SEM with moderation analysis (cross-lagged-model) in R

Question

I want to do structural equation modeling with three moderators. My variables are attractiveness (X), self-worth (Y), age (A), gender (G) and social status (S). The data is longitudinal and collected in two waves: t1 and t2. In order to find out which relation exists between X and Y, in which direction this relation goes and how the relation is moderated by A, G and S, I want to use a cross-lagged-model where X_t2 and Y_t2 are the outcome variables. I use the R-package lavaan. The model looks like the following:

modelCLP <- '
  # regressions
    X_t2 ~ X_t1 + Y_t1 + A + G + S + Y_t1 * A + Y_t1 * G + Y_t1 * S   
    Y_t2 ~ Y_t1 + X_t2 + A + G + S + X_t1 * A + X_t1 * G + X_t1 * S 
  
  # co-movements
    X_t2 ~~ Y_t2
    X_t1 ~~ Y_t1
 
'
fit <- sem(modelCLP, data = datenB)
summary(fit, standardized = TRUE, fit.measures = TRUE)

The problem with my output is that I get the same results for the moderators in equation 1 and for the moderators in equation 2. When I do three separate analyses for the moderators I get three different results. When i calculate the model above, I get theses results:

lavaan 0.6-10 ended normally after 20 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        13
  Number of equality constraints                     4
                                                      
                                                  Used       Total
  Number of observations                           871        2406
                                                                  
Model Test User Model:
                                                      
  Test statistic                                14.959
  Degrees of freedom                                 4
  P-value (Chi-square)                           0.005

Model Test Baseline Model:

  Test statistic                              1024.222
  Degrees of freedom                                11
  P-value                                        0.000

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.989
  Tucker-Lewis Index (TLI)                       0.970

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -1967.499
  Loglikelihood unrestricted model (H1)      -1960.020
                                                      
  Akaike (AIC)                                3952.999
  Bayesian (BIC)                              3995.926
  Sample-size adjusted Bayesian (BIC)         3967.344

Root Mean Square Error of Approximation:

  RMSEA                                          0.056
  90 Percent confidence interval - lower         0.028
  90 Percent confidence interval - upper         0.088
  P-value RMSEA <= 0.05                          0.320

Standardized Root Mean Square Residual:

  SRMR                                           0.018

Parameter Estimates:

  Standard errors                             Standard
  Information                                 Expected
  Information saturated (h1) model          Structured

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  X_t2 ~                                                                
    X_t1              0.382    0.018   21.245    0.000    0.382    0.600
    Y_t1              0.100    0.034    2.902    0.004    0.100    0.083
    A       (Y_t1)    0.002    0.002    1.395    0.163    0.002    0.037
    G       (Y_t1)    0.002    0.002    1.395    0.163    0.002    0.001
    S       (Y_t1)    0.002    0.002    1.395    0.163    0.002    0.003
  Y_t2 ~                                                                
    Y_t1              0.716    0.034   21.180    0.000    0.716    0.594
    X_t1              0.064    0.018    3.617    0.000    0.064    0.100
    A       (X_t1)    0.004    0.001    2.724    0.006    0.004    0.071
    G       (X_t1)    0.004    0.001    2.724    0.006    0.004    0.002
    S       (X_t1)    0.004    0.001    2.724    0.006    0.004    0.006

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
 .X_t2 ~~                                                               
   .Y_t2              0.104    0.020    5.287    0.000    0.104    0.182

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .X_t2              0.580    0.028   20.869    0.000    0.580    0.581
   .Y_t2              0.560    0.027   20.869    0.000    0.560    0.559

What can I do in order to get different results for the three moderators? Is there a better way to do a SEM with multiple moderators in R?

score 0 · Answer 1 · answered Jun 06 '22 at 17:42

I am not sure what exactly is being done by lavaan in your code, but I believe maybe 'A', 'G', and 'S' are considered constrains in the model.

For what I know, we need to prepare the interaction (moderation) terms before running the SEM analysis in almost (?) all tools... There are several ways to do so.

One is computing factor scores for the latent variables and generate the interaction terms as product among factor score and moderator.
Another way to do so in R, without computing factor scores is, for example, to use the function indProd() from semTools package.
From your code, it appears you are not dealing with latent variables, so, compute the product among the variables would be sufficient:

modelCLP$A_Y_t1=modelCLP$A*modelCLP$Y_t1
modelCLP$G_Y_t1=modelCLP$G*modelCLP$Y_t1
modelCLP$S_Y_t1=modelCLP$S*modelCLP$Y_t1
modelCLP$A_X_t1=modelCLP$A*modelCLP$Y_t1
modelCLP$G_X_t1=modelCLP$G*modelCLP$X_t1
modelCLP$S_X_t1=modelCLP$S*modelCLP$X_t1

    modelCLP <- '
      # regressions
    X_t2 ~ X_t1 + Y_t1 + A + G + S + A_Y_t1 + G_Y_t1  + S_Y_t1   
    Y_t2 ~ Y_t1 + X_t2 + A + G + S + A_X_t1 + G_X_t1 + S_X_t1      
      # co-movements
    X_t2 ~~ Y_t2
    X_t1 ~~ Y_t1'

Note: you possibly need to add covariances among all variables (including these interaction terms).

fit <- sem(modelCLP, data = datenB)
summary(fit, standardized = TRUE, fit.measures = TRUE)

SEM with moderation analysis (cross-lagged-model) in R

1 Answers1