167
## BS:VSC:DT3_ 0.033 0.063 0.274 -0.072 -0.448 -0.141 -0.616Since the models are now all not singular, we can continue to explore the data through post-hoc comparisons.
# Means of Block * VisuoSpatialCongruency interaction
emmeans_interaction_DT1_I <- emmeans(lmm_model_DT1_I, ~ Block * VisuoSpatialCongruency| DT1_I)
emmeans_interaction_DT1_I2 <- emmeans(lmm_model_DT1_I, ~ Block * DT1_I| VisuoSpatialCongruency)
emmeans_interaction_DT1_I3 <- emmeans(lmm_model_DT1_I, ~ VisuoSpatialCongruency * DT1_I| Block)
emmeans_interaction_DT2_F <- emmeans(lmm_model_DT2_F, ~ Block * VisuoSpatialCongruency| DT2_F)
emmeans_interaction_DT2_F2 <- emmeans(lmm_model_DT2_F, ~ Block * DT2_F| VisuoSpatialCongruency)
emmeans_interaction_DT2_F3 <- emmeans(lmm_model_DT2_F, ~ VisuoSpatialCongruency * DT2_F| Block)
emmeans_interaction_DT3_P <- emmeans(lmm_model_DT3_P, ~ Block * VisuoSpatialCongruency| DT3_P)
emmeans_interaction_DT3_P2 <- emmeans(lmm_model_DT3_P, ~ Block * DT3_P| VisuoSpatialCongruency)
emmeans_interaction_DT3_P3 <- emmeans(lmm_model_DT3_P, ~ VisuoSpatialCongruency * DT3_P| Block)
# Means of Block
emmeans_block_DT1_I <- emmeans(lmm_model_DT1_I, ~ Block| DT1_I)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_DT2_F <- emmeans(lmm_model_DT2_F, ~ Block| DT2_F)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_DT3_P <- emmeans(lmm_model_DT3_P, ~ Block| DT3_P)## NOTE: Results may be misleading due to involvement in interactions# Means of VisuoSpatialCongruency
emmeans_visuo_DT1_I <- emmeans(lmm_model_DT1_I, ~ VisuoSpatialCongruency| DT1_I)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_DT2_F <- emmeans(lmm_model_DT2_F, ~ VisuoSpatialCongruency| DT2_F)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_DT3_P <- emmeans(lmm_model_DT3_P, ~ VisuoSpatialCongruency| DT3_P)## NOTE: Results may be misleading due to involvement in interactions#
# Post hoc comparisons of Block * VisuoSpatialCongruency
posthoc_interaction_DT1_I <- pairs(emmeans_interaction_DT1_I, adjust = "bonferroni")
posthoc_interaction_DT1_I2 <- pairs(emmeans_interaction_DT1_I2, adjust = "bonferroni")
posthoc_interaction_DT1_I3 <- pairs(emmeans_interaction_DT1_I3, adjust = "bonferroni")
posthoc_interaction_DT2_F <- pairs(emmeans_interaction_DT2_F, adjust = "bonferroni")
posthoc_interaction_DT2_F2 <- pairs(emmeans_interaction_DT2_F2, adjust = "bonferroni")
posthoc_interaction_DT2_F3 <- pairs(emmeans_interaction_DT2_F3, adjust = "bonferroni")
posthoc_interaction_DT3_P <- pairs(emmeans_interaction_DT3_P, adjust = "bonferroni")
posthoc_interaction_DT3_P2 <- pairs(emmeans_interaction_DT3_P2, adjust = "bonferroni")
posthoc_interaction_DT3_P3 <- pairs(emmeans_interaction_DT3_P3, adjust = "bonferroni")
# Post hoc comparisons of Block
posthoc_block_DT1_I <- contrast(emmeans_block_DT1_I, adjust = "bonferroni")
posthoc_block_DT2_F <- contrast(emmeans_block_DT2_F, adjust = "bonferroni")
posthoc_block_DT3_P <- contrast(emmeans_block_DT3_P, adjust = "bonferroni")
# Post hoc comparisons of VisuoSpatialCongruency
posthoc_visuo_DT1_I <- contrast(emmeans_visuo_DT1_I, adjust = "bonferroni")
posthoc_visuo_DT2_F <- contrast(emmeans_visuo_DT2_F, adjust = "bonferroni")
posthoc_visuo_DT3_P <- contrast(emmeans_visuo_DT3_P, adjust = "bonferroni")
#
#post hoc summary of Block * VisuoSpatialCongruency
summary(posthoc_interaction_DT1_I)## DT1_I = 57.4:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -10.26 9.03 31.0 -1.137 1.0000
## A cong - A inc -123.16 12.04 30.9 -10.230 <.0001
## A cong - S inc -120.55 12.31 31.0 -9.790 <.0001
## S cong - A inc -112.90 16.32 31.0 -6.918 <.0001
## S cong - S inc -110.28 10.63 30.9 -10.370 <.0001
## A inc - S inc 2.61 14.70 30.9 0.178 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_DT1_I2)## VisuoSpatialCongruency = cong:
## contrast estimate SE df t.ratio
## A DT1_I57.4162393162393 - S DT1_I57.4162393162393 -10.26 9.03 31.0 -1.137
## p.value
## 0.2644
##
## VisuoSpatialCongruency = inc:
## contrast estimate SE df t.ratio
## A DT1_I57.4162393162393 - S DT1_I57.4162393162393 2.61 14.70 30.9 0.178
## p.value
## 0.8599
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_DT1_I3)## Block = A:
## contrast estimate SE df
## cong DT1_I57.4162393162393 - inc DT1_I57.4162393162393 -123 12.0 30.9
## t.ratio p.value
## -10.230 <.0001
##
## Block = S:
## contrast estimate SE df
## cong DT1_I57.4162393162393 - inc DT1_I57.4162393162393 -110 10.6 30.9
## t.ratio p.value
## -10.370 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_DT2_F)## DT2_F = 34.6:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -10.56 8.67 31.0 -1.218 1.0000
## A cong - A inc -123.09 12.07 30.9 -10.198 <.0001
## A cong - S inc -120.74 12.14 30.9 -9.943 <.0001
## S cong - A inc -112.53 16.09 30.9 -6.995 <.0001
## S cong - S inc -110.18 10.68 30.9 -10.315 <.0001
## A inc - S inc 2.35 14.58 30.9 0.161 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_DT2_F2)## VisuoSpatialCongruency = cong:
## contrast estimate SE df t.ratio
## A DT2_F34.6141025641026 - S DT2_F34.6141025641026 -10.56 8.67 31.0 -1.218
## p.value
## 0.2324
##
## VisuoSpatialCongruency = inc:
## contrast estimate SE df t.ratio
## A DT2_F34.6141025641026 - S DT2_F34.6141025641026 2.35 14.58 30.9 0.161
## p.value
## 0.8730
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_DT2_F3)## Block = A:
## contrast estimate SE df
## cong DT2_F34.6141025641026 - inc DT2_F34.6141025641026 -123 12.1 30.9
## t.ratio p.value
## -10.198 <.0001
##
## Block = S:
## contrast estimate SE df
## cong DT2_F34.6141025641026 - inc DT2_F34.6141025641026 -110 10.7 30.9
## t.ratio p.value
## -10.315 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_DT3_P)## DT3_P = 7.93:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.73 9.81 31.0 -0.992 1.0000
## A cong - A inc -123.26 11.87 30.9 -10.383 <.0001
## A cong - S inc -120.15 11.67 30.9 -10.297 <.0001
## S cong - A inc -113.52 16.66 31.0 -6.816 <.0001
## S cong - S inc -110.41 10.60 30.9 -10.412 <.0001
## A inc - S inc 3.11 14.60 30.9 0.213 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_DT3_P2)## VisuoSpatialCongruency = cong:
## contrast estimate SE df t.ratio
## A DT3_P7.93333333333333 - S DT3_P7.93333333333333 -9.73 9.81 31.0 -0.992
## p.value
## 0.3288
##
## VisuoSpatialCongruency = inc:
## contrast estimate SE df t.ratio
## A DT3_P7.93333333333333 - S DT3_P7.93333333333333 3.11 14.60 30.9 0.213
## p.value
## 0.8326
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_DT3_P3)## Block = A:
## contrast estimate SE df
## cong DT3_P7.93333333333333 - inc DT3_P7.93333333333333 -123 11.9 30.9
## t.ratio p.value
## -10.383 <.0001
##
## Block = S:
## contrast estimate SE df
## cong DT3_P7.93333333333333 - inc DT3_P7.93333333333333 -110 10.6 30.9
## t.ratio p.value
## -10.412 <.0001
##
## Degrees-of-freedom method: kenward-roger#post hoc summary of Block
summary(posthoc_block_DT1_I)## DT1_I = 57.4:
## contrast estimate SE df t.ratio p.value
## A effect -1.91 5.35 31 -0.358 1.0000
## S effect 1.91 5.35 31 0.358 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_DT2_F)## DT2_F = 34.6:
## contrast estimate SE df t.ratio p.value
## A effect -2.05 5.21 31 -0.394 1.0000
## S effect 2.05 5.21 31 0.394 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_DT3_P)## DT3_P = 7.93:
## contrast estimate SE df t.ratio p.value
## A effect -1.66 5.42 31 -0.306 1.0000
## S effect 1.66 5.42 31 0.306 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 tests#post hoc summary of VisuoSpatialCongruency
summary(posthoc_visuo_DT1_I)## DT1_I = 57.4:
## contrast estimate SE df t.ratio p.value
## cong effect -58.4 4.86 31 -11.999 <.0001
## inc effect 58.4 4.86 31 11.999 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_DT2_F)## DT2_F = 34.6:
## contrast estimate SE df t.ratio p.value
## cong effect -58.3 4.86 30.9 -11.993 <.0001
## inc effect 58.3 4.86 30.9 11.993 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_DT3_P)## DT3_P = 7.93:
## contrast estimate SE df t.ratio p.value
## cong effect -58.4 4.73 31 -12.358 <.0001
## inc effect 58.4 4.73 31 12.358 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 tests##Social Interaction Participants were asked to self-report about their social interactions levels. Three question regarding social interaction involvement were presented on a VAS scale from 0 to 100, stating: (1) “How involved were you in social interactions before the pandemic”; (2) “How involved have you been in social interactions in the past week?”; (3) “How much would you like to be involved in social interactions right now?”.
Here we considered the scores to each question as covariate for our LMM.
#LMM + Social Interaction scores as covariate
lmm_model_SI_1 <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * SI_1 + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
lmm_model_SI_2 <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * SI_2 + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
lmm_model_SI_3 <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * SI_3 + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
#verifysingularity
isSingular(lmm_model_SI_1)## [1] FALSEisSingular(lmm_model_SI_2)## [1] FALSEisSingular(lmm_model_SI_3)## [1] FALSE#summary
summary(lmm_model_SI_1)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * SI_1 + (1 + Block *
## VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28749.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0709 -0.5733 -0.1286 0.3779 5.9469
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8721 93.39
## BlockS 2031 45.07 0.01
## VisuoSpatialCongruencyinc 3430 58.56 0.09 -0.44
## BlockS:VisuoSpatialCongruencyinc 1964 44.32 -0.21 0.33 -0.56
## Residual 11570 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 291.52638 36.96929 30.95468 7.886
## BlockS 15.03051 21.79999 30.82700 0.689
## VisuoSpatialCongruencyinc 114.73008 26.68716 32.43165 4.299
## SI_1 0.57030 0.60154 30.94777 0.948
## BlockS:VisuoSpatialCongruencyinc 18.72185 26.17616 32.49892 0.715
## BlockS:SI_1 -0.09599 0.35483 30.86364 -0.271
## VisuoSpatialCongruencyinc:SI_1 0.15526 0.43393 32.38197 0.358
## BlockS:VisuoSpatialCongruencyinc:SI_1 -0.57563 0.42576 32.46498 -1.352
## Pr(>|t|)
## (Intercept) 6.76e-09 ***
## BlockS 0.495683
## VisuoSpatialCongruencyinc 0.000147 ***
## SI_1 0.350441
## BlockS:VisuoSpatialCongruencyinc 0.479577
## BlockS:SI_1 0.788563
## VisuoSpatialCongruencyinc:SI_1 0.722811
## BlockS:VisuoSpatialCongruencyinc:SI_1 0.185722
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC SI_1 BlS:VSC BS:SI_ VSC:SI
## BlockS -0.103
## VsSptlCngrn -0.019 -0.135
## SI_1 -0.891 0.091 0.017
## BlckS:VsSpC -0.040 -0.142 -0.606 0.036
## BlockS:SI_1 0.091 -0.890 0.121 -0.102 0.126
## VsSptC:SI_1 0.017 0.121 -0.892 -0.019 0.541 -0.136
## BS:VSC:SI_1 0.036 0.126 0.541 -0.040 -0.891 -0.142 -0.605summary(lmm_model_SI_2)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * SI_2 + (1 + Block *
## VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28744.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0797 -0.5677 -0.1297 0.3789 5.9390
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8988 94.81
## BlockS 1930 43.93 0.00
## VisuoSpatialCongruencyinc 3348 57.86 0.09 -0.49
## BlockS:VisuoSpatialCongruencyinc 1371 37.03 -0.30 0.62 -0.58
## Residual 11568 107.55
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 319.92868 39.13572 31.01549 8.175
## BlockS -10.96131 22.43196 31.03162 -0.489
## VisuoSpatialCongruencyinc 107.03476 27.40002 31.69557 3.906
## SI_2 0.05128 0.63706 30.98981 0.081
## BlockS:VisuoSpatialCongruencyinc 46.84145 25.42120 32.72173 1.843
## BlockS:SI_2 0.37406 0.36468 30.85401 1.026
## VisuoSpatialCongruencyinc:SI_2 0.29846 0.44777 32.05035 0.667
## BlockS:VisuoSpatialCongruencyinc:SI_2 -1.08174 0.41456 32.80940 -2.609
## Pr(>|t|)
## (Intercept) 3.1e-09 ***
## BlockS 0.628527
## VisuoSpatialCongruencyinc 0.000461 ***
## SI_2 0.936356
## BlockS:VisuoSpatialCongruencyinc 0.074462 .
## BlockS:SI_2 0.312996
## VisuoSpatialCongruencyinc:SI_2 0.509827
## BlockS:VisuoSpatialCongruencyinc:SI_2 0.013558 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC SI_2 BlS:VSC BS:SI_ VSC:SI
## BlockS -0.116
## VsSptlCngrn -0.016 -0.163
## SI_2 -0.900 0.104 0.014
## BlckS:VsSpC -0.071 -0.059 -0.597 0.064
## BlockS:SI_2 0.104 -0.900 0.147 -0.115 0.053
## VsSptC:SI_2 0.014 0.146 -0.900 -0.015 0.539 -0.164
## BS:VSC:SI_2 0.064 0.053 0.540 -0.071 -0.900 -0.057 -0.602summary(lmm_model_SI_3)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * SI_3 + (1 + Block *
## VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28747.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0822 -0.5784 -0.1177 0.3790 5.9359
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8800 93.81
## BlockS 1776 42.14 -0.06
## VisuoSpatialCongruencyinc 3434 58.60 0.10 -0.48
## BlockS:VisuoSpatialCongruencyinc 2152 46.39 -0.23 0.44 -0.56
## Residual 11569 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 293.27443 41.15387 31.00987 7.126
## BlockS -25.65543 23.23724 31.06243 -1.104
## VisuoSpatialCongruencyinc 118.86422 29.68326 32.98933 4.004
## SI_3 0.52738 0.67067 30.98321 0.786
## BlockS:VisuoSpatialCongruencyinc 9.50294 29.77659 33.61382 0.319
## BlockS:SI_3 0.63217 0.37822 30.88655 1.671
## VisuoSpatialCongruencyinc:SI_3 0.07794 0.48360 32.88780 0.161
## BlockS:VisuoSpatialCongruencyinc:SI_3 -0.39644 0.48437 33.36096 -0.818
## Pr(>|t|)
## (Intercept) 5.22e-08 ***
## BlockS 0.278044
## VisuoSpatialCongruencyinc 0.000332 ***
## SI_3 0.437636
## BlockS:VisuoSpatialCongruencyinc 0.751594
## BlockS:SI_3 0.104736
## VisuoSpatialCongruencyinc:SI_3 0.872943
## BlockS:VisuoSpatialCongruencyinc:SI_3 0.418904
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC SI_3 BlS:VSC BS:SI_ VSC:SI
## BlockS -0.159
## VsSptlCngrn -0.013 -0.148
## SI_3 -0.912 0.145 0.012
## BlckS:VsSpC -0.056 -0.096 -0.605 0.051
## BlockS:SI_3 0.145 -0.912 0.135 -0.159 0.086
## VsSptC:SI_3 0.012 0.135 -0.914 -0.012 0.553 -0.149
## BS:VSC:SI_3 0.051 0.086 0.554 -0.057 -0.914 -0.094 -0.606Since the models are not singular, we can continue to explore the data through post-hoc comparisons.
# Means of Block * VisuoSpatialCongruency interaction
emmeans_interaction_SI_1 <- emmeans(lmm_model_SI_1, ~ Block * VisuoSpatialCongruency| SI_1)
emmeans_interaction_SI_12 <- emmeans(lmm_model_SI_1, ~ Block * SI_1| VisuoSpatialCongruency)
emmeans_interaction_SI_13 <- emmeans(lmm_model_SI_1, ~ VisuoSpatialCongruency * SI_1| Block)
emmeans_interaction_SI_2 <- emmeans(lmm_model_SI_2, ~ Block * VisuoSpatialCongruency| SI_2)
emmeans_interaction_SI_22 <- emmeans(lmm_model_SI_2, ~ Block * SI_2| VisuoSpatialCongruency)
emmeans_interaction_SI_23 <- emmeans(lmm_model_SI_2, ~ VisuoSpatialCongruency * SI_2| Block)
emmeans_interaction_SI_3 <- emmeans(lmm_model_SI_3, ~ Block * VisuoSpatialCongruency| SI_3)
emmeans_interaction_SI_32 <- emmeans(lmm_model_SI_3, ~ Block * SI_3| VisuoSpatialCongruency)
emmeans_interaction_SI_33 <- emmeans(lmm_model_SI_3, ~ VisuoSpatialCongruency * SI_3| Block)
# Means of Block
emmeans_block_SI_1 <- emmeans(lmm_model_SI_1, ~ Block| SI_1)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_SI_2 <- emmeans(lmm_model_SI_2, ~ Block| SI_2)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_SI_3 <- emmeans(lmm_model_SI_3, ~ Block| SI_3)## NOTE: Results may be misleading due to involvement in interactions# Means of VisuoSpatialCongruency
emmeans_visuo_SI_1 <- emmeans(lmm_model_SI_1, ~ VisuoSpatialCongruency| SI_1)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_SI_2 <- emmeans(lmm_model_SI_2, ~ VisuoSpatialCongruency| SI_2)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_SI_3 <- emmeans(lmm_model_SI_3, ~ VisuoSpatialCongruency| SI_3)## NOTE: Results may be misleading due to involvement in interactions#
# Post hoc comparisons of Block * VisuoSpatialCongruency
posthoc_interaction_SI_1 <- pairs(emmeans_interaction_SI_1, adjust = "bonferroni")
posthoc_interaction_SI_12 <- pairs(emmeans_interaction_SI_12, adjust = "bonferroni")
posthoc_interaction_SI_13 <- pairs(emmeans_interaction_SI_13, adjust = "bonferroni")
posthoc_interaction_SI_2 <- pairs(emmeans_interaction_SI_2, adjust = "bonferroni")
posthoc_interaction_SI_22 <- pairs(emmeans_interaction_SI_22, adjust = "bonferroni")
posthoc_interaction_SI_23 <- pairs(emmeans_interaction_SI_23, adjust = "bonferroni")
posthoc_interaction_SI_3 <- pairs(emmeans_interaction_SI_3, adjust = "bonferroni")
posthoc_interaction_SI_32 <- pairs(emmeans_interaction_SI_32, adjust = "bonferroni")
posthoc_interaction_SI_33 <- pairs(emmeans_interaction_SI_33, adjust = "bonferroni")
# Post hoc comparisons of Block
posthoc_block_SI_1 <- contrast(emmeans_block_SI_1, adjust = "bonferroni")
posthoc_block_SI_2 <- contrast(emmeans_block_SI_2, adjust = "bonferroni")
posthoc_block_SI_3 <- contrast(emmeans_block_SI_3, adjust = "bonferroni")
# Post hoc comparisons of VisuoSpatialCongruency
posthoc_visuo_SI_1 <- contrast(emmeans_visuo_SI_1, adjust = "bonferroni")
posthoc_visuo_SI_2 <- contrast(emmeans_visuo_SI_2, adjust = "bonferroni")
posthoc_visuo_SI_3 <- contrast(emmeans_visuo_SI_3, adjust = "bonferroni")
#
#post hoc summary of Block * VisuoSpatialCongruency
summary(posthoc_interaction_SI_1)## SI_1 = 54.7:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.78 9.93 31.0 -0.986 1.0000
## A cong - A inc -123.22 12.06 30.9 -10.213 <.0001
## A cong - S inc -120.26 12.12 31.0 -9.918 <.0001
## S cong - A inc -113.43 16.63 31.0 -6.820 <.0001
## S cong - S inc -110.47 10.72 30.9 -10.309 <.0001
## A inc - S inc 2.96 14.34 30.9 0.207 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_SI_12)## VisuoSpatialCongruency = cong:
## contrast estimate SE df t.ratio
## A SI_154.6649572649573 - S SI_154.6649572649573 -9.78 9.93 31.0 -0.986
## p.value
## 0.3320
##
## VisuoSpatialCongruency = inc:
## contrast estimate SE df t.ratio
## A SI_154.6649572649573 - S SI_154.6649572649573 2.96 14.34 30.9 0.207
## p.value
## 0.8377
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_SI_13)## Block = A:
## contrast estimate SE df
## cong SI_154.6649572649573 - inc SI_154.6649572649573 -123 12.1 30.9
## t.ratio p.value
## -10.213 <.0001
##
## Block = S:
## contrast estimate SE df
## cong SI_154.6649572649573 - inc SI_154.6649572649573 -110 10.7 30.9
## t.ratio p.value
## -10.309 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_SI_2)## SI_2 = 55.4:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.77 9.77 31.0 -1.000 1.0000
## A cong - A inc -123.57 11.96 30.9 -10.332 <.0001
## A cong - S inc -120.24 12.31 31.0 -9.770 <.0001
## S cong - A inc -113.81 16.65 31.0 -6.836 <.0001
## S cong - S inc -110.47 10.35 30.9 -10.674 <.0001
## A inc - S inc 3.33 14.35 30.9 0.232 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_SI_22)## VisuoSpatialCongruency = cong:
## contrast estimate SE df t.ratio
## A SI_255.4115384615385 - S SI_255.4115384615385 -9.77 9.77 31.0 -1.000
## p.value
## 0.3253
##
## VisuoSpatialCongruency = inc:
## contrast estimate SE df t.ratio
## A SI_255.4115384615385 - S SI_255.4115384615385 3.33 14.35 30.9 0.232
## p.value
## 0.8178
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_SI_23)## Block = A:
## contrast estimate SE df
## cong SI_255.4115384615385 - inc SI_255.4115384615385 -124 12.0 30.9
## t.ratio p.value
## -10.332 <.0001
##
## Block = S:
## contrast estimate SE df
## cong SI_255.4115384615385 - inc SI_255.4115384615385 -110 10.3 30.9
## t.ratio p.value
## -10.674 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_SI_3)## SI_3 = 56.3:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.92 9.53 31.0 -1.041 1.0000
## A cong - A inc -123.25 12.07 30.9 -10.211 <.0001
## A cong - S inc -120.36 12.32 31.0 -9.772 <.0001
## S cong - A inc -113.33 16.47 31.0 -6.880 <.0001
## S cong - S inc -110.45 10.84 30.9 -10.185 <.0001
## A inc - S inc 2.89 14.68 30.9 0.197 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_SI_32)## VisuoSpatialCongruency = cong:
## contrast estimate SE df t.ratio
## A SI_356.2675213675214 - S SI_356.2675213675214 -9.92 9.53 31.0 -1.041
## p.value
## 0.3061
##
## VisuoSpatialCongruency = inc:
## contrast estimate SE df t.ratio
## A SI_356.2675213675214 - S SI_356.2675213675214 2.89 14.68 30.9 0.197
## p.value
## 0.8453
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_SI_33)## Block = A:
## contrast estimate SE df
## cong SI_356.2675213675214 - inc SI_356.2675213675214 -123 12.1 30.9
## t.ratio p.value
## -10.211 <.0001
##
## Block = S:
## contrast estimate SE df
## cong SI_356.2675213675214 - inc SI_356.2675213675214 -110 10.8 30.9
## t.ratio p.value
## -10.185 <.0001
##
## Degrees-of-freedom method: kenward-roger#post hoc summary of Block
summary(posthoc_block_SI_1)## SI_1 = 54.7:
## contrast estimate SE df t.ratio p.value
## A effect -1.71 5.4 31 -0.316 1.0000
## S effect 1.71 5.4 31 0.316 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_SI_2)## SI_2 = 55.4:
## contrast estimate SE df t.ratio p.value
## A effect -1.61 5.48 31 -0.294 1.0000
## S effect 1.61 5.48 31 0.294 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_SI_3)## SI_3 = 56.3:
## contrast estimate SE df t.ratio p.value
## A effect -1.76 5.4 31 -0.325 1.0000
## S effect 1.76 5.4 31 0.325 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 tests#post hoc summary of VisuoSpatialCongruency
summary(posthoc_visuo_SI_1)## SI_1 = 54.7:
## contrast estimate SE df t.ratio p.value
## cong effect -58.4 4.87 31 -11.990 <.0001
## inc effect 58.4 4.87 31 11.990 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_SI_2)## SI_2 = 55.4:
## contrast estimate SE df t.ratio p.value
## cong effect -58.5 4.86 31 -12.046 <.0001
## inc effect 58.5 4.86 31 12.046 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_SI_3)## SI_3 = 56.3:
## contrast estimate SE df t.ratio p.value
## cong effect -58.4 4.87 31 -11.989 <.0001
## inc effect 58.4 4.87 31 11.989 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 tests#Proprioceptive Drift Before starting the experiment and after each stroking (two per block), participants were asked to verbally report the felt location of the hidden left index finger. Therefore, the data were collected in three time points: baseline, session 1, and 2. These values of proprioceptive drift across each block are considered as covariate in the following LMM. Here we considered the scores to each question as covariate for our LMM.
#LMM + Social Interaction scores as covariate
lmm_model_Baseline <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * Baseline + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
lmm_model_Drift1 <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * Drift1 + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
lmm_model_Drift2 <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * Drift2 + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
#verifysingularity
isSingular(lmm_model_Baseline)## [1] FALSEisSingular(lmm_model_Drift1)## [1] FALSEisSingular(lmm_model_Drift2)## [1] FALSE#summary
summary(lmm_model_Baseline)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * Baseline + (1 +
## Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28738.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0781 -0.5720 -0.1317 0.3779 5.9400
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8365 91.46
## BlockS 2087 45.69 0.06
## VisuoSpatialCongruencyinc 3443 58.68 0.10 -0.43
## BlockS:VisuoSpatialCongruencyinc 2288 47.83 -0.23 0.28 -0.56
## Residual 11569 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 363.1779 51.2995 34.8900 7.080
## BlockS -52.2800 54.9072 33.7410 -0.952
## VisuoSpatialCongruencyinc 136.1053 62.2382 32.5433 2.187
## Baseline -2.7798 3.3402 30.2561 -0.832
## BlockS:VisuoSpatialCongruencyinc -21.2618 66.0237 38.9328 -0.322
## BlockS:Baseline 4.1033 3.6500 33.0538 1.124
## VisuoSpatialCongruencyinc:Baseline -0.8802 4.1959 32.1563 -0.210
## BlockS:VisuoSpatialCongruencyinc:Baseline 0.6162 4.4104 37.5086 0.140
## Pr(>|t|)
## (Intercept) 3.07e-08 ***
## BlockS 0.3478
## VisuoSpatialCongruencyinc 0.0361 *
## Baseline 0.4118
## BlockS:VisuoSpatialCongruencyinc 0.7492
## BlockS:Baseline 0.2690
## VisuoSpatialCongruencyinc:Baseline 0.8352
## BlockS:VisuoSpatialCongruencyinc:Baseline 0.8896
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC Baseln BlS:VSC BlcS:B VsSC:B
## BlockS -0.876
## VsSptlCngrn 0.003 -0.003
## Baseline -0.947 0.920 -0.003
## BlckS:VsSpC -0.006 -0.037 -0.945 0.001
## BlockS:Bsln 0.898 -0.983 -0.002 -0.948 0.030
## VsSptlCng:B -0.003 -0.003 -0.981 0.003 0.941 0.003
## BlckS:VSC:B 0.002 0.030 0.948 -0.001 -0.982 -0.028 -0.966summary(lmm_model_Drift1)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * Drift1 + (1 +
## Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28732.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0732 -0.5780 -0.1211 0.3798 5.9451
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8726 93.41
## BlockS 2139 46.25 -0.04
## VisuoSpatialCongruencyinc 3421 58.49 0.11 -0.45
## BlockS:VisuoSpatialCongruencyinc 1949 44.15 -0.21 0.37 -0.56
## Residual 11569 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 350.6040 72.4928 46.8902 4.836
## BlockS 22.6458 53.9005 30.2547 0.420
## VisuoSpatialCongruencyinc 107.1639 65.3372 34.7867 1.640
## Drift1 -1.8976 4.8019 46.2458 -0.395
## BlockS:VisuoSpatialCongruencyinc -70.8024 64.3300 32.6071 -1.101
## BlockS:Drift1 -0.8769 3.6056 30.1591 -0.243
## VisuoSpatialCongruencyinc:Drift1 1.0962 4.3735 34.8871 0.251
## BlockS:VisuoSpatialCongruencyinc:Drift1 3.9500 4.3046 32.5042 0.918
## Pr(>|t|)
## (Intercept) 1.47e-05 ***
## BlockS 0.677
## VisuoSpatialCongruencyinc 0.110
## Drift1 0.695
## BlockS:VisuoSpatialCongruencyinc 0.279
## BlockS:Drift1 0.809
## VisuoSpatialCongruencyinc:Drift1 0.804
## BlockS:VisuoSpatialCongruencyinc:Drift1 0.366
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC Drift1 BlS:VSC BlS:D1 VSC:D1
## BlockS -0.444
## VsSptlCngrn 0.011 -0.119
## Drift1 -0.973 0.450 -0.011
## BlckS:VsSpC -0.028 -0.079 -0.705 0.027
## BlckS:Drft1 0.445 -0.982 0.115 -0.457 0.076
## VsSptlCn:D1 -0.011 0.115 -0.983 0.011 0.697 -0.117
## BlcS:VSC:D1 0.027 0.076 0.697 -0.027 -0.983 -0.078 -0.709summary(lmm_model_Drift2)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * Drift2 + (1 +
## Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28731.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0820 -0.5831 -0.1202 0.3817 5.9361
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8556 92.50
## BlockS 1937 44.01 -0.01
## VisuoSpatialCongruencyinc 3435 58.61 0.11 -0.44
## BlockS:VisuoSpatialCongruencyinc 2013 44.86 -0.25 0.45 -0.60
## Residual 11569 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 388.688 63.353 48.120 6.135
## BlockS 50.385 47.856 30.959 1.053
## VisuoSpatialCongruencyinc 106.406 56.026 34.215 1.899
## Drift2 -4.428 4.103 47.964 -1.079
## BlockS:VisuoSpatialCongruencyinc -79.992 57.658 32.816 -1.387
## BlockS:Drift2 -2.638 3.119 30.922 -0.846
## VisuoSpatialCongruencyinc:Drift2 1.132 3.676 34.417 0.308
## BlockS:VisuoSpatialCongruencyinc:Drift2 4.437 3.772 32.816 1.176
## Pr(>|t|)
## (Intercept) 1.54e-07 ***
## BlockS 0.301
## VisuoSpatialCongruencyinc 0.066 .
## Drift2 0.286
## BlockS:VisuoSpatialCongruencyinc 0.175
## BlockS:Drift2 0.404
## VisuoSpatialCongruencyinc:Drift2 0.760
## BlockS:VisuoSpatialCongruencyinc:Drift2 0.248
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC Drift2 BlS:VSC BlS:D2 VSC:D2
## BlockS -0.237
## VsSptlCngrn 0.016 -0.119
## Drift2 -0.965 0.239 -0.016
## BlckS:VsSpC -0.053 -0.084 -0.634 0.051
## BlckS:Drft2 0.249 -0.979 0.115 -0.258 0.081
## VsSptlCn:D2 -0.016 0.116 -0.977 0.016 0.622 -0.118
## BlcS:VSC:D2 0.050 0.080 0.627 -0.052 -0.978 -0.081 -0.642Since the models are not singular, we can continue to explore the data through post-hoc comparisons.
# Means of Block * VisuoSpatialCongruency interaction
emmeans_interaction_Baseline <- emmeans(lmm_model_Baseline, ~ Block * VisuoSpatialCongruency| Baseline)
emmeans_interaction_Baseline2 <- emmeans(lmm_model_Baseline, ~ Block * Baseline| VisuoSpatialCongruency)
emmeans_interaction_Baseline3 <- emmeans(lmm_model_Baseline, ~ VisuoSpatialCongruency * Baseline| Block)
emmeans_interaction_Drift1 <- emmeans(lmm_model_Drift1, ~ Block * VisuoSpatialCongruency| Drift1)
emmeans_interaction_Drift12 <- emmeans(lmm_model_Drift1, ~ Block * Drift1| VisuoSpatialCongruency)
emmeans_interaction_Drift13 <- emmeans(lmm_model_Drift1, ~ VisuoSpatialCongruency * Drift1| Block)
emmeans_interaction_Drift2 <- emmeans(lmm_model_Drift2, ~ Block * VisuoSpatialCongruency| Drift2)
emmeans_interaction_Drift22 <- emmeans(lmm_model_Drift2, ~ Block * Drift2| VisuoSpatialCongruency)
emmeans_interaction_Drift23 <- emmeans(lmm_model_Drift2, ~ VisuoSpatialCongruency * Drift2| Block)
# Means of Block
emmeans_block_Baseline <- emmeans(lmm_model_Baseline, ~ Block| Baseline)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_Drift1 <- emmeans(lmm_model_Drift1, ~ Block| Drift1)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_Drift2 <- emmeans(lmm_model_Drift2, ~ Block| Drift2)## NOTE: Results may be misleading due to involvement in interactions# Means of VisuoSpatialCongruency
emmeans_visuo_Baseline <- emmeans(lmm_model_Baseline, ~ VisuoSpatialCongruency| Baseline)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_Drift1 <- emmeans(lmm_model_Drift1, ~ VisuoSpatialCongruency| Drift1)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_Drift2 <- emmeans(lmm_model_Drift2, ~ VisuoSpatialCongruency| Drift2)## NOTE: Results may be misleading due to involvement in interactions#
# Post hoc comparisons of Block * VisuoSpatialCongruency
posthoc_interaction_Baseline <- pairs(emmeans_interaction_Baseline, adjust = "bonferroni")
posthoc_interaction_Baseline2 <- pairs(emmeans_interaction_Baseline2, adjust = "bonferroni")
posthoc_interaction_Baseline3 <- pairs(emmeans_interaction_Baseline3, adjust = "bonferroni")
posthoc_interaction_Drift1 <- pairs(emmeans_interaction_Drift1, adjust = "bonferroni")
posthoc_interaction_Drift12 <- pairs(emmeans_interaction_Drift12, adjust = "bonferroni")
posthoc_interaction_Drift13 <- pairs(emmeans_interaction_Drift13, adjust = "bonferroni")
posthoc_interaction_Drift2 <- pairs(emmeans_interaction_Drift2, adjust = "bonferroni")
posthoc_interaction_Drift22 <- pairs(emmeans_interaction_Drift22, adjust = "bonferroni")
posthoc_interaction_Drift23 <- pairs(emmeans_interaction_Drift23, adjust = "bonferroni")
# Post hoc comparisons of Block
posthoc_block_Baseline <- contrast(emmeans_block_Baseline, adjust = "bonferroni")
posthoc_block_Drift1 <- contrast(emmeans_block_Drift1, adjust = "bonferroni")
posthoc_block_Drift2 <- contrast(emmeans_block_Drift2, adjust = "bonferroni")
# Post hoc comparisons of VisuoSpatialCongruency
posthoc_visuo_Baseline <- contrast(emmeans_visuo_Baseline, adjust = "bonferroni")
posthoc_visuo_Drift1 <- contrast(emmeans_visuo_Drift1, adjust = "bonferroni")
posthoc_visuo_Drift2 <- contrast(emmeans_visuo_Drift2, adjust = "bonferroni")
#
#post hoc summary of Block * VisuoSpatialCongruency
summary(posthoc_interaction_Baseline)## Baseline = 15.5:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -11.145 10.5 31.3 -1.058 1.0000
## A cong - A inc -122.500 12.7 31.9 -9.615 <.0001
## A cong - S inc -121.907 12.7 31.9 -9.590 <.0001
## S cong - A inc -111.355 17.5 31.8 -6.373 <.0001
## S cong - S inc -110.762 10.9 31.1 -10.121 <.0001
## A inc - S inc 0.593 15.5 30.5 0.038 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_Baseline2)## VisuoSpatialCongruency = cong:
## contrast estimate SE df
## A Baseline15.4569848845593 - S Baseline15.4569848845593 -11.145 10.5 31.3
## t.ratio p.value
## -1.058 0.2984
##
## VisuoSpatialCongruency = inc:
## contrast estimate SE df
## A Baseline15.4569848845593 - S Baseline15.4569848845593 0.593 15.5 30.5
## t.ratio p.value
## 0.038 0.9698
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_Baseline3)## Block = A:
## contrast estimate SE
## cong Baseline15.4569848845593 - inc Baseline15.4569848845593 -122 12.7
## df t.ratio p.value
## 31.9 -9.615 <.0001
##
## Block = S:
## contrast estimate SE
## cong Baseline15.4569848845593 - inc Baseline15.4569848845593 -111 10.9
## df t.ratio p.value
## 31.1 -10.121 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_Drift1)## Drift1 = 14.7:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.75 10.1 30.3 -0.967 1.0000
## A cong - A inc -123.28 12.1 30.9 -10.228 <.0001
## A cong - S inc -120.31 12.3 30.4 -9.782 <.0001
## S cong - A inc -113.53 16.8 30.6 -6.743 <.0001
## S cong - S inc -110.55 10.7 30.9 -10.346 <.0001
## A inc - S inc 2.97 14.6 30.4 0.203 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_Drift12)## VisuoSpatialCongruency = cong:
## contrast estimate SE df t.ratio
## A Drift114.7024266690847 - S Drift114.7024266690847 -9.75 10.1 30.3 -0.967
## p.value
## 0.3413
##
## VisuoSpatialCongruency = inc:
## contrast estimate SE df t.ratio
## A Drift114.7024266690847 - S Drift114.7024266690847 2.97 14.6 30.4 0.203
## p.value
## 0.8402
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_Drift13)## Block = A:
## contrast estimate SE df
## cong Drift114.7024266690847 - inc Drift114.7024266690847 -123 12.1 30.9
## t.ratio p.value
## -10.228 <.0001
##
## Block = S:
## contrast estimate SE df
## cong Drift114.7024266690847 - inc Drift114.7024266690847 -111 10.7 30.9
## t.ratio p.value
## -10.346 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_Drift2)## Drift2 = 15:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -10.83 9.81 30.5 -1.104 1.0000
## A cong - A inc -123.38 12.08 30.9 -10.215 <.0001
## A cong - S inc -120.74 12.41 30.6 -9.727 <.0001
## S cong - A inc -112.56 16.55 30.8 -6.800 <.0001
## S cong - S inc -109.92 10.47 30.9 -10.502 <.0001
## A inc - S inc 2.64 14.80 30.6 0.178 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_Drift22)## VisuoSpatialCongruency = cong:
## contrast estimate SE df
## A Drift214.9922327549613 - S Drift214.9922327549613 -10.83 9.81 30.5
## t.ratio p.value
## -1.104 0.2783
##
## VisuoSpatialCongruency = inc:
## contrast estimate SE df
## A Drift214.9922327549613 - S Drift214.9922327549613 2.64 14.80 30.6
## t.ratio p.value
## 0.178 0.8596
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_Drift23)## Block = A:
## contrast estimate SE df
## cong Drift214.9922327549613 - inc Drift214.9922327549613 -123 12.1 30.9
## t.ratio p.value
## -10.215 <.0001
##
## Block = S:
## contrast estimate SE df
## cong Drift214.9922327549613 - inc Drift214.9922327549613 -110 10.5 30.9
## t.ratio p.value
## -10.502 <.0001
##
## Degrees-of-freedom method: kenward-roger#post hoc summary of Block
summary(posthoc_block_Baseline)## Baseline = 15.5:
## contrast estimate SE df t.ratio p.value
## A effect -2.64 5.79 30.7 -0.455 1.0000
## S effect 2.64 5.79 30.7 0.455 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_Drift1)## Drift1 = 14.7:
## contrast estimate SE df t.ratio p.value
## A effect -1.69 5.54 30.3 -0.306 1.0000
## S effect 1.69 5.54 30.3 0.306 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_Drift2)## Drift2 = 15:
## contrast estimate SE df t.ratio p.value
## A effect -2.05 5.52 30.5 -0.371 1.0000
## S effect 2.05 5.52 30.5 0.371 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 tests#post hoc summary of VisuoSpatialCongruency
summary(posthoc_visuo_Baseline)## Baseline = 15.5:
## contrast estimate SE df t.ratio p.value
## cong effect -58.3 4.98 32.7 -11.713 <.0001
## inc effect 58.3 4.98 32.7 11.713 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_Drift1)## Drift1 = 14.7:
## contrast estimate SE df t.ratio p.value
## cong effect -58.5 4.86 30.9 -12.019 <.0001
## inc effect 58.5 4.86 30.9 12.019 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_Drift2)## Drift2 = 15:
## contrast estimate SE df t.ratio p.value
## cong effect -58.3 4.8 31 -12.158 <.0001
## inc effect 58.3 4.8 31 12.158 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 tests##Perceived Similarity Participants also responded to some brief questions explicitly verifying the comfortability of the social-touch experience and the perceived similarity with the experimenter. Specifically, based on Myers & Hodges (2011); Goldstein & Cialdini (2007); Batson et al. (1997), as a measure of Perceived Similarity, we asked participants on a 9-point Likert scale, ranging from “Not at all” to “Extremely”, to what extent they felt: (1) Sharing similar attributes with the experimenter; (2) A shared identity with the experimenter; (3) Being similar to the experimenter. Moreover, we asked how comfortable they were with the touch during the experiment on a Visual Analog Scale (VAS) scale from 0 to 100.
Here we considered the scores to each question as covariate for our LMM.
#LMM + Social Interaction scores as covariate
lmm_model_TC <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * TouchComfortability + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
lmm_model_SA <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * SimilarAttributes + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
lmm_model_SI <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * SharedIdentity + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
lmm_model_S <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * Similarity + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
#verifysingularity
isSingular(lmm_model_TC)## [1] FALSEisSingular(lmm_model_SA)## [1] FALSEisSingular(lmm_model_SI)## [1] FALSEisSingular(lmm_model_S)## [1] FALSE#summary
summary(lmm_model_TC)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * TouchComfortability +
## (1 + Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28748.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0743 -0.5767 -0.1183 0.3802 5.9438
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8769 93.64
## BlockS 2046 45.23 0.01
## VisuoSpatialCongruencyinc 3405 58.35 0.11 -0.41
## BlockS:VisuoSpatialCongruencyinc 2317 48.13 -0.31 0.35 -0.60
## Residual 11570 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error
## (Intercept) 319.72389 47.11610
## BlockS 45.40885 58.09743
## VisuoSpatialCongruencyinc 138.67058 51.43791
## TouchComfortability 0.03602 0.52281
## BlockS:VisuoSpatialCongruencyinc -97.74935 66.51605
## BlockS:TouchComfortability -0.40842 0.66078
## VisuoSpatialCongruencyinc:TouchComfortability -0.18417 0.59577
## BlockS:VisuoSpatialCongruencyinc:TouchComfortability 0.97845 0.76188
## df t value Pr(>|t|)
## (Intercept) 39.39936 6.786 4.02e-08
## BlockS 30.79919 0.782 0.4404
## VisuoSpatialCongruencyinc 33.61700 2.696 0.0109
## TouchComfortability 33.82423 0.069 0.9455
## BlockS:VisuoSpatialCongruencyinc 39.64204 -1.470 0.1496
## BlockS:TouchComfortability 30.99206 -0.618 0.5410
## VisuoSpatialCongruencyinc:TouchComfortability 33.54350 -0.309 0.7591
## BlockS:VisuoSpatialCongruencyinc:TouchComfortability 40.19853 1.284 0.2064
##
## (Intercept) ***
## BlockS
## VisuoSpatialCongruencyinc *
## TouchComfortability
## BlockS:VisuoSpatialCongruencyinc
## BlockS:TouchComfortability
## VisuoSpatialCongruencyinc:TouchComfortability
## BlockS:VisuoSpatialCongruencyinc:TouchComfortability
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC TchCmf BlS:VSC BlS:TC VSC:TC
## BlockS -0.302
## VsSptlCngrn 0.022 -0.064
## TchCmfrtblt -0.934 0.317 -0.023
## BlckS:VsSpC -0.052 -0.148 -0.595 0.048
## BlckS:TchCm 0.326 -0.985 0.061 -0.350 0.144
## VsSptlCn:TC -0.023 0.061 -0.972 0.024 0.585 -0.062
## BlcS:VSC:TC 0.045 0.142 0.598 -0.048 -0.982 -0.142 -0.615summary(lmm_model_SA)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * SimilarAttributes +
## (1 + Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28732.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0714 -0.5750 -0.1251 0.3783 5.9466
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8758 93.59
## BlockS 2048 45.26 0.02
## VisuoSpatialCongruencyinc 3355 57.92 0.09 -0.43
## BlockS:VisuoSpatialCongruencyinc 2246 47.39 -0.26 0.34 -0.54
## Residual 11570 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 339.007 32.350 48.083
## BlockS 7.619 25.250 30.971
## VisuoSpatialCongruencyinc 133.051 27.600 34.537
## SimilarAttributes -3.418 5.795 47.792
## BlockS:VisuoSpatialCongruencyinc -28.981 30.281 33.390
## BlockS:SimilarAttributes 0.707 4.552 31.102
## VisuoSpatialCongruencyinc:SimilarAttributes -2.063 5.238 35.332
## BlockS:VisuoSpatialCongruencyinc:SimilarAttributes 3.311 5.610 34.307
## t value Pr(>|t|)
## (Intercept) 10.479 5.24e-14 ***
## BlockS 0.302 0.765
## VisuoSpatialCongruencyinc 4.821 2.83e-05 ***
## SimilarAttributes -0.590 0.558
## BlockS:VisuoSpatialCongruencyinc -0.957 0.345
## BlockS:SimilarAttributes 0.155 0.878
## VisuoSpatialCongruencyinc:SimilarAttributes -0.394 0.696
## BlockS:VisuoSpatialCongruencyinc:SimilarAttributes 0.590 0.559
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC SmlrAt BlS:VSC BlS:SA VSC:SA
## BlockS -0.129
## VsSptlCngrn -0.011 -0.112
## SmlrAttrbts -0.854 0.129 0.007
## BlckS:VsSpC -0.060 -0.139 -0.571 0.052
## BlckS:SmlrA 0.210 -0.914 0.096 -0.246 0.122
## VsSptlCn:SA 0.006 0.100 -0.901 -0.006 0.519 -0.107
## BlcS:VSC:SA 0.046 0.116 0.559 -0.055 -0.913 -0.117 -0.621summary(lmm_model_SI)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * SharedIdentity +
## (1 + Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28730.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0788 -0.5714 -0.1231 0.3795 5.9391
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 9068 95.22
## BlockS 1723 41.50 -0.04
## VisuoSpatialCongruencyinc 3425 58.53 0.09 -0.46
## BlockS:VisuoSpatialCongruencyinc 2278 47.73 -0.25 0.38 -0.55
## Residual 11570 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 336.1413 23.9195 48.6494
## BlockS 32.0143 22.8826 30.9951
## VisuoSpatialCongruencyinc 120.5813 23.1907 34.8162
## SharedIdentity -3.3376 4.1695 32.5023
## BlockS:VisuoSpatialCongruencyinc -10.7266 28.1536 39.2151
## BlockS:SharedIdentity -4.8338 4.9476 31.8384
## VisuoSpatialCongruencyinc:SharedIdentity 0.6699 5.0125 34.7096
## BlockS:VisuoSpatialCongruencyinc:SharedIdentity -0.5245 6.1511 42.7759
## t value Pr(>|t|)
## (Intercept) 14.053 < 2e-16 ***
## BlockS 1.399 0.172
## VisuoSpatialCongruencyinc 5.200 8.89e-06 ***
## SharedIdentity -0.800 0.429
## BlockS:VisuoSpatialCongruencyinc -0.381 0.705
## BlockS:SharedIdentity -0.977 0.336
## VisuoSpatialCongruencyinc:SharedIdentity 0.134 0.894
## BlockS:VisuoSpatialCongruencyinc:SharedIdentity -0.085 0.932
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC ShrdId BlS:VSC BlS:SI VSC:SI
## BlockS -0.320
## VsSptlCngrn 0.002 -0.071
## ShardIdntty -0.698 0.400 -0.013
## BlckS:VsSpC -0.043 -0.145 -0.622 0.026
## BlckS:ShrdI 0.344 -0.909 0.047 -0.493 0.130
## VsSptlCn:SI -0.010 0.050 -0.854 0.015 0.570 -0.054
## BlcS:VSC:SI 0.020 0.126 0.577 -0.029 -0.899 -0.133 -0.676summary(lmm_model_S)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * Similarity + (1 +
## Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28732.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0699 -0.5732 -0.1256 0.3757 5.9481
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8681 93.17
## BlockS 2151 46.38 -0.01
## VisuoSpatialCongruencyinc 3247 56.98 0.14 -0.44
## BlockS:VisuoSpatialCongruencyinc 2268 47.62 -0.30 0.30 -0.53
## Residual 11570 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 314.057 27.008 48.054 11.628
## BlockS 15.490 24.961 30.594 0.621
## VisuoSpatialCongruencyinc 141.403 24.947 36.185 5.668
## Similarity 1.998 4.878 38.762 0.410
## BlockS:VisuoSpatialCongruencyinc -36.190 29.328 36.877 -1.234
## BlockS:Similarity -1.401 4.830 31.168 -0.290
## VisuoSpatialCongruencyinc:Similarity -4.198 5.073 36.836 -0.828
## BlockS:VisuoSpatialCongruencyinc:Similarity 5.307 5.835 39.372 0.910
## Pr(>|t|)
## (Intercept) 1.42e-15 ***
## BlockS 0.539
## VisuoSpatialCongruencyinc 1.90e-06 ***
## Similarity 0.684
## BlockS:VisuoSpatialCongruencyinc 0.225
## BlockS:Similarity 0.774
## VisuoSpatialCongruencyinc:Similarity 0.413
## BlockS:VisuoSpatialCongruencyinc:Similarity 0.369
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC Smlrty BlS:VSC BlcS:S VsSC:S
## BlockS -0.211
## VsSptlCngrn 0.025 -0.098
## Similarity -0.784 0.232 -0.025
## BlckS:VsSpC -0.069 -0.160 -0.581 0.053
## BlckS:Smlrt 0.284 -0.908 0.079 -0.362 0.138
## VsSptlCng:S -0.023 0.081 -0.881 0.030 0.529 -0.089
## BlckS:VSC:S 0.045 0.132 0.568 -0.059 -0.906 -0.133 -0.646Since the models are not singular, we can continue to explore the data through post-hoc comparisons.
# Means of Block * VisuoSpatialCongruency interaction
emmeans_interaction_TC <- emmeans(lmm_model_TC, ~ Block * VisuoSpatialCongruency| TouchComfortability)
emmeans_interaction_TC2 <- emmeans(lmm_model_TC, ~ Block * TouchComfortability| VisuoSpatialCongruency)
emmeans_interaction_TC3 <- emmeans(lmm_model_TC, ~ VisuoSpatialCongruency * TouchComfortability| Block)
emmeans_interaction_SA <- emmeans(lmm_model_SA, ~ Block * VisuoSpatialCongruency| SimilarAttributes)
emmeans_interaction_SA2 <- emmeans(lmm_model_SA, ~ Block * SimilarAttributes| VisuoSpatialCongruency)
emmeans_interaction_SA3 <- emmeans(lmm_model_SA, ~ VisuoSpatialCongruency * SimilarAttributes| Block)
emmeans_interaction_SI <- emmeans(lmm_model_SI, ~ Block * VisuoSpatialCongruency| SharedIdentity)
emmeans_interaction_SI2 <- emmeans(lmm_model_SI, ~ Block * SharedIdentity| VisuoSpatialCongruency)
emmeans_interaction_SI3 <- emmeans(lmm_model_SI, ~ VisuoSpatialCongruency * SharedIdentity| Block)
emmeans_interaction_S <- emmeans(lmm_model_S, ~ Block * VisuoSpatialCongruency| Similarity)
emmeans_interaction_S2 <- emmeans(lmm_model_S, ~ Block * Similarity| VisuoSpatialCongruency)
emmeans_interaction_S3 <- emmeans(lmm_model_S, ~ VisuoSpatialCongruency * Similarity| Block)
# Means of Block
emmeans_block_TC <- emmeans(lmm_model_TC, ~ Block| TouchComfortability)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_SA <- emmeans(lmm_model_SA, ~ Block| SimilarAttributes)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_SI <- emmeans(lmm_model_SI, ~ Block| SharedIdentity)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_S <- emmeans(lmm_model_S, ~ Block| Similarity)## NOTE: Results may be misleading due to involvement in interactions# Means of VisuoSpatialCongruency
emmeans_visuo_TC <- emmeans(lmm_model_TC, ~ VisuoSpatialCongruency| TouchComfortability)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_SA <- emmeans(lmm_model_SA, ~ VisuoSpatialCongruency| SimilarAttributes)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_SI <- emmeans(lmm_model_SI, ~ VisuoSpatialCongruency| SharedIdentity)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_S <- emmeans(lmm_model_S, ~ VisuoSpatialCongruency| Similarity)## NOTE: Results may be misleading due to involvement in interactions#
# Post hoc comparisons of Block * VisuoSpatialCongruency
posthoc_interaction_TC <- pairs(emmeans_interaction_TC, adjust = "bonferroni")
posthoc_interaction_TC2 <- pairs(emmeans_interaction_TC2, adjust = "bonferroni")
posthoc_interaction_TC3 <- pairs(emmeans_interaction_TC3, adjust = "bonferroni")
posthoc_interaction_SA <- pairs(emmeans_interaction_SA, adjust = "bonferroni")
posthoc_interaction_SA2 <- pairs(emmeans_interaction_SA2, adjust = "bonferroni")
posthoc_interaction_SA3 <- pairs(emmeans_interaction_SA3, adjust = "bonferroni")
posthoc_interaction_SI <- pairs(emmeans_interaction_SI, adjust = "bonferroni")
posthoc_interaction_SI2 <- pairs(emmeans_interaction_SI2, adjust = "bonferroni")
posthoc_interaction_SI3 <- pairs(emmeans_interaction_SI3, adjust = "bonferroni")
posthoc_interaction_S <- pairs(emmeans_interaction_S, adjust = "bonferroni")
posthoc_interaction_S2 <- pairs(emmeans_interaction_S2, adjust = "bonferroni")
posthoc_interaction_S3 <- pairs(emmeans_interaction_S3, adjust = "bonferroni")
# Post hoc comparisons of Block
posthoc_block_TC <- contrast(emmeans_block_TC, adjust = "bonferroni")
posthoc_block_SA <- contrast(emmeans_block_SA, adjust = "bonferroni")
posthoc_block_SI <- contrast(emmeans_block_SI, adjust = "bonferroni")
posthoc_block_S <- contrast(emmeans_block_S, adjust = "bonferroni")
# Post hoc comparisons of VisuoSpatialCongruency
posthoc_visuo_TC <- contrast(emmeans_visuo_TC, adjust = "bonferroni")
posthoc_visuo_SA <- contrast(emmeans_visuo_SA, adjust = "bonferroni")
posthoc_visuo_SI <- contrast(emmeans_visuo_SI, adjust = "bonferroni")
posthoc_visuo_S <- contrast(emmeans_visuo_S, adjust = "bonferroni")
#
#post hoc summary of Block * VisuoSpatialCongruency
summary(posthoc_interaction_TC)## TouchComfortability = 85.7:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -10.40 10.1 30.4 -1.027 1.0000
## A cong - A inc -122.89 12.1 31.0 -10.169 <.0001
## A cong - S inc -119.40 12.6 30.8 -9.481 <.0001
## S cong - A inc -112.48 16.6 31.0 -6.762 <.0001
## S cong - S inc -109.00 10.6 31.1 -10.246 <.0001
## A inc - S inc 3.48 15.1 30.8 0.231 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_TC2)## VisuoSpatialCongruency = cong:
## contrast
## A TouchComfortability85.708547008547 - S TouchComfortability85.708547008547
## estimate SE df t.ratio p.value
## -10.40 10.1 30.4 -1.027 0.3125
##
## VisuoSpatialCongruency = inc:
## contrast
## A TouchComfortability85.708547008547 - S TouchComfortability85.708547008547
## estimate SE df t.ratio p.value
## 3.48 15.1 30.8 0.231 0.8191
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_TC3)## Block = A:
## contrast
## cong TouchComfortability85.708547008547 - inc TouchComfortability85.708547008547
## estimate SE df t.ratio p.value
## -123 12.1 31.0 -10.169 <.0001
##
## Block = S:
## contrast
## cong TouchComfortability85.708547008547 - inc TouchComfortability85.708547008547
## estimate SE df t.ratio p.value
## -109 10.6 31.1 -10.246 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_SA)## SimilarAttributes = 4.96:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -11.12 10.3 32.1 -1.077 1.0000
## A cong - A inc -122.83 12.0 31.0 -10.216 <.0001
## A cong - S inc -121.38 12.9 32.1 -9.427 <.0001
## S cong - A inc -111.70 16.8 32.0 -6.646 <.0001
## S cong - S inc -110.26 11.0 30.9 -10.013 <.0001
## A inc - S inc 1.44 15.1 32.3 0.095 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_SA2)## VisuoSpatialCongruency = cong:
## contrast
## A SimilarAttributes4.95726495726496 - S SimilarAttributes4.95726495726496
## estimate SE df t.ratio p.value
## -11.12 10.3 32.1 -1.077 0.2894
##
## VisuoSpatialCongruency = inc:
## contrast
## A SimilarAttributes4.95726495726496 - S SimilarAttributes4.95726495726496
## estimate SE df t.ratio p.value
## 1.44 15.1 32.3 0.095 0.9245
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_SA3)## Block = A:
## contrast
## cong SimilarAttributes4.95726495726496 - inc SimilarAttributes4.95726495726496
## estimate SE df t.ratio p.value
## -123 12 31.0 -10.216 <.0001
##
## Block = S:
## contrast
## cong SimilarAttributes4.95726495726496 - inc SimilarAttributes4.95726495726496
## estimate SE df t.ratio p.value
## -110 11 30.9 -10.013 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_SI)## SharedIdentity = 4.11:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -12.144 9.56 30.2 -1.271 1.0000
## A cong - A inc -123.335 12.09 31.1 -10.204 <.0001
## A cong - S inc -122.597 12.33 30.4 -9.944 <.0001
## S cong - A inc -111.191 16.36 30.9 -6.796 <.0001
## S cong - S inc -110.452 10.97 30.9 -10.073 <.0001
## A inc - S inc 0.738 14.66 30.6 0.050 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_SI2)## VisuoSpatialCongruency = cong:
## contrast estimate
## A SharedIdentity4.11068376068376 - S SharedIdentity4.11068376068376 -12.144
## SE df t.ratio p.value
## 9.56 30.2 -1.271 0.2136
##
## VisuoSpatialCongruency = inc:
## contrast estimate
## A SharedIdentity4.11068376068376 - S SharedIdentity4.11068376068376 0.738
## SE df t.ratio p.value
## 14.66 30.6 0.050 0.9601
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_SI3)## Block = A:
## contrast
## cong SharedIdentity4.11068376068376 - inc SharedIdentity4.11068376068376
## estimate SE df t.ratio p.value
## -123 12.1 31.1 -10.204 <.0001
##
## Block = S:
## contrast
## cong SharedIdentity4.11068376068376 - inc SharedIdentity4.11068376068376
## estimate SE df t.ratio p.value
## -110 11.0 30.9 -10.073 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_S)## Similarity = 4.58:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.08 10.5 31.3 -0.864 1.0000
## A cong - A inc -122.19 11.9 31.1 -10.264 <.0001
## A cong - S inc -119.37 12.8 31.6 -9.323 <.0001
## S cong - A inc -113.12 16.9 31.8 -6.701 <.0001
## S cong - S inc -110.29 11.0 30.9 -9.999 <.0001
## A inc - S inc 2.83 15.2 31.8 0.186 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_S2)## VisuoSpatialCongruency = cong:
## contrast estimate SE df
## A Similarity4.57606837606838 - S Similarity4.57606837606838 -9.08 10.5 31.3
## t.ratio p.value
## -0.864 0.3943
##
## VisuoSpatialCongruency = inc:
## contrast estimate SE df
## A Similarity4.57606837606838 - S Similarity4.57606837606838 2.83 15.2 31.8
## t.ratio p.value
## 0.186 0.8535
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_S3)## Block = A:
## contrast estimate SE
## cong Similarity4.57606837606838 - inc Similarity4.57606837606838 -122 11.9
## df t.ratio p.value
## 31.1 -10.264 <.0001
##
## Block = S:
## contrast estimate SE
## cong Similarity4.57606837606838 - inc Similarity4.57606837606838 -110 11.0
## df t.ratio p.value
## 30.9 -9.999 <.0001
##
## Degrees-of-freedom method: kenward-roger#post hoc summary of Block
summary(posthoc_block_TC)## TouchComfortability = 85.7:
## contrast estimate SE df t.ratio p.value
## A effect -1.73 5.63 30.6 -0.307 1.0000
## S effect 1.73 5.63 30.6 0.307 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_SA)## SimilarAttributes = 4.96:
## contrast estimate SE df t.ratio p.value
## A effect -2.42 5.69 32.5 -0.425 1.0000
## S effect 2.42 5.69 32.5 0.425 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_SI)## SharedIdentity = 4.11:
## contrast estimate SE df t.ratio p.value
## A effect -2.85 5.36 30.5 -0.532 1.0000
## S effect 2.85 5.36 30.5 0.532 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_S)## Similarity = 4.58:
## contrast estimate SE df t.ratio p.value
## A effect -1.56 5.73 31.7 -0.273 1.0000
## S effect 1.56 5.73 31.7 0.273 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 tests#post hoc summary of VisuoSpatialCongruency
summary(posthoc_visuo_TC)## TouchComfortability = 85.7:
## contrast estimate SE df t.ratio p.value
## cong effect -58 4.77 31.2 -12.161 <.0001
## inc effect 58 4.77 31.2 12.161 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_SA)## SimilarAttributes = 4.96:
## contrast estimate SE df t.ratio p.value
## cong effect -58.3 4.86 31.2 -11.981 <.0001
## inc effect 58.3 4.86 31.2 11.981 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_SI)## SharedIdentity = 4.11:
## contrast estimate SE df t.ratio p.value
## cong effect -58.4 4.87 31.2 -11.994 <.0001
## inc effect 58.4 4.87 31.2 11.994 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_S)## Similarity = 4.58:
## contrast estimate SE df t.ratio p.value
## cong effect -58.1 4.82 31.3 -12.062 <.0001
## inc effect 58.1 4.82 31.3 12.062 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 tests##SRHI-Q Participants completed a questionnaire assessing the strength of the ‘social’ rubber hand illusion (SRHI-Q), adapted from a validated questionnaire developed by Longo et al. (2008). This questionnaire assessed the strength of the illusion in the paradigm through three components: Ownership, Location and Hand Loss. It consisted of 13 statements (listed below) measured on a 7-point Likert scale, ranging from “Strongly disagree” to “Strongly agree” with responses scoring -3 to 3, respectively. Thus, negative scores corresponded to disagreement with the statements, while positive scores corresponded to agreement with the statements.
Here we considered the scores to each question as covariate for our LMM.
#LMM + Social Interaction scores as covariate
lmm_model_Ownership <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * Ownership + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
lmm_model_Location <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * Location + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
lmm_model_HandLoss <- lmer(RTNoOutlier ~ Block * VisuoSpatialCongruency * HandLoss + (1 + Block * VisuoSpatialCongruency| Subject), control = lmerControl(optimizer = "bobyqa"), data = SRHI)
#verifysingularity
isSingular(lmm_model_Ownership)## [1] FALSEisSingular(lmm_model_Location)## [1] FALSEisSingular(lmm_model_HandLoss)## [1] FALSE#summary
summary(lmm_model_Ownership)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * Ownership + (1 +
## Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28723.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1106 -0.5788 -0.1321 0.3841 5.9078
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8431 91.82
## BlockS 2227 47.20 0.02
## VisuoSpatialCongruencyinc 3210 56.66 0.19 -0.43
## BlockS:VisuoSpatialCongruencyinc 2232 47.25 -0.33 0.22 -0.62
## Residual 11569 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 330.239 21.891 45.336 15.086
## BlockS 9.077 17.665 32.694 0.514
## VisuoSpatialCongruencyinc 106.503 20.621 34.682 5.165
## Ownership 3.831 7.295 32.739 0.525
## BlockS:VisuoSpatialCongruencyinc 20.068 21.605 37.331 0.929
## BlockS:Ownership 1.393 8.448 31.976 0.165
## VisuoSpatialCongruencyinc:Ownership -8.455 8.561 32.870 -0.988
## BlockS:VisuoSpatialCongruencyinc:Ownership 20.403 9.892 41.581 2.063
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## BlockS 0.6108
## VisuoSpatialCongruencyinc 9.98e-06 ***
## Ownership 0.6030
## BlockS:VisuoSpatialCongruencyinc 0.3589
## BlockS:Ownership 0.8701
## VisuoSpatialCongruencyinc:Ownership 0.3305
## BlockS:VisuoSpatialCongruencyinc:Ownership 0.0454 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC Ownrsh BlS:VSC BlcS:O VsSC:O
## BlockS -0.454
## VsSptlCngrn 0.045 -0.087
## Ownership 0.654 -0.626 0.030
## BlckS:VsSpC -0.081 -0.087 -0.798 -0.041
## BlckS:Ownrs -0.375 0.786 -0.052 -0.570 -0.064
## VsSptlCng:O 0.023 -0.051 0.821 0.034 -0.722 -0.065
## BlckS:VSC:O -0.032 -0.071 -0.625 -0.048 0.809 -0.131 -0.760summary(lmm_model_Location)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * Location + (1 +
## Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28728.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0955 -0.5754 -0.1269 0.3797 5.9226
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8707 93.31
## BlockS 2141 46.27 -0.01
## VisuoSpatialCongruencyinc 3310 57.53 0.14 -0.42
## BlockS:VisuoSpatialCongruencyinc 2352 48.50 -0.30 0.27 -0.55
## Residual 11569 107.56
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 324.8968 22.0460 45.1715 14.737
## BlockS 9.5488 16.3156 34.5660 0.585
## VisuoSpatialCongruencyinc 112.9148 19.6932 34.6423 5.734
## Location 1.2204 8.0557 35.3073 0.152
## BlockS:VisuoSpatialCongruencyinc -0.4746 19.6728 36.1205 -0.024
## BlockS:Location 1.9375 7.9635 31.6853 0.243
## VisuoSpatialCongruencyinc:Location -5.8716 8.9081 34.5078 -0.659
## BlockS:VisuoSpatialCongruencyinc:Location 8.7325 9.7475 38.2307 0.896
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## BlockS 0.562
## VisuoSpatialCongruencyinc 1.79e-06 ***
## Location 0.880
## BlockS:VisuoSpatialCongruencyinc 0.981
## BlockS:Location 0.809
## VisuoSpatialCongruencyinc:Location 0.514
## BlockS:VisuoSpatialCongruencyinc:Location 0.376
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC Locatn BlS:VSC BlcS:L VsSC:L
## BlockS -0.537
## VsSptlCngrn 0.027 -0.079
## Location 0.647 -0.745 0.023
## BlckS:VsSpC -0.070 -0.039 -0.825 -0.030
## BlockS:Lctn -0.377 0.637 -0.057 -0.583 0.007
## VsSptlCng:L 0.019 -0.037 0.797 0.028 -0.750 -0.070
## BlckS:VSC:L -0.030 -0.003 -0.602 -0.047 0.704 -0.093 -0.758summary(lmm_model_HandLoss)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RTNoOutlier ~ Block * VisuoSpatialCongruency * HandLoss + (1 +
## Block * VisuoSpatialCongruency | Subject)
## Data: SRHI
## Control: lmerControl(optimizer = "bobyqa")
##
## REML criterion at convergence: 28728
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0739 -0.5713 -0.1275 0.3832 5.9447
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 8833 93.99
## BlockS 2098 45.81 -0.01
## VisuoSpatialCongruencyinc 3415 58.44 0.10 -0.44
## BlockS:VisuoSpatialCongruencyinc 2092 45.74 -0.30 0.35 -0.55
## Residual 11568 107.55
## Number of obs: 2340, groups: Subject, 33
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 322.7822 16.9252 30.4972 19.071
## BlockS 9.9318 10.0556 29.4520 0.988
## VisuoSpatialCongruencyinc 123.1672 12.0501 32.1588 10.221
## HandLoss -0.7772 7.5941 32.0154 -0.102
## BlockS:VisuoSpatialCongruencyinc -13.4481 12.0373 32.3338 -1.117
## BlockS:HandLoss -1.4387 8.5358 32.0319 -0.169
## VisuoSpatialCongruencyinc:HandLoss 0.7334 8.6994 32.9116 0.084
## BlockS:VisuoSpatialCongruencyinc:HandLoss 8.3474 9.9661 39.6166 0.838
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## BlockS 0.331
## VisuoSpatialCongruencyinc 1.25e-11 ***
## HandLoss 0.919
## BlockS:VisuoSpatialCongruencyinc 0.272
## BlockS:HandLoss 0.867
## VisuoSpatialCongruencyinc:HandLoss 0.933
## BlockS:VisuoSpatialCongruencyinc:HandLoss 0.407
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlockS VsSptC HndLss BlS:VSC BlS:HL VSC:HL
## BlockS -0.116
## VsSptlCngrn -0.011 -0.140
## HandLoss -0.029 0.019 0.001
## BlckS:VsSpC -0.098 -0.120 -0.596 0.001
## BlckS:HndLs 0.017 -0.070 0.003 -0.596 0.008
## VsSptlCn:HL 0.000 0.004 -0.042 0.028 0.029 -0.061
## BlcS:VSC:HL 0.001 0.009 0.029 -0.041 -0.050 -0.090 -0.744Since the models are not singular, we can continue to explore the data through post-hoc comparisons.
# Means of Block * VisuoSpatialCongruency interaction
emmeans_interaction_Ownership <- emmeans(lmm_model_Ownership, ~ Block * VisuoSpatialCongruency| Ownership)
emmeans_interaction_Ownership2 <- emmeans(lmm_model_Ownership, ~ Block * Ownership| VisuoSpatialCongruency)
emmeans_interaction_Ownership3 <- emmeans(lmm_model_Ownership, ~ VisuoSpatialCongruency * Ownership| Block)
emmeans_interaction_Location <- emmeans(lmm_model_Location, ~ Block * VisuoSpatialCongruency| Location)
emmeans_interaction_Location2 <- emmeans(lmm_model_Location, ~ Block * Location| VisuoSpatialCongruency)
emmeans_interaction_Location3 <- emmeans(lmm_model_Location, ~ VisuoSpatialCongruency * Location| Block)
emmeans_interaction_HandLoss <- emmeans(lmm_model_HandLoss, ~ Block * VisuoSpatialCongruency| HandLoss)
emmeans_interaction_HandLoss2 <- emmeans(lmm_model_HandLoss, ~ Block * HandLoss| VisuoSpatialCongruency)
emmeans_interaction_HandLoss3 <- emmeans(lmm_model_HandLoss, ~ VisuoSpatialCongruency * HandLoss| Block)
# Means of Block
emmeans_block_Ownership <- emmeans(lmm_model_Ownership, ~ Block| Ownership)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_Location <- emmeans(lmm_model_Location, ~ Block| Location)## NOTE: Results may be misleading due to involvement in interactionsemmeans_block_HandLoss <- emmeans(lmm_model_HandLoss, ~ Block| HandLoss)## NOTE: Results may be misleading due to involvement in interactions# Means of VisuoSpatialCongruency
emmeans_visuo_Ownership <- emmeans(lmm_model_Ownership, ~ VisuoSpatialCongruency| Ownership)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_Location <- emmeans(lmm_model_Location, ~ VisuoSpatialCongruency| Location)## NOTE: Results may be misleading due to involvement in interactionsemmeans_visuo_HandLoss <- emmeans(lmm_model_HandLoss, ~ VisuoSpatialCongruency| HandLoss)## NOTE: Results may be misleading due to involvement in interactions#
# Post hoc comparisons of Block * VisuoSpatialCongruency
posthoc_interaction_Ownership <- pairs(emmeans_interaction_Ownership, adjust = "bonferroni")
posthoc_interaction_Ownership2 <- pairs(emmeans_interaction_Ownership2, adjust = "bonferroni")
posthoc_interaction_Ownership3 <- pairs(emmeans_interaction_Ownership3, adjust = "bonferroni")
posthoc_interaction_Location <- pairs(emmeans_interaction_Location, adjust = "bonferroni")
posthoc_interaction_Location2 <- pairs(emmeans_interaction_Location2, adjust = "bonferroni")
posthoc_interaction_Location3 <- pairs(emmeans_interaction_Location3, adjust = "bonferroni")
posthoc_interaction_HandLoss <- pairs(emmeans_interaction_HandLoss, adjust = "bonferroni")
posthoc_interaction_HandLoss2 <- pairs(emmeans_interaction_HandLoss2, adjust = "bonferroni")
posthoc_interaction_HandLoss3 <- pairs(emmeans_interaction_HandLoss3, adjust = "bonferroni")
# Post hoc comparisons of Block
posthoc_block_Ownership <- contrast(emmeans_block_Ownership, adjust = "bonferroni")
posthoc_block_Location <- contrast(emmeans_block_Location, adjust = "bonferroni")
posthoc_block_HandLoss <- contrast(emmeans_block_HandLoss, adjust = "bonferroni")
# Post hoc comparisons of VisuoSpatialCongruency
posthoc_visuo_Ownership <- contrast(emmeans_visuo_Ownership, adjust = "bonferroni")
posthoc_visuo_Location <- contrast(emmeans_visuo_Location, adjust = "bonferroni")
posthoc_visuo_HandLoss <- contrast(emmeans_visuo_HandLoss, adjust = "bonferroni")
#
#post hoc summary of Block * VisuoSpatialCongruency
summary(posthoc_interaction_Ownership)## Ownership = -1.67:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -6.75 11.0 31.6 -0.612 1.0000
## A cong - A inc -120.61 12.1 31.4 -9.956 <.0001
## A cong - S inc -113.39 12.3 32.1 -9.252 <.0001
## S cong - A inc -113.86 17.4 33.0 -6.560 <.0001
## S cong - S inc -106.63 10.5 31.0 -10.181 <.0001
## A inc - S inc 7.23 15.4 32.5 0.468 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_Ownership2)## VisuoSpatialCongruency = cong:
## contrast estimate SE
## (A Ownership-1.66863247863248) - (S Ownership-1.66863247863248) -6.75 11.0
## df t.ratio p.value
## 31.6 -0.612 0.5447
##
## VisuoSpatialCongruency = inc:
## contrast estimate SE
## (A Ownership-1.66863247863248) - (S Ownership-1.66863247863248) 7.23 15.4
## df t.ratio p.value
## 32.5 0.468 0.6426
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_Ownership3)## Block = A:
## contrast estimate
## (cong Ownership-1.66863247863248) - (inc Ownership-1.66863247863248) -121
## SE df t.ratio p.value
## 12.1 31.4 -9.956 <.0001
##
## Block = S:
## contrast estimate
## (cong Ownership-1.66863247863248) - (inc Ownership-1.66863247863248) -107
## SE df t.ratio p.value
## 10.5 31.0 -10.181 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_Location)## Location = -1.21:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -7.20 13.0 36.4 -0.554 1.0000
## A cong - A inc -120.04 13.0 31.7 -9.247 <.0001
## A cong - S inc -116.17 14.9 38.4 -7.792 <.0001
## S cong - A inc -112.84 19.2 38.7 -5.888 <.0001
## S cong - S inc -108.97 11.5 31.3 -9.443 <.0001
## A inc - S inc 3.87 18.0 38.4 0.215 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_Location2)## VisuoSpatialCongruency = cong:
## contrast estimate SE df
## (A Location-1.2133547008547) - (S Location-1.2133547008547) -7.20 13 36.4
## t.ratio p.value
## -0.554 0.5828
##
## VisuoSpatialCongruency = inc:
## contrast estimate SE df
## (A Location-1.2133547008547) - (S Location-1.2133547008547) 3.87 18 38.4
## t.ratio p.value
## 0.215 0.8311
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_Location3)## Block = A:
## contrast estimate SE
## (cong Location-1.2133547008547) - (inc Location-1.2133547008547) -120 13.0
## df t.ratio p.value
## 31.7 -9.247 <.0001
##
## Block = S:
## contrast estimate SE
## (cong Location-1.2133547008547) - (inc Location-1.2133547008547) -109 11.5
## df t.ratio p.value
## 31.3 -9.443 <.0001
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_HandLoss)## HandLoss = 0.0573:
## contrast estimate SE df t.ratio p.value
## A cong - S cong -9.85 10.0 30.0 -0.981 1.0000
## A cong - A inc -123.21 12.0 30.9 -10.228 <.0001
## A cong - S inc -120.09 12.4 30.2 -9.653 <.0001
## S cong - A inc -113.36 16.7 30.5 -6.780 <.0001
## S cong - S inc -110.24 10.8 31.0 -10.197 <.0001
## A inc - S inc 3.12 14.7 30.1 0.212 1.0000
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 6 testssummary(posthoc_interaction_HandLoss2)## VisuoSpatialCongruency = cong:
## contrast estimate SE df
## A HandLoss0.0572649572649573 - S HandLoss0.0572649572649573 -9.85 10.0 30.0
## t.ratio p.value
## -0.981 0.3342
##
## VisuoSpatialCongruency = inc:
## contrast estimate SE df
## A HandLoss0.0572649572649573 - S HandLoss0.0572649572649573 3.12 14.7 30.1
## t.ratio p.value
## 0.212 0.8335
##
## Degrees-of-freedom method: kenward-rogersummary(posthoc_interaction_HandLoss3)## Block = A:
## contrast estimate SE
## cong HandLoss0.0572649572649573 - inc HandLoss0.0572649572649573 -123 12.0
## df t.ratio p.value
## 30.9 -10.228 <.0001
##
## Block = S:
## contrast estimate SE
## cong HandLoss0.0572649572649573 - inc HandLoss0.0572649572649573 -110 10.8
## df t.ratio p.value
## 31.0 -10.197 <.0001
##
## Degrees-of-freedom method: kenward-roger#post hoc summary of Block
summary(posthoc_block_Ownership)## Ownership = -1.67:
## contrast estimate SE df t.ratio p.value
## A effect 0.118 5.89 32.1 0.020 1.0000
## S effect -0.118 5.89 32.1 -0.020 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_Location)## Location = -1.21:
## contrast estimate SE df t.ratio p.value
## A effect -0.831 6.99 37.5 -0.119 1.0000
## S effect 0.831 6.99 37.5 0.119 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_block_HandLoss)## HandLoss = 0.0573:
## contrast estimate SE df t.ratio p.value
## A effect -1.68 5.53 30.1 -0.304 1.0000
## S effect 1.68 5.53 30.1 0.304 1.0000
##
## Results are averaged over the levels of: VisuoSpatialCongruency
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 tests#post hoc summary of VisuoSpatialCongruency
summary(posthoc_visuo_Ownership)## Ownership = -1.67:
## contrast estimate SE df t.ratio p.value
## cong effect -56.8 4.67 32.4 -12.175 <.0001
## inc effect 56.8 4.67 32.4 12.175 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_Location)## Location = -1.21:
## contrast estimate SE df t.ratio p.value
## cong effect -57.3 4.98 35.1 -11.489 <.0001
## inc effect 57.3 4.98 35.1 11.489 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 testssummary(posthoc_visuo_HandLoss)## HandLoss = 0.0573:
## contrast estimate SE df t.ratio p.value
## cong effect -58.4 4.87 31 -11.989 <.0001
## inc effect 58.4 4.87 31 11.989 <.0001
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: kenward-roger
## P value adjustment: bonferroni method for 2 tests