SEM - Time-dependent explanatory variable in latent growth model

[Andre Martinez]

Hello,

I am using the SEM procedure to build a latent growth model for longitudinal data (repeated variable = cog at times 0, 1, and 2).

I am able to include baseline covariates (eg sex in the example below). I would like to include a time-dependent covariate Y measured at times 0, 1, and 2 and I do not seem to be able to make it work. Any advice ?

sem ///
(cog0 <- Intercept@1 Slope@0 _cons@0) ///
(cog1 <- Intercept@1 Slope@1 _cons@0) ///
(cog2 <- Intercept@1 Slope@2 _cons@0) ///
(Intercept <- sex _cons) (Slope <- sex _cons ) , latent(Intercept Slope) ///
var(e.cog0@var2 e.cog1@var2 e.cog2@var2) cov(e.Intercept*e.Slope ) ///

Thank you

André

[Dick Campbell]

You need to tell us what happens when you run this rather than just stating that you can't make it work. Please show your code along with the output you get including error messages. Also, the output will be a lot easier to read if you use code tags.

[wbuchanan]

It doesn't look like you have any time varying covariates in your syntax nor do you describe how they are supposed to fit into your model (e.g., do they directly effect the latent means, the manifest variables, are they autoregressive, etc...).

[Andre Martinez]

Thank you. It's my first post, I will try to do better next time :-)

The time-dependent variable Y is measured at the same time as COG at each time (0,1,2) and I would like Y to influence COG at each time, ie like in the model below. Y is not autoregressive.

sem ///
(cog0 <- Intercept@1 Slope@0 y0@a0 _cons@0) ///
(cog1 <- Intercept@1 Slope@1 y1@a1 _cons@0) ///
(cog2 <- Intercept@1 Slope@2 y2@a2 _cons@0) ///
(Intercept <- sex _cons) (Slope <- sex _cons ) , ///
latent(Intercept Slope) ///
var(e.cog0@var2 e.cog1@var2 e.cog2@var2) cov(e.Intercept*e.Slope )

With this syntax, the model fails to converge (Iteration 300: log likelihood = 115284.02 (not concave) and does not change so I need to stop it). I suppose I am doing something wrong as a mixed model using the same data converges without any difficulty.

Thank you for your help.

André

[Dick Campbell]

Can you please provide the SEM output? I want to see how SEM interprets your model.

[Andre Martinez]

Thank you Dick.

The following model (without the time dependent time-variable Y; this model is a typical latent growth model as in the SEM documentation of Stata)

sem    (cog0 <- Intercept@1 Slope@0 _cons@0) ///
          (cog1 <- Intercept@1 Slope@1 _cons@0) ///
          (cog2 <- Intercept@1 Slope@2 _cons@0) ///
(Intercept <- sex _cons) (Slope <- sex _cons ) , latent(Intercept Slope) ///
var(e.cog0@var2 e.cog1@var2 e.cog2@var2) cov(e.Intercept*e.Slope )

gives this output

Structural equation model                       Number of obs     =      2,521
Estimation method  = ml
Log likelihood     = -8578.3219

 ( 1)  [cog0]Intercept = 1
 ( 2)  [cog1]Intercept = 1
 ( 3)  [cog1]Slope = 1
 ( 4)  [cog2]Intercept = 1
 ( 5)  [cog2]Slope = 2
 ( 6)  [var(e.cog0)]_cons - [var(e.cog2)]_cons = 0
 ( 7)  [var(e.cog1)]_cons - [var(e.cog2)]_cons = 0
 ( 8)  [cog0]_cons = 0
 ( 9)  [cog1]_cons = 0
 (10)  [cog2]_cons = 0
-----------------------------------------------------------------------------------------
                        |                 OIM
                        |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------------+----------------------------------------------------------------
Structural              |
  Intercept <-          |
                    sex |  -.1419539   .0292636    -4.85   0.000    -.1993094   -.0845983
                  _cons |   .3087704    .023284    13.26   0.000     .2631346    .3544062
  ----------------------+----------------------------------------------------------------
  Slope <-              |
                    sex |  -.0053852   .0134301    -0.40   0.688    -.0317078    .0209373
                  _cons |  -.1226473   .0106859   -11.48   0.000    -.1435912   -.1017034
------------------------+----------------------------------------------------------------
Measurement             |
  cog0 <-               |
              Intercept |          1  (constrained)
                  _cons |          0  (constrained)
  ----------------------+----------------------------------------------------------------
  cog1 <-               |
              Intercept |          1  (constrained)
                  Slope |          1  (constrained)
                  _cons |          0  (constrained)
  ----------------------+----------------------------------------------------------------
  cog2 <-               |
              Intercept |          1  (constrained)
                  Slope |          2  (constrained)
                  _cons |          0  (constrained)
------------------------+----------------------------------------------------------------
             var(e.cog0)|   .1600242   .0045073                      .1514295    .1691066
             var(e.cog1)|   .1600242   .0045073                      .1514295    .1691066
             var(e.cog2)|   .1600242   .0045073                      .1514295    .1691066
        var(e.Intercept)|   .3681304   .0146158                      .3405703    .3979209
            var(e.Slope)|   .0256114   .0037322                      .0192482     .034078
------------------------+----------------------------------------------------------------
cov(e.Intercept,e.Slope)|   .0065308   .0053133     1.23   0.219    -.0038831    .0169448
-----------------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(4)   =     45.83, Prob > chi2 = 0.0000

But the model that includes the time-dependent variable Y influencing COG at each time does not converge, so there is no output for me to show

sem ///
(cog0 <- Intercept@1 Slope@0 y0@a0 _cons@0) ///
(cog1 <- Intercept@1 Slope@1 y1@a1 _cons@0) ///
(cog2 <- Intercept@1 Slope@2 y2@a2 _cons@0) ///
(Intercept <- sex _cons) (Slope <- sex _cons ) , ///
latent(Intercept Slope) ///
var(e.cog0@var2 e.cog1@var2 e.cog2@var2) cov(e.Intercept*e.Slope )

Thank you for your help

[Dick Campbell]

[Dick Campbell]

Sorry, I just accidentally posted an empty note.

You might want to take a look at Alan Acock's book, Discovering Structural Equation Modeling Using Stata. Chapter 4 of that book contains an example of exactly what you want to do. Here is his code setup.

use bmiworking.dta, clear   
recode drkdays* (.a/.e=.)
center drkdays* deswgt97

/* This model cannot be fit in Small Stata */
sem   (Intercept@1 Slope@0 c_drkdays01   -> bmi01) ///
      (Intercept@1 Slope@1 c_drkdays02   -> bmi02) /// 
      (Intercept@1 Slope@2 c_drkdays03   -> bmi03) ///                                                                     
      (Intercept@1 Slope@4 c_drkdays05   -> bmi05) ///                                                                     
      (Intercept@1 Slope@5 c_drkdays06   -> bmi06) ///                                                                     
      (Intercept@1 Slope@6 c_drkdays07   -> bmi07) ///                                                                     
      (Intercept@1 Slope@7 c_drkdays08   -> bmi08) ///
      (Intercept@1 Slope@8 c_drkdays09   -> bmi09) ///
      (Intercept Slope <- male c_deswgt _cons)           ///
      if bmi01~=.|bmi02~=.|bmi03~=.|bmi05~=.|bmi06~=.|  ///
      bmi07~=.|bmi08~=.|bmi09~=.,  ///         
      cov(e.Intercept*e.Slope)  ///
      method(mlmv) noconstant 
estat eqgof
estat gof, stats(all)
estat mindices

Looking at your code, it appears that you are having trouble relating the TVC's to the outcomes. In Acock's code you will note that each of the time varying bmi outcomes is predicted by the intercept, a time-coded slope value and a time-specific covariate, e.g. (Intercept@1 Slope@4 c_drkdays05 -> bmi05) /// I can't quite figure out the logic underlying your code, but I think if you base what you are trying to do on Acock's example you should be fine. I highly recommend his book.

[Andre Martinez]

Thank you very much Dick. This is very useful. It looks like this is what I am doing, but there must be a problem related to the data, as it fails to converge. I will try to run other examples. I ordered the book, it seems very useful.
Thanks for your help
André