Chapter 6 Week7_1: Lavaan Lab 4 Mediated Moderation & Moderated Mediation
In this lab, we will learn how to:
- Estimate the mediated moderation model
- Estimate the moderated mediation model
- Bootstrap the effects
- Conduct simple slope analyses
6.1 PART 1: Mediated Moderation (Indirect Conditional effect)
6.1.1 Step 1: Read-in Data
Imagine that we extended our CBT study by adding a mediator: the average number of daily negative thoughts reported at the end of six weeks.
The hypothesis we will test is that NegThoughts mediates the CBT*NeedCog -> Depression path
Let’s read this dataset in:
cbtData <- read.csv(file = "dataInClass.csv", header = T, sep = ',')This time we work with the continuous version of the moderator: NeedCogCont.
Let’s examine their means and standard deviations:
apply(cbtData[,-c(1,2)], 2, mean)## CBTDummy NeedCog NegThoughts Depression
## 0.500000000 0.309000000 -1.944249996 -1.589356290
## NeedCogCont
## 0.005925852apply(cbtData[,-c(1,2)], 2, sd)## CBTDummy NeedCog NegThoughts Depression
## 0.5002502 0.4623124 3.1877174 5.6506763
## NeedCogCont
## 0.9974319Why dropping the first two variables?
- The first two variables ID and CBT are not numerical and have no means.
NeedCogCont has been standardized already, which is helpful.
- If not, don’t forget to use scale() function to center the continuous variables.
6.1.2 Step 2: Create the interaction term for Moderation Analysis
To test the moderation effect, we have to manually create a product term in the dataset before running our model:
cbtData$CBTxNeedCogCont <- cbtData$CBTDummy * cbtData$NeedCogContLet’s look at cbtData again:
head(cbtData)## ID CBT CBTDummy NeedCog NegThoughts
## 1 1 CBT Treatment 1 0 -4.1453029
## 2 2 Information Only 0 1 2.1775218
## 3 3 CBT Treatment 1 0 -1.5551349
## 4 4 Information Only 0 0 0.1679286
## 5 5 Information Only 0 1 2.5103192
## 6 6 CBT Treatment 1 0 -3.1626670
## Depression NeedCogCont CBTxNeedCogCont
## 1 -5.802172 0.0182802 0.0182802
## 2 5.496665 1.4238703 0.0000000
## 3 -1.950566 -1.0151726 -1.0151726
## 4 2.655801 -0.8547152 0.0000000
## 5 6.855488 0.6759705 0.0000000
## 6 -2.968198 -0.9123426 -0.91234266.1.3 Step 3: Write the syntax and Fit the model
load the package:
library(lavaan)Follow the two equations to write the model syntax:
ex1MedModerationBasic <- "
# label the coefficients:
NegThoughts ~ a_m1*CBTxNeedCogCont + a_m2*NeedCogCont + a_m3*CBTDummy
Depression ~ b1*CBTDummy + b2*NeedCogCont + b3*CBTxNeedCogCont + bM*NegThoughts
#Define New Parameter Using :=
#Mediated Moderation effect
MedMod_ab := a_m1*bM
TotalMod := MedMod_ab + b3
" Since we included the intercept term, we need to ask sem() to include the meanstructure:
ex1fit <- lavaan::sem(model = ex1MedModerationBasic,
data = cbtData,
fixed.x = FALSE,
meanstructure = TRUE)
summary(ex1fit, ci = T)## lavaan 0.6-12 ended normally after 38 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 20
##
## Number of observations 1000
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## NegThoughts ~
## CBTxNCC (a_m1) -3.071 0.064 -48.104 0.000
## NdCgCnt (a_m2) 2.000 0.044 45.075 0.000
## CBTDmmy (a_m3) -5.060 0.064 -79.562 0.000
## Depression ~
## CBTDmmy (b1) -1.240 0.137 -9.055 0.000
## NdCgCnt (b2) 0.141 0.061 2.292 0.022
## CBTxNCC (b3) -0.109 0.092 -1.180 0.238
## NgThght (bM) 1.582 0.025 62.899 0.000
## ci.lower ci.upper
##
## -3.196 -2.945
## 1.913 2.087
## -5.185 -4.936
##
## -1.509 -0.972
## 0.020 0.261
## -0.290 0.072
## 1.533 1.631
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## CBTxNeedCogCont ~~
## NeedCogCont 0.480 0.027 18.055 0.000
## CBTDummy -0.008 0.011 -0.764 0.445
## NeedCogCont ~~
## CBTDummy -0.020 0.016 -1.249 0.212
## ci.lower ci.upper
##
## 0.428 0.532
## -0.030 0.013
##
## -0.051 0.011
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .NegThoughts 0.523 0.045 11.618 0.000
## .Depression 2.104 0.038 55.199 0.000
## CBTxNeedCogCnt -0.017 0.022 -0.764 0.445
## NeedCogCont 0.006 0.032 0.188 0.851
## CBTDummy 0.500 0.016 31.623 0.000
## ci.lower ci.upper
## 0.434 0.611
## 2.029 2.179
## -0.060 0.026
## -0.056 0.068
## 0.469 0.531
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .NegThoughts 1.010 0.045 22.361 0.000
## .Depression 0.639 0.029 22.361 0.000
## CBTxNeedCogCnt 0.480 0.021 22.361 0.000
## NeedCogCont 0.994 0.044 22.361 0.000
## CBTDummy 0.250 0.011 22.361 0.000
## ci.lower ci.upper
## 0.921 1.098
## 0.583 0.695
## 0.438 0.522
## 0.907 1.081
## 0.228 0.272
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|)
## MedMod_ab -4.858 0.127 -38.211 0.000
## TotalMod -4.967 0.113 -43.943 0.000
## ci.lower ci.upper
## -5.107 -4.609
## -5.188 -4.745Are we done?
6.1.4 Step 4: Bootstrap Version
We need to request Bootstrap because this involves testing a mediation effect MedMod_ab.
Remember to set a seed:
set.seed(2022)
ex1Boot <- lavaan::sem(model = ex1MedModerationBasic,
data = cbtData,
fixed.x = FALSE,
meanstructure = TRUE,
se = "bootstrap",
bootstrap = 1000) - This requires the full dataset - need more than the covariance matrix.
- se = “bootstrap” requests bootstrap standard errors.
- bootstrap = 1000 requests 1000 bootstrap samples.
Request BC confidence interval:
parameterEstimates(ex1Boot,
level = 0.95,
boot.ci.type="bca.simple",
standardized = TRUE)## Warning in norm.inter(t, adj.alpha): extreme order
## statistics used as endpoints## lhs op rhs label est
## 1 NegThoughts ~ CBTxNeedCogCont a_m1 -3.071
## 2 NegThoughts ~ NeedCogCont a_m2 2.000
## 3 NegThoughts ~ CBTDummy a_m3 -5.060
## 4 Depression ~ CBTDummy b1 -1.240
## 5 Depression ~ NeedCogCont b2 0.141
## 6 Depression ~ CBTxNeedCogCont b3 -0.109
## 7 Depression ~ NegThoughts bM 1.582
## 8 NegThoughts ~~ NegThoughts 1.010
## 9 Depression ~~ Depression 0.639
## 10 CBTxNeedCogCont ~~ CBTxNeedCogCont 0.480
## 11 CBTxNeedCogCont ~~ NeedCogCont 0.480
## 12 CBTxNeedCogCont ~~ CBTDummy -0.008
## 13 NeedCogCont ~~ NeedCogCont 0.994
## 14 NeedCogCont ~~ CBTDummy -0.020
## 15 CBTDummy ~~ CBTDummy 0.250
## 16 NegThoughts ~1 0.523
## 17 Depression ~1 2.104
## 18 CBTxNeedCogCont ~1 -0.017
## 19 NeedCogCont ~1 0.006
## 20 CBTDummy ~1 0.500
## 21 MedMod_ab := a_m1*bM MedMod_ab -4.858
## 22 TotalMod := MedMod_ab+b3 TotalMod -4.967
## se z pvalue ci.lower ci.upper std.lv std.all
## 1 0.067 -45.675 0.000 -3.195 -2.922 -3.071 -0.668
## 2 0.048 42.047 0.000 1.902 2.093 2.000 0.626
## 3 0.064 -78.764 0.000 -5.183 -4.930 -5.060 -0.794
## 4 0.133 -9.337 0.000 -1.493 -0.979 -1.240 -0.110
## 5 0.059 2.379 0.017 0.020 0.256 0.141 0.025
## 6 0.088 -1.232 0.218 -0.270 0.071 -0.109 -0.013
## 7 0.024 65.833 0.000 1.539 1.632 1.582 0.892
## 8 0.042 23.885 0.000 0.937 1.109 1.010 0.099
## 9 0.030 21.077 0.000 0.585 0.708 0.639 0.020
## 10 0.034 14.292 0.000 0.411 0.545 0.480 1.000
## 11 0.034 14.314 0.000 0.412 0.545 0.480 0.695
## 12 0.011 -0.781 0.435 -0.030 0.013 -0.008 -0.024
## 13 0.044 22.749 0.000 0.909 1.078 0.994 1.000
## 14 0.016 -1.258 0.208 -0.051 0.013 -0.020 -0.040
## 15 0.000 619.383 0.000 0.250 0.250 0.250 1.000
## 16 0.046 11.401 0.000 0.436 0.616 0.523 0.164
## 17 0.038 54.754 0.000 2.029 2.177 2.104 0.373
## 18 0.021 -0.781 0.435 -0.059 0.026 -0.017 -0.024
## 19 0.031 0.190 0.849 -0.062 0.063 0.006 0.006
## 20 0.016 30.669 0.000 0.466 0.528 0.500 1.000
## 21 0.125 -38.863 0.000 -5.089 -4.602 -4.858 -0.596
## 22 0.118 -42.112 0.000 -5.195 -4.720 -4.967 -0.609
## std.nox
## 1 -0.964
## 2 0.628
## 3 -1.588
## 4 -0.220
## 5 0.025
## 6 -0.019
## 7 0.892
## 8 0.099
## 9 0.020
## 10 0.480
## 11 0.480
## 12 -0.008
## 13 0.994
## 14 -0.020
## 15 0.250
## 16 0.164
## 17 0.373
## 18 -0.017
## 19 0.006
## 20 0.500
## 21 -0.860
## 22 -0.879Warning message:
In norm.inter(t, adj.alpha) : extreme order statistics used as endpoints
https://rcompanion.org/handbook/E_04.html
The BCa (bias corrected, accelerated) is often cited as the best for theoretical reasons. The percentile method is also cited as typically good. However, if you get the “extreme order statistics used as endpoints” warning message, use a different test. For small data sets, the interval from BCa may be wider than for some other methods.
6.1.5 Step 5: Effect size measures
Measure 1: Completely Standardized Indirect Effect (CSIE)
beta_a_m1 = -0.668
beta_bM = 0.892
es1 = beta_a_m1*beta_bM
es1## [1] -0.595856- According to Cohen, .01-.09 is small, .10-.25 is medium, and .25 + is large
- This is a large mediation effect
Measure 2:
- Use unstandardized parameter estimates:
TotalMod = -4.967
MedMod_ab = -4.858
prop = MedMod_ab/TotalMod #97.8%
prop## [1] 0.9780552b3 = -0.109 # pvalue=0.218 # nonsig- Mediated% = indirect effect / total effect = ab / c
- Consistent mediation
- Complete mediation as the remaining direct effect is nonsig and prop > 80%
6.2 PART 2: Moderated Mediation (Conditional Indirect effect)
In this lab, we’ll test this first-stage moderated mediation model in which NeedCog moderates the CBT -> NegThoughts path
6.2.1 Step 1: Product Term
We already have the product term in the dataset:
cbtData$CBTxNeedCogCont <- cbtData$CBTDummy * cbtData$NeedCogContIf NeedCog moderates the NegThoughts -> Depression path, then we center NegThoughts and create a product term between centered NegThoughts*NeedCogCont (making sense?)
6.2.2 Step 2: Write the syntax and Fit the model
ex2ModMediationBasic <- "
NegThoughts ~ a1*CBTDummy + a2*NeedCogCont + a3*CBTxNeedCogCont
Depression ~ b*NegThoughts + cprime*CBTDummy
"We’ll need to define the Index of Moderated Mediation in the syntax:
ex2ModMediation <- "
#Regressions
NegThoughts ~ a1*CBTDummy + a2*NeedCogCont + a3*CBTxNeedCogCont
Depression ~ b*NegThoughts + cprime*CBTDummy
#Index of Moderated Mediation
IndexOfModMed := a3*b
" ex2ModMediationBasic <- "
NegThoughts ~ a1*CBTDummy + a2*NeedCogCont + a3*CBTxNeedCogCont
Depression ~ b*NegThoughts + cprime*CBTDummy
" # NegThoughts ~ CBTDummy:NeedCogCont6.2.3 Step 3: Bootstrap Version
Since this model involves tests of indirect effects
let’s jump to the bootstrap test:
set.seed(2022)
ex2Boot <- lavaan::sem(model = ex2ModMediation,
data = cbtData,
fixed.x = FALSE,
meanstructure = TRUE,
se = "bootstrap",
bootstrap = 1000) You can further request a BC (bias-corrected) by adding an argument boot.ci.type = “bca.simple” to parameterEstimates():
parameterEstimates(ex2Boot,
level = 0.95,
boot.ci.type="bca.simple",
standardized = TRUE)## Warning in norm.inter(t, adj.alpha): extreme order
## statistics used as endpoints## lhs op rhs label est
## 1 NegThoughts ~ CBTDummy a1 -5.060
## 2 NegThoughts ~ NeedCogCont a2 2.000
## 3 NegThoughts ~ CBTxNeedCogCont a3 -3.071
## 4 Depression ~ NegThoughts b 1.617
## 5 Depression ~ CBTDummy cprime -1.066
## 6 NegThoughts ~~ NegThoughts 1.010
## 7 Depression ~~ Depression 0.645
## 8 CBTDummy ~~ CBTDummy 0.250
## 9 CBTDummy ~~ NeedCogCont -0.020
## 10 CBTDummy ~~ CBTxNeedCogCont -0.008
## 11 NeedCogCont ~~ NeedCogCont 0.994
## 12 NeedCogCont ~~ CBTxNeedCogCont 0.480
## 13 CBTxNeedCogCont ~~ CBTxNeedCogCont 0.480
## 14 NegThoughts ~1 0.523
## 15 Depression ~1 2.089
## 16 CBTDummy ~1 0.500
## 17 NeedCogCont ~1 0.006
## 18 CBTxNeedCogCont ~1 -0.017
## 19 IndexOfModMed := a3*b IndexOfModMed -4.967
## se z pvalue ci.lower ci.upper std.lv std.all
## 1 0.064 -78.764 0.000 -5.183 -4.930 -5.060 -0.794
## 2 0.048 42.047 0.000 1.902 2.093 2.000 0.626
## 3 0.067 -45.675 0.000 -3.195 -2.922 -3.071 -0.668
## 4 0.013 124.544 0.000 1.592 1.642 1.617 0.912
## 5 0.084 -12.758 0.000 -1.216 -0.899 -1.066 -0.094
## 6 0.042 23.885 0.000 0.937 1.109 1.010 0.099
## 7 0.031 21.047 0.000 0.592 0.714 0.645 0.020
## 8 0.000 619.383 0.000 0.250 0.250 0.250 1.000
## 9 0.016 -1.258 0.208 -0.051 0.013 -0.020 -0.040
## 10 0.011 -0.781 0.435 -0.030 0.013 -0.008 -0.024
## 11 0.044 22.749 0.000 0.909 1.078 0.994 1.000
## 12 0.034 14.314 0.000 0.412 0.545 0.480 0.695
## 13 0.034 14.292 0.000 0.411 0.545 0.480 1.000
## 14 0.046 11.401 0.000 0.436 0.616 0.523 0.164
## 15 0.037 56.930 0.000 2.021 2.160 2.089 0.370
## 16 0.016 30.669 0.000 0.468 0.531 0.500 1.000
## 17 0.031 0.190 0.849 -0.062 0.063 0.006 0.006
## 18 0.021 -0.781 0.435 -0.059 0.026 -0.017 -0.024
## 19 0.114 -43.431 0.000 -5.180 -4.727 -4.967 -0.609
## std.nox
## 1 -1.588
## 2 0.628
## 3 -0.964
## 4 0.912
## 5 -0.189
## 6 0.099
## 7 0.020
## 8 0.250
## 9 -0.020
## 10 -0.008
## 11 0.994
## 12 0.480
## 13 0.480
## 14 0.164
## 15 0.370
## 16 0.500
## 17 0.006
## 18 -0.017
## 19 -0.879Defined Parameters:
Estimate Std.Err ci.lower ci.upper std.all
IndexOfModMed -4.967 0.114 -5.180 -4.727 -0.609NeedCogCont significantly moderates CBT -> NegThoughts -> Depression indirect effect through moderating the first stage of the indirect effect
- Since we expect the effect of CBT on Depression to be negative (CBT reduces Depression)
- And IndexOfModMed is also negative
- We’ll say NeedCogCont strengthens the indirect effect of CBT on Depression through NegThoughts
- The higher need for cognition, the stronger the indirect effect, and the more effect mediated by NegThoughts
6.2.4 Step 4: Simple Slopes
As a follow-up analysis to a significant moderation effect, we conduct simple slope anlaysis:
Let’s use pick-a-point (Rogosa, 1980) and plot the indirect effects at designated levels of NeedCogCont:
mean(cbtData$NeedCogCont) #0## [1] 0.005925852sd(cbtData$NeedCogCont) # 1## [1] 0.9974319Three representative levels:
mean(cbtData$NeedCogCont) - sd(cbtData$NeedCogCont) # -1## [1] -0.991506mean(cbtData$NeedCogCont) #0## [1] 0.005925852mean(cbtData$NeedCogCont) + sd(cbtData$NeedCogCont) # 1## [1] 1.003358let’s define the Conditional Indirect Effects in the syntax:
ex3ModMediation <- "
#Regressions
NegThoughts ~ a1*CBTDummy + a2*NeedCogCont + a3*CBTxNeedCogCont
Depression ~ b*NegThoughts + cprime*CBTDummy
#Index of Moderated Mediation
IndexOfModMed := a3*b
#Simple Slopes
aSSLow := a1+a3*(-1)
aSSMean := a1+a3*0
aSSHigh := a1+a3*1
#Conditional Indirect Effects
abLow := aSSLow*b
abMean := aSSMean*b
abHigh := aSSHigh*b
" set.seed(2022)
ex3Boot <- lavaan::sem(model = ex3ModMediation,
data = cbtData,
se = "bootstrap",
bootstrap = 1000,
fixed.x=FALSE,
meanstructure = TRUE) parameterEstimates(ex3Boot,
level = 0.95,
boot.ci.type="bca.simple",
standardized = TRUE)## Warning in norm.inter(t, adj.alpha): extreme order
## statistics used as endpoints## lhs op rhs label
## 1 NegThoughts ~ CBTDummy a1
## 2 NegThoughts ~ NeedCogCont a2
## 3 NegThoughts ~ CBTxNeedCogCont a3
## 4 Depression ~ NegThoughts b
## 5 Depression ~ CBTDummy cprime
## 6 NegThoughts ~~ NegThoughts
## 7 Depression ~~ Depression
## 8 CBTDummy ~~ CBTDummy
## 9 CBTDummy ~~ NeedCogCont
## 10 CBTDummy ~~ CBTxNeedCogCont
## 11 NeedCogCont ~~ NeedCogCont
## 12 NeedCogCont ~~ CBTxNeedCogCont
## 13 CBTxNeedCogCont ~~ CBTxNeedCogCont
## 14 NegThoughts ~1
## 15 Depression ~1
## 16 CBTDummy ~1
## 17 NeedCogCont ~1
## 18 CBTxNeedCogCont ~1
## 19 IndexOfModMed := a3*b IndexOfModMed
## 20 aSSLow := a1+a3*(-1) aSSLow
## 21 aSSMean := a1+a3*0 aSSMean
## 22 aSSHigh := a1+a3*1 aSSHigh
## 23 abLow := aSSLow*b abLow
## 24 abMean := aSSMean*b abMean
## 25 abHigh := aSSHigh*b abHigh
## est se z pvalue ci.lower ci.upper std.lv
## 1 -5.060 0.064 -78.764 0.000 -5.183 -4.930 -5.060
## 2 2.000 0.048 42.047 0.000 1.902 2.093 2.000
## 3 -3.071 0.067 -45.675 0.000 -3.195 -2.922 -3.071
## 4 1.617 0.013 124.544 0.000 1.592 1.642 1.617
## 5 -1.066 0.084 -12.758 0.000 -1.216 -0.899 -1.066
## 6 1.010 0.042 23.885 0.000 0.937 1.109 1.010
## 7 0.645 0.031 21.047 0.000 0.592 0.714 0.645
## 8 0.250 0.000 619.383 0.000 0.250 0.250 0.250
## 9 -0.020 0.016 -1.258 0.208 -0.051 0.013 -0.020
## 10 -0.008 0.011 -0.781 0.435 -0.030 0.013 -0.008
## 11 0.994 0.044 22.749 0.000 0.909 1.078 0.994
## 12 0.480 0.034 14.314 0.000 0.412 0.545 0.480
## 13 0.480 0.034 14.292 0.000 0.411 0.545 0.480
## 14 0.523 0.046 11.401 0.000 0.436 0.616 0.523
## 15 2.089 0.037 56.930 0.000 2.021 2.160 2.089
## 16 0.500 0.016 30.669 0.000 0.468 0.531 0.500
## 17 0.006 0.031 0.190 0.849 -0.062 0.063 0.006
## 18 -0.017 0.021 -0.781 0.435 -0.059 0.026 -0.017
## 19 -4.967 0.114 -43.431 0.000 -5.180 -4.727 -4.967
## 20 -1.990 0.092 -21.679 0.000 -2.176 -1.813 -1.990
## 21 -5.060 0.064 -78.724 0.000 -5.183 -4.930 -5.060
## 22 -8.131 0.094 -86.243 0.000 -8.313 -7.942 -8.131
## 23 -3.218 0.151 -21.338 0.000 -3.532 -2.941 -3.218
## 24 -8.185 0.121 -67.625 0.000 -8.433 -7.944 -8.185
## 25 -13.152 0.181 -72.721 0.000 -13.513 -12.779 -13.152
## std.all std.nox
## 1 -0.794 -1.588
## 2 0.626 0.628
## 3 -0.668 -0.964
## 4 0.912 0.912
## 5 -0.094 -0.189
## 6 0.099 0.099
## 7 0.020 0.020
## 8 1.000 0.250
## 9 -0.040 -0.020
## 10 -0.024 -0.008
## 11 1.000 0.994
## 12 0.695 0.480
## 13 1.000 0.480
## 14 0.164 0.164
## 15 0.370 0.370
## 16 1.000 0.500
## 17 0.006 0.006
## 18 -0.024 -0.017
## 19 -0.609 -0.879
## 20 -0.126 -0.624
## 21 -0.794 -1.588
## 22 -1.462 -2.552
## 23 -0.115 -0.570
## 24 -0.725 -1.449
## 25 -1.334 -2.329Defined Parameters:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper std.all
IndexOfModMed -4.967 0.114 -43.431 0.000 -5.180 -4.727 -0.609
aSSLow -1.990 0.092 -21.679 0.000 -2.176 -1.813 -0.126
aSSMean -5.060 0.064 -78.724 0.000 -5.183 -4.930 -0.794
aSSHigh -8.131 0.094 -86.243 0.000 -8.313 -7.942 -1.462
abLow -3.218 0.151 -21.338 0.000 -3.532 -2.941 -0.115
abMean -8.185 0.121 -67.625 0.000 -8.433 -7.944 -0.725
abHigh -13.152 0.181 -72.721 0.000 -13.513 -12.779 -1.334
b 1.617 0.013 124.544 0.000 1.592 1.642 0.912
cprime -1.066 0.084 -12.758 0.000 -1.216 -0.899 -0.094 What does a1 tell you?
What does a2 tell you?
What does a3 tell you?
What does IndexOfModMed tell you?
What does aSSLow tell you?
What does aSSMean tell you?
What does aSSHigh tell you?
What does b tell you?
What does abLow tell you?
What does abMean tell you?
What does abHigh tell you?
What does cprime tell you?
the simple slopes of CBT -> NegThoughts (a path) are all negative at three levels of the moderator
the indirect effects of CBT -> NegThoughts -> Depression (ab) are all negative at three levels of the moderator
6.2.5 Step 5 JOHNSON-NEYMAN INTERVAL
Although johnson_neyman() does not work on lavaan fitted object (yet), one can use a try-and-error approach to figure out the region of significance:
First, obtain the minimum and maximum of the moderator NeedCogCont:
min(cbtData$NeedCogCont) # -2.83## [1] -2.829197max(cbtData$NeedCogCont) # 3.31## [1] 3.310095ex4_JN <- "
#Regressions
NegThoughts ~ a1*CBTDummy + a2*NeedCogCont + a3*CBTxNeedCogCont
Depression ~ b*NegThoughts + cprime*CBTDummy
#Index of Moderated Mediation
IndexOfModMed := a3*b
#Simple Slopes
aSSMin := a1+a3*(-2.83)
aSSMin1 := a1+a3*(-1.75)
aSSMin2 := a1+a3*(-1.74)
aSSMin3 := a1+a3*(-1.58)
aSSMin4 := a1+a3*(-1.57)
aSSLow := a1+a3*(-1)
aSSMean := a1+a3*0
aSSHigh := a1+a3*1
aSSMax := a1+a3*(3.31)
#Conditional Indirect Effects
abMin := (a1+a3*(-2.83))*b
abMin1 := (a1+a3*(-1.75))*b # cutoff1
abMin2 := (a1+a3*(-1.74))*b
abMin3 := (a1+a3*(-1.58))*b
abMin4 := (a1+a3*(-1.57))*b # cutoff2
abLow := aSSLow*b
abMean := aSSMean*b
abHigh := aSSHigh*b
abMax := (a1+a3*(3.31))*b
" set.seed(2022)
ex4Boot <- lavaan::sem(model = ex4_JN,
data = cbtData,
se = "bootstrap",
bootstrap = 1000,
fixed.x=FALSE,
meanstructure = TRUE) parameterEstimates(ex4Boot,
level = 0.95,
boot.ci.type="bca.simple")## Warning in norm.inter(t, adj.alpha): extreme order
## statistics used as endpoints## lhs op rhs label
## 1 NegThoughts ~ CBTDummy a1
## 2 NegThoughts ~ NeedCogCont a2
## 3 NegThoughts ~ CBTxNeedCogCont a3
## 4 Depression ~ NegThoughts b
## 5 Depression ~ CBTDummy cprime
## 6 NegThoughts ~~ NegThoughts
## 7 Depression ~~ Depression
## 8 CBTDummy ~~ CBTDummy
## 9 CBTDummy ~~ NeedCogCont
## 10 CBTDummy ~~ CBTxNeedCogCont
## 11 NeedCogCont ~~ NeedCogCont
## 12 NeedCogCont ~~ CBTxNeedCogCont
## 13 CBTxNeedCogCont ~~ CBTxNeedCogCont
## 14 NegThoughts ~1
## 15 Depression ~1
## 16 CBTDummy ~1
## 17 NeedCogCont ~1
## 18 CBTxNeedCogCont ~1
## 19 IndexOfModMed := a3*b IndexOfModMed
## 20 aSSMin := a1+a3*(-2.83) aSSMin
## 21 aSSMin1 := a1+a3*(-1.75) aSSMin1
## 22 aSSMin2 := a1+a3*(-1.74) aSSMin2
## 23 aSSMin3 := a1+a3*(-1.58) aSSMin3
## 24 aSSMin4 := a1+a3*(-1.57) aSSMin4
## 25 aSSLow := a1+a3*(-1) aSSLow
## 26 aSSMean := a1+a3*0 aSSMean
## 27 aSSHigh := a1+a3*1 aSSHigh
## 28 aSSMax := a1+a3*(3.31) aSSMax
## 29 abMin := (a1+a3*(-2.83))*b abMin
## 30 abMin1 := (a1+a3*(-1.75))*b abMin1
## 31 abMin2 := (a1+a3*(-1.74))*b abMin2
## 32 abMin3 := (a1+a3*(-1.58))*b abMin3
## 33 abMin4 := (a1+a3*(-1.57))*b abMin4
## 34 abLow := aSSLow*b abLow
## 35 abMean := aSSMean*b abMean
## 36 abHigh := aSSHigh*b abHigh
## 37 abMax := (a1+a3*(3.31))*b abMax
## est se z pvalue ci.lower ci.upper
## 1 -5.060 0.064 -78.764 0.000 -5.183 -4.930
## 2 2.000 0.048 42.047 0.000 1.902 2.093
## 3 -3.071 0.067 -45.675 0.000 -3.195 -2.922
## 4 1.617 0.013 124.544 0.000 1.592 1.642
## 5 -1.066 0.084 -12.758 0.000 -1.216 -0.899
## 6 1.010 0.042 23.885 0.000 0.937 1.109
## 7 0.645 0.031 21.047 0.000 0.592 0.714
## 8 0.250 0.000 619.383 0.000 0.250 0.250
## 9 -0.020 0.016 -1.258 0.208 -0.051 0.013
## 10 -0.008 0.011 -0.781 0.435 -0.030 0.013
## 11 0.994 0.044 22.749 0.000 0.909 1.078
## 12 0.480 0.034 14.314 0.000 0.412 0.545
## 13 0.480 0.034 14.292 0.000 0.411 0.545
## 14 0.523 0.046 11.401 0.000 0.436 0.616
## 15 2.089 0.037 56.930 0.000 2.021 2.160
## 16 0.500 0.016 30.669 0.000 0.468 0.531
## 17 0.006 0.031 0.190 0.849 -0.062 0.063
## 18 -0.017 0.021 -0.781 0.435 -0.059 0.026
## 19 -4.967 0.114 -43.431 0.000 -5.180 -4.727
## 20 3.630 0.199 18.215 0.000 3.204 4.011
## 21 0.313 0.133 2.363 0.018 0.029 0.562
## 22 0.283 0.132 2.141 0.032 0.000 0.530
## 23 -0.209 0.123 -1.701 0.089 -0.471 0.018
## 24 -0.239 0.122 -1.960 0.050 -0.500 -0.013
## 25 -1.990 0.092 -21.679 0.000 -2.176 -1.813
## 26 -5.060 0.064 -78.724 0.000 -5.183 -4.930
## 27 -8.131 0.094 -86.243 0.000 -8.313 -7.942
## 28 -15.224 0.233 -65.232 0.000 -15.658 -14.751
## 29 5.871 0.324 18.092 0.000 5.185 6.487
## 30 0.507 0.214 2.363 0.018 0.047 0.904
## 31 0.457 0.213 2.141 0.032 -0.001 0.853
## 32 -0.338 0.199 -1.700 0.089 -0.759 0.030
## 33 -0.387 0.198 -1.959 0.050 -0.807 -0.020
## 34 -3.218 0.151 -21.338 0.000 -3.532 -2.941
## 35 -8.185 0.121 -67.625 0.000 -8.433 -7.944
## 36 -13.152 0.181 -72.721 0.000 -13.513 -12.779
## 37 -24.624 0.418 -58.964 0.000 -25.391 -23.738So our regions of significance are:
- \([-2.83, -1.75]\): In which the ab are positive and significant. Participants with this level of NeegCog experienced elevated levels of depression due to CBT because CBT induces more negative thoughts among them.
- \((-1.75, -1.57)\): In which the ab are NOT significant.
- \([-1.57, 3.31]\): In which the ab are negative and significant. Participants with this level of NeegCog experienced reduced levels of depression due to CBT because CBT reduced negative thoughts for them.