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library(emmeans)

Set up

Full_data_all <- read_csv("Full_data_all.csv")
## New names:
## Rows: 259 Columns: 274
## ── Column specification
## ──────────────────────────────────────────────────────── Delimiter: "," chr
## (2): Prolific_ID, Group dbl (272): ...1, X, ...3, ID, B_IUS_1, B_IUS_2,
## B_IUS_3, B_IUS_4, B_IUS_5, B...
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## • `` -> `...1`
## • `...1` -> `...3`

H2a IUS: difference in change in cognitive IUS over time between groups

Baseline to post

IUS_BP <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_IUS_total", "B_POST_IUS_total")
## Formatting table as needed
IUS_BP_long <- IUS_BP %>%
  pivot_longer(cols = c(A_PRE_IUS_total, B_POST_IUS_total),
               names_to = "Time",
               values_to = "IUS_Score")
IUS_MEM_BP <- lmer(IUS_Score ~ Group * Time + (1|ID), data = IUS_BP_long, REML = TRUE)
summary(IUS_MEM_BP)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: IUS_Score ~ Group * Time + (1 | ID)
##    Data: IUS_BP_long
## 
## REML criterion at convergence: 3592.2
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.95161 -0.44757  0.00781  0.41532  2.86841 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 71.13    8.434   
##  Residual             24.28    4.927   
## Number of obs: 516, groups:  ID, 259
## 
## Fixed effects:
##                                          Estimate Std. Error       df t value
## (Intercept)                               41.0800     1.3814 328.7093  29.738
## GroupB_Controls                            0.9483     1.6758 328.7093   0.566
## GroupC_Intervention                        1.9880     1.6836 328.7093   1.181
## TimeB_POST_IUS_total                      -0.2800     0.9854 254.2485  -0.284
## GroupB_Controls:TimeB_POST_IUS_total      -3.5879     1.1955 254.2485  -3.001
## GroupC_Intervention:TimeB_POST_IUS_total  -6.0437     1.2044 254.6121  -5.018
##                                          Pr(>|t|)    
## (Intercept)                               < 2e-16 ***
## GroupB_Controls                           0.57186    
## GroupC_Intervention                       0.23854    
## TimeB_POST_IUS_total                      0.77654    
## GroupB_Controls:TimeB_POST_IUS_total      0.00296 ** 
## GroupC_Intervention:TimeB_POST_IUS_total 9.81e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) GrpB_C GrpC_I TB_POS GB_C:T
## GrpB_Cntrls -0.824                            
## GrpC_Intrvn -0.820  0.676                     
## TB_POST_IUS -0.357  0.294  0.293              
## GB_C:TB_POS  0.294 -0.357 -0.241 -0.824       
## GC_I:TB_POS  0.292 -0.241 -0.356 -0.818  0.674
anova  (IUS_MEM_BP)
## Type III Analysis of Variance Table with Satterthwaite's method
##             Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
## Group        10.89    5.45     2 256.08  0.2243    0.7992    
## Time       1394.73 1394.73     1 254.53 57.4503 6.459e-13 ***
## Group:Time  617.82  308.91     2 254.58 12.7243 5.407e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(IUS_MEM_BP,
                  pred.labels=c("Intercept", "Psychoeducation Control", "Mindset Intervention","Time (Post)", "Psychoeducation Control x Time","Mindset Intervention x Time"),
                  dv.labels=c("Intolerance of Uncertainty (IUS-12 Score)"),
                  string.std_ci = "std. 95% CI",
                  string.std = "std. Beta",
                  show.std = TRUE,
                  show.est = FALSE)
  Intolerance of Uncertainty (IUS-12 Score)
Predictors std. Beta std. 95% CI p
Intercept 0.09 -0.18 – 0.36 <0.001
Psychoeducation Control 0.09 -0.23 – 0.42 0.572
Mindset Intervention 0.20 -0.13 – 0.53 0.238
Time (Post) -0.03 -0.22 – 0.17 0.776
Psychoeducation Control x Time -0.36 -0.59 – -0.12 0.003
Mindset Intervention x Time -0.60 -0.84 – -0.37 <0.001
Random Effects
σ2 24.28
τ00 ID 71.13
ICC 0.75
N ID 259
Observations 516
Marginal R2 / Conditional R2 0.056 / 0.760
parameters::standardise_parameters(IUS_MEM_BP)
## # Standardization method: refit
## 
## Parameter                                | Std. Coef. |         95% CI
## ----------------------------------------------------------------------
## (Intercept)                              |       0.09 | [-0.18,  0.36]
## GroupB_Controls                          |       0.09 | [-0.23,  0.42]
## GroupC_Intervention                      |       0.20 | [-0.13,  0.53]
## TimeB_POST_IUS_total                     |      -0.03 | [-0.22,  0.17]
## GroupB_Controls:TimeB_POST_IUS_total     |      -0.36 | [-0.59, -0.12]
## GroupC_Intervention:TimeB_POST_IUS_total |      -0.60 | [-0.84, -0.37]

Effect of time for the intervention group

IUS_I_p <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_IUS_total", "B_POST_IUS_total") %>% 
  filter(Group == "C_Intervention")
## Formatting table as needed
IUS_I_long_p <- IUS_I_p %>%
  pivot_longer(cols = c(A_PRE_IUS_total, B_POST_IUS_total),
               names_to = "Time",
               values_to = "IUS_Score")
IUS_MEM_I_p <- lmer(IUS_Score ~ Time + (1|ID), data = IUS_I_long_p, REML = TRUE)
summary(IUS_MEM_I_p)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: IUS_Score ~ Time + (1 | ID)
##    Data: IUS_I_long_p
## 
## REML criterion at convergence: 1458.8
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.51489 -0.43453  0.03273  0.35595  2.42007 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 69.41    8.331   
##  Residual             33.77    5.812   
## Number of obs: 204, groups:  ID, 103
## 
## Fixed effects:
##                      Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)           43.0680     1.0009 139.9412   43.03  < 2e-16 ***
## TimeB_POST_IUS_total  -6.3200     0.8165 100.8777   -7.74 7.84e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## TB_POST_IUS -0.401
anova  (IUS_MEM_I_p)
## Type III Analysis of Variance Table with Satterthwaite's method
##      Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
## Time 2023.5  2023.5     1 100.88  59.912 7.843e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(IUS_MEM_I_p)
  IUS Score
Predictors Estimates CI p
(Intercept) 43.07 41.09 – 45.04 <0.001
Time [B_POST_IUS_total] -6.32 -7.93 – -4.71 <0.001
Random Effects
σ2 33.77
τ00 ID 69.41
ICC 0.67
N ID 103
Observations 204
Marginal R2 / Conditional R2 0.089 / 0.702
parameters::standardise_parameters(IUS_MEM_I_p)
## # Standardization method: refit
## 
## Parameter            | Std. Coef. |         95% CI
## --------------------------------------------------
## (Intercept)          |       0.29 | [ 0.11,  0.48]
## TimeB_POST_IUS_total |      -0.59 | [-0.75, -0.44]

Effect of time for the psychoed group

IUS_C_p <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_IUS_total", "B_POST_IUS_total") %>% 
  filter(Group == "B_Controls")
## Formatting table as needed
IUS_C_long_p <- IUS_C_p %>%
  pivot_longer(cols = c(A_PRE_IUS_total, B_POST_IUS_total),
               names_to = "Time",
               values_to = "IUS_Score")
IUS_MEM_C_p <- lmer(IUS_Score ~ Time + (1|ID), data = IUS_C_long_p, REML = TRUE)
summary(IUS_MEM_C_p)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: IUS_Score ~ Time + (1 | ID)
##    Data: IUS_C_long_p
## 
## REML criterion at convergence: 1466.3
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.89613 -0.42593 -0.04266  0.47538  2.98785 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 82.41    9.078   
##  Residual             19.72    4.441   
## Number of obs: 212, groups:  ID, 106
## 
## Fixed effects:
##                      Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)           42.0283     0.9816 127.1907   42.81  < 2e-16 ***
## TimeB_POST_IUS_total  -3.8679     0.6100 105.0000   -6.34 5.87e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## TB_POST_IUS -0.311
anova  (IUS_MEM_C_p)
## Type III Analysis of Variance Table with Satterthwaite's method
##      Sum Sq Mean Sq NumDF DenDF F value    Pr(>F)    
## Time 792.92  792.92     1   105    40.2 5.866e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(IUS_MEM_C_p)
  IUS Score
Predictors Estimates CI p
(Intercept) 42.03 40.09 – 43.96 <0.001
Time [B_POST_IUS_total] -3.87 -5.07 – -2.67 <0.001
Random Effects
σ2 19.72
τ00 ID 82.41
ICC 0.81
N ID 106
Observations 212
Marginal R2 / Conditional R2 0.035 / 0.814
parameters::standardise_parameters(IUS_MEM_C_p)
## # Standardization method: refit
## 
## Parameter            | Std. Coef. |         95% CI
## --------------------------------------------------
## (Intercept)          |       0.19 | [ 0.00,  0.38]
## TimeB_POST_IUS_total |      -0.38 | [-0.49, -0.26]

Effect of time for the ECs group

IUS_EC_p <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_IUS_total", "B_POST_IUS_total") %>% 
  filter(Group == "A_ECs")
## Formatting table as needed
IUS_EC_long_p <- IUS_EC_p %>%
  pivot_longer(cols = c(A_PRE_IUS_total, B_POST_IUS_total),
               names_to = "Time",
               values_to = "IUS_Score")
IUS_MEM_EC_p <- lmer(IUS_Score ~ Time + (1|ID), data = IUS_EC_long_p, REML = TRUE)
summary(IUS_MEM_EC_p)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: IUS_Score ~ Time + (1 | ID)
##    Data: IUS_EC_long_p
## 
## REML criterion at convergence: 650
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.7648 -0.5669  0.0155  0.4452  2.4970 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 50.40    7.10    
##  Residual             14.59    3.82    
## Number of obs: 100, groups:  ID, 50
## 
## Fixed effects:
##                      Estimate Std. Error     df t value Pr(>|t|)    
## (Intercept)            41.080      1.140 61.197  36.030   <2e-16 ***
## TimeB_POST_IUS_total   -0.280      0.764 49.000  -0.366    0.716    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## TB_POST_IUS -0.335
anova  (IUS_MEM_EC_p)
## Type III Analysis of Variance Table with Satterthwaite's method
##      Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Time   1.96    1.96     1    49  0.1343 0.7156
sjPlot::tab_model(IUS_MEM_EC_p)
  IUS Score
Predictors Estimates CI p
(Intercept) 41.08 38.82 – 43.34 <0.001
Time [B_POST_IUS_total] -0.28 -1.80 – 1.24 0.715
Random Effects
σ2 14.59
τ00 ID 50.40
ICC 0.78
N ID 50
Observations 100
Marginal R2 / Conditional R2 0.000 / 0.776
parameters::standardise_parameters(IUS_MEM_EC_p)
## # Standardization method: refit
## 
## Parameter            | Std. Coef. |        95% CI
## -------------------------------------------------
## (Intercept)          |       0.02 | [-0.26, 0.30]
## TimeB_POST_IUS_total |      -0.03 | [-0.22, 0.15]

Cohen’s d

# IUS - post
m.ef_ius_p<-emmeans(IUS_MEM_BP, "Time", "Group")
eff_size(m.ef_ius_p, sigma = sigma(IUS_MEM_BP), edf = df.residual(IUS_MEM_BP))
## Group = A_ECs:
##  contrast                           effect.size    SE  df lower.CL upper.CL
##  A_PRE_IUS_total - B_POST_IUS_total      0.0568 0.200 329   -0.337     0.45
## 
## Group = B_Controls:
##  contrast                           effect.size    SE  df lower.CL upper.CL
##  A_PRE_IUS_total - B_POST_IUS_total      0.7850 0.140 329    0.510     1.06
## 
## Group = C_Intervention:
##  contrast                           effect.size    SE  df lower.CL upper.CL
##  A_PRE_IUS_total - B_POST_IUS_total      1.2834 0.146 329    0.996     1.57
## 
## sigma used for effect sizes: 4.927 
## Degrees-of-freedom method: inherited from kenward-roger when re-gridding 
## Confidence level used: 0.95

Baseline to 1W

IUS_B1W <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_IUS_total", "C_W1_IUS_total")
## Formatting table as needed
IUS_B1W_long <- IUS_B1W %>%
  pivot_longer(cols = c(A_PRE_IUS_total, C_W1_IUS_total),
               names_to = "Time",
               values_to = "IUS_Score")
IUS_MEM_B1W <- lmer(IUS_Score ~ Group * Time + (1|ID), data = IUS_B1W_long, REML = TRUE)
summary(IUS_MEM_B1W)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: IUS_Score ~ Group * Time + (1 | ID)
##    Data: IUS_B1W_long
## 
## REML criterion at convergence: 3541.4
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -3.05745 -0.40449 -0.00329  0.45694  2.90920 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 64.04    8.003   
##  Residual             24.69    4.969   
## Number of obs: 511, groups:  ID, 259
## 
## Fixed effects:
##                                        Estimate Std. Error       df t value
## (Intercept)                             41.0800     1.3321 334.4251  30.837
## GroupB_Controls                          0.9483     1.6161 334.4251   0.587
## GroupC_Intervention                      1.9880     1.6236 334.4251   1.224
## TimeC_W1_IUS_total                       0.8991     1.0114 251.5502   0.889
## GroupB_Controls:TimeC_W1_IUS_total      -2.7707     1.2233 251.1429  -2.265
## GroupC_Intervention:TimeC_W1_IUS_total  -5.4023     1.2307 251.3348  -4.390
##                                        Pr(>|t|)    
## (Intercept)                             < 2e-16 ***
## GroupB_Controls                          0.5577    
## GroupC_Intervention                      0.2217    
## TimeC_W1_IUS_total                       0.3749    
## GroupB_Controls:TimeC_W1_IUS_total       0.0244 *  
## GroupC_Intervention:TimeC_W1_IUS_total 1.67e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) GrpB_C GrpC_I TC_W1_ GB_C:T
## GrpB_Cntrls -0.824                            
## GrpC_Intrvn -0.820  0.676                     
## TmC_W1_IUS_ -0.366  0.302  0.301              
## GB_C:TC_W1_  0.303 -0.368 -0.249 -0.827       
## GC_I:TC_W1_  0.301 -0.248 -0.367 -0.822  0.679
anova  (IUS_MEM_B1W)
## Type III Analysis of Variance Table with Satterthwaite's method
##            Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
## Group        5.54    2.77     2 256.11  0.1122 0.8938692    
## Time       372.30  372.30     1 251.08 15.0803 0.0001318 ***
## Group:Time 499.29  249.64     2 250.97 10.1120 5.976e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(IUS_MEM_B1W,
                  pred.labels=c("Intercept", "Psychoeducation Control", "Mindset Intervention", "Time (1 Week)", "Psychoeducation Control x Time","Mindset Intervention x Time"),
                  dv.labels=c("Intolerance of Uncertainty (IUS-12 Score"),
                  string.std_ci = "std. 95% CI",
                  string.std = "std. Beta",
                  show.std = TRUE,
                  show.est = FALSE)
  Intolerance of Uncertainty (IUS-12 Score
Predictors std. Beta std. 95% CI p
Intercept -0.01 -0.28 – 0.27 <0.001
Psychoeducation Control 0.10 -0.23 – 0.43 0.558
Mindset Intervention 0.21 -0.13 – 0.55 0.221
Time (1 Week) 0.09 -0.11 – 0.30 0.374
Psychoeducation Control x Time -0.29 -0.55 – -0.04 0.024
Mindset Intervention x Time -0.57 -0.82 – -0.31 <0.001
Random Effects
σ2 24.69
τ00 ID 64.04
ICC 0.72
N ID 259
Observations 511
Marginal R2 / Conditional R2 0.027 / 0.729
parameters::standardise_parameters(IUS_MEM_B1W)
## # Standardization method: refit
## 
## Parameter                              | Std. Coef. |         95% CI
## --------------------------------------------------------------------
## (Intercept)                            |  -7.24e-03 | [-0.28,  0.27]
## GroupB_Controls                        |       0.10 | [-0.23,  0.43]
## GroupC_Intervention                    |       0.21 | [-0.13,  0.55]
## TimeC_W1_IUS_total                     |       0.09 | [-0.11,  0.30]
## GroupB_Controls:TimeC_W1_IUS_total     |      -0.29 | [-0.55, -0.04]
## GroupC_Intervention:TimeC_W1_IUS_total |      -0.57 | [-0.82, -0.31]

Effect of time in the intervention group

IUS_I_1w <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_IUS_total", "C_W1_IUS_total") %>% 
  filter(Group == "C_Intervention")
## Formatting table as needed
IUS_I_long_1w <- IUS_I_1w %>%
  pivot_longer(cols = c(A_PRE_IUS_total, C_W1_IUS_total),
               names_to = "Time",
               values_to = "IUS_Score")
IUS_MEM_I_1w <- lmer(IUS_Score ~ Time + (1|ID), data = IUS_I_long_1w, REML = TRUE)
summary(IUS_MEM_I_1w)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: IUS_Score ~ Time + (1 | ID)
##    Data: IUS_I_long_1w
## 
## REML criterion at convergence: 1433.3
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.75154 -0.41446  0.07427  0.44626  2.56493 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 61.29    7.829   
##  Residual             31.45    5.608   
## Number of obs: 203, groups:  ID, 103
## 
## Fixed effects:
##                    Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)         43.0680     0.9489 140.1867  45.386  < 2e-16 ***
## TimeC_W1_IUS_total  -4.4842     0.7912  99.1655  -5.668 1.42e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## TmC_W1_IUS_ -0.407
anova  (IUS_MEM_I_1w)
## Type III Analysis of Variance Table with Satterthwaite's method
##      Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
## Time 1010.4  1010.4     1 99.166  32.123 1.424e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(IUS_MEM_I_1w)
  IUS Score
Predictors Estimates CI p
(Intercept) 43.07 41.20 – 44.94 <0.001
Time [C_W1_IUS_total] -4.48 -6.04 – -2.92 <0.001
Random Effects
σ2 31.45
τ00 ID 61.29
ICC 0.66
N ID 103
Observations 203
Marginal R2 / Conditional R2 0.052 / 0.678
parameters::standardise_parameters(IUS_MEM_I_1w)
## # Standardization method: refit
## 
## Parameter          | Std. Coef. |         95% CI
## ------------------------------------------------
## (Intercept)        |       0.21 | [ 0.02,  0.41]
## TimeC_W1_IUS_total |      -0.46 | [-0.62, -0.30]

Effect of time in the control group

IUS_C_1w <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_IUS_total", "C_W1_IUS_total") %>% 
  filter(Group == "B_Controls")
## Formatting table as needed
IUS_C_long_1w <- IUS_C_1w %>%
  pivot_longer(cols = c(A_PRE_IUS_total, C_W1_IUS_total),
               names_to = "Time",
               values_to = "IUS_Score")
IUS_MEM_C_1w <- lmer(IUS_Score ~ Time + (1|ID), data = IUS_C_long_1w, REML = TRUE)
summary(IUS_MEM_C_1w)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: IUS_Score ~ Time + (1 | ID)
##    Data: IUS_C_long_1w
## 
## REML criterion at convergence: 1467.1
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.1362 -0.4476 -0.0080  0.4750  2.3101 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 74.91    8.655   
##  Residual             23.94    4.893   
## Number of obs: 210, groups:  ID, 106
## 
## Fixed effects:
##                    Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)         42.0283     0.9657 133.0949  43.520  < 2e-16 ***
## TimeC_W1_IUS_total  -1.8758     0.6778 103.7076  -2.768  0.00669 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## TmC_W1_IUS_ -0.345
anova  (IUS_MEM_C_1w)
## Type III Analysis of Variance Table with Satterthwaite's method
##      Sum Sq Mean Sq NumDF  DenDF F value   Pr(>F)   
## Time 183.38  183.38     1 103.71  7.6596 0.006689 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(IUS_MEM_C_1w)
  IUS Score
Predictors Estimates CI p
(Intercept) 42.03 40.12 – 43.93 <0.001
Time [C_W1_IUS_total] -1.88 -3.21 – -0.54 0.006
Random Effects
σ2 23.94
τ00 ID 74.91
ICC 0.76
N ID 106
Observations 210
Marginal R2 / Conditional R2 0.009 / 0.760
parameters::standardise_parameters(IUS_MEM_C_1w)
## # Standardization method: refit
## 
## Parameter          | Std. Coef. |         95% CI
## ------------------------------------------------
## (Intercept)        |       0.09 | [-0.10,  0.28]
## TimeC_W1_IUS_total |      -0.19 | [-0.32, -0.05]

Effect of time in the EC group

IUS_EC_1w <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_IUS_total", "C_W1_IUS_total") %>% 
  filter(Group == "A_ECs")
## Formatting table as needed
IUS_EC_long_1w <- IUS_EC_1w %>%
  pivot_longer(cols = c(A_PRE_IUS_total, C_W1_IUS_total),
               names_to = "Time",
               values_to = "IUS_Score")
IUS_MEM_EC_1w <- lmer(IUS_Score ~ Time + (1|ID), data = IUS_EC_long_1w, REML = TRUE)
summary(IUS_MEM_EC_1w)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: IUS_Score ~ Time + (1 | ID)
##    Data: IUS_EC_long_1w
## 
## REML criterion at convergence: 624.4
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.7506 -0.4373 -0.1144  0.3660  1.9978 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 45.92    6.776   
##  Residual             12.25    3.500   
## Number of obs: 98, groups:  ID, 50
## 
## Fixed effects:
##                    Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)         41.0800     1.0786 60.1817  38.087   <2e-16 ***
## TimeC_W1_IUS_total   0.8932     0.7129 47.6699   1.253    0.216    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## TmC_W1_IUS_ -0.319
anova  (IUS_MEM_EC_1w)
## Type III Analysis of Variance Table with Satterthwaite's method
##      Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Time  19.23   19.23     1 47.67  1.5701 0.2163
sjPlot::tab_model(IUS_MEM_EC_1w)
  IUS Score
Predictors Estimates CI p
(Intercept) 41.08 38.94 – 43.22 <0.001
Time [C_W1_IUS_total] 0.89 -0.52 – 2.31 0.213
Random Effects
σ2 12.25
τ00 ID 45.92
ICC 0.79
N ID 50
Observations 98
Marginal R2 / Conditional R2 0.003 / 0.790
parameters::standardise_parameters(IUS_MEM_EC_1w)
## # Standardization method: refit
## 
## Parameter          | Std. Coef. |        95% CI
## -----------------------------------------------
## (Intercept)        |      -0.06 | [-0.34, 0.22]
## TimeC_W1_IUS_total |       0.12 | [-0.07, 0.30]

Cohen’s d

# IUS - post
m.ef_ius_1w<-emmeans(IUS_MEM_B1W, "Time", "Group")
eff_size(m.ef_ius_1w, sigma = sigma(IUS_MEM_B1W), edf = df.residual(IUS_MEM_B1W))
## Group = A_ECs:
##  contrast                         effect.size    SE  df lower.CL upper.CL
##  A_PRE_IUS_total - C_W1_IUS_total      -0.181 0.204 334   -0.582     0.22
## 
## Group = B_Controls:
##  contrast                         effect.size    SE  df lower.CL upper.CL
##  A_PRE_IUS_total - C_W1_IUS_total       0.377 0.139 334    0.103     0.65
## 
## Group = C_Intervention:
##  contrast                         effect.size    SE  df lower.CL upper.CL
##  A_PRE_IUS_total - C_W1_IUS_total       0.906 0.144 334    0.623     1.19
## 
## sigma used for effect sizes: 4.969 
## Degrees-of-freedom method: inherited from kenward-roger when re-gridding 
## Confidence level used: 0.95

Baseline to 1M

IUS_B1M <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_IUS_total", "D_M1_IUS_total")
## Formatting table as needed
IUS_B1M_long <- IUS_B1M %>%
  pivot_longer(cols = c(A_PRE_IUS_total, D_M1_IUS_total),
               names_to = "Time",
               values_to = "IUS_Score")
IUS_MEM_B1M <- lmer(IUS_Score ~ Group * Time + (1|ID), data = IUS_B1M_long, REML = TRUE)
summary(IUS_MEM_B1M)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: IUS_Score ~ Group * Time + (1 | ID)
##    Data: IUS_B1M_long
## 
## REML criterion at convergence: 3427.6
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.95787 -0.46559  0.01777  0.50003  2.25579 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 59.99    7.745   
##  Residual             29.75    5.454   
## Number of obs: 488, groups:  ID, 259
## 
## Fixed effects:
##                                        Estimate Std. Error       df t value
## (Intercept)                             41.0800     1.3397 343.4368  30.664
## GroupB_Controls                          0.9483     1.6252 343.4368   0.583
## GroupC_Intervention                      1.9880     1.6328 343.4368   1.218
## TimeD_M1_IUS_total                       2.2079     1.1512 235.9671   1.918
## GroupB_Controls:TimeD_M1_IUS_total      -3.9626     1.3951 235.8181  -2.840
## GroupC_Intervention:TimeD_M1_IUS_total  -6.9119     1.4023 235.8887  -4.929
##                                        Pr(>|t|)    
## (Intercept)                             < 2e-16 ***
## GroupB_Controls                          0.5599    
## GroupC_Intervention                      0.2242    
## TimeD_M1_IUS_total                       0.0563 .  
## GroupB_Controls:TimeD_M1_IUS_total       0.0049 ** 
## GroupC_Intervention:TimeD_M1_IUS_total 1.56e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) GrpB_C GrpC_I TD_M1_ GB_C:T
## GrpB_Cntrls -0.824                            
## GrpC_Intrvn -0.820  0.676                     
## TmD_M1_IUS_ -0.386  0.318  0.317              
## GB_C:TD_M1_  0.318 -0.386 -0.261 -0.825       
## GC_I:TD_M1_  0.317 -0.261 -0.386 -0.821  0.677
anova  (IUS_MEM_B1M)
## Type III Analysis of Variance Table with Satterthwaite's method
##            Sum Sq Mean Sq NumDF  DenDF F value   Pr(>F)    
## Group       28.24   14.12     2 257.23  0.4747 0.622614    
## Time       207.73  207.73     1 235.80  6.9828 0.008781 ** 
## Group:Time 736.40  368.20     2 235.76 12.3767 7.74e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(IUS_MEM_B1M,
                  pred.labels=c("Intercept", "Psychoeducation Control", "Mindset Intervention", "Time (1 Month)", "Psychoeducation Control x Time","Mindset Intervention x Time"),
                  dv.labels=c("Intolerance of Uncertainty (IUS-12 Score)"),
                  string.std_ci = "std. 95% CI",
                  string.std = "std. Beta",
                  show.std = TRUE,
                  show.est = FALSE)
  Intolerance of Uncertainty (IUS-12 Score)
Predictors std. Beta std. 95% CI p
Intercept -0.02 -0.30 – 0.25 <0.001
Psychoeducation Control 0.10 -0.23 – 0.43 0.560
Mindset Intervention 0.21 -0.13 – 0.54 0.224
Time (1 Month) 0.23 -0.01 – 0.47 0.056
Psychoeducation Control x Time -0.41 -0.70 – -0.13 0.005
Mindset Intervention x Time -0.72 -1.01 – -0.43 <0.001
Random Effects
σ2 29.75
τ00 ID 59.99
ICC 0.67
N ID 259
Observations 488
Marginal R2 / Conditional R2 0.032 / 0.679
parameters::standardise_parameters(IUS_MEM_B1M)
## # Standardization method: refit
## 
## Parameter                              | Std. Coef. |         95% CI
## --------------------------------------------------------------------
## (Intercept)                            |      -0.02 | [-0.30,  0.25]
## GroupB_Controls                        |       0.10 | [-0.23,  0.43]
## GroupC_Intervention                    |       0.21 | [-0.13,  0.54]
## TimeD_M1_IUS_total                     |       0.23 | [-0.01,  0.47]
## GroupB_Controls:TimeD_M1_IUS_total     |      -0.41 | [-0.70, -0.13]
## GroupC_Intervention:TimeD_M1_IUS_total |      -0.72 | [-1.01, -0.43]

Effect of time in the intervention group

IUS_I_1m <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_IUS_total", "D_M1_IUS_total") %>% 
  filter(Group == "C_Intervention")
## Formatting table as needed
IUS_I_long_1m <- IUS_I_1m %>%
  pivot_longer(cols = c(A_PRE_IUS_total, D_M1_IUS_total),
               names_to = "Time",
               values_to = "IUS_Score")
IUS_MEM_I_1m <- lmer(IUS_Score ~ Time + (1|ID), data = IUS_I_long_1m, REML = TRUE)
summary(IUS_MEM_I_1m)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: IUS_Score ~ Time + (1 | ID)
##    Data: IUS_I_long_1m
## 
## REML criterion at convergence: 1377.6
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.21864 -0.50213  0.02461  0.53633  2.12054 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 59.37    7.705   
##  Residual             33.76    5.811   
## Number of obs: 194, groups:  ID, 103
## 
## Fixed effects:
##                    Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)         43.0680     0.9509 140.9831  45.290  < 2e-16 ***
## TimeD_M1_IUS_total  -4.7031     0.8523  94.9404  -5.518 2.96e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## TmD_M1_IUS_ -0.404
anova  (IUS_MEM_I_1m)
## Type III Analysis of Variance Table with Satterthwaite's method
##      Sum Sq Mean Sq NumDF DenDF F value    Pr(>F)    
## Time 1028.1  1028.1     1 94.94  30.449 2.961e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(IUS_MEM_I_1m)
  IUS Score
Predictors Estimates CI p
(Intercept) 43.07 41.19 – 44.94 <0.001
Time [D_M1_IUS_total] -4.70 -6.38 – -3.02 <0.001
Random Effects
σ2 33.76
τ00 ID 59.37
ICC 0.64
N ID 103
Observations 194
Marginal R2 / Conditional R2 0.056 / 0.658
parameters::standardise_parameters(IUS_MEM_I_1m)
## # Standardization method: refit
## 
## Parameter          | Std. Coef. |         95% CI
## ------------------------------------------------
## (Intercept)        |       0.22 | [ 0.03,  0.41]
## TimeD_M1_IUS_total |      -0.47 | [-0.64, -0.30]

Effect of time in the control group

IUS_C_1m <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_IUS_total", "D_M1_IUS_total") %>% 
  filter(Group == "B_Controls")
## Formatting table as needed
IUS_C_long_1m <- IUS_C_1m %>%
  pivot_longer(cols = c(A_PRE_IUS_total, D_M1_IUS_total),
               names_to = "Time",
               values_to = "IUS_Score")
IUS_MEM_C_1m <- lmer(IUS_Score ~ Time + (1|ID), data = IUS_C_long_1m, REML = TRUE)
summary(IUS_MEM_C_1m)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: IUS_Score ~ Time + (1 | ID)
##    Data: IUS_C_long_1m
## 
## REML criterion at convergence: 1431.8
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.78127 -0.44321  0.07034  0.45684  2.03174 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 69.93    8.363   
##  Residual             33.21    5.763   
## Number of obs: 200, groups:  ID, 106
## 
## Fixed effects:
##                    Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)         42.0283     0.9864 139.0853   42.61   <2e-16 ***
## TimeD_M1_IUS_total  -1.7574     0.8329  95.8821   -2.11   0.0375 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## TmD_M1_IUS_ -0.381
anova  (IUS_MEM_C_1m)
## Type III Analysis of Variance Table with Satterthwaite's method
##      Sum Sq Mean Sq NumDF  DenDF F value  Pr(>F)  
## Time 147.85  147.85     1 95.882  4.4519 0.03747 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(IUS_MEM_C_1m)
  IUS Score
Predictors Estimates CI p
(Intercept) 42.03 40.08 – 43.97 <0.001
Time [D_M1_IUS_total] -1.76 -3.40 – -0.11 0.036
Random Effects
σ2 33.21
τ00 ID 69.93
ICC 0.68
N ID 106
Observations 200
Marginal R2 / Conditional R2 0.007 / 0.680
parameters::standardise_parameters(IUS_MEM_C_1m)
## # Standardization method: refit
## 
## Parameter          | Std. Coef. |         95% CI
## ------------------------------------------------
## (Intercept)        |       0.07 | [-0.12,  0.26]
## TimeD_M1_IUS_total |      -0.17 | [-0.34, -0.01]

Effect of time in the EC group

IUS_EC_1m <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_IUS_total", "D_M1_IUS_total") %>% 
  filter(Group == "A_ECs")
## Formatting table as needed
IUS_EC_long_1m <- IUS_EC_1m %>%
  pivot_longer(cols = c(A_PRE_IUS_total, D_M1_IUS_total),
               names_to = "Time",
               values_to = "IUS_Score")
IUS_MEM_EC_1m <- lmer(IUS_Score ~ Time + (1|ID), data = IUS_EC_long_1m, REML = TRUE)
summary(IUS_MEM_EC_1m)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: IUS_Score ~ Time + (1 | ID)
##    Data: IUS_EC_long_1m
## 
## REML criterion at convergence: 601
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.1175 -0.4876 -0.1018  0.5149  1.5792 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 40.03    6.327   
##  Residual             13.84    3.720   
## Number of obs: 94, groups:  ID, 50
## 
## Fixed effects:
##                    Estimate Std. Error     df t value Pr(>|t|)    
## (Intercept)          41.080      1.038 61.951  39.577  < 2e-16 ***
## TimeD_M1_IUS_total    2.197      0.787 44.914   2.791  0.00768 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## TmD_M1_IUS_ -0.339
anova  (IUS_MEM_EC_1m)
## Type III Analysis of Variance Table with Satterthwaite's method
##      Sum Sq Mean Sq NumDF  DenDF F value   Pr(>F)   
## Time 107.85  107.85     1 44.914  7.7919 0.007679 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(IUS_MEM_EC_1m)
  IUS Score
Predictors Estimates CI p
(Intercept) 41.08 39.02 – 43.14 <0.001
Time [D_M1_IUS_total] 2.20 0.63 – 3.76 0.006
Random Effects
σ2 13.84
τ00 ID 40.03
ICC 0.74
N ID 50
Observations 94
Marginal R2 / Conditional R2 0.022 / 0.749
parameters::standardise_parameters(IUS_MEM_EC_1m)
## # Standardization method: refit
## 
## Parameter          | Std. Coef. |        95% CI
## -----------------------------------------------
## (Intercept)        |      -0.14 | [-0.42, 0.13]
## TimeD_M1_IUS_total |       0.29 | [ 0.09, 0.50]

Cohen’s d

# IUS - post
m.ef_ius_1m<-emmeans(IUS_MEM_B1M, "Time", "Group")
eff_size(m.ef_ius_1m, sigma = sigma(IUS_MEM_B1M), edf = df.residual(IUS_MEM_B1M))
## Group = A_ECs:
##  contrast                         effect.size    SE  df lower.CL upper.CL
##  A_PRE_IUS_total - D_M1_IUS_total      -0.405 0.212 342  -0.8209   0.0112
## 
## Group = B_Controls:
##  contrast                         effect.size    SE  df lower.CL upper.CL
##  A_PRE_IUS_total - D_M1_IUS_total       0.322 0.145 342   0.0367   0.6067
## 
## Group = C_Intervention:
##  contrast                         effect.size    SE  df lower.CL upper.CL
##  A_PRE_IUS_total - D_M1_IUS_total       0.862 0.149 342   0.5685   1.1564
## 
## sigma used for effect sizes: 5.454 
## Degrees-of-freedom method: inherited from kenward-roger when re-gridding 
## Confidence level used: 0.95

H2a GM: difference in change in growth mindsets over time between groups

Baseline to post

GM_BP <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_GM", "B_POST_GM")
## Formatting table as needed
GM_BP_long <- GM_BP %>%
  pivot_longer(cols = c(A_PRE_GM, B_POST_GM),
               names_to = "Time",
               values_to = "GM_Score")
GM_MEM_BP <- lmer(GM_Score ~ Group * Time + (1|ID), data = GM_BP_long, REML = TRUE)
summary(GM_MEM_BP)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: GM_Score ~ Group * Time + (1 | ID)
##    Data: GM_BP_long
## 
## REML criterion at convergence: 1673.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.5473 -0.4356 -0.0320  0.4087  2.9611 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 1.471    1.2128  
##  Residual             0.614    0.7836  
## Number of obs: 516, groups:  ID, 259
## 
## Fixed effects:
##                                   Estimate Std. Error       df t value Pr(>|t|)
## (Intercept)                         2.7400     0.2042 341.6189  13.418  < 2e-16
## GroupB_Controls                     0.4015     0.2477 341.6189   1.621 0.105989
## GroupC_Intervention                 0.1629     0.2489 341.6189   0.655 0.513178
## TimeB_POST_GM                       0.0400     0.1567 254.5431   0.255 0.798745
## GroupB_Controls:TimeB_POST_GM      -0.5306     0.1901 254.5431  -2.791 0.005657
## GroupC_Intervention:TimeB_POST_GM  -0.7237     0.1915 254.9544  -3.779 0.000196
##                                      
## (Intercept)                       ***
## GroupB_Controls                      
## GroupC_Intervention                  
## TimeB_POST_GM                        
## GroupB_Controls:TimeB_POST_GM     ** 
## GroupC_Intervention:TimeB_POST_GM ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) GrpB_C GrpC_I TB_POS GB_C:T
## GrpB_Cntrls -0.824                            
## GrpC_Intrvn -0.820  0.676                     
## TmB_POST_GM -0.384  0.316  0.315              
## GB_C:TB_POS  0.316 -0.384 -0.260 -0.824       
## GC_I:TB_POS  0.314 -0.259 -0.383 -0.818  0.674
anova  (GM_MEM_BP)
## Type III Analysis of Variance Table with Satterthwaite's method
##             Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
## Group       2.0352  1.0176     2 256.34  1.6574 0.1926771    
## Time       16.3667 16.3667     1 254.86 26.6558   4.9e-07 ***
## Group:Time  8.8331  4.4165     2 254.92  7.1931 0.0009142 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(GM_MEM_BP,
                  pred.labels=c("Intercept", "Psychoeducation Control", "Mindset Intervention", "Time (Post)", "Psychoeducation Control x Time","Mindset Intervention x Time"),
                  dv.labels=c("Growth Mindsets about Uncertainty Tolerance"),
                  string.std_ci = "std. 95% CI",
                  string.std = "std. Beta",
                  show.std = TRUE,
                  show.est = FALSE)
  Growth Mindsets about Uncertainty Tolerance
Predictors std. Beta std. 95% CI p
Intercept 0.00 -0.27 – 0.27 <0.001
Psychoeducation Control 0.27 -0.06 – 0.60 0.106
Mindset Intervention 0.11 -0.22 – 0.44 0.513
Time (Post) 0.03 -0.18 – 0.24 0.799
Psychoeducation Control x Time -0.36 -0.61 – -0.11 0.005
Mindset Intervention x Time -0.49 -0.75 – -0.24 <0.001
Random Effects
σ2 0.61
τ00 ID 1.47
ICC 0.71
N ID 259
Observations 516
Marginal R2 / Conditional R2 0.043 / 0.718
parameters::standardise_parameters(GM_MEM_BP)
## # Standardization method: refit
## 
## Parameter                         | Std. Coef. |         95% CI
## ---------------------------------------------------------------
## (Intercept)                       |   1.11e-03 | [-0.27,  0.27]
## GroupB_Controls                   |       0.27 | [-0.06,  0.60]
## GroupC_Intervention               |       0.11 | [-0.22,  0.44]
## TimeB_POST_GM                     |       0.03 | [-0.18,  0.24]
## GroupB_Controls:TimeB_POST_GM     |      -0.36 | [-0.61, -0.11]
## GroupC_Intervention:TimeB_POST_GM |      -0.49 | [-0.75, -0.24]

Effect of time for the intervention group

GM_I_p <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_GM", "B_POST_GM") %>% 
  filter(Group == "C_Intervention")
## Formatting table as needed
GM_I_long_p <- GM_I_p %>%
  pivot_longer(cols = c(A_PRE_GM, B_POST_GM),
               names_to = "Time",
               values_to = "GM_Score")
GM_MEM_I_p <- lmer(GM_Score ~ Time + (1|ID), data = GM_I_long_p, REML = TRUE)
summary(GM_MEM_I_p)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: GM_Score ~ Time + (1 | ID)
##    Data: GM_I_long_p
## 
## REML criterion at convergence: 677.1
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.1963 -0.4652 -0.1065  0.4509  2.7023 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 1.2470   1.1167  
##  Residual             0.7763   0.8811  
## Number of obs: 204, groups:  ID, 103
## 
## Fixed effects:
##               Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)     2.9029     0.1402 147.4341  20.712  < 2e-16 ***
## TimeB_POST_GM  -0.6839     0.1238 101.2984  -5.526 2.55e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## TmB_POST_GM -0.435
anova  (GM_MEM_I_p)
## Type III Analysis of Variance Table with Satterthwaite's method
##      Sum Sq Mean Sq NumDF DenDF F value   Pr(>F)    
## Time 23.709  23.709     1 101.3  30.539 2.55e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(GM_MEM_I_p)
  GM Score
Predictors Estimates CI p
(Intercept) 2.90 2.63 – 3.18 <0.001
Time [B_POST_GM] -0.68 -0.93 – -0.44 <0.001
Random Effects
σ2 0.78
τ00 ID 1.25
ICC 0.62
N ID 103
Observations 204
Marginal R2 / Conditional R2 0.055 / 0.637
parameters::standardise_parameters(GM_MEM_I_p)
## # Standardization method: refit
## 
## Parameter     | Std. Coef. |         95% CI
## -------------------------------------------
## (Intercept)   |       0.23 | [ 0.04,  0.42]
## TimeB_POST_GM |      -0.47 | [-0.63, -0.30]

Effect of time for the psychoed group

GM_C_p <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_GM", "B_POST_GM") %>% 
  filter(Group == "B_Controls")
## Formatting table as needed
GM_C_long_p <- GM_C_p %>%
  pivot_longer(cols = c(A_PRE_GM, B_POST_GM),
               names_to = "Time",
               values_to = "GM_Score")
GM_MEM_C_p <- lmer(GM_Score ~ Time + (1|ID), data = GM_C_long_p, REML = TRUE)
summary(GM_MEM_C_p)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: GM_Score ~ Time + (1 | ID)
##    Data: GM_C_long_p
## 
## REML criterion at convergence: 684.4
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.29531 -0.50719 -0.06417  0.45981  2.33778 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 1.5642   1.2507  
##  Residual             0.5738   0.7575  
## Number of obs: 212, groups:  ID, 106
## 
## Fixed effects:
##               Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)     3.1415     0.1420 136.7834  22.121  < 2e-16 ***
## TimeB_POST_GM  -0.4906     0.1040 105.0000  -4.715 7.47e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## TmB_POST_GM -0.366
anova  (GM_MEM_C_p)
## Type III Analysis of Variance Table with Satterthwaite's method
##      Sum Sq Mean Sq NumDF DenDF F value    Pr(>F)    
## Time 12.755  12.755     1   105   22.23 7.468e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(GM_MEM_C_p)
  GM Score
Predictors Estimates CI p
(Intercept) 3.14 2.86 – 3.42 <0.001
Time [B_POST_GM] -0.49 -0.70 – -0.29 <0.001
Random Effects
σ2 0.57
τ00 ID 1.56
ICC 0.73
N ID 106
Observations 212
Marginal R2 / Conditional R2 0.027 / 0.739
parameters::standardise_parameters(GM_MEM_C_p)
## # Standardization method: refit
## 
## Parameter     | Std. Coef. |         95% CI
## -------------------------------------------
## (Intercept)   |       0.17 | [-0.02,  0.36]
## TimeB_POST_GM |      -0.33 | [-0.47, -0.19]

Effect of time for the ECs group

GM_EC_p <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_GM", "B_POST_GM") %>% 
  filter(Group == "A_ECs")
## Formatting table as needed
GM_EC_long_p <- GM_EC_p %>%
  pivot_longer(cols = c(A_PRE_GM, B_POST_GM),
               names_to = "Time",
               values_to = "GM_Score")
GM_MEM_EC_p <- lmer(GM_Score ~ Time + (1|ID), data = GM_EC_long_p, REML = TRUE)
summary(GM_MEM_EC_p)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: GM_Score ~ Time + (1 | ID)
##    Data: GM_EC_long_p
## 
## REML criterion at convergence: 302.7
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.32797 -0.24433  0.00479  0.22845  2.78488 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 1.7376   1.3182  
##  Residual             0.3665   0.6054  
## Number of obs: 100, groups:  ID, 50
## 
## Fixed effects:
##               Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)     2.7400     0.2051 58.2658   13.36   <2e-16 ***
## TimeB_POST_GM   0.0400     0.1211 49.0000    0.33    0.743    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## TmB_POST_GM -0.295
anova  (GM_MEM_EC_p)
## Type III Analysis of Variance Table with Satterthwaite's method
##      Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Time   0.04    0.04     1    49  0.1091 0.7425
sjPlot::tab_model(GM_MEM_EC_p)
  GM Score
Predictors Estimates CI p
(Intercept) 2.74 2.33 – 3.15 <0.001
Time [B_POST_GM] 0.04 -0.20 – 0.28 0.742
Random Effects
σ2 0.37
τ00 ID 1.74
ICC 0.83
N ID 50
Observations 100
Marginal R2 / Conditional R2 0.000 / 0.826
parameters::standardise_parameters(GM_MEM_EC_p)
## # Standardization method: refit
## 
## Parameter     | Std. Coef. |        95% CI
## ------------------------------------------
## (Intercept)   |      -0.01 | [-0.30, 0.27]
## TimeB_POST_GM |       0.03 | [-0.14, 0.19]

Cohen’s d

# GM - post
m.ef_GM_p<-emmeans(GM_MEM_BP, "Time", "Group")
eff_size(m.ef_GM_p, sigma = sigma(GM_MEM_BP), edf = df.residual(GM_MEM_BP))
## Group = A_ECs:
##  contrast             effect.size    SE  df lower.CL upper.CL
##  A_PRE_GM - B_POST_GM      -0.051 0.200 341   -0.444    0.342
## 
## Group = B_Controls:
##  contrast             effect.size    SE  df lower.CL upper.CL
##  A_PRE_GM - B_POST_GM       0.626 0.139 341    0.353    0.899
## 
## Group = C_Intervention:
##  contrast             effect.size    SE  df lower.CL upper.CL
##  A_PRE_GM - B_POST_GM       0.873 0.143 341    0.591    1.154
## 
## sigma used for effect sizes: 0.7836 
## Degrees-of-freedom method: inherited from kenward-roger when re-gridding 
## Confidence level used: 0.95

Baseline to 1W

GM_B1W <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_GM", "C_W1_GM")
## Formatting table as needed
GM_B1W_long <- GM_B1W %>%
  pivot_longer(cols = c(A_PRE_GM, C_W1_GM),
               names_to = "Time",
               values_to = "GM_Score")
GM_MEM_B1W <- lmer(GM_Score ~ Group * Time + (1|ID), data = GM_B1W_long, REML = TRUE)
summary(GM_MEM_B1W)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: GM_Score ~ Group * Time + (1 | ID)
##    Data: GM_B1W_long
## 
## REML criterion at convergence: 1747.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.2664 -0.5109 -0.1518  0.4940  2.7870 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 1.038    1.019   
##  Residual             1.010    1.005   
## Number of obs: 511, groups:  ID, 259
## 
## Fixed effects:
##                                 Estimate Std. Error       df t value Pr(>|t|)
## (Intercept)                       2.7400     0.2024 403.7332  13.539   <2e-16
## GroupB_Controls                   0.4015     0.2455 403.7332   1.635   0.1027
## GroupC_Intervention               0.1629     0.2467 403.7332   0.661   0.5093
## TimeC_W1_GM                      -0.0784     0.2041 253.9941  -0.384   0.7012
## GroupB_Controls:TimeC_W1_GM      -0.2376     0.2470 253.3522  -0.962   0.3370
## GroupC_Intervention:TimeC_W1_GM  -0.5133     0.2484 253.6544  -2.066   0.0398
##                                    
## (Intercept)                     ***
## GroupB_Controls                    
## GroupC_Intervention                
## TimeC_W1_GM                        
## GroupB_Controls:TimeC_W1_GM        
## GroupC_Intervention:TimeC_W1_GM *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) GrpB_C GrpC_I TC_W1_ GB_C:T
## GrpB_Cntrls -0.824                            
## GrpC_Intrvn -0.820  0.676                     
## TimeC_W1_GM -0.489  0.403  0.401              
## GB_C:TC_W1_  0.404 -0.490 -0.332 -0.826       
## GC_I:TC_W1_  0.402 -0.331 -0.490 -0.822  0.679
anova  (GM_MEM_B1W)
## Type III Analysis of Variance Table with Satterthwaite's method
##             Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
## Group       5.0659  2.5329     2 256.72  2.5080 0.0834210 .  
## Time       12.1159 12.1159     1 253.25 11.9969 0.0006256 ***
## Group:Time  4.6763  2.3381     2 253.08  2.3152 0.1008383    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(GM_MEM_B1W,
                  pred.labels=c("Intercept", "Psychoeducation Control", "Mindset Intervention", "Time (1 Week)", "Psychoeducation Control x Time","Mindset Intervention x Time"),
                  dv.labels=c("Growth Mindsets about Uncertainty Tolerance"),
                  string.std_ci = "std. 95% CI",
                  string.std = "std. Beta",
                  show.std = TRUE,
                  show.est = FALSE,
                  emph.p = FALSE)
  Growth Mindsets about Uncertainty Tolerance
Predictors std. Beta std. 95% CI p
Intercept -0.03 -0.31 – 0.24 <0.001
Psychoeducation Control 0.28 -0.06 – 0.61 0.103
Mindset Intervention 0.11 -0.22 – 0.45 0.509
Time (1 Week) -0.05 -0.33 – 0.22 0.701
Psychoeducation Control x Time -0.16 -0.50 – 0.17 0.337
Mindset Intervention x Time -0.35 -0.69 – -0.02 0.039
Random Effects
σ2 1.01
τ00 ID 1.04
ICC 0.51
N ID 259
Observations 511
Marginal R2 / Conditional R2 0.035 / 0.524
parameters::standardise_parameters(GM_MEM_B1W)
## # Standardization method: refit
## 
## Parameter                       | Std. Coef. |         95% CI
## -------------------------------------------------------------
## (Intercept)                     |      -0.03 | [-0.31,  0.24]
## GroupB_Controls                 |       0.28 | [-0.06,  0.61]
## GroupC_Intervention             |       0.11 | [-0.22,  0.45]
## TimeC_W1_GM                     |      -0.05 | [-0.33,  0.22]
## GroupB_Controls:TimeC_W1_GM     |      -0.16 | [-0.50,  0.17]
## GroupC_Intervention:TimeC_W1_GM |      -0.35 | [-0.69, -0.02]

Effect of time in the intervention group

GM_I_1w <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_GM", "C_W1_GM") %>% 
  filter(Group == "C_Intervention")
## Formatting table as needed
GM_I_long_1w <- GM_I_1w %>%
  pivot_longer(cols = c(A_PRE_GM, C_W1_GM),
               names_to = "Time",
               values_to = "GM_Score")
GM_MEM_I_1w <- lmer(GM_Score ~ Time + (1|ID), data = GM_I_long_1w, REML = TRUE)
summary(GM_MEM_I_1w)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: GM_Score ~ Time + (1 | ID)
##    Data: GM_I_long_1w
## 
## REML criterion at convergence: 669.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.0272 -0.5347 -0.1665  0.4495  2.6449 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 0.9190   0.9586  
##  Residual             0.8902   0.9435  
## Number of obs: 203, groups:  ID, 103
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)   2.9029     0.1325 160.1284  21.903  < 2e-16 ***
## TimeC_W1_GM  -0.5918     0.1330  99.8615  -4.451 2.23e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## TimeC_W1_GM -0.490
anova  (GM_MEM_I_1w)
## Type III Analysis of Variance Table with Satterthwaite's method
##      Sum Sq Mean Sq NumDF  DenDF F value   Pr(>F)    
## Time 17.635  17.635     1 99.862  19.809 2.23e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(GM_MEM_I_1w)
  GM Score
Predictors Estimates CI p
(Intercept) 2.90 2.64 – 3.16 <0.001
Time [C_W1_GM] -0.59 -0.85 – -0.33 <0.001
Random Effects
σ2 0.89
τ00 ID 0.92
ICC 0.51
N ID 103
Observations 203
Marginal R2 / Conditional R2 0.046 / 0.531
parameters::standardise_parameters(GM_MEM_I_1w)
## # Standardization method: refit
## 
## Parameter   | Std. Coef. |         95% CI
## -----------------------------------------
## (Intercept) |       0.21 | [ 0.02,  0.40]
## TimeC_W1_GM |      -0.43 | [-0.62, -0.24]

Effect of time in the control group

GM_C_1w <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_GM", "C_W1_GM") %>% 
  filter(Group == "B_Controls")
## Formatting table as needed
GM_C_long_1w <- GM_C_1w %>%
  pivot_longer(cols = c(A_PRE_GM, C_W1_GM),
               names_to = "Time",
               values_to = "GM_Score")
GM_MEM_C_1w <- lmer(GM_Score ~ Time + (1|ID), data = GM_C_long_1w, REML = TRUE)
summary(GM_MEM_C_1w)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: GM_Score ~ Time + (1 | ID)
##    Data: GM_C_long_1w
## 
## REML criterion at convergence: 721.6
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -1.91277 -0.54284 -0.07926  0.49810  2.19714 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 1.2837   1.1330  
##  Residual             0.9229   0.9607  
## Number of obs: 210, groups:  ID, 106
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)   3.1415     0.1443 156.1787  21.774   <2e-16 ***
## TimeC_W1_GM  -0.3162     0.1330 104.0931  -2.378   0.0192 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## TimeC_W1_GM -0.454
anova  (GM_MEM_C_1w)
## Type III Analysis of Variance Table with Satterthwaite's method
##      Sum Sq Mean Sq NumDF  DenDF F value  Pr(>F)  
## Time 5.2187  5.2187     1 104.09  5.6548 0.01923 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(GM_MEM_C_1w)
  GM Score
Predictors Estimates CI p
(Intercept) 3.14 2.86 – 3.43 <0.001
Time [C_W1_GM] -0.32 -0.58 – -0.05 0.018
Random Effects
σ2 0.92
τ00 ID 1.28
ICC 0.58
N ID 106
Observations 210
Marginal R2 / Conditional R2 0.011 / 0.586
parameters::standardise_parameters(GM_MEM_C_1w)
## # Standardization method: refit
## 
## Parameter   | Std. Coef. |         95% CI
## -----------------------------------------
## (Intercept) |       0.10 | [-0.09,  0.30]
## TimeC_W1_GM |      -0.21 | [-0.39, -0.04]

Effect of time in the EC group

GM_EC_1w <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_GM", "C_W1_GM") %>% 
  filter(Group == "A_ECs")
## Formatting table as needed
GM_EC_long_1w <- GM_EC_1w %>%
  pivot_longer(cols = c(A_PRE_GM, C_W1_GM),
               names_to = "Time",
               values_to = "GM_Score")
GM_MEM_EC_1w <- lmer(GM_Score ~ Time + (1|ID), data = GM_EC_long_1w, REML = TRUE)
summary(GM_MEM_EC_1w)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: GM_Score ~ Time + (1 | ID)
##    Data: GM_EC_long_1w
## 
## REML criterion at convergence: 350.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.7863 -0.6582 -0.1036  0.4625  2.4339 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 0.7595   0.8715  
##  Residual             1.4472   1.2030  
## Number of obs: 98, groups:  ID, 50
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)  2.74000    0.21008 86.32366  13.043   <2e-16 ***
## TimeC_W1_GM -0.07678    0.24394 48.82968  -0.315    0.754    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## TimeC_W1_GM -0.565
anova  (GM_MEM_EC_1w)
## Type III Analysis of Variance Table with Satterthwaite's method
##       Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Time 0.14335 0.14335     1 48.83  0.0991 0.7543
sjPlot::tab_model(GM_MEM_EC_1w)
  GM Score
Predictors Estimates CI p
(Intercept) 2.74 2.32 – 3.16 <0.001
Time [C_W1_GM] -0.08 -0.56 – 0.41 0.754
Random Effects
σ2 1.45
τ00 ID 0.76
ICC 0.34
N ID 50
Observations 98
Marginal R2 / Conditional R2 0.001 / 0.345
parameters::standardise_parameters(GM_MEM_EC_1w)
## # Standardization method: refit
## 
## Parameter   | Std. Coef. |        95% CI
## ----------------------------------------
## (Intercept) |       0.02 | [-0.26, 0.31]
## TimeC_W1_GM |      -0.05 | [-0.38, 0.28]

Cohen’s d

# GM - post
m.ef_GM_1w<-emmeans(GM_MEM_B1W, "Time", "Group")
eff_size(m.ef_GM_1w, sigma = sigma(GM_MEM_B1W), edf = df.residual(GM_MEM_B1W))
## Group = A_ECs:
##  contrast           effect.size    SE  df lower.CL upper.CL
##  A_PRE_GM - C_W1_GM       0.078 0.203 403  -0.3213    0.477
## 
## Group = B_Controls:
##  contrast           effect.size    SE  df lower.CL upper.CL
##  A_PRE_GM - C_W1_GM       0.314 0.139 403   0.0417    0.587
## 
## Group = C_Intervention:
##  contrast           effect.size    SE  df lower.CL upper.CL
##  A_PRE_GM - C_W1_GM       0.589 0.142 403   0.3094    0.868
## 
## sigma used for effect sizes: 1.005 
## Degrees-of-freedom method: inherited from kenward-roger when re-gridding 
## Confidence level used: 0.95

Baseline to 1M

GM_B1M <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_GM", "D_M1_GM")
## Formatting table as needed
GM_B1M_long <- GM_B1M %>%
  pivot_longer(cols = c(A_PRE_GM, D_M1_GM),
               names_to = "Time",
               values_to = "GM_Score")
GM_MEM_B1M <- lmer(GM_Score ~ Group * Time + (1|ID), data = GM_B1M_long, REML = TRUE)
summary(GM_MEM_B1M)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: GM_Score ~ Group * Time + (1 | ID)
##    Data: GM_B1M_long
## 
## REML criterion at convergence: 1639.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.3875 -0.5367 -0.1142  0.4999  2.8661 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 1.0920   1.0450  
##  Residual             0.8918   0.9444  
## Number of obs: 487, groups:  ID, 259
## 
## Fixed effects:
##                                  Estimate Std. Error        df t value Pr(>|t|)
## (Intercept)                       2.74000    0.19919 375.54541  13.756   <2e-16
## GroupB_Controls                   0.40151    0.24164 375.54541   1.662   0.0974
## GroupC_Intervention               0.16291    0.24277 375.54541   0.671   0.5026
## TimeD_M1_GM                      -0.03867    0.19861 235.43449  -0.195   0.8458
## GroupB_Controls:TimeD_M1_GM      -0.30728    0.24103 235.51016  -1.275   0.2036
## GroupC_Intervention:TimeD_M1_GM  -0.59125    0.24193 235.33298  -2.444   0.0153
##                                    
## (Intercept)                     ***
## GroupB_Controls                 .  
## GroupC_Intervention                
## TimeD_M1_GM                        
## GroupB_Controls:TimeD_M1_GM        
## GroupC_Intervention:TimeD_M1_GM *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) GrpB_C GrpC_I TD_M1_ GB_C:T
## GrpB_Cntrls -0.824                            
## GrpC_Intrvn -0.820  0.676                     
## TimeD_M1_GM -0.451  0.372  0.370              
## GB_C:TD_M1_  0.372 -0.451 -0.305 -0.824       
## GC_I:TD_M1_  0.370 -0.305 -0.451 -0.821  0.676
anova  (GM_MEM_B1M)
## Type III Analysis of Variance Table with Satterthwaite's method
##             Sum Sq Mean Sq NumDF  DenDF F value   Pr(>F)    
## Group       4.3400  2.1700     2 254.05  2.4332 0.089803 .  
## Time       11.8930 11.8930     1 235.41 13.3353 0.000321 ***
## Group:Time  5.5615  2.7807     2 235.41  3.1180 0.046079 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(GM_MEM_B1M,
                  pred.labels=c("Intercept", "Psychoeducation Control", "Mindset Intervention", "Time (1 Month)", "Psychoeducation Control x Time","Mindset Intervention x Time"),
                  dv.labels=c("Growth Mindsets about Uncertainty Tolerance"),
                  string.std_ci = "std. 95% CI",
                  string.std = "std. Beta",
                  show.std = TRUE,
                  show.est = FALSE)
  Growth Mindsets about Uncertainty Tolerance
Predictors std. Beta std. 95% CI p
Intercept -0.03 -0.30 – 0.25 <0.001
Psychoeducation Control 0.28 -0.05 – 0.61 0.097
Mindset Intervention 0.11 -0.22 – 0.45 0.503
Time (1 Month) -0.03 -0.30 – 0.25 0.846
Psychoeducation Control x Time -0.21 -0.55 – 0.12 0.203
Mindset Intervention x Time -0.41 -0.75 – -0.08 0.015
Random Effects
σ2 0.89
τ00 ID 1.09
ICC 0.55
N ID 259
Observations 487
Marginal R2 / Conditional R2 0.039 / 0.568
parameters::standardise_parameters(GM_MEM_B1M)
## # Standardization method: refit
## 
## Parameter                       | Std. Coef. |         95% CI
## -------------------------------------------------------------
## (Intercept)                     |      -0.03 | [-0.30,  0.25]
## GroupB_Controls                 |       0.28 | [-0.05,  0.61]
## GroupC_Intervention             |       0.11 | [-0.22,  0.45]
## TimeD_M1_GM                     |      -0.03 | [-0.30,  0.25]
## GroupB_Controls:TimeD_M1_GM     |      -0.21 | [-0.55,  0.12]
## GroupC_Intervention:TimeD_M1_GM |      -0.41 | [-0.75, -0.08]

Effect of time in the intervention group

GM_I_1m <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_GM", "D_M1_GM") %>% 
  filter(Group == "C_Intervention")
## Formatting table as needed
GM_I_long_1m <- GM_I_1m %>%
  pivot_longer(cols = c("A_PRE_GM", "D_M1_GM"),
               names_to = "Time",
               values_to = "GM_Score")
GM_MEM_I_1m <- lmer(GM_Score ~ Time + (1|ID), data = GM_I_long_1m, REML = TRUE)
summary(GM_MEM_I_1m)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: GM_Score ~ Time + (1 | ID)
##    Data: GM_I_long_1m
## 
## REML criterion at convergence: 648.4
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.9867 -0.5532 -0.1672  0.4949  2.5917 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 0.9846   0.9923  
##  Residual             0.9103   0.9541  
## Number of obs: 194, groups:  ID, 103
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)   2.9029     0.1356 153.6770   21.40  < 2e-16 ***
## TimeD_M1_GM  -0.6317     0.1395  94.7042   -4.53 1.72e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## TimeD_M1_GM -0.467
anova  (GM_MEM_I_1m)
## Type III Analysis of Variance Table with Satterthwaite's method
##      Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
## Time 18.677  18.677     1 94.704  20.517 1.722e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(GM_MEM_I_1m)
  GM Score
Predictors Estimates CI p
(Intercept) 2.90 2.64 – 3.17 <0.001
Time [D_M1_GM] -0.63 -0.91 – -0.36 <0.001
Random Effects
σ2 0.91
τ00 ID 0.98
ICC 0.52
N ID 103
Observations 194
Marginal R2 / Conditional R2 0.050 / 0.544
parameters::standardise_parameters(GM_MEM_I_1m)
## # Standardization method: refit
## 
## Parameter   | Std. Coef. |         95% CI
## -----------------------------------------
## (Intercept) |       0.22 | [ 0.03,  0.41]
## TimeD_M1_GM |      -0.45 | [-0.64, -0.25]

Effect of time in the Control group

GM_C_1m <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_GM", "D_M1_GM") %>% 
  filter(Group == "B_Controls")
## Formatting table as needed
GM_C_long_1m <- GM_C_1m %>%
  pivot_longer(cols = c("A_PRE_GM", "D_M1_GM"),
               names_to = "Time",
               values_to = "GM_Score")
GM_MEM_C_1m <- lmer(GM_Score ~ Time + (1|ID), data = GM_C_long_1m, REML = TRUE)
summary(GM_MEM_C_1m)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: GM_Score ~ Time + (1 | ID)
##    Data: GM_C_long_1m
## 
## REML criterion at convergence: 675.1
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -1.95946 -0.57782 -0.05595  0.48663  1.97716 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 1.2394   1.113   
##  Residual             0.8612   0.928   
## Number of obs: 199, groups:  ID, 106
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)   3.1415     0.1408 148.6405   22.32   <2e-16 ***
## TimeD_M1_GM  -0.3467     0.1344  95.3134   -2.58   0.0114 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## TimeD_M1_GM -0.430
anova  (GM_MEM_C_1m)
## Type III Analysis of Variance Table with Satterthwaite's method
##      Sum Sq Mean Sq NumDF  DenDF F value  Pr(>F)  
## Time 5.7344  5.7344     1 95.313  6.6585 0.01139 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(GM_MEM_C_1m)
  GM Score
Predictors Estimates CI p
(Intercept) 3.14 2.86 – 3.42 <0.001
Time [D_M1_GM] -0.35 -0.61 – -0.08 0.011
Random Effects
σ2 0.86
τ00 ID 1.24
ICC 0.59
N ID 106
Observations 199
Marginal R2 / Conditional R2 0.014 / 0.596
parameters::standardise_parameters(GM_MEM_C_1m)
## # Standardization method: refit
## 
## Parameter   | Std. Coef. |         95% CI
## -----------------------------------------
## (Intercept) |       0.11 | [-0.08,  0.30]
## TimeD_M1_GM |      -0.24 | [-0.42, -0.06]

Effect of time in the EC group

GM_EC_1m <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_GM", "D_M1_GM") %>% 
  filter(Group == "A_ECs")
## Formatting table as needed
GM_EC_long_1m <- GM_EC_1m %>%
  pivot_longer(cols = c(A_PRE_GM, D_M1_GM),
               names_to = "Time",
               values_to = "GM_Score")
GM_MEM_EC_1m <- lmer(GM_Score ~ Time + (1|ID), data = GM_EC_long_1m, REML = TRUE)
summary(GM_MEM_EC_1m)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: GM_Score ~ Time + (1 | ID)
##    Data: GM_EC_long_1m
## 
## REML criterion at convergence: 315.1
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.33742 -0.58035  0.03805  0.43870  2.84681 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 1.0070   1.0035  
##  Residual             0.9155   0.9568  
## Number of obs: 94, groups:  ID, 50
## 
## Fixed effects:
##             Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)  2.74000    0.19609 73.62077  13.973   <2e-16 ***
## TimeD_M1_GM -0.03961    0.20106 45.56175  -0.197    0.845    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## TimeD_M1_GM -0.464
anova  (GM_MEM_EC_1m)
## Type III Analysis of Variance Table with Satterthwaite's method
##        Sum Sq  Mean Sq NumDF  DenDF F value Pr(>F)
## Time 0.035534 0.035534     1 45.562  0.0388 0.8447
sjPlot::tab_model(GM_MEM_EC_1m)
  GM Score
Predictors Estimates CI p
(Intercept) 2.74 2.35 – 3.13 <0.001
Time [D_M1_GM] -0.04 -0.44 – 0.36 0.844
Random Effects
σ2 0.92
τ00 ID 1.01
ICC 0.52
N ID 50
Observations 94
Marginal R2 / Conditional R2 0.000 / 0.524
parameters::standardise_parameters(GM_MEM_EC_1m)
## # Standardization method: refit
## 
## Parameter   | Std. Coef. |        95% CI
## ----------------------------------------
## (Intercept) |       0.02 | [-0.26, 0.30]
## TimeD_M1_GM |      -0.03 | [-0.32, 0.26]

Cohen’s d

# GM - 1m
m.ef_GM_1m <- emmeans(GM_MEM_B1M, "Time", "Group")
eff_size(m.ef_GM_1m, sigma = sigma(GM_MEM_B1M), edf = df.residual(GM_MEM_B1M))
## Group = A_ECs:
##  contrast           effect.size    SE  df lower.CL upper.CL
##  A_PRE_GM - D_M1_GM      0.0409 0.210 376  -0.3727    0.455
## 
## Group = B_Controls:
##  contrast           effect.size    SE  df lower.CL upper.CL
##  A_PRE_GM - D_M1_GM      0.3663 0.145 376   0.0809    0.652
## 
## Group = C_Intervention:
##  contrast           effect.size    SE  df lower.CL upper.CL
##  A_PRE_GM - D_M1_GM      0.6670 0.148 376   0.3762    0.958
## 
## sigma used for effect sizes: 0.9444 
## Degrees-of-freedom method: inherited from kenward-roger when re-gridding 
## Confidence level used: 0.95

H2b PHQ: difference in change in PHQ over time between groups

Baseline to 1W

PHQ_B1W <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_PHQ_total", "C_W1_PHQ_total")
## Formatting table as needed
PHQ_B1W_long <- PHQ_B1W %>%
  pivot_longer(cols = c(A_PRE_PHQ_total, C_W1_PHQ_total),
               names_to = "Time",
               values_to = "PHQ_Score")
PHQ_MEM_B1W <- lmer(PHQ_Score ~ Group * Time + (1|ID), data = PHQ_B1W_long, REML = TRUE)
summary(PHQ_MEM_B1W)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: PHQ_Score ~ Group * Time + (1 | ID)
##    Data: PHQ_B1W_long
## 
## REML criterion at convergence: 3069.4
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.70427 -0.49822 -0.04073  0.44204  3.13898 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 24.53    4.953   
##  Residual             10.07    3.173   
## Number of obs: 510, groups:  ID, 259
## 
## Fixed effects:
##                                        Estimate Std. Error       df t value
## (Intercept)                              9.9600     0.8318 339.2793  11.974
## GroupB_Controls                         -0.5166     1.0091 339.2793  -0.512
## GroupC_Intervention                      0.7196     1.0138 339.2793   0.710
## TimeC_W1_PHQ_total                      -0.1012     0.6458 252.0371  -0.157
## GroupB_Controls:TimeC_W1_PHQ_total      -0.7976     0.7821 251.8019  -1.020
## GroupC_Intervention:TimeC_W1_PHQ_total  -1.3587     0.7858 251.8141  -1.729
##                                        Pr(>|t|)    
## (Intercept)                              <2e-16 ***
## GroupB_Controls                           0.609    
## GroupC_Intervention                       0.478    
## TimeC_W1_PHQ_total                        0.876    
## GroupB_Controls:TimeC_W1_PHQ_total        0.309    
## GroupC_Intervention:TimeC_W1_PHQ_total    0.085 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) GrpB_C GrpC_I TC_W1_ GB_C:T
## GrpB_Cntrls -0.824                            
## GrpC_Intrvn -0.820  0.676                     
## TmC_W1_PHQ_ -0.375  0.309  0.308              
## GB_C:TC_W1_  0.309 -0.375 -0.254 -0.826       
## GC_I:TC_W1_  0.308 -0.254 -0.375 -0.822  0.679
anova  (PHQ_MEM_B1W)
## Type III Analysis of Variance Table with Satterthwaite's method
##            Sum Sq Mean Sq NumDF  DenDF F value  Pr(>F)   
## Group      18.876   9.438     2 257.38  0.9375 0.39294   
## Time       75.005  75.005     1 251.69  7.4503 0.00679 **
## Group:Time 30.533  15.266     2 251.61  1.5164 0.22149   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(PHQ_MEM_B1W,
                  pred.labels=c("Intercept", "Psychoeducation Control", "Mindset Intervention", "Time (1 Week)", "Psychoeducation Control x Time","Mindset Intervention x Time"),
                  dv.labels=c("Depression (PHQ-8 Score)"),
                  string.std_ci = "std. 95% CI",
                  string.std = "std. Beta",
                  show.std = TRUE,
                  show.est = FALSE)
  Depression (PHQ-8 Score)
Predictors std. Beta std. 95% CI p
Intercept 0.07 -0.21 – 0.34 <0.001
Psychoeducation Control -0.09 -0.42 – 0.25 0.609
Mindset Intervention 0.12 -0.22 – 0.46 0.478
Time (1 Week) -0.02 -0.23 – 0.20 0.875
Psychoeducation Control x Time -0.13 -0.39 – 0.13 0.308
Mindset Intervention x Time -0.23 -0.49 – 0.03 0.084
Random Effects
σ2 10.07
τ00 ID 24.53
ICC 0.71
N ID 259
Observations 510
Marginal R2 / Conditional R2 0.015 / 0.713
parameters::standardise_parameters(PHQ_MEM_B1W)
## # Standardization method: refit
## 
## Parameter                              | Std. Coef. |        95% CI
## -------------------------------------------------------------------
## (Intercept)                            |       0.07 | [-0.21, 0.34]
## GroupB_Controls                        |      -0.09 | [-0.42, 0.25]
## GroupC_Intervention                    |       0.12 | [-0.22, 0.46]
## TimeC_W1_PHQ_total                     |      -0.02 | [-0.23, 0.20]
## GroupB_Controls:TimeC_W1_PHQ_total     |      -0.13 | [-0.39, 0.13]
## GroupC_Intervention:TimeC_W1_PHQ_total |      -0.23 | [-0.49, 0.03]

Baseline to 1M

PHQ_B1M <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_PHQ_total", "D_M1_PHQ_total")
## Formatting table as needed
PHQ_B1M_long <- PHQ_B1M %>%
  pivot_longer(cols = c(A_PRE_PHQ_total, D_M1_PHQ_total),
               names_to = "Time",
               values_to = "PHQ_Score")
PHQ_MEM_B1M <- lmer(PHQ_Score ~ Group * Time + (1|ID), data = PHQ_B1M_long, REML = TRUE)
summary(PHQ_MEM_B1M)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: PHQ_Score ~ Group * Time + (1 | ID)
##    Data: PHQ_B1M_long
## 
## REML criterion at convergence: 3028.1
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.64448 -0.55044 -0.09744  0.49965  2.79846 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 21.46    4.633   
##  Residual             15.15    3.892   
## Number of obs: 487, groups:  ID, 259
## 
## Fixed effects:
##                                        Estimate Std. Error       df t value
## (Intercept)                              9.9600     0.8557 367.8141  11.640
## GroupB_Controls                         -0.5166     1.0381 367.8141  -0.498
## GroupC_Intervention                      0.7196     1.0429 367.8141   0.690
## TimeD_M1_PHQ_total                       0.6244     0.8271 240.0648   0.755
## GroupB_Controls:TimeD_M1_PHQ_total      -1.8086     0.9995 239.3565  -1.810
## GroupC_Intervention:TimeD_M1_PHQ_total  -2.9746     1.0045 239.4295  -2.961
##                                        Pr(>|t|)    
## (Intercept)                             < 2e-16 ***
## GroupB_Controls                         0.61902    
## GroupC_Intervention                     0.49062    
## TimeD_M1_PHQ_total                      0.45104    
## GroupB_Controls:TimeD_M1_PHQ_total      0.07161 .  
## GroupC_Intervention:TimeD_M1_PHQ_total  0.00337 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) GrpB_C GrpC_I TD_M1_ GB_C:T
## GrpB_Cntrls -0.824                            
## GrpC_Intrvn -0.820  0.676                     
## TmD_M1_PHQ_ -0.428  0.353  0.351              
## GB_C:TD_M1_  0.354 -0.430 -0.291 -0.828       
## GC_I:TD_M1_  0.352 -0.291 -0.430 -0.823  0.681
anova  (PHQ_MEM_B1M)
## Type III Analysis of Variance Table with Satterthwaite's method
##             Sum Sq Mean Sq NumDF  DenDF F value  Pr(>F)  
## Group       35.957  17.979     2 258.66  1.1869 0.30684  
## Time        96.897  96.897     1 239.05  6.3966 0.01208 *
## Group:Time 134.059  67.029     2 238.81  4.4250 0.01297 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(PHQ_MEM_B1M,
                  pred.labels=c("Intercept", "Psychoeducation Control", "Mindset Intervention", "Time (1 Month)", "Psychoeducation Control x Time","Mindset Intervention x Time"),
                  dv.labels=c("Depression (PHQ-8 Score)"),
                  string.std_ci = "std. 95% CI",
                  string.std = "std. Beta",
                  show.std = TRUE,
                  show.est = FALSE)
  Depression (PHQ-8 Score)
Predictors std. Beta std. 95% CI p
Intercept 0.09 -0.18 – 0.37 <0.001
Psychoeducation Control -0.08 -0.42 – 0.25 0.619
Mindset Intervention 0.12 -0.22 – 0.45 0.491
Time (1 Month) 0.10 -0.16 – 0.37 0.451
Psychoeducation Control x Time -0.30 -0.62 – 0.03 0.071
Mindset Intervention x Time -0.49 -0.81 – -0.16 0.003
Random Effects
σ2 15.15
τ00 ID 21.46
ICC 0.59
N ID 259
Observations 487
Marginal R2 / Conditional R2 0.026 / 0.597
parameters::standardise_parameters(PHQ_MEM_B1M)
## # Standardization method: refit
## 
## Parameter                              | Std. Coef. |         95% CI
## --------------------------------------------------------------------
## (Intercept)                            |       0.09 | [-0.18,  0.37]
## GroupB_Controls                        |      -0.08 | [-0.42,  0.25]
## GroupC_Intervention                    |       0.12 | [-0.22,  0.45]
## TimeD_M1_PHQ_total                     |       0.10 | [-0.16,  0.37]
## GroupB_Controls:TimeD_M1_PHQ_total     |      -0.30 | [-0.62,  0.03]
## GroupC_Intervention:TimeD_M1_PHQ_total |      -0.49 | [-0.81, -0.16]

Effect of time in the intervention group

PHQ_I_1m <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_PHQ_total", "D_M1_PHQ_total") %>% 
  filter(Group == "C_Intervention")
## Formatting table as needed
PHQ_I_long_1m <- PHQ_I_1m %>%
  pivot_longer(cols = c("A_PRE_PHQ_total", "D_M1_PHQ_total"),
               names_to = "Time",
               values_to = "PHQ_Score")
PHQ_MEM_I_1m <- lmer(PHQ_Score ~ Time + (1|ID), data = PHQ_I_long_1m, REML = TRUE)
summary(PHQ_MEM_I_1m)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: PHQ_Score ~ Time + (1 | ID)
##    Data: PHQ_I_long_1m
## 
## REML criterion at convergence: 1192.6
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.30041 -0.55128 -0.08312  0.51684  2.64008 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 20.39    4.516   
##  Residual             13.80    3.714   
## Number of obs: 194, groups:  ID, 103
## 
## Fixed effects:
##                    Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)         10.6796     0.5761 145.9837   18.54  < 2e-16 ***
## TimeD_M1_PHQ_total  -2.3508     0.5441  95.7256   -4.32 3.81e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## TmD_M1_PHQ_ -0.427
anova  (PHQ_MEM_I_1m)
## Type III Analysis of Variance Table with Satterthwaite's method
##      Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
## Time 257.49  257.49     1 95.726  18.663 3.811e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(PHQ_MEM_I_1m)
  PHQ Score
Predictors Estimates CI p
(Intercept) 10.68 9.54 – 11.82 <0.001
Time [D_M1_PHQ_total] -2.35 -3.42 – -1.28 <0.001
Random Effects
σ2 13.80
τ00 ID 20.39
ICC 0.60
N ID 103
Observations 194
Marginal R2 / Conditional R2 0.039 / 0.612
parameters::standardise_parameters(PHQ_MEM_I_1m)
## # Standardization method: refit
## 
## Parameter          | Std. Coef. |         95% CI
## ------------------------------------------------
## (Intercept)        |       0.18 | [-0.01,  0.37]
## TimeD_M1_PHQ_total |      -0.39 | [-0.57, -0.21]

Effect of time in the Control group

PHQ_C_1m <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_PHQ_total", "D_M1_PHQ_total") %>% 
  filter(Group == "B_Controls")
## Formatting table as needed
PHQ_C_long_1m <- PHQ_C_1m %>%
  pivot_longer(cols = c("A_PRE_PHQ_total", "D_M1_PHQ_total"),
               names_to = "Time",
               values_to = "PHQ_Score")
PHQ_MEM_C_1m <- lmer(PHQ_Score ~ Time + (1|ID), data = PHQ_C_long_1m, REML = TRUE)
summary(PHQ_MEM_C_1m)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: PHQ_Score ~ Time + (1 | ID)
##    Data: PHQ_C_long_1m
## 
## REML criterion at convergence: 1265.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.3651 -0.6137 -0.1412  0.5123  2.5367 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 19.77    4.447   
##  Residual             18.70    4.325   
## Number of obs: 200, groups:  ID, 106
## 
## Fixed effects:
##                    Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)          9.4434     0.6025 159.5745  15.675   <2e-16 ***
## TimeD_M1_PHQ_total  -1.1978     0.6221  98.5457  -1.926    0.057 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## TmD_M1_PHQ_ -0.471
anova  (PHQ_MEM_C_1m)
## Type III Analysis of Variance Table with Satterthwaite's method
##      Sum Sq Mean Sq NumDF  DenDF F value  Pr(>F)  
## Time 69.341  69.341     1 98.546  3.7077 0.05704 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(PHQ_MEM_C_1m)
  PHQ Score
Predictors Estimates CI p
(Intercept) 9.44 8.26 – 10.63 <0.001
Time [D_M1_PHQ_total] -1.20 -2.42 – 0.03 0.056
Random Effects
σ2 18.70
τ00 ID 19.77
ICC 0.51
N ID 106
Observations 200
Marginal R2 / Conditional R2 0.009 / 0.518
parameters::standardise_parameters(PHQ_MEM_C_1m)
## # Standardization method: refit
## 
## Parameter          | Std. Coef. |        95% CI
## -----------------------------------------------
## (Intercept)        |       0.10 | [-0.09, 0.29]
## TimeD_M1_PHQ_total |      -0.19 | [-0.39, 0.00]

Effect of time in the EC group

PHQ_EC_1m <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_PHQ_total", "D_M1_PHQ_total") %>% 
  filter(Group == "A_ECs")
## Formatting table as needed
PHQ_EC_long_1m <- PHQ_EC_1m %>%
  pivot_longer(cols = c(A_PRE_PHQ_total, D_M1_PHQ_total),
               names_to = "Time",
               values_to = "PHQ_Score")
PHQ_MEM_EC_1m <- lmer(PHQ_Score ~ Time + (1|ID), data = PHQ_EC_long_1m, REML = TRUE)
summary(PHQ_MEM_EC_1m)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: PHQ_Score ~ Time + (1 | ID)
##    Data: PHQ_EC_long_1m
## 
## REML criterion at convergence: 564.1
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.8858 -0.4652 -0.1043  0.5389  1.7733 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 27.42    5.236   
##  Residual             10.19    3.192   
## Number of obs: 93, groups:  ID, 50
## 
## Fixed effects:
##                    Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)          9.9600     0.8673 62.0927   11.48   <2e-16 ***
## TimeD_M1_PHQ_total   0.6818     0.6819 43.8551    1.00    0.323    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## TmD_M1_PHQ_ -0.345
anova  (PHQ_MEM_EC_1m)
## Type III Analysis of Variance Table with Satterthwaite's method
##      Sum Sq Mean Sq NumDF  DenDF F value Pr(>F)
## Time 10.188  10.188     1 43.855  0.9999 0.3228
sjPlot::tab_model(PHQ_MEM_EC_1m)
  PHQ Score
Predictors Estimates CI p
(Intercept) 9.96 8.24 – 11.68 <0.001
Time [D_M1_PHQ_total] 0.68 -0.67 – 2.04 0.320
Random Effects
σ2 10.19
τ00 ID 27.42
ICC 0.73
N ID 50
Observations 93
Marginal R2 / Conditional R2 0.003 / 0.730
parameters::standardise_parameters(PHQ_MEM_EC_1m)
## # Standardization method: refit
## 
## Parameter          | Std. Coef. |        95% CI
## -----------------------------------------------
## (Intercept)        |      -0.03 | [-0.31, 0.25]
## TimeD_M1_PHQ_total |       0.11 | [-0.11, 0.33]

Cohen’s d

# phq - 1m
m.ef_phq_1m <- emmeans(PHQ_MEM_B1M, "Time", "Group")
eff_size(m.ef_phq_1m, sigma = sigma(PHQ_MEM_B1M), edf = df.residual(PHQ_MEM_B1M))
## Group = A_ECs:
##  contrast                         effect.size    SE  df lower.CL upper.CL
##  A_PRE_PHQ_total - D_M1_PHQ_total      -0.160 0.213 366  -0.5786    0.258
## 
## Group = B_Controls:
##  contrast                         effect.size    SE  df lower.CL upper.CL
##  A_PRE_PHQ_total - D_M1_PHQ_total       0.304 0.145 366   0.0201    0.588
## 
## Group = C_Intervention:
##  contrast                         effect.size    SE  df lower.CL upper.CL
##  A_PRE_PHQ_total - D_M1_PHQ_total       0.604 0.148 366   0.3132    0.894
## 
## sigma used for effect sizes: 3.892 
## Degrees-of-freedom method: inherited from kenward-roger when re-gridding 
## Confidence level used: 0.95

H2b GAD: difference in change in GAD over time between groups

Baseline to 1W

# Merging across timepoints
GAD_B1W <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_GAD_total", "C_W1_GAD_total")
## Formatting table as needed
GAD_B1W_long <- GAD_B1W %>%
  pivot_longer(cols = c(A_PRE_GAD_total, C_W1_GAD_total),
               names_to = "Time",
               values_to = "GAD_Score")
GAD_MEM_B1W <- lmer(GAD_Score ~ Group * Time + (1|ID), data = GAD_B1W_long, REML = TRUE)
summary(GAD_MEM_B1W)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: GAD_Score ~ Group * Time + (1 | ID)
##    Data: GAD_B1W_long
## 
## REML criterion at convergence: 3025.1
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.0453 -0.4584 -0.0843  0.4595  3.1840 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 22.202   4.712   
##  Residual              9.297   3.049   
## Number of obs: 510, groups:  ID, 259
## 
## Fixed effects:
##                                        Estimate Std. Error       df t value
## (Intercept)                              8.0200     0.7937 340.7093  10.104
## GroupB_Controls                          0.4706     0.9629 340.7093   0.489
## GroupC_Intervention                      1.2616     0.9674 340.7093   1.304
## TimeC_W1_GAD_total                       0.3104     0.6206 252.2282   0.500
## GroupB_Controls:TimeC_W1_GAD_total      -0.9286     0.7516 251.9901  -1.236
## GroupC_Intervention:TimeC_W1_GAD_total  -1.3167     0.7551 252.0024  -1.744
##                                        Pr(>|t|)    
## (Intercept)                              <2e-16 ***
## GroupB_Controls                          0.6254    
## GroupC_Intervention                      0.1931    
## TimeC_W1_GAD_total                       0.6174    
## GroupB_Controls:TimeC_W1_GAD_total       0.2178    
## GroupC_Intervention:TimeC_W1_GAD_total   0.0824 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) GrpB_C GrpC_I TC_W1_ GB_C:T
## GrpB_Cntrls -0.824                            
## GrpC_Intrvn -0.820  0.676                     
## TmC_W1_GAD_ -0.378  0.311  0.310              
## GB_C:TC_W1_  0.312 -0.378 -0.256 -0.826       
## GC_I:TC_W1_  0.310 -0.256 -0.378 -0.822  0.679
anova  (GAD_MEM_B1W)
## Type III Analysis of Variance Table with Satterthwaite's method
##            Sum Sq Mean Sq NumDF  DenDF F value Pr(>F)
## Group       7.671  3.8355     2 257.54  0.4125 0.6624
## Time       21.411 21.4112     1 251.88  2.3030 0.1304
## Group:Time 28.314 14.1572     2 251.80  1.5228 0.2201
sjPlot::tab_model(GAD_MEM_B1W,
                  pred.labels=c("Intercept", "Psychoeducation Control", "Mindset Intervention", "Time (1 Week)", "Psychoeducation Control x Time","Mindset Intervention x Time"),
                  dv.labels=c("Anxiety (GAD-7 Score)"),
                  string.std_ci = "std. 95% CI",
                  string.std = "std. Beta",
                  show.std = TRUE,
                  show.est = FALSE)
  Anxiety (GAD-7 Score)
Predictors std. Beta std. 95% CI p
Intercept -0.07 -0.35 – 0.20 <0.001
Psychoeducation Control 0.08 -0.25 – 0.42 0.625
Mindset Intervention 0.22 -0.11 – 0.56 0.193
Time (1 Week) 0.06 -0.16 – 0.27 0.617
Psychoeducation Control x Time -0.17 -0.43 – 0.10 0.217
Mindset Intervention x Time -0.23 -0.50 – 0.03 0.082
Random Effects
σ2 9.30
τ00 ID 22.20
ICC 0.70
N ID 259
Observations 510
Marginal R2 / Conditional R2 0.007 / 0.707
parameters::standardise_parameters(GAD_MEM_B1W)
## # Standardization method: refit
## 
## Parameter                              | Std. Coef. |        95% CI
## -------------------------------------------------------------------
## (Intercept)                            |      -0.07 | [-0.35, 0.20]
## GroupB_Controls                        |       0.08 | [-0.25, 0.42]
## GroupC_Intervention                    |       0.22 | [-0.11, 0.56]
## TimeC_W1_GAD_total                     |       0.06 | [-0.16, 0.27]
## GroupB_Controls:TimeC_W1_GAD_total     |      -0.17 | [-0.43, 0.10]
## GroupC_Intervention:TimeC_W1_GAD_total |      -0.23 | [-0.50, 0.03]

Baseline to 1M

# Merging across timepoints
GAD_B1M <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_GAD_total", "D_M1_GAD_total")
## Formatting table as needed
GAD_B1M_long <- GAD_B1M %>%
  pivot_longer(cols = c(A_PRE_GAD_total, D_M1_GAD_total),
               names_to = "Time",
               values_to = "GAD_Score")
GAD_MEM_B1M <- lmer(GAD_Score ~ Group * Time + (1|ID), data = GAD_B1M_long, REML = TRUE)
summary(GAD_MEM_B1M)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: GAD_Score ~ Group * Time + (1 | ID)
##    Data: GAD_B1M_long
## 
## REML criterion at convergence: 2951
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.26184 -0.51370 -0.07266  0.47118  2.72886 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 19.51    4.417   
##  Residual             12.64    3.555   
## Number of obs: 486, groups:  ID, 259
## 
## Fixed effects:
##                                        Estimate Std. Error       df t value
## (Intercept)                              8.0200     0.8018 361.1090  10.002
## GroupB_Controls                          0.4706     0.9727 361.1090   0.484
## GroupC_Intervention                      1.2616     0.9772 361.1090   1.291
## TimeD_M1_GAD_total                       1.2587     0.7560 238.1128   1.665
## GroupB_Controls:TimeD_M1_GAD_total      -2.2184     0.9147 237.6716  -2.425
## GroupC_Intervention:TimeD_M1_GAD_total  -3.0251     0.9181 237.5072  -3.295
##                                        Pr(>|t|)    
## (Intercept)                             < 2e-16 ***
## GroupB_Controls                         0.62884    
## GroupC_Intervention                     0.19755    
## TimeD_M1_GAD_total                      0.09724 .  
## GroupB_Controls:TimeD_M1_GAD_total      0.01605 *  
## GroupC_Intervention:TimeD_M1_GAD_total  0.00113 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) GrpB_C GrpC_I TD_M1_ GB_C:T
## GrpB_Cntrls -0.824                            
## GrpC_Intrvn -0.820  0.676                     
## TmD_M1_GAD_ -0.417  0.344  0.342              
## GB_C:TD_M1_  0.345 -0.418 -0.283 -0.826       
## GC_I:TD_M1_  0.343 -0.283 -0.418 -0.823  0.681
anova  (GAD_MEM_B1M)
## Type III Analysis of Variance Table with Satterthwaite's method
##             Sum Sq Mean Sq NumDF  DenDF F value   Pr(>F)   
## Group        7.574   3.787     2 258.32  0.2997 0.741299   
## Time        24.554  24.554     1 237.32  1.9431 0.164633   
## Group:Time 137.971  68.986     2 237.14  5.4594 0.004808 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(GAD_MEM_B1M,
                  pred.labels=c("Intercept", "Psychoeducation Control", "Mindset Intervention", "Time (1 Month)", "Psychoeducation Control x Time","Mindset Intervention x Time"),
                  dv.labels=c("Anxiety (GAD-7 Score)"),
                  string.std_ci = "std. 95% CI",
                  string.std = "std. Beta",
                  show.std = TRUE,
                  show.est = FALSE)
  Anxiety (GAD-7 Score)
Predictors std. Beta std. 95% CI p
Intercept -0.05 -0.32 – 0.23 <0.001
Psychoeducation Control 0.08 -0.25 – 0.42 0.629
Mindset Intervention 0.22 -0.12 – 0.56 0.197
Time (1 Month) 0.22 -0.04 – 0.48 0.097
Psychoeducation Control x Time -0.39 -0.70 – -0.07 0.016
Mindset Intervention x Time -0.53 -0.85 – -0.21 0.001
Random Effects
σ2 12.64
τ00 ID 19.51
ICC 0.61
N ID 259
Observations 486
Marginal R2 / Conditional R2 0.016 / 0.613
parameters::standardise_parameters(GAD_MEM_B1M)
## # Standardization method: refit
## 
## Parameter                              | Std. Coef. |         95% CI
## --------------------------------------------------------------------
## (Intercept)                            |      -0.05 | [-0.32,  0.23]
## GroupB_Controls                        |       0.08 | [-0.25,  0.42]
## GroupC_Intervention                    |       0.22 | [-0.12,  0.56]
## TimeD_M1_GAD_total                     |       0.22 | [-0.04,  0.48]
## GroupB_Controls:TimeD_M1_GAD_total     |      -0.39 | [-0.70, -0.07]
## GroupC_Intervention:TimeD_M1_GAD_total |      -0.53 | [-0.85, -0.21]

Effect of time in the intervention group

GAD_I <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_GAD_total", "C_W1_GAD_total", "D_M1_GAD_total") %>% 
  filter(Group == "C_Intervention")
## Formatting table as needed
GAD_I_long <- GAD_I %>%
  pivot_longer(cols = c("A_PRE_GAD_total", "C_W1_GAD_total", "D_M1_GAD_total"),
               names_to = "Time",
               values_to = "GAD_Score")
GAD_MEM_I <- lmer(GAD_Score ~ Time + (1|ID), data = GAD_I_long, REML = TRUE)
summary(GAD_MEM_I)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: GAD_Score ~ Time + (1 | ID)
##    Data: GAD_I_long
## 
## REML criterion at convergence: 1726.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.8905 -0.4758 -0.0769  0.5231  2.7194 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 21.53    4.640   
##  Residual             10.86    3.296   
## Number of obs: 294, groups:  ID, 103
## 
## Fixed effects:
##                    Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)          9.2816     0.5608 160.4682  16.552  < 2e-16 ***
## TimeC_W1_GAD_total  -1.0187     0.4640 190.5491  -2.195 0.029351 *  
## TimeD_M1_GAD_total  -1.8024     0.4800 192.1943  -3.755 0.000229 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) TC_W1_
## TmC_W1_GAD_ -0.405       
## TmD_M1_GAD_ -0.392  0.472
anova  (GAD_MEM_I)
## Type III Analysis of Variance Table with Satterthwaite's method
##      Sum Sq Mean Sq NumDF  DenDF F value    Pr(>F)    
## Time 155.64  77.819     2 191.83  7.1649 0.0009978 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(GAD_MEM_I)
  GAD Score
Predictors Estimates CI p
(Intercept) 9.28 8.18 – 10.39 <0.001
Time [C_W1_GAD_total] -1.02 -1.93 – -0.11 0.029
Time [D_M1_GAD_total] -1.80 -2.75 – -0.86 <0.001
Random Effects
σ2 10.86
τ00 ID 21.53
ICC 0.66
N ID 103
Observations 294
Marginal R2 / Conditional R2 0.016 / 0.670
parameters::standardise_parameters(GAD_MEM_I)
## # Standardization method: refit
## 
## Parameter          | Std. Coef. |         95% CI
## ------------------------------------------------
## (Intercept)        |       0.15 | [-0.04,  0.34]
## TimeC_W1_GAD_total |      -0.18 | [-0.34, -0.02]
## TimeD_M1_GAD_total |      -0.31 | [-0.48, -0.15]

Effect of time in the Control group

GAD_C <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_GAD_total", "C_W1_GAD_total", "D_M1_GAD_total") %>% 
  filter(Group == "B_Controls")
## Formatting table as needed
GAD_C_long <- GAD_C %>%
  pivot_longer(cols = c("A_PRE_GAD_total", "C_W1_GAD_total", "D_M1_GAD_total"),
               names_to = "Time",
               values_to = "GAD_Score")
GAD_MEM_C <- lmer(GAD_Score ~ Time + (1|ID), data = GAD_C_long, REML = TRUE)
summary(GAD_MEM_C)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: GAD_Score ~ Time + (1 | ID)
##    Data: GAD_C_long
## 
## REML criterion at convergence: 1788.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.7651 -0.4670 -0.1016  0.5054  3.2095 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 22.48    4.741   
##  Residual             11.47    3.387   
## Number of obs: 302, groups:  ID, 106
## 
## Fixed effects:
##                    Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)          8.4906     0.5659 164.7207  15.003   <2e-16 ***
## TimeC_W1_GAD_total  -0.6425     0.4703 195.2577  -1.366   0.1734    
## TimeD_M1_GAD_total  -0.9632     0.4877 197.0825  -1.975   0.0497 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) TC_W1_
## TmC_W1_GAD_ -0.407       
## TmD_M1_GAD_ -0.392  0.474
anova  (GAD_MEM_C)
## Type III Analysis of Variance Table with Satterthwaite's method
##      Sum Sq Mean Sq NumDF  DenDF F value Pr(>F)
## Time 47.478  23.739     2 196.44  2.0693  0.129
sjPlot::tab_model(GAD_MEM_C)
  GAD Score
Predictors Estimates CI p
(Intercept) 8.49 7.38 – 9.60 <0.001
Time [C_W1_GAD_total] -0.64 -1.57 – 0.28 0.173
Time [D_M1_GAD_total] -0.96 -1.92 – -0.00 0.049
Random Effects
σ2 11.47
τ00 ID 22.48
ICC 0.66
N ID 106
Observations 302
Marginal R2 / Conditional R2 0.005 / 0.664
parameters::standardise_parameters(GAD_MEM_C)
## # Standardization method: refit
## 
## Parameter          | Std. Coef. |         95% CI
## ------------------------------------------------
## (Intercept)        |       0.09 | [-0.10,  0.29]
## TimeC_W1_GAD_total |      -0.11 | [-0.27,  0.05]
## TimeD_M1_GAD_total |      -0.17 | [-0.33,  0.00]

Effect of time in the EC group

GAD_EC <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_GAD_total", "C_W1_GAD_total", "D_M1_GAD_total") %>% 
  filter(Group == "A_ECs")
## Formatting table as needed
GAD_EC_long <- GAD_EC %>%
  pivot_longer(cols = c(A_PRE_GAD_total, C_W1_GAD_total, D_M1_GAD_total),
               names_to = "Time",
               values_to = "GAD_Score")
GAD_MEM_EC <- lmer(GAD_Score ~ Time + (1|ID), data = GAD_EC_long, REML = TRUE)
summary(GAD_MEM_EC)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: GAD_Score ~ Time + (1 | ID)
##    Data: GAD_EC_long
## 
## REML criterion at convergence: 812.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.4036 -0.4894 -0.0713  0.4865  3.4462 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 18.47    4.297   
##  Residual             10.24    3.200   
## Number of obs: 141, groups:  ID, 50
## 
## Fixed effects:
##                    Estimate Std. Error      df t value Pr(>|t|)    
## (Intercept)          8.0200     0.7577 79.1032  10.584   <2e-16 ***
## TimeC_W1_GAD_total   0.4472     0.6492 90.0523   0.689    0.493    
## TimeD_M1_GAD_total   1.3070     0.6753 91.0193   1.935    0.056 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) TC_W1_
## TmC_W1_GAD_ -0.416       
## TmD_M1_GAD_ -0.400  0.465
anova  (GAD_MEM_EC)
## Type III Analysis of Variance Table with Satterthwaite's method
##      Sum Sq Mean Sq NumDF  DenDF F value Pr(>F)
## Time 38.943  19.472     2 90.832  1.9017 0.1552
sjPlot::tab_model(GAD_MEM_EC)
  GAD Score
Predictors Estimates CI p
(Intercept) 8.02 6.52 – 9.52 <0.001
Time [C_W1_GAD_total] 0.45 -0.84 – 1.73 0.492
Time [D_M1_GAD_total] 1.31 -0.03 – 2.64 0.055
Random Effects
σ2 10.24
τ00 ID 18.47
ICC 0.64
N ID 50
Observations 141
Marginal R2 / Conditional R2 0.010 / 0.647
parameters::standardise_parameters(GAD_MEM_EC)
## # Standardization method: refit
## 
## Parameter          | Std. Coef. |        95% CI
## -----------------------------------------------
## (Intercept)        |      -0.09 | [-0.36, 0.19]
## TimeC_W1_GAD_total |       0.08 | [-0.16, 0.32]
## TimeD_M1_GAD_total |       0.24 | [-0.01, 0.49]

Cohen’s d

# gad - 1m
m.ef_gad_1m <- emmeans(GAD_MEM_B1M, "Time", "Group")
eff_size(m.ef_gad_1m, sigma = sigma(GAD_MEM_B1M), edf = df.residual(GAD_MEM_B1M))
## Group = A_ECs:
##  contrast                         effect.size    SE  df lower.CL upper.CL
##  A_PRE_GAD_total - D_M1_GAD_total      -0.354 0.213 359  -0.7731   0.0649
## 
## Group = B_Controls:
##  contrast                         effect.size    SE  df lower.CL upper.CL
##  A_PRE_GAD_total - D_M1_GAD_total       0.270 0.145 359  -0.0155   0.5555
## 
## Group = C_Intervention:
##  contrast                         effect.size    SE  df lower.CL upper.CL
##  A_PRE_GAD_total - D_M1_GAD_total       0.497 0.147 359   0.2069   0.7869
## 
## sigma used for effect sizes: 3.555 
## Degrees-of-freedom method: inherited from kenward-roger when re-gridding 
## Confidence level used: 0.95

E2 FI: Change in functional impairment over time across groups

Baseline to 1W

# Merging across timepoints
FI_B1W <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_FI_total", "C_W1_FI_total")
## Formatting table as needed
FI_B1W_long <- FI_B1W %>%
  pivot_longer(cols = c(A_PRE_FI_total, C_W1_FI_total),
               names_to = "Time",
               values_to = "FI_Score")
FI_MEM_B1W <- lmer(FI_Score ~ Group * Time + (1|ID), data = FI_B1W_long, REML = TRUE)
summary(FI_MEM_B1W)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: FI_Score ~ Group * Time + (1 | ID)
##    Data: FI_B1W_long
## 
## REML criterion at convergence: 2740.6
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.86590 -0.50210 -0.00798  0.48671  2.80124 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 9.039    3.007   
##  Residual             6.577    2.565   
## Number of obs: 510, groups:  ID, 259
## 
## Fixed effects:
##                                        Estimate Std. Error        df t value
## (Intercept)                             9.86000    0.55886 380.24977  17.643
## GroupB_Controls                         0.16830    0.67797 380.24977   0.248
## GroupC_Intervention                     0.61573    0.68113 380.24977   0.904
## TimeC_W1_FI_total                       0.09842    0.52127 252.70546   0.189
## GroupB_Controls:TimeC_W1_FI_total      -0.30400    0.63140 252.38770  -0.481
## GroupC_Intervention:TimeC_W1_FI_total  -1.05347    0.63439 252.40409  -1.661
##                                       Pr(>|t|)    
## (Intercept)                             <2e-16 ***
## GroupB_Controls                          0.804    
## GroupC_Intervention                      0.367    
## TimeC_W1_FI_total                        0.850    
## GroupB_Controls:TimeC_W1_FI_total        0.631    
## GroupC_Intervention:TimeC_W1_FI_total    0.098 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) GrpB_C GrpC_I TC_W1_ GB_C:T
## GrpB_Cntrls -0.824                            
## GrpC_Intrvn -0.820  0.676                     
## TmC_W1_FI_t -0.452  0.372  0.370              
## GB_C:TC_W1_  0.373 -0.452 -0.306 -0.826       
## GC_I:TC_W1_  0.371 -0.306 -0.452 -0.822  0.678
anova  (FI_MEM_B1W)
## Type III Analysis of Variance Table with Satterthwaite's method
##             Sum Sq Mean Sq NumDF  DenDF F value Pr(>F)
## Group       0.2043  0.1022     2 256.87  0.0155 0.9846
## Time       14.0165 14.0165     1 252.24  2.1312 0.1456
## Group:Time 23.2052 11.6026     2 252.13  1.7642 0.1734
sjPlot::tab_model(FI_MEM_B1W, 
                  pred.labels=c("Intercept", "Psychoeducation Control", "Mindset Intervention", "Time (1 Week)", "Psychoeducation Control x Time","Mindset Intervention x Time"),
                  dv.labels=c("Functional Impairment"),
                  string.std_ci = "std. 95% CI",
                  string.std = "std. Beta",
                  show.std = TRUE,
                  show.est = FALSE)
  Functional Impairment
Predictors std. Beta std. 95% CI p
Intercept -0.03 -0.30 – 0.25 <0.001
Psychoeducation Control 0.04 -0.29 – 0.38 0.804
Mindset Intervention 0.16 -0.18 – 0.49 0.366
Time (1 Week) 0.02 -0.23 – 0.28 0.850
Psychoeducation Control x Time -0.08 -0.39 – 0.24 0.630
Mindset Intervention x Time -0.27 -0.58 – 0.05 0.097
Random Effects
σ2 6.58
τ00 ID 9.04
ICC 0.58
N ID 259
Observations 510
Marginal R2 / Conditional R2 0.006 / 0.581
parameters::standardise_parameters(FI_MEM_B1W)
## # Standardization method: refit
## 
## Parameter                             | Std. Coef. |        95% CI
## ------------------------------------------------------------------
## (Intercept)                           |      -0.03 | [-0.30, 0.25]
## GroupB_Controls                       |       0.04 | [-0.29, 0.38]
## GroupC_Intervention                   |       0.16 | [-0.18, 0.49]
## TimeC_W1_FI_total                     |       0.02 | [-0.23, 0.28]
## GroupB_Controls:TimeC_W1_FI_total     |      -0.08 | [-0.39, 0.24]
## GroupC_Intervention:TimeC_W1_FI_total |      -0.27 | [-0.58, 0.05]

Baseline to 1M

# Merging across timepoints
FI_B1M <- Full_data_all %>% 
  dplyr::select("ID", "Group", "A_PRE_FI_total", "D_M1_FI_total")
## Formatting table as needed
FI_B1M_long <- FI_B1M %>%
  pivot_longer(cols = c(A_PRE_FI_total, D_M1_FI_total),
               names_to = "Time",
               values_to = "FI_Score")
FI_MEM_B1M <- lmer(FI_Score ~ Group * Time + (1|ID), data = FI_B1M_long, REML = TRUE)
summary(FI_MEM_B1M)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: FI_Score ~ Group * Time + (1 | ID)
##    Data: FI_B1M_long
## 
## REML criterion at convergence: 2627.3
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.39593 -0.49332 -0.00673  0.48809  2.50102 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  ID       (Intercept) 10.482   3.238   
##  Residual              5.891   2.427   
## Number of obs: 489, groups:  ID, 259
## 
## Fixed effects:
##                                       Estimate Std. Error       df t value
## (Intercept)                             9.8600     0.5722 351.6690  17.230
## GroupB_Controls                         0.1683     0.6942 351.6690   0.242
## GroupC_Intervention                     0.6157     0.6974 351.6690   0.883
## TimeD_M1_FI_total                      -0.1205     0.5119 237.2371  -0.235
## GroupB_Controls:TimeD_M1_FI_total      -0.5991     0.6203 237.0764  -0.966
## GroupC_Intervention:TimeD_M1_FI_total  -0.9938     0.6226 236.9204  -1.596
##                                       Pr(>|t|)    
## (Intercept)                             <2e-16 ***
## GroupB_Controls                          0.809    
## GroupC_Intervention                      0.378    
## TimeD_M1_FI_total                        0.814    
## GroupB_Controls:TimeD_M1_FI_total        0.335    
## GroupC_Intervention:TimeD_M1_FI_total    0.112    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) GrpB_C GrpC_I TD_M1_ GB_C:T
## GrpB_Cntrls -0.824                            
## GrpC_Intrvn -0.820  0.676                     
## TmD_M1_FI_t -0.402  0.332  0.330              
## GB_C:TD_M1_  0.332 -0.403 -0.272 -0.825       
## GC_I:TD_M1_  0.331 -0.273 -0.403 -0.822  0.678
anova  (FI_MEM_B1M)
## Type III Analysis of Variance Table with Satterthwaite's method
##            Sum Sq Mean Sq NumDF  DenDF F value   Pr(>F)   
## Group       1.403   0.702     2 256.73  0.1191 0.887779   
## Time       44.086  44.086     1 236.88  7.4834 0.006698 **
## Group:Time 15.160   7.580     2 236.79  1.2867 0.278109   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
sjPlot::tab_model(FI_MEM_B1M, 
                  pred.labels=c("Intercept", "Psychoeducation Control", "Mindset Intervention", "Time (1 Month)", "Psychoeducation Control x Time","Mindset Intervention x Time"),
                  dv.labels=c("Functional Impairment"),
                  string.std_ci = "std. 95% CI",
                  string.std = "std. Beta",
                  show.std = TRUE,
                  show.est = FALSE)
  Functional Impairment
Predictors std. Beta std. 95% CI p
Intercept 0.01 -0.27 – 0.29 <0.001
Psychoeducation Control 0.04 -0.29 – 0.38 0.809
Mindset Intervention 0.15 -0.19 – 0.49 0.378
Time (1 Month) -0.03 -0.28 – 0.22 0.814
Psychoeducation Control x Time -0.15 -0.45 – 0.15 0.335
Mindset Intervention x Time -0.25 -0.55 – 0.06 0.111
Random Effects
σ2 5.89
τ00 ID 10.48
ICC 0.64
N ID 259
Observations 489
Marginal R2 / Conditional R2 0.012 / 0.644
parameters::standardise_parameters(FI_MEM_B1M)
## # Standardization method: refit
## 
## Parameter                             | Std. Coef. |        95% CI
## ------------------------------------------------------------------
## (Intercept)                           |       0.01 | [-0.27, 0.29]
## GroupB_Controls                       |       0.04 | [-0.29, 0.38]
## GroupC_Intervention                   |       0.15 | [-0.19, 0.49]
## TimeD_M1_FI_total                     |      -0.03 | [-0.28, 0.22]
## GroupB_Controls:TimeD_M1_FI_total     |      -0.15 | [-0.45, 0.15]
## GroupC_Intervention:TimeD_M1_FI_total |      -0.25 | [-0.55, 0.06]