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.

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.

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    0.064

To 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    0.064

Multiple-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   -0.002

Testing 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   -0.002
---
title: "EPSY 906/CLDP 948 Example 9: Path Analysis for Mediation"
output:
  html_notebook:
    smart: false
---

## Path Analysis for Mediation

```{r setup, include=TRUE}
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.](picture1.png)

![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.](picture2.png)

```{r import, include=TRUE}
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).

```{r singlegroup, include=TRUE}
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)
```
To show how bootstrap confidence intervals are found, we use the following syntax:

```{r boot1, include=TRUE}

singleGroupEstimatesBootstrap = lavaan(model = singleGroupSyntax, data = mindData, estimator = "ML", mimic = "mplus", se = "bootstrap")
summary(singleGroupEstimatesBootstrap, fit.measures = TRUE, rsquare = TRUE, standardized = TRUE)
```

### Multiple-Group Path Model (all parameters estimated separately by gender)


```{r multigroup, include=TRUE}
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)
```

Testing 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:

```{r boot2, include=TRUE}

multiGroupEstimatesBootstrap = lavaan(model = multiGroupSyntax, data = mindData, estimator = "ML", mimic = "mplus", se = "bootstrap", group = "sex")
summary(multiGroupEstimatesBootstrap, fit.measures = TRUE, rsquare = TRUE, standardized = TRUE)
```
