R Notebook
Preliminaries
library(readr)
library(tidyverse)
library(corrplot)
library(lavaan)
library(rstatix)
library(GGally)
Predictors_18 <- read_csv("Predictors_18.csv")
Mediator_36 <- read_csv("Mediator_36.csv")
Outcomes60_formatted <- read_csv("Outcomes60_formatted.csv")Combine datasets
full <- full_join(Outcomes60_formatted, Mediator_36, by="Blind_ID")
full <- full_join(full, Predictors_18, by="Blind_ID") %>%
rename(
ELI = CELF_ELI_standard_score,
RLI = CELF_RLI_standard_score,
WAI = WAI_Total,
ERRNI = ERRNI_comps,
logRT = meanlogRT,
Vocab = VocabTotal
)Get descriptive stats
full %>%
get_summary_stats(type="common")Get joint distributions
full %>%
dplyr::select("logCTC", "logAWC", "logRT", "Vocab", "LUI_Total", "ELI", "RLI", "WAI", "ERRNI") %>%
ggpairs()
Two participants with exceptionally low LUI score (see scatterplots above). We’ll fit model with and without them.
full2 <- full %>%
filter(LUI_Total > 100)full2 %>%
dplyr::select("logCTC", "logAWC", "logRT", "Vocab", "LUI_Total", "ELI", "RLI", "WAI", "ERRNI") %>%
ggpairs()
Correlation Plot
full %>%
dplyr::select("logCTC", "logAWC", "logRT", "Vocab", "LUI_Total", "ELI", "RLI", "WAI", "ERRNI") %>%
cor(use="pairwise.complete.obs") %>%
corrplot()
With two participants removed
full2 %>%
dplyr::select("logCTC", "logAWC", "logRT", "Vocab", "LUI_Total", "ELI", "RLI", "WAI", "ERRNI") %>%
cor(use="pairwise.complete.obs") %>%
corrplot()
Include all observations
Direct effects can be seen in the regressions. Indirect effects and total effects are in the defined parameters blocked EERNI_CTC_I = indirect effect of CTC (through LUI) on ERRNI, etc. EERNI_CTC_T = total effect direct effect + indirect effect. I used bootstrapped standard errors because indirect effects have non-normal sampling distributions.
model <- '
# direct effects
ERRNI ~ b11*logCTC + b12*logAWC + b13*logRT + b14*Vocab + b15*LUI_Total
WAI ~ c11*logCTC + c12*logAWC + c13*logRT + c14*Vocab + c15*LUI_Total
RLI ~ d11*logCTC + d12*logAWC + d13*logRT + d14*Vocab + d15*LUI_Total
ELI ~ e11*logCTC + e12*logAWC + e13*logRT + e14*Vocab + e15*LUI_Total
# mediators
LUI_Total ~ f1*logCTC + f2*logAWC + f3*logRT + f4*Vocab
# cov
ERRNI ~~ WAI
ERRNI ~~ ELI
ERRNI ~~ RLI
WAI ~~ ELI
WAI ~~ RLI
RLI ~~ ELI
# indirect effects
ERRNI_CTC_I := b15*f1
ERRNI_AWC_I := b15*f2
ERRNI_RT_I := b15*f3
ERRNI_Vocab_I := b15*f4
WAI_CTC_I := c15*f1
WAI_AWC_I := c15*f2
WAI_RT_I := c15*f3
WAI_Vocab_I := c15*f4
RLI_CTC_I := d15*f1
RLI_AWC_I := d15*f2
RLI_RT_I := d15*f3
RLI_Vocab_I := d15*f4
ELI_CTC_I := e15*f1
ELI_AWC_I := e15*f2
ELI_RT_I := e15*f3
ELI_Vocab_I := e15*f4
# total effects
ERRNI_CTC_T := b11 + (b15*f1)
ERRNI_AWC_T := b12 + (b15*f2)
ERRNI_RT_T := b13 + (b15*f3)
ERRNI_Vocab_T := b14 + (b15*f4)
WAI_CTC_T := c11 + (c15*f1)
WAI_AWC_T := c12 + (c15*f2)
WAI_RT_T := c13 + (c15*f3)
WAI_Vocab_T := c14 + (c15*f4)
RLI_CTC_T := d11 + (d15*f1)
RLI_AWC_T := d12 + (d15*f2)
RLI_RT_T := d13 + (d15*f3)
RLI_Vocab_T := d14 + (d15*f4)
ELI_CTC_T := e11 + (e15*f1)
ELI_AWC_T := e12 + (e15*f2)
ELI_RT_T := e13 + (e15*f3)
ELI_Vocab_T := e14 + (e15*f4)
'
#m1 <- sem(model, data=full, missing="ml", se="bootstrap", bootstrap=9999)
#write_rds(m1, "models/m1.rds" )
m1 <- read_rds("models/m1.rds")summarise model, get
summary(m1, standardized=TRUE)## lavaan 0.6-12 ended normally after 219 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 40
##
## Number of observations 85
## Number of missing patterns 4
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Parameter Estimates:
##
## Standard errors Bootstrap
## Number of requested bootstrap draws 9999
## Number of successful bootstrap draws 9999
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## ERRNI ~
## logCTC (b11) -0.211 0.350 -0.602 0.547 -0.211 -0.090
## logAWC (b12) -0.061 0.384 -0.160 0.873 -0.061 -0.022
## logRT (b13) -2.031 0.706 -2.877 0.004 -2.031 -0.297
## Vocab (b14) 0.002 0.002 0.904 0.366 0.002 0.139
## LUI_Totl (b15) 0.010 0.010 1.030 0.303 0.010 0.141
## WAI ~
## logCTC (c11) -0.465 1.814 -0.256 0.798 -0.465 -0.050
## logAWC (c12) 2.476 2.033 1.218 0.223 2.476 0.223
## logRT (c13) -3.049 3.325 -0.917 0.359 -3.049 -0.111
## Vocab (c14) -0.004 0.006 -0.691 0.489 -0.004 -0.085
## LUI_Totl (c15) 0.085 0.043 1.973 0.048 0.085 0.298
## RLI ~
## logCTC (d11) 1.713 3.925 0.436 0.663 1.713 0.068
## logAWC (d12) -4.337 4.261 -1.018 0.309 -4.337 -0.144
## logRT (d13) -20.666 7.566 -2.731 0.006 -20.666 -0.279
## Vocab (d14) -0.015 0.017 -0.887 0.375 -0.015 -0.115
## LUI_Totl (d15) 0.286 0.131 2.187 0.029 0.286 0.370
## ELI ~
## logCTC (e11) 0.926 2.990 0.310 0.757 0.926 0.045
## logAWC (e12) -0.383 3.581 -0.107 0.915 -0.383 -0.016
## logRT (e13) -10.306 5.350 -1.927 0.054 -10.306 -0.170
## Vocab (e14) 0.022 0.012 1.797 0.072 0.022 0.209
## LUI_Totl (e15) 0.270 0.090 3.019 0.003 0.270 0.428
## LUI_Total ~
## logCTC (f1) 1.938 4.709 0.412 0.681 1.938 0.059
## logAWC (f2) 6.755 5.581 1.210 0.226 6.755 0.173
## logRT (f3) -5.027 8.134 -0.618 0.537 -5.027 -0.052
## Vocab (f4) 0.068 0.019 3.584 0.000 0.068 0.404
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .ERRNI ~~
## .WAI 1.801 0.638 2.822 0.005 1.801 0.357
## .ELI 1.195 0.974 1.227 0.220 1.195 0.129
## .RLI 2.871 1.403 2.047 0.041 2.871 0.218
## .WAI ~~
## .ELI 10.646 3.961 2.687 0.007 10.646 0.287
## .RLI 22.886 5.341 4.285 0.000 22.886 0.435
## .RLI ~~
## .ELI 43.463 10.924 3.979 0.000 43.463 0.449
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .ERRNI 14.010 5.299 2.644 0.008 14.010 11.468
## .WAI 15.142 22.466 0.674 0.500 15.142 3.103
## .RLI 236.439 64.122 3.687 0.000 236.439 17.870
## .ELI 132.924 45.703 2.908 0.004 132.924 12.289
## .LUI_Total 86.082 66.028 1.304 0.192 86.082 5.025
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .ERRNI 1.262 0.197 6.395 0.000 1.262 0.846
## .WAI 20.154 2.620 7.692 0.000 20.154 0.846
## .RLI 137.217 18.986 7.227 0.000 137.217 0.784
## .ELI 68.216 9.694 7.037 0.000 68.216 0.583
## .LUI_Total 212.691 53.656 3.964 0.000 212.691 0.725
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## ERRNI_CTC_I 0.020 0.066 0.298 0.766 0.020 0.008
## ERRNI_AWC_I 0.068 0.106 0.646 0.518 0.068 0.025
## ERRNI_RT_I -0.051 0.123 -0.411 0.681 -0.051 -0.007
## ERRNI_Vocab_I 0.001 0.001 0.943 0.346 0.001 0.057
## WAI_CTC_I 0.164 0.423 0.388 0.698 0.164 0.018
## WAI_AWC_I 0.573 0.680 0.842 0.400 0.573 0.052
## WAI_RT_I -0.426 0.779 -0.547 0.584 -0.426 -0.016
## WAI_Vocab_I 0.006 0.004 1.467 0.142 0.006 0.120
## RLI_CTC_I 0.554 1.410 0.393 0.695 0.554 0.022
## RLI_AWC_I 1.930 2.148 0.898 0.369 1.930 0.064
## RLI_RT_I -1.436 2.523 -0.569 0.569 -1.436 -0.019
## RLI_Vocab_I 0.020 0.012 1.605 0.109 0.020 0.149
## ELI_CTC_I 0.524 1.291 0.406 0.685 0.524 0.025
## ELI_AWC_I 1.827 1.889 0.967 0.334 1.827 0.074
## ELI_RT_I -1.359 2.318 -0.586 0.558 -1.359 -0.022
## ELI_Vocab_I 0.018 0.010 1.881 0.060 0.018 0.173
## ERRNI_CTC_T -0.191 0.354 -0.540 0.589 -0.191 -0.082
## ERRNI_AWC_T 0.007 0.388 0.018 0.986 0.007 0.002
## ERRNI_RT_T -2.082 0.707 -2.945 0.003 -2.082 -0.304
## ERRNI_Vocab_T 0.002 0.002 1.367 0.172 0.002 0.196
## WAI_CTC_T -0.300 1.838 -0.163 0.870 -0.300 -0.032
## WAI_AWC_T 3.049 1.985 1.536 0.125 3.049 0.275
## WAI_RT_T -3.475 3.414 -1.018 0.309 -3.475 -0.127
## WAI_Vocab_T 0.002 0.006 0.302 0.762 0.002 0.035
## RLI_CTC_T 2.266 4.214 0.538 0.591 2.266 0.089
## RLI_AWC_T -2.407 4.580 -0.526 0.599 -2.407 -0.080
## RLI_RT_T -22.103 8.137 -2.716 0.007 -22.103 -0.298
## RLI_Vocab_T 0.004 0.017 0.267 0.789 0.004 0.034
## ELI_CTC_T 1.450 3.030 0.479 0.632 1.450 0.070
## ELI_AWC_T 1.444 3.654 0.395 0.693 1.444 0.059
## ELI_RT_T -11.665 5.243 -2.225 0.026 -11.665 -0.192
## ELI_Vocab_T 0.041 0.013 3.222 0.001 0.041 0.382Marginally significant direct effect of RT on ELI, significant effect on RLI and EERNI. Nothing on WAI. No indirect effects of vocab. Some total effects, but hard to know what to make of those. Not much going on CTC or AWC.
Since we have very little power, try cutting those paths.
model2 <- '
# direct effects
ERRNI ~ b13*logRT + b14*Vocab + b15*LUI_Total
WAI ~ c13*logRT + c14*Vocab + c15*LUI_Total
RLI ~ d13*logRT + d14*Vocab + d15*LUI_Total
ELI ~ e13*logRT + e14*Vocab + e15*LUI_Total
# mediators
LUI_Total ~ f3*logRT + f4*Vocab
# cov
ERRNI ~~ WAI
ERRNI ~~ ELI
ERRNI ~~ RLI
WAI ~~ ELI
WAI ~~ RLI
RLI ~~ ELI
# indirect effects
ERRNI_RT_I := b15*f3
ERRNI_Vocab_I := b15*f4
WAI_RT_I := c15*f3
WAI_Vocab_I := c15*f4
RLI_RT_I := d15*f3
RLI_Vocab_I := d15*f4
ELI_RT_I := e15*f3
ELI_Vocab_I := e15*f4
# total effects
ERRNI_RT_T := b13 + (b15*f3)
ERRNI_Vocab_T := b14 + (b15*f4)
WAI_RT_T := c13 + (c15*f3)
WAI_Vocab_T := c14 + (c15*f4)
RLI_RT_T := d13 + (d15*f3)
RLI_Vocab_T := d14 + (d15*f4)
ELI_RT_T := e13 + (e15*f3)
ELI_Vocab_T := e14 + (e15*f4)
'
#m2 <- sem(model2, full, missing="ml", se="bootstrap", bootstrap=9999)
#write_rds(m2, "models/m2.rds")
m2 <-read_rds("models/m2.rds")summary(m2, standardized=TRUE)## lavaan 0.6-12 ended normally after 156 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 30
##
## Number of observations 85
## Number of missing patterns 4
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Parameter Estimates:
##
## Standard errors Bootstrap
## Number of requested bootstrap draws 9999
## Number of successful bootstrap draws 9999
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## ERRNI ~
## logRT (b13) -1.878 0.722 -2.600 0.009 -1.878 -0.274
## Vocab (b14) 0.001 0.002 0.801 0.423 0.001 0.115
## LUI_Totl (b15) 0.008 0.010 0.807 0.420 0.008 0.113
## WAI ~
## logRT (c13) -2.857 2.829 -1.010 0.313 -2.857 -0.104
## Vocab (c14) -0.004 0.006 -0.734 0.463 -0.004 -0.091
## LUI_Totl (c15) 0.098 0.040 2.471 0.013 0.098 0.346
## RLI ~
## logRT (d13) -21.604 7.585 -2.848 0.004 -21.604 -0.293
## Vocab (d14) -0.013 0.017 -0.744 0.457 -0.013 -0.097
## LUI_Totl (d15) 0.257 0.131 1.955 0.051 0.257 0.334
## ELI ~
## logRT (e13) -10.880 5.168 -2.105 0.035 -10.880 -0.179
## Vocab (e14) 0.024 0.012 2.055 0.040 0.024 0.222
## LUI_Totl (e15) 0.273 0.085 3.232 0.001 0.273 0.433
## LUI_Total ~
## logRT (f3) -7.517 7.499 -1.002 0.316 -7.517 -0.078
## Vocab (f4) 0.076 0.017 4.594 0.000 0.076 0.451
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .ERRNI ~~
## .WAI 1.734 0.662 2.621 0.009 1.734 0.335
## .ELI 1.183 0.995 1.189 0.235 1.183 0.127
## .RLI 2.954 1.439 2.052 0.040 2.954 0.222
## .WAI ~~
## .ELI 10.771 4.240 2.540 0.011 10.771 0.284
## .RLI 21.611 5.480 3.944 0.000 21.611 0.400
## .RLI ~~
## .ELI 43.268 10.745 4.027 0.000 43.268 0.444
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .ERRNI 11.375 5.059 2.249 0.025 11.375 9.311
## .WAI 32.883 19.346 1.700 0.089 32.883 6.739
## .RLI 215.546 56.035 3.847 0.000 215.546 16.362
## .ELI 138.371 37.150 3.725 0.000 138.371 12.791
## .LUI_Total 179.057 50.708 3.531 0.000 179.057 10.455
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .ERRNI 1.276 0.194 6.568 0.000 1.276 0.855
## .WAI 20.988 2.775 7.564 0.000 20.988 0.881
## .RLI 138.818 19.118 7.261 0.000 138.818 0.800
## .ELI 68.342 9.549 7.157 0.000 68.342 0.584
## .LUI_Total 225.746 55.974 4.033 0.000 225.746 0.770
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## ERRNI_RT_I -0.061 0.117 -0.521 0.602 -0.061 -0.009
## ERRNI_Vocab_I 0.001 0.001 0.781 0.435 0.001 0.051
## WAI_RT_I -0.740 0.807 -0.917 0.359 -0.740 -0.027
## WAI_Vocab_I 0.008 0.004 1.919 0.055 0.008 0.156
## RLI_RT_I -1.929 2.118 -0.911 0.362 -1.929 -0.026
## RLI_Vocab_I 0.020 0.012 1.649 0.099 0.020 0.151
## ELI_RT_I -2.054 2.087 -0.984 0.325 -2.054 -0.034
## ELI_Vocab_I 0.021 0.009 2.197 0.028 0.021 0.195
## ERRNI_RT_T -1.939 0.709 -2.735 0.006 -1.939 -0.283
## ERRNI_Vocab_T 0.002 0.002 1.254 0.210 0.002 0.166
## WAI_RT_T -3.597 2.773 -1.297 0.195 -3.597 -0.131
## WAI_Vocab_T 0.003 0.005 0.576 0.565 0.003 0.065
## RLI_RT_T -23.534 7.924 -2.970 0.003 -23.534 -0.319
## RLI_Vocab_T 0.007 0.016 0.445 0.656 0.007 0.054
## ELI_RT_T -12.934 5.083 -2.545 0.011 -12.934 -0.213
## ELI_Vocab_T 0.045 0.011 3.926 0.000 0.045 0.418When those other parameters are removed, clear effects for LWL RT on the outcomes. Marginally significant effects of vocabulary through LUI.
Refit models to dataset with two low LUI scores removed.
#m3 <- sem(model, data=full2, missing="ml", se="bootstrap", bootstrap=9999)
#m4 <- sem(model2, data=full2, missing="ml", se="bootstrap", bootstrap=9999)
#write_rds(m3, "models/m3.rds")
#write_rds(m4, "models/m4.rds")
m3 <- read_rds("models/m3.rds")
m4 <- read_rds("models/m4.rds")summary(m3, standardized=TRUE)## lavaan 0.6-12 ended normally after 217 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 40
##
## Number of observations 78
## Number of missing patterns 2
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Parameter Estimates:
##
## Standard errors Bootstrap
## Number of requested bootstrap draws 9999
## Number of successful bootstrap draws 9999
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## ERRNI ~
## logCTC (b11) -0.131 0.377 -0.349 0.727 -0.131 -0.058
## logAWC (b12) -0.118 0.411 -0.288 0.773 -0.118 -0.043
## logRT (b13) -2.134 0.736 -2.900 0.004 -2.134 -0.318
## Vocab (b14) 0.003 0.002 1.248 0.212 0.003 0.206
## LUI_Totl (b15) -0.001 0.012 -0.111 0.912 -0.001 -0.015
## WAI ~
## logCTC (c11) 0.161 1.857 0.087 0.931 0.161 0.019
## logAWC (c12) 2.071 2.073 0.999 0.318 2.071 0.199
## logRT (c13) -3.093 3.489 -0.887 0.375 -3.093 -0.121
## Vocab (c14) -0.003 0.006 -0.517 0.605 -0.003 -0.071
## LUI_Totl (c15) 0.025 0.043 0.573 0.567 0.025 0.075
## RLI ~
## logCTC (d11) 2.484 4.232 0.587 0.557 2.484 0.108
## logAWC (d12) -4.715 4.307 -1.095 0.274 -4.715 -0.170
## logRT (d13) -26.493 7.734 -3.426 0.001 -26.493 -0.388
## Vocab (d14) -0.016 0.018 -0.882 0.378 -0.016 -0.127
## LUI_Totl (d15) 0.107 0.121 0.885 0.376 0.107 0.121
## ELI ~
## logCTC (e11) 1.842 2.887 0.638 0.524 1.842 0.105
## logAWC (e12) -0.565 3.395 -0.166 0.868 -0.565 -0.027
## logRT (e13) -11.753 5.422 -2.168 0.030 -11.753 -0.225
## Vocab (e14) 0.028 0.012 2.250 0.024 0.028 0.296
## LUI_Totl (e15) 0.109 0.071 1.536 0.124 0.109 0.161
## LUI_Total ~
## logCTC (f1) 4.251 4.023 1.057 0.291 4.251 0.163
## logAWC (f2) 3.002 4.666 0.643 0.520 3.002 0.096
## logRT (f3) -5.942 8.084 -0.735 0.462 -5.942 -0.077
## Vocab (f4) 0.051 0.014 3.590 0.000 0.051 0.366
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .ERRNI ~~
## .WAI 1.737 0.712 2.438 0.015 1.737 0.347
## .ELI 0.264 0.988 0.267 0.789 0.264 0.031
## .RLI 1.998 1.417 1.410 0.159 1.998 0.160
## .WAI ~~
## .ELI 7.224 3.723 1.940 0.052 7.224 0.209
## .RLI 20.195 5.337 3.784 0.000 20.195 0.404
## .RLI ~~
## .ELI 32.108 9.601 3.344 0.001 32.108 0.372
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .ERRNI 16.264 5.534 2.939 0.003 16.264 13.338
## .WAI 23.837 22.512 1.059 0.290 23.837 5.122
## .RLI 299.614 63.058 4.751 0.000 299.614 24.192
## .ELI 160.636 43.655 3.680 0.000 160.636 16.940
## .LUI_Total 117.012 64.375 1.818 0.069 117.012 8.348
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .ERRNI 1.246 0.212 5.871 0.000 1.246 0.838
## .WAI 20.045 2.693 7.443 0.000 20.045 0.926
## .RLI 124.613 17.485 7.127 0.000 124.613 0.812
## .ELI 59.711 8.816 6.773 0.000 59.711 0.664
## .LUI_Total 139.310 18.532 7.517 0.000 139.310 0.709
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## ERRNI_CTC_I -0.006 0.071 -0.080 0.937 -0.006 -0.003
## ERRNI_AWC_I -0.004 0.067 -0.060 0.952 -0.004 -0.001
## ERRNI_RT_I 0.008 0.123 0.065 0.948 0.008 0.001
## ERRNI_Vocab_I -0.000 0.001 -0.107 0.915 -0.000 -0.006
## WAI_CTC_I 0.105 0.255 0.412 0.680 0.105 0.012
## WAI_AWC_I 0.074 0.292 0.254 0.799 0.074 0.007
## WAI_RT_I -0.147 0.505 -0.291 0.771 -0.147 -0.006
## WAI_Vocab_I 0.001 0.002 0.544 0.586 0.001 0.027
## RLI_CTC_I 0.455 0.773 0.589 0.556 0.455 0.020
## RLI_AWC_I 0.321 0.870 0.370 0.712 0.321 0.012
## RLI_RT_I -0.636 1.516 -0.420 0.675 -0.636 -0.009
## RLI_Vocab_I 0.005 0.007 0.838 0.402 0.005 0.044
## ELI_CTC_I 0.464 0.569 0.816 0.415 0.464 0.026
## ELI_AWC_I 0.328 0.711 0.461 0.645 0.328 0.015
## ELI_RT_I -0.649 1.153 -0.562 0.574 -0.649 -0.012
## ELI_Vocab_I 0.006 0.004 1.316 0.188 0.006 0.059
## ERRNI_CTC_T -0.137 0.365 -0.375 0.707 -0.137 -0.061
## ERRNI_AWC_T -0.122 0.410 -0.298 0.765 -0.122 -0.045
## ERRNI_RT_T -2.126 0.729 -2.918 0.004 -2.126 -0.316
## ERRNI_Vocab_T 0.002 0.002 1.292 0.196 0.002 0.200
## WAI_CTC_T 0.267 1.837 0.145 0.885 0.267 0.031
## WAI_AWC_T 2.146 2.027 1.058 0.290 2.146 0.206
## WAI_RT_T -3.240 3.523 -0.920 0.358 -3.240 -0.126
## WAI_Vocab_T -0.002 0.006 -0.354 0.723 -0.002 -0.044
## RLI_CTC_T 2.939 4.218 0.697 0.486 2.939 0.128
## RLI_AWC_T -4.394 4.331 -1.014 0.310 -4.394 -0.158
## RLI_RT_T -27.129 8.033 -3.377 0.001 -27.129 -0.397
## RLI_Vocab_T -0.010 0.016 -0.629 0.529 -0.010 -0.082
## ELI_CTC_T 2.306 2.892 0.797 0.425 2.306 0.131
## ELI_AWC_T -0.237 3.300 -0.072 0.943 -0.237 -0.011
## ELI_RT_T -12.401 5.463 -2.270 0.023 -12.401 -0.237
## ELI_Vocab_T 0.034 0.012 2.851 0.004 0.034 0.355No indirect effects of vocab, though direct effect on ELI.
summary(m4, standardized=TRUE )## lavaan 0.6-12 ended normally after 149 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 30
##
## Number of observations 78
## Number of missing patterns 2
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Parameter Estimates:
##
## Standard errors Bootstrap
## Number of requested bootstrap draws 9999
## Number of successful bootstrap draws 9999
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## ERRNI ~
## logRT (b13) -2.038 0.727 -2.803 0.005 -2.038 -0.303
## Vocab (b14) 0.002 0.002 1.251 0.211 0.002 0.191
## LUI_Totl (b15) -0.004 0.012 -0.306 0.760 -0.004 -0.041
## WAI ~
## logRT (c13) -3.280 2.807 -1.168 0.243 -3.280 -0.128
## Vocab (c14) -0.003 0.006 -0.460 0.646 -0.003 -0.064
## LUI_Totl (c15) 0.044 0.041 1.060 0.289 0.044 0.131
## RLI ~
## logRT (d13) -28.065 7.593 -3.696 0.000 -28.065 -0.411
## Vocab (d14) -0.013 0.017 -0.729 0.466 -0.013 -0.102
## LUI_Totl (d15) 0.091 0.120 0.753 0.451 0.091 0.103
## ELI ~
## logRT (e13) -13.043 5.211 -2.503 0.012 -13.043 -0.249
## Vocab (e14) 0.030 0.012 2.602 0.009 0.030 0.321
## LUI_Totl (e15) 0.122 0.066 1.841 0.066 0.122 0.180
## LUI_Total ~
## logRT (f3) -9.650 7.380 -1.307 0.191 -9.650 -0.125
## Vocab (f4) 0.061 0.013 4.686 0.000 0.061 0.436
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .ERRNI ~~
## .WAI 1.645 0.736 2.236 0.025 1.645 0.321
## .ELI 0.207 1.007 0.206 0.837 0.207 0.024
## .RLI 2.082 1.452 1.434 0.152 2.082 0.165
## .WAI ~~
## .ELI 7.618 4.084 1.865 0.062 7.618 0.215
## .RLI 19.103 5.500 3.473 0.001 19.103 0.371
## .RLI ~~
## .ELI 32.082 9.601 3.342 0.001 32.082 0.368
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .ERRNI 13.977 5.135 2.722 0.006 13.977 11.463
## .WAI 43.400 18.860 2.301 0.021 43.400 9.326
## .RLI 282.343 54.865 5.146 0.000 282.343 22.797
## .ELI 173.454 36.097 4.805 0.000 173.454 18.288
## .LUI_Total 196.470 49.619 3.960 0.000 196.470 14.017
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .ERRNI 1.257 0.208 6.041 0.000 1.257 0.845
## .WAI 20.938 2.886 7.254 0.000 20.938 0.967
## .RLI 126.604 18.094 6.997 0.000 126.604 0.825
## .ELI 60.171 8.888 6.770 0.000 60.171 0.669
## .LUI_Total 148.938 20.259 7.352 0.000 148.938 0.758
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## ERRNI_RT_I 0.034 0.137 0.249 0.803 0.034 0.005
## ERRNI_Vocab_I -0.000 0.001 -0.293 0.770 -0.000 -0.018
## WAI_RT_I -0.421 0.613 -0.687 0.492 -0.421 -0.016
## WAI_Vocab_I 0.003 0.003 1.025 0.305 0.003 0.057
## RLI_RT_I -0.876 1.587 -0.552 0.581 -0.876 -0.013
## RLI_Vocab_I 0.006 0.007 0.745 0.456 0.006 0.045
## ELI_RT_I -1.174 1.185 -0.991 0.322 -1.174 -0.022
## ELI_Vocab_I 0.007 0.005 1.631 0.103 0.007 0.078
## ERRNI_RT_T -2.004 0.729 -2.750 0.006 -2.004 -0.298
## ERRNI_Vocab_T 0.002 0.002 1.247 0.212 0.002 0.173
## WAI_RT_T -3.700 2.849 -1.299 0.194 -3.700 -0.144
## WAI_Vocab_T -0.000 0.006 -0.058 0.954 -0.000 -0.007
## RLI_RT_T -28.941 7.723 -3.747 0.000 -28.941 -0.424
## RLI_Vocab_T -0.007 0.015 -0.469 0.639 -0.007 -0.057
## ELI_RT_T -14.217 5.265 -2.700 0.007 -14.217 -0.272
## ELI_Vocab_T 0.038 0.011 3.418 0.001 0.038 0.399Still no indirect effects of vocab.
sessionInfo()## R version 4.1.3 (2022-03-10)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows Server x64 (build 17763)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=Dutch_Netherlands.1252 LC_CTYPE=Dutch_Netherlands.1252
## [3] LC_MONETARY=Dutch_Netherlands.1252 LC_NUMERIC=C
## [5] LC_TIME=Dutch_Netherlands.1252
##
## attached base packages:
## [1] stats graphics grDevices datasets utils methods base
##
## other attached packages:
## [1] GGally_2.1.2 rstatix_0.7.0 lavaan_0.6-12 corrplot_0.92
## [5] forcats_0.5.1 stringr_1.4.0 dplyr_1.0.9 purrr_0.3.4
## [9] tidyr_1.2.0 tibble_3.1.8 ggplot2_3.3.6 tidyverse_1.3.2
## [13] readr_2.1.2
##
## loaded via a namespace (and not attached):
## [1] httr_1.4.4 sass_0.4.2 bit64_4.0.5
## [4] vroom_1.5.7 jsonlite_1.8.0 carData_3.0-5
## [7] modelr_0.1.8 bslib_0.4.0 assertthat_0.2.1
## [10] highr_0.9 stats4_4.1.3 renv_0.15.4
## [13] googlesheets4_1.0.1 cellranger_1.1.0 yaml_2.3.5
## [16] pbivnorm_0.6.0 pillar_1.8.0 backports_1.4.1
## [19] glue_1.6.2 digest_0.6.29 RColorBrewer_1.1-3
## [22] rvest_1.0.2 colorspace_2.0-3 htmltools_0.5.3
## [25] plyr_1.8.7 pkgconfig_2.0.3 broom_1.0.0
## [28] haven_2.5.0 scales_1.2.0 tzdb_0.3.0
## [31] googledrive_2.0.0 farver_2.1.1 generics_0.1.3
## [34] car_3.1-0 ellipsis_0.3.2 cachem_1.0.6
## [37] withr_2.5.0 cli_3.3.0 mnormt_2.1.0
## [40] magrittr_2.0.3 crayon_1.5.1 readxl_1.4.0
## [43] evaluate_0.16 fs_1.5.2 fansi_1.0.3
## [46] xml2_1.3.3 tools_4.1.3 hms_1.1.1
## [49] gargle_1.2.0 lifecycle_1.0.1 munsell_0.5.0
## [52] reprex_2.0.2 compiler_4.1.3 jquerylib_0.1.4
## [55] rlang_1.0.4 grid_4.1.3 rstudioapi_0.13
## [58] labeling_0.4.2 rmarkdown_2.16 gtable_0.3.0
## [61] reshape_0.8.9 abind_1.4-5 DBI_1.1.3
## [64] R6_2.5.1 lubridate_1.8.0 knitr_1.39
## [67] bit_4.0.4 fastmap_1.1.0 utf8_1.2.2
## [70] stringi_1.7.6 parallel_4.1.3 Rcpp_1.0.9
## [73] vctrs_0.4.1 dbplyr_2.2.1 tidyselect_1.1.2
## [76] xfun_0.32