EPSY 906/CLDP 948 Example 9: Path Analysis for Mediation
Path Analysis for Mediation
if (!require(lavaan)) install.packages("lavaan")
library(lavaan)A sample of 653 undergraduates completed the six measures depicted in Figure 1 (residual covariances among the mediators are not shown for diagram clarity). Table 3 shows the correlations of the six variables by gender.
The research questions were as follows: (1) To what extent do these four mediators account for the relationship between mindfulness and warmth towards feminists? (2) How do these direct and indirect effects differ by gender?
Accordingly, we will begin with a single-group model, and then examine a multiple-group model in which all parameters are estimated separately for men and women. From there, one would proceed by constraining specific direct and indirect effects to be equal across genders and note the decrease in model fit in doing so.
Figure 1 from: Gervais, S. J. & Hoffman, L. (2013). Just think about it: Mindfulness, sexism, and prejudice towards feminists. Sex Roles, 68(5), 283-295.
Table 3 from: Gervais, S. J. & Hoffman, L. (2013). Just think about it: Mindfulness, sexism, and prejudice towards feminists. Sex Roles, 68(5), 283-295.
mindData = read.csv(file = "Mindfull_Example.csv", col.names = c("in1", "SexMW", "age", "Mind1",
"Mind2", "Hostile", "Benev",
"Intern", "Extern", "NonTrado",
"Career", "Fem", "WomMov"), na.strings = "-999")
#Center mindfulness at 2 (out of 1 to 4)
mindData$Mind1C = mindData$Mind1-2
#Mean of feminists and womens' movement
mindData$NonTrad = (mindData$Fem + mindData$WomMov)/2
#label sex variable
mindData$sex = NA_character_
mindData$sex[which(mindData$SexMW == 0)] = "Male"
mindData$sex[which(mindData$SexMW == 1)] = "Female"Single-Group Path Model
Note that H0=H1, meaning that the model is just-identified (and thus fits perfectly).
singleGroupSyntax = "
#intercept and variance labels
Mind1C ~ (Xint)*1; Mind1C ~~ (Xvar)*Mind1C;
Intern ~ (M1int)*1; Intern ~~ (M1var)*Intern;
Extern ~ (M2int)*1; Extern ~~ (M2var)*Extern;
Hostile ~ (M3int)*1; Hostile ~~ (M3var)*Hostile;
Benev ~ (M4int)*1; Benev ~~ (M4var)*Benev;
NonTrad ~ (Yint)*1; NonTrad ~~ (Yvar)*NonTrad;
#Left side of model
Intern ~ (XtoM1)*Mind1C
Extern ~ (XtoM2)*Mind1C
Hostile ~ (XtoM3)*Mind1C
Benev ~ (XtoM4)*Mind1C
#All predictors of right-hand side
NonTrad ~ (XtoY)*Mind1C + (M1toY)*Intern + (M2toY)*Extern + (M3toY)*Hostile + (M4toY)*Benev
#Residual Covariances
Intern ~~ (Cov1)*Extern + (Cov2)*Hostile + (Cov3)*Benev
Extern ~~ (Cov4)*Hostile + (Cov5)*Benev
Hostile ~~ (Cov6)*Benev
#Indirect effects:
XtoM1toY := XtoM1*M1toY
XtoM2toY := XtoM2*M2toY
XtoM3toY := XtoM3*M3toY
XtoM4toY := XtoM4*M4toY
totalXtoY := XtoM1*M1toY + XtoM2*M2toY + XtoM3*M3toY + XtoM4*M4toY + XtoY
"
singleGroupEstimates = lavaan(model = singleGroupSyntax, data = mindData, estimator = "MLR", mimic = "mplus")
summary(singleGroupEstimates, fit.measures = TRUE, rsquare = TRUE, standardized = TRUE)lavaan (0.5-23.1097) converged normally after 56 iterations
Number of observations 652
Number of missing patterns 3
Estimator ML Robust
Minimum Function Test Statistic 0.000 0.000
Degrees of freedom 0 0
Minimum Function Value 0.0000000000000
Scaling correction factor NA
for the Yuan-Bentler correction (Mplus variant)
Model test baseline model:
Minimum Function Test Statistic 439.497 395.635
Degrees of freedom 15 15
P-value 0.000 0.000
User model versus baseline model:
Comparative Fit Index (CFI) 1.000 1.000
Tucker-Lewis Index (TLI) 1.000 1.000
Robust Comparative Fit Index (CFI) NA
Robust Tucker-Lewis Index (TLI) NA
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5402.398 -5402.398
Loglikelihood unrestricted model (H1) -5402.398 -5402.398
Number of free parameters 27 27
Akaike (AIC) 10858.795 10858.795
Bayesian (BIC) 10979.756 10979.756
Sample-size adjusted Bayesian (BIC) 10894.032 10894.032
Root Mean Square Error of Approximation:
RMSEA 0.000 0.000
90 Percent Confidence Interval 0.000 0.000 0.000 0.000
P-value RMSEA <= 0.05 NA NA
Robust RMSEA 0.000
90 Percent Confidence Interval 0.000 0.000
Standardized Root Mean Square Residual:
SRMR 0.000 0.000
Parameter Estimates:
Information Observed
Standard Errors Robust.huber.white
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Intern ~
Mind1C (XtM1) 0.332 0.120 2.759 0.006 0.332 0.111
Extern ~
Mind1C (XtM2) 0.042 0.105 0.394 0.694 0.042 0.015
Hostile ~
Mind1C (XtM3) -0.195 0.071 -2.734 0.006 -0.195 -0.102
Benev ~
Mind1C (XtM4) -0.050 0.065 -0.764 0.445 -0.050 -0.028
NonTrad ~
Mind1C (XtoY) -0.009 0.213 -0.043 0.966 -0.009 -0.002
Intern (M1tY) 0.567 0.075 7.529 0.000 0.567 0.309
Extern (M2tY) 0.057 0.074 0.761 0.447 0.057 0.028
Hostile (M3tY) -0.812 0.111 -7.334 0.000 -0.812 -0.282
Benev (M4tY) -0.220 0.110 -1.993 0.046 -0.220 -0.071
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Intern ~~
.Extern (Cov1) 0.603 0.077 7.855 0.000 0.603 0.377
.Hostile (Cov2) -0.373 0.053 -7.103 0.000 -0.373 -0.338
.Benev (Cov3) -0.003 0.045 -0.074 0.941 -0.003 -0.003
.Extern ~~
.Hostile (Cov4) 0.036 0.045 0.813 0.416 0.036 0.036
.Benev (Cov5) 0.147 0.043 3.389 0.001 0.147 0.153
.Hostile ~~
.Benev (Cov6) 0.111 0.031 3.616 0.000 0.111 0.168
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Mind1C (Xint) 0.834 0.017 48.182 0.000 0.834 1.887
.Intern (M1nt) 4.971 0.115 43.281 0.000 4.971 3.759
.Extern (M2nt) 4.063 0.100 40.820 0.000 4.063 3.340
.Hostile (M3nt) 4.069 0.067 60.995 0.000 4.069 4.824
.Benev (M4nt) 4.109 0.059 69.504 0.000 4.109 5.211
.NonTrad (Yint) 7.471 0.846 8.835 0.000 7.471 3.078
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Mind1C (Xvar) 0.195 0.012 16.396 0.000 0.195 1.000
.Intern (M1vr) 1.727 0.087 19.873 0.000 1.727 0.988
.Extern (M2vr) 1.480 0.081 18.160 0.000 1.480 1.000
.Hostile (M3vr) 0.704 0.047 14.996 0.000 0.704 0.990
.Benev (M4vr) 0.621 0.038 16.337 0.000 0.621 0.999
.NonTrad (Yvar) 4.399 0.248 17.765 0.000 4.399 0.747
R-Square:
Estimate
Intern 0.012
Extern 0.000
Hostile 0.010
Benev 0.001
NonTrad 0.253
Defined Parameters:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
XtoM1toY 0.188 0.073 2.590 0.010 0.188 0.034
XtoM2toY 0.002 0.007 0.345 0.730 0.002 0.000
XtoM3toY 0.158 0.062 2.567 0.010 0.158 0.029
XtoM4toY 0.011 0.016 0.692 0.489 0.011 0.002
totalXtoY 0.351 0.236 1.489 0.137 0.351 0.064To show how bootstrap confidence intervals are found, we use the following syntax:
summary(singleGroupEstimatesBootstrap, fit.measures = TRUE, rsquare = TRUE, standardized = TRUE)
lavaan (0.5-23.1097) converged normally after 56 iterations
Number of observations 652
Number of missing patterns 3
Estimator ML
Minimum Function Test Statistic 0.000
Degrees of freedom 0
Minimum Function Value 0.0000000000000
Model test baseline model:
Minimum Function Test Statistic 439.497
Degrees of freedom 15
P-value 0.000
User model versus baseline model:
Comparative Fit Index (CFI) 1.000
Tucker-Lewis Index (TLI) 1.000
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5402.398
Loglikelihood unrestricted model (H1) -5402.398
Number of free parameters 27
Akaike (AIC) 10858.795
Bayesian (BIC) 10979.756
Sample-size adjusted Bayesian (BIC) 10894.032
Root Mean Square Error of Approximation:
RMSEA 0.000
90 Percent Confidence Interval 0.000 0.000
P-value RMSEA <= 0.05 NA
Standardized Root Mean Square Residual:
SRMR 0.000
Parameter Estimates:
Information Observed
Standard Errors Bootstrap
Number of requested bootstrap draws 1000
Number of successful bootstrap draws 997
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Intern ~
Mind1C (XtM1) 0.332 0.123 2.712 0.007 0.332 0.111
Extern ~
Mind1C (XtM2) 0.042 0.105 0.396 0.692 0.042 0.015
Hostile ~
Mind1C (XtM3) -0.195 0.070 -2.786 0.005 -0.195 -0.102
Benev ~
Mind1C (XtM4) -0.050 0.067 -0.738 0.460 -0.050 -0.028
NonTrad ~
Mind1C (XtoY) -0.009 0.210 -0.043 0.965 -0.009 -0.002
Intern (M1tY) 0.567 0.077 7.378 0.000 0.567 0.309
Extern (M2tY) 0.057 0.074 0.765 0.444 0.057 0.028
Hostile (M3tY) -0.812 0.113 -7.209 0.000 -0.812 -0.282
Benev (M4tY) -0.220 0.107 -2.061 0.039 -0.220 -0.071
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Intern ~~
.Extern (Cov1) 0.603 0.074 8.137 0.000 0.603 0.377
.Hostile (Cov2) -0.373 0.054 -6.879 0.000 -0.373 -0.338
.Benev (Cov3) -0.003 0.045 -0.074 0.941 -0.003 -0.003
.Extern ~~
.Hostile (Cov4) 0.036 0.044 0.819 0.413 0.036 0.036
.Benev (Cov5) 0.147 0.043 3.434 0.001 0.147 0.153
.Hostile ~~
.Benev (Cov6) 0.111 0.031 3.549 0.000 0.111 0.168
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Mind1C (Xint) 0.834 0.017 50.172 0.000 0.834 1.887
.Intern (M1nt) 4.971 0.115 43.231 0.000 4.971 3.759
.Extern (M2nt) 4.063 0.099 41.134 0.000 4.063 3.340
.Hostile (M3nt) 4.069 0.066 61.954 0.000 4.069 4.824
.Benev (M4nt) 4.109 0.060 68.020 0.000 4.109 5.211
.NonTrad (Yint) 7.471 0.841 8.881 0.000 7.471 3.078
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Mind1C (Xvar) 0.195 0.012 16.335 0.000 0.195 1.000
.Intern (M1vr) 1.727 0.086 20.020 0.000 1.727 0.988
.Extern (M2vr) 1.480 0.079 18.806 0.000 1.480 1.000
.Hostile (M3vr) 0.704 0.047 14.960 0.000 0.704 0.990
.Benev (M4vr) 0.621 0.037 16.569 0.000 0.621 0.999
.NonTrad (Yvar) 4.399 0.245 17.975 0.000 4.399 0.747
R-Square:
Estimate
Intern 0.012
Extern 0.000
Hostile 0.010
Benev 0.001
NonTrad 0.253
Defined Parameters:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
XtoM1toY 0.188 0.074 2.540 0.011 0.188 0.034
XtoM2toY 0.002 0.010 0.226 0.821 0.002 0.000
XtoM3toY 0.158 0.061 2.584 0.010 0.158 0.029
XtoM4toY 0.011 0.018 0.616 0.538 0.011 0.002
totalXtoY 0.351 0.230 1.522 0.128 0.351 0.064Multiple-Group Path Model (all parameters estimated separately by gender)
multiGroupSyntax = "
#intercept and variance labels
Mind1C ~ c(fXint, mXint)*1; Mind1C ~~ c(fXvar, mXvar)*Mind1C;
Intern ~ c(fM1int, mM1int)*1; Intern ~~ c(fM1var, mM1var)*Intern;
Extern ~ c(fM2int, mM2int)*1; Extern ~~ c(fM2var, mM2var)*Extern;
Hostile ~ c(fM3int, mM3int)*1; Hostile ~~ c(fM3var, mM3var)*Hostile;
Benev ~ c(fM4int, mM4int)*1; Benev ~~ c(fM4var, mM4var)*Benev;
NonTrad ~ c(fYint, mYint)*1; NonTrad ~~ c(fYvar, mYvar)*NonTrad;
#Left side of model
Intern ~ c(fXtoM1, mXtoM1)*Mind1C
Extern ~ c(fXtoM2, mXtoM2)*Mind1C
Hostile ~ c(fXtoM3, mXtoM3)*Mind1C
Benev ~ c(fXtoM4, mXtoM4)*Mind1C
#All predictors of right-hand side
NonTrad ~ c(fXtoY, mXtoY)*Mind1C + c(fM1toY, mM1toY)*Intern +
c(fM2toY, mM2toY)*Extern + c(fM3toY, mM3toY)*Hostile +
c(fM4toY, mM4toY)*Benev
#Residual Covariances
Intern ~~ c(fCov1, mCov1)*Extern + c(fCov2, mCov2)*Hostile + c(fCov3, mCov3)*Benev
Extern ~~ c(fCov4, mCov4)*Hostile + c(fCov5, mCov5)*Benev
Hostile ~~ c(fCov6, mCov6)*Benev
#Indirect effects:
fXtoM1toY := fXtoM1*fM1toY
fXtoM2toY := fXtoM2*fM2toY
fXtoM3toY := fXtoM3*fM3toY
fXtoM4toY := fXtoM4*fM4toY
mXtoM1toY := mXtoM1*mM1toY
mXtoM2toY := mXtoM2*mM2toY
mXtoM3toY := mXtoM3*mM3toY
mXtoM4toY := mXtoM4*mM4toY
#Differences in direct effect paths
dXtoM1 := mXtoM1 - fXtoM1
dXtoM2 := mXtoM2 - fXtoM2
dXtoM3 := mXtoM3 - fXtoM3
dXtoM4 := mXtoM4 - fXtoM4
dM1toY := mM1toY - fM1toY
dM2toY := mM2toY - fM2toY
dM3toY := mM3toY - fM3toY
dM4toY := mM4toY - fM4toY
"
multiGroupEstimates = lavaan(model = multiGroupSyntax, data = mindData, estimator = "MLR", mimic = "mplus", group = "sex")
summary(multiGroupEstimates, fit.measures = TRUE, rsquare = TRUE, standardized = TRUE)lavaan (0.5-23.1097) converged normally after 97 iterations
Number of observations per group
Female 380
Male 272
Number of missing patterns per group
Female 3
Male 3
Estimator ML Robust
Minimum Function Test Statistic 0.000 0.000
Degrees of freedom 0 0
Minimum Function Value 0.0000000000000
Scaling correction factor NA
for the Yuan-Bentler correction (Mplus variant)
Chi-square for each group:
Female 0.000 0.000
Male 0.000 0.000
Model test baseline model:
Minimum Function Test Statistic 398.511 362.153
Degrees of freedom 30 30
P-value 0.000 0.000
User model versus baseline model:
Comparative Fit Index (CFI) 1.000 1.000
Tucker-Lewis Index (TLI) 1.000 1.000
Robust Comparative Fit Index (CFI) NA
Robust Tucker-Lewis Index (TLI) NA
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5323.242 -5323.242
Loglikelihood unrestricted model (H1) -5323.242 -5323.242
Number of free parameters 54 54
Akaike (AIC) 10754.485 10754.485
Bayesian (BIC) 10996.407 10996.407
Sample-size adjusted Bayesian (BIC) 10824.957 10824.957
Root Mean Square Error of Approximation:
RMSEA 0.000 0.000
90 Percent Confidence Interval 0.000 0.000 0.000 0.000
P-value RMSEA <= 0.05 NA NA
Robust RMSEA 0.000
90 Percent Confidence Interval 0.000 0.000
Standardized Root Mean Square Residual:
SRMR 0.000 0.000
Parameter Estimates:
Information Observed
Standard Errors Robust.huber.white
Group 1 [Female]:
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Intern ~
Mind1C (fXM1) 0.099 0.146 0.676 0.499 0.099 0.036
Extern ~
Mind1C (fXM2) -0.117 0.133 -0.874 0.382 -0.117 -0.044
Hostile ~
Mind1C (fXM3) -0.181 0.081 -2.250 0.024 -0.181 -0.109
Benev ~
Mind1C (fXM4) 0.138 0.079 1.762 0.078 0.138 0.081
NonTrad ~
Mind1C (fXtY) -0.126 0.254 -0.498 0.618 -0.126 -0.026
Intern (fM1Y) 0.449 0.105 4.264 0.000 0.449 0.247
Extern (fM2Y) 0.084 0.099 0.841 0.401 0.084 0.045
Hostile (fM3Y) -0.535 0.161 -3.328 0.001 -0.535 -0.180
Benev (fM4Y) -0.159 0.151 -1.054 0.292 -0.159 -0.055
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Intern ~~
.Extern (fCv1) 0.556 0.085 6.556 0.000 0.556 0.383
.Hostile (fCv2) -0.184 0.047 -3.900 0.000 -0.184 -0.205
.Benev (fCv3) -0.012 0.050 -0.233 0.816 -0.012 -0.013
.Extern ~~
.Hostile (fCv4) 0.023 0.044 0.522 0.602 0.023 0.026
.Benev (fCv5) 0.157 0.052 3.000 0.003 0.157 0.171
.Hostile ~~
.Benev (fCv6) 0.118 0.032 3.656 0.000 0.118 0.210
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Mind1C (fXnt) 0.847 0.023 36.886 0.000 0.847 1.892
.Intern (fM1n) 5.414 0.138 39.269 0.000 5.414 4.457
.Extern (fM2n) 4.200 0.125 33.482 0.000 4.200 3.504
.Hostile (fM3n) 3.853 0.077 50.063 0.000 3.853 5.185
.Benev (fM4n) 3.848 0.074 51.657 0.000 3.848 5.025
.NonTrad (fYnt) 7.172 1.081 6.633 0.000 7.172 3.256
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Mind1C (fXvr) 0.200 0.015 13.042 0.000 0.200 1.000
.Intern (fM1v) 1.473 0.089 16.634 0.000 1.473 0.999
.Extern (fM2v) 1.433 0.105 13.603 0.000 1.433 0.998
.Hostile (fM3v) 0.545 0.043 12.743 0.000 0.545 0.988
.Benev (fM4v) 0.583 0.046 12.659 0.000 0.583 0.993
.NonTrad (fYvr) 4.230 0.303 13.972 0.000 4.230 0.872
R-Square:
Estimate
Intern 0.001
Extern 0.002
Hostile 0.012
Benev 0.007
NonTrad 0.128
Group 2 [Male]:
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Intern ~
Mind1C (mXM1) 0.624 0.199 3.131 0.002 0.624 0.195
Extern ~
Mind1C (mXM2) 0.274 0.166 1.651 0.099 0.274 0.095
Hostile ~
Mind1C (mXM3) -0.167 0.126 -1.321 0.186 -0.167 -0.081
Benev ~
Mind1C (mXM4) -0.307 0.111 -2.768 0.006 -0.307 -0.167
NonTrad ~
Mind1C (mXtY) 0.212 0.364 0.582 0.561 0.212 0.038
Intern (mM1Y) 0.557 0.107 5.184 0.000 0.557 0.319
Extern (mM2Y) 0.045 0.110 0.408 0.683 0.045 0.023
Hostile (mM3Y) -0.847 0.155 -5.460 0.000 -0.847 -0.311
Benev (mM4Y) -0.175 0.170 -1.026 0.305 -0.175 -0.058
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Intern ~~
.Extern (mCv1) 0.643 0.132 4.870 0.000 0.643 0.383
.Hostile (mCv2) -0.470 0.088 -5.350 0.000 -0.470 -0.390
.Benev (mCv3) 0.117 0.074 1.593 0.111 0.117 0.110
.Extern ~~
.Hostile (mCv4) 0.058 0.077 0.744 0.457 0.058 0.053
.Benev (mCv5) 0.154 0.067 2.288 0.022 0.154 0.158
.Hostile ~~
.Benev (mCv6) 0.031 0.048 0.651 0.515 0.031 0.045
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Mind1C (mXnt) 0.816 0.026 31.051 0.000 0.816 1.883
.Intern (mM1n) 4.392 0.185 23.753 0.000 4.392 3.167
.Extern (mM2n) 3.871 0.158 24.499 0.000 3.871 3.117
.Hostile (mM3n) 4.334 0.113 38.350 0.000 4.334 4.877
.Benev (mM4n) 4.459 0.092 48.257 0.000 4.459 5.591
.NonTrad (mYnt) 6.868 1.261 5.447 0.000 6.868 2.840
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Mind1C (mXvr) 0.188 0.019 10.019 0.000 0.188 1.000
.Intern (mM1v) 1.850 0.147 12.629 0.000 1.850 0.962
.Extern (mM2v) 1.528 0.127 12.066 0.000 1.528 0.991
.Hostile (mM3v) 0.784 0.076 10.360 0.000 0.784 0.993
.Benev (mM4v) 0.618 0.059 10.412 0.000 0.618 0.972
.NonTrad (mYvr) 4.126 0.396 10.407 0.000 4.126 0.705
R-Square:
Estimate
Intern 0.038
Extern 0.009
Hostile 0.007
Benev 0.028
NonTrad 0.295
Defined Parameters:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
fXtoM1toY 0.044 0.066 0.671 0.502 0.044 0.009
fXtoM2toY -0.010 0.015 -0.644 0.520 -0.010 -0.002
fXtoM3toY 0.097 0.053 1.846 0.065 0.097 0.020
fXtoM4toY -0.022 0.024 -0.937 0.349 -0.022 -0.004
mXtoM1toY 0.347 0.127 2.724 0.006 0.347 0.062
mXtoM2toY 0.012 0.030 0.409 0.683 0.012 0.002
mXtoM3toY 0.142 0.112 1.269 0.204 0.142 0.025
mXtoM4toY 0.054 0.058 0.921 0.357 0.054 0.010
dXtoM1 0.525 0.247 2.127 0.033 0.525 0.159
dXtoM2 0.390 0.213 1.834 0.067 0.390 0.139
dXtoM3 0.014 0.150 0.095 0.924 0.014 0.028
dXtoM4 -0.445 0.136 -3.277 0.001 -0.445 -0.248
dM1toY 0.108 0.150 0.718 0.473 0.108 0.072
dM2toY -0.039 0.148 -0.263 0.793 -0.039 -0.023
dM3toY -0.312 0.223 -1.397 0.162 -0.312 -0.131
dM4toY -0.015 0.227 -0.068 0.946 -0.015 -0.002Testing differences between paths across groups can be done in three different ways (in order of most to least work): 1. Constrain paths to be equal; re-estimate the model (for direct or indirect effects; same procedure as when testing invariance) 2. Univariate Wald test of differences between single paths (for direct effects) using defined parameters (multiple per model) -- See last model
To show how bootstrap confidence intervals are found, we use the following syntax:
summary(multiGroupEstimatesBootstrap, fit.measures = TRUE, rsquare = TRUE, standardized = TRUE)
lavaan (0.5-23.1097) converged normally after 97 iterations
Number of observations per group
Female 380
Male 272
Number of missing patterns per group
Female 3
Male 3
Estimator ML
Minimum Function Test Statistic 0.000
Degrees of freedom 0
Minimum Function Value 0.0000000000000
Chi-square for each group:
Female 0.000
Male 0.000
Model test baseline model:
Minimum Function Test Statistic 398.511
Degrees of freedom 30
P-value 0.000
User model versus baseline model:
Comparative Fit Index (CFI) 1.000
Tucker-Lewis Index (TLI) 1.000
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -5323.242
Loglikelihood unrestricted model (H1) -5323.242
Number of free parameters 54
Akaike (AIC) 10754.485
Bayesian (BIC) 10996.407
Sample-size adjusted Bayesian (BIC) 10824.957
Root Mean Square Error of Approximation:
RMSEA 0.000
90 Percent Confidence Interval 0.000 0.000
P-value RMSEA <= 0.05 NA
Standardized Root Mean Square Residual:
SRMR 0.000
Parameter Estimates:
Information Observed
Standard Errors Bootstrap
Number of requested bootstrap draws 1000
Number of successful bootstrap draws 995
Group 1 [Female]:
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Intern ~
Mind1C (fXM1) 0.099 0.148 0.666 0.505 0.099 0.036
Extern ~
Mind1C (fXM2) -0.117 0.136 -0.858 0.391 -0.117 -0.044
Hostile ~
Mind1C (fXM3) -0.181 0.084 -2.170 0.030 -0.181 -0.109
Benev ~
Mind1C (fXM4) 0.138 0.081 1.718 0.086 0.138 0.081
NonTrad ~
Mind1C (fXtY) -0.126 0.259 -0.488 0.626 -0.126 -0.026
Intern (fM1Y) 0.449 0.111 4.034 0.000 0.449 0.247
Extern (fM2Y) 0.084 0.102 0.819 0.413 0.084 0.045
Hostile (fM3Y) -0.535 0.162 -3.295 0.001 -0.535 -0.180
Benev (fM4Y) -0.159 0.154 -1.034 0.301 -0.159 -0.055
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Intern ~~
.Extern (fCv1) 0.556 0.087 6.360 0.000 0.556 0.383
.Hostile (fCv2) -0.184 0.047 -3.921 0.000 -0.184 -0.205
.Benev (fCv3) -0.012 0.050 -0.235 0.815 -0.012 -0.013
.Extern ~~
.Hostile (fCv4) 0.023 0.044 0.526 0.599 0.023 0.026
.Benev (fCv5) 0.157 0.051 3.093 0.002 0.157 0.171
.Hostile ~~
.Benev (fCv6) 0.118 0.032 3.726 0.000 0.118 0.210
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Mind1C (fXnt) 0.847 0.022 37.938 0.000 0.847 1.892
.Intern (fM1n) 5.414 0.139 38.975 0.000 5.414 4.457
.Extern (fM2n) 4.200 0.126 33.388 0.000 4.200 3.504
.Hostile (fM3n) 3.853 0.077 50.094 0.000 3.853 5.185
.Benev (fM4n) 3.848 0.075 51.097 0.000 3.848 5.025
.NonTrad (fYnt) 7.172 1.114 6.438 0.000 7.172 3.256
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Mind1C (fXvr) 0.200 0.015 13.543 0.000 0.200 1.000
.Intern (fM1v) 1.473 0.091 16.191 0.000 1.473 0.999
.Extern (fM2v) 1.433 0.106 13.551 0.000 1.433 0.998
.Hostile (fM3v) 0.545 0.043 12.804 0.000 0.545 0.988
.Benev (fM4v) 0.583 0.045 12.883 0.000 0.583 0.993
.NonTrad (fYvr) 4.230 0.303 13.949 0.000 4.230 0.872
R-Square:
Estimate
Intern 0.001
Extern 0.002
Hostile 0.012
Benev 0.007
NonTrad 0.128
Group 2 [Male]:
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Intern ~
Mind1C (mXM1) 0.624 0.207 3.017 0.003 0.624 0.195
Extern ~
Mind1C (mXM2) 0.274 0.173 1.580 0.114 0.274 0.095
Hostile ~
Mind1C (mXM3) -0.167 0.131 -1.274 0.202 -0.167 -0.081
Benev ~
Mind1C (mXM4) -0.307 0.111 -2.758 0.006 -0.307 -0.167
NonTrad ~
Mind1C (mXtY) 0.212 0.371 0.571 0.568 0.212 0.038
Intern (mM1Y) 0.557 0.111 5.024 0.000 0.557 0.319
Extern (mM2Y) 0.045 0.114 0.393 0.695 0.045 0.023
Hostile (mM3Y) -0.847 0.158 -5.353 0.000 -0.847 -0.311
Benev (mM4Y) -0.175 0.171 -1.023 0.306 -0.175 -0.058
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Intern ~~
.Extern (mCv1) 0.643 0.131 4.892 0.000 0.643 0.383
.Hostile (mCv2) -0.470 0.090 -5.216 0.000 -0.470 -0.390
.Benev (mCv3) 0.117 0.073 1.609 0.108 0.117 0.110
.Extern ~~
.Hostile (mCv4) 0.058 0.080 0.724 0.469 0.058 0.053
.Benev (mCv5) 0.154 0.068 2.262 0.024 0.154 0.158
.Hostile ~~
.Benev (mCv6) 0.031 0.048 0.650 0.516 0.031 0.045
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Mind1C (mXnt) 0.816 0.027 29.985 0.000 0.816 1.883
.Intern (mM1n) 4.392 0.195 22.474 0.000 4.392 3.167
.Extern (mM2n) 3.871 0.163 23.771 0.000 3.871 3.117
.Hostile (mM3n) 4.334 0.116 37.477 0.000 4.334 4.877
.Benev (mM4n) 4.459 0.093 47.874 0.000 4.459 5.591
.NonTrad (mYnt) 6.868 1.230 5.585 0.000 6.868 2.840
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Mind1C (mXvr) 0.188 0.018 10.384 0.000 0.188 1.000
.Intern (mM1v) 1.850 0.146 12.644 0.000 1.850 0.962
.Extern (mM2v) 1.528 0.124 12.307 0.000 1.528 0.991
.Hostile (mM3v) 0.784 0.075 10.510 0.000 0.784 0.993
.Benev (mM4v) 0.618 0.060 10.249 0.000 0.618 0.972
.NonTrad (mYvr) 4.126 0.400 10.325 0.000 4.126 0.705
R-Square:
Estimate
Intern 0.038
Extern 0.009
Hostile 0.007
Benev 0.028
NonTrad 0.295
Defined Parameters:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
fXtoM1toY 0.044 0.071 0.627 0.531 0.044 0.009
fXtoM2toY -0.010 0.021 -0.470 0.638 -0.010 -0.002
fXtoM3toY 0.097 0.056 1.725 0.084 0.097 0.020
fXtoM4toY -0.022 0.026 -0.841 0.400 -0.022 -0.004
mXtoM1toY 0.347 0.136 2.562 0.010 0.347 0.062
mXtoM2toY 0.012 0.038 0.322 0.748 0.012 0.002
mXtoM3toY 0.142 0.118 1.194 0.232 0.142 0.025
mXtoM4toY 0.054 0.060 0.896 0.370 0.054 0.010
dXtoM1 0.525 0.256 2.053 0.040 0.525 0.159
dXtoM2 0.390 0.219 1.784 0.074 0.390 0.139
dXtoM3 0.014 0.157 0.091 0.927 0.014 0.028
dXtoM4 -0.445 0.137 -3.256 0.001 -0.445 -0.248
dM1toY 0.108 0.157 0.689 0.491 0.108 0.072
dM2toY -0.039 0.152 -0.256 0.798 -0.039 -0.023
dM3toY -0.312 0.222 -1.409 0.159 -0.312 -0.131
dM4toY -0.015 0.230 -0.067 0.947 -0.015 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