Mediation in Latent Growth Curve Models

[Judith B.]

I'm a complete newbie to R, and learning as I'm going. I haven't had much luck trying to find syntax to conduct a mediation analysis in latent growth curve modeling framework.  Using lavaan I've been able to run mediation and latent growth curve models separately, but my attempts to to integrate those two has failed.

I would appreciate it if someone was willing to share some code they have. I have one predictor and one mediator variable (both measured at time 1), and a dependent variable measured at time 1, time 2, and time 3.

Thanks!

[Terrence Jorgensen]

I've been able to run mediation and latent growth curve models separately, but my attempts to to integrate those two has failed.

My advice would be to draw a path diagram of your hypothesized model.  If you can draw it, you can translate it into syntax using "~" for regression paths (or "=~" for factor loadings) and "~~" for (co)variances.

I would appreciate it if someone was willing to share some code they have. I have one predictor and one mediator variable (both measured at time 1), and a dependent variable measured at time 1, time 2, and time 3.

So your dependent variables in the mediation model are the growth factors (latent intercept and slope)?  Simply regress those onto your mediator, and regress the mediator onto your predictor.

Terrence D. Jorgensen

Postdoctoral Researcher, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

UvA web page: http://www.uva.nl/profile/t.d.jorgensen

[Judith B.]

Hi Terrence,
thanks! I think I fixed my mistakes, including several error messages I received. My model looks like this.


Essentially, I'm examining whether CSI4.tot at time 0 mediates the association between "BF_Ex.A" and subsequent changes in CSI4.tot at times 1 through 5.

Here is my syntax:

mediation.model <- ' 
             #latent growth variables
                 #DV intercept
                   i =~ 1*CSI4.tot.1 + 1*CSI4.tot.2 + 1*CSI4.tot.3 + 1*CSI4.tot.4 + 1*CSI4.tot.5
                 #DV slope
                   s =~ 1*CSI4.tot.1 + 2*CSI4.tot.2 + 3*CSI4.tot.3 + 4*CSI4.tot.4 + 5*CSI4.tot.5
             #Specifying intercept for CSI4.tot.0
                  CSI4.tot.0 ~ 1
             #direct effect
                   i ~ c*BF_Ex.A
                  s ~ c*BF_Ex.A
             # mediator
                   CSI4.tot.0 ~ a*BF_Ex.A
                   i ~ b*CSI4.tot.0
                  s ~ b*CSI4.tot.0
             # indirect effect (a*b)
                   ab := a*b 
             # total effect
                   total := c + (a*b)
'

fit.growth<-growth(mediation.model, data = dset, se = "bootstrap")
summary(fit.growth)

I can run this model without getting any error messages, but I am not absolutely confident that my code is accurate. Some feedback would be appreciated.

Thanks!

[Terrence Jorgensen]

You should also estimate the intercept of i and of s, but the growth() function should add those parameters automatically.  You also need to use different labels for the effects on i and on s (using b and c for both constrains those effects to be equal, which is not what you want to do).  You can use {ib, ic} for effects on i, and {sb, sc} for effects on s.

[Judith B.]

Thanks again, Terrence.
Just to be sure, given that the growth() function automatically estimates the latent variable intercepts, there is nothing else I need to do, correct?
Does this code and output look accurate then?


Code:

mediation.model <- ' 
                      #latent growth variables (note: only DV is growth factor in this model)

                        #DV intercept
                        i =~ 1*CSI4.tot.1 + 1*CSI4.tot.2 + 1*CSI4.tot.3 + 1*CSI4.tot.4 + 1*CSI4.tot.5
                        #DV slope
                        s =~ 1*CSI4.tot.1 + 2*CSI4.tot.2 + 3*CSI4.tot.3 + 4*CSI4.tot.4 + 5*CSI4.tot.5
                      #Specifying intercept for CSI4.tot.0
                        CSI4.tot.0 ~ 1
                      #direct effect

                        i ~ {ic}*BF_Ex.A
                        s ~ {sc}*BF_Ex.A

                      # mediator
                        CSI4.tot.0 ~ a*BF_Ex.A

                        i ~  {ib}*CSI4.tot.0
                        s ~ {sb}*CSI4.tot.0
                     # indirect effect (a*{sb})
                        ab := a*{sb} 
                      # total effect
                        total := {sc} + (a*{sb})

'

fit.growth<-growth(mediation.model, data = dset, se = "bootstrap")
summary(fit.growth)

Output:

lavaan (0.5-23.1097) converged normally after  47 iterations

                                                  Used       Total
  Number of observations                           165         600

  Estimator                                         ML
  Minimum Function Test Statistic               55.211
  Degrees of freedom                                16
  P-value (Chi-square)                           0.000

Parameter Estimates:

  Information                                 Observed
  Standard Errors                            Bootstrap
  Number of requested bootstrap draws             1000
  Number of successful bootstrap draws            1000

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  i =~                                                
    CSI4.tot.1        1.000                           
    CSI4.tot.2        1.000                           
    CSI4.tot.3        1.000                           
    CSI4.tot.4        1.000                           
    CSI4.tot.5        1.000                           
  s =~                                                
    CSI4.tot.1        1.000                           
    CSI4.tot.2        2.000                           
    CSI4.tot.3        3.000                           
    CSI4.tot.4        4.000                           
    CSI4.tot.5        5.000                           

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)
  i ~                                                 
    BF_Ex.A   (ic)    0.097    0.077    1.251    0.211
  s ~                                                 
    BF_Ex.A   (sc)   -0.005    0.022   -0.210    0.834
  CSI4.tot.0 ~                                        
    BF_Ex.A    (a)   -0.034    0.089   -0.381    0.703
  i ~                                                 
    CSI4.tt.0 (ib)    0.887    0.054   16.485    0.000
  s ~                                                 
    CSI4.tt.0 (sb)   -0.038    0.017   -2.213    0.027

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)
 .i ~~                                                
   .s                -0.853    0.253   -3.365    0.001

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)
   .CSI4.tot.0        9.028    0.657   13.737    0.000
   .CSI4.tot.1        0.000                           
   .CSI4.tot.2        0.000                           
   .CSI4.tot.3        0.000                           
   .CSI4.tot.4        0.000                           
   .CSI4.tot.5        0.000                           
   .i                -0.327    0.741   -0.441    0.659
   .s                 1.122    0.230    4.878    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .CSI4.tot.1        2.569    0.555    4.631    0.000
   .CSI4.tot.2        2.977    0.608    4.895    0.000
   .CSI4.tot.3        4.290    0.811    5.293    0.000
   .CSI4.tot.4        2.018    0.305    6.624    0.000
   .CSI4.tot.5        0.728    0.489    1.487    0.137
   .CSI4.tot.0       13.276    1.438    9.230    0.000
   .i                 7.605    1.284    5.924    0.000
   .s                 0.534    0.082    6.524    0.000

Defined Parameters:
                   Estimate  Std.Err  z-value  P(>|z|)
    ab                0.001    0.004    0.352    0.725
    total            -0.003    0.022   -0.150    0.881

Thanks!

[Terrence Jorgensen]

Does this code and output look accurate then?

Those curly braces should not be there, and you could also calculate the indirect effect on i, but it looks like it worked (all the expected estimates are in the output).

[ahmad]

Hi, following up on this point, I’m wondering how we can extend this model to a moderated mediation framework using multiple-group SEM. Specifically, if we want to examine the moderating effects of sex on the direct, indirect, and total effects in this latent growth mediation model, should we constrain any parameters in the latent growth model portion? Or can we treat this model as a standard mediation model and simply test the moderating role of sex across groups?

Thank,

A