Control variables in longitudinal model
Message/Author
 james rosenthal posted on Monday, January 26, 2009 - 10:20 am
Dr. Muthen(s):

I am working with 5000 cases/children referred to the child welfare system, each with 4 waves of data. I am going to model the relationship between the number of placements between waves and score on a behavior problems measure. Label the four number of placement variables np1, np2, np3, and np4 and the four behavior variables b1,b2,b3, and b4. My basic model is:

!placement on placement;
np2 on np1;
np3 on np2;
np4 on np3;
!behavior on behavior;
b2 on b1;
b3 on b2;
b4 on b3;
!behavior on placement;
b1 on np1;
b2 on np2;
b3 on np3;
b4 on np4;
!placement on behavior;
np2 on b1;
np3 on b2;
np4 on b3;

I need suggestions on how to integrate two types control variables into the analysis: 1) those constant across waves (gender, initial type of maltreatment, and ethnicity) and 2) those that change by wave (age group, type of placement residing in, and length of time resided in placement).

Do I simply enter the control variables into the above regressions? Would building a growth factor help? Should I build the controls into the model?

Any suggestions would be appreciated.

Thanks.

Jim
 Linda K. Muthen posted on Monday, January 26, 2009 - 4:26 pm
If you want an autoregressive model as you have specified, you could do the following where gender is a time-invariant covariate and tv is a time-varying covariate:

np2 on np1 gender tv2;
np3 on np2 gender tv3;
np4 on np3 gender tv4;

If you use a latent growth curve model, you regress the growth factors on the time-invariant covariates and the outcome on the time-varying covariates.
 james rosenthal posted on Tuesday, January 27, 2009 - 7:19 am
Linda:

also, could i use a multiple groups strategy to examine whether a covariate/control has a significant effect on the overall model?

For instance (sticking with the model statement that i wrote out on the prior email). could i state that model statement for, say, boys, and then repeat the entire model statement for girls? would doing so provide a test of whether gender contributes significantly to the overall model?

thanks again.

jim
 Linda K. Muthen posted on Tuesday, January 27, 2009 - 8:16 am
You could use a categorical covariates as a grouping variable to test differences across groups in not only intercepts but also regression coefficients.
 james rosenthal posted on Tuesday, January 27, 2009 - 8:45 am
Linda:

I had pictured testing a categorical covariate as a grouping variable by comparing some sort of (probably?) chi-square based measure of model fit of the model with and without the covariate.

could you possibly provide some guidance on 1) how to test intercepts, 2) how to test regression coefficients, 3) how one would get an overall chi-square test (or other related test) of whether the covariate was contributing significantly.

If i simply repeated the model statement for the second group?, what does that test and not test (coefficients? intercepts?) or is such a statement way off track.

Jim
 Linda K. Muthen posted on Tuesday, January 27, 2009 - 10:42 am
The Topic 1 short course handout shows how to use chi-square difference testing with multiple group analysis to test the difference of parameters across groups. There is also a video of the Topic 1 short course available. Difference testing using chi-square or the loglikelihood is also discussed in Chapter 13 of the Mplus User's Guide in the multiple group discussion.
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