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 patrick sturgis posted on Wednesday, May 03, 2006 - 2:58 pm
I am estimating a cross-lagged model on panel data where I have an X and a Y measured at 3 occasions. X is a categorical (binary) variable, Y is a count variable. So I have:

x3 on x2 y2;
y3 on x2 y2;
x2 on x1 y1;
y2 on x1 y1;


For this type of model, it is important to model covariances between disturbance terms of endogenous variables. so I want to estimate:

x3 with y3;
x2 with y2;
x3 with x2;
y3 with y2;

however, even using the theta parameterization, I cannot seem to estimate the variance of the disturbance term of the count variables (y1-y3). How should I deal with this? Thank you for your help,

Patrick
 Bengt O. Muthen posted on Thursday, May 04, 2006 - 11:32 am
Mplus does not include residual variances for Poisson regression with a dependent variable that is a count variable - this is in line with regular Poisson regression analysis where such a residual is absent. The Theta parameterization is not in effect for count outcomes. You can, however, in Mplus define a residual by defining a factor that influences the dependent count variable, e.g. when regressing y on a covariate x,

f by y@0;

y on x f@1;

which would estimate a residual variance in the form of the factor variance for f. With say 2 dependent variables that are counts, you can hereby correlate the residuals across the 2 regressions.
 patrick sturgis posted on Thursday, May 04, 2006 - 1:16 pm
Thank you Bengt

do you have a reference for this approach?

Patrick
 Bengt O. Muthen posted on Thursday, May 04, 2006 - 9:04 pm
This is in line with approaches used in the Hidden Markov references given in the Mplus User's Guide: Mooijaart (1998) and Langeheine & van de Pol(2002).
 patrick sturgis posted on Saturday, May 06, 2006 - 12:48 am
Bengt

so I would use theta paramterization to deal with the binary variables and not specify the count variables as counts in this specification?

Patrick
 Bengt O. Muthen posted on Saturday, May 06, 2006 - 10:42 am
Sorry, somehow my answer above ended up in the wrong thread - we were talking Poisson modeling, not latent class modeling.

So you would treat the outcomes as a blend of categorical and counts and use ML estimation (no other choice with counts). Note that you would only covary 2 sets of residuals,

x3 with y3;
x2 with y2;

You have regression relations for the other 2 that you listed.

With ML estimation you don't have access to Theta, so you have to bring in a dummy factor. Take for example the first residual covariance of x3 with y3:

fy3 by y3@0; fy3@1;
fx3 by x3@0; fx3@1;
y3 on fy3@1;
x3 on fx3@1;
fy3 with fx3;

The last statement gives you the residual covariance you wanted. I am not sure if it is identified, but you can try. No reference for this; just utilizing Mplus.
 patrick sturgis posted on Monday, May 08, 2006 - 3:38 am
thanks for the clarification. One (hopefully) final thing - do I specify the observed count variables as counts in this specification? i.e.:

count are Y3 Y2;
 Bengt O. Muthen posted on Monday, May 08, 2006 - 8:54 am
That's right.
 Jacqueline Homel posted on Friday, February 01, 2013 - 12:34 pm
I am estimating a parallel process latent growth model with four outcomes, over three timepoints. Three outcomes are continuous and the fourth is a count of conduct problems (from 0 to 7). This is my input:

USEVAR are TDer3 TDer4 TDer5 TDef3 TDef4 TDef5 dep3 dep4 dep5 cdc73 cdc74 cdc75;
count are cdc73 cdc74 cdc75 ;
Analysis:
Algorithm = integration ;
Integration =montecarlo(5000) ;
MODEL:
ider sder | TDer3@0 TDer4@2.8 TDer5@4.6 ;
idef sdef | TDef3@0 TDef4@2.8 TDef5@4.6 ;
idep sdep | dep3@0 dep4@2.8 dep5@4.6 ;
icond scond | cdc73@0 cdc74@2.8 cdc75@4.6 ;

I want to covary the residual variances for the observed variables. As an experiment I tried the approach outlined above for cdc73 and dep3, and it ran:

fcd3dep3 by cdc73@1 dep3 ;
fcd3dep3@1 ; [fcd3dep3@0] ;

However, I would need nine residual covariances in total and each of these adds a dimension of integration. Is there an alternative method that would be faster?
 Bengt O. Muthen posted on Saturday, February 02, 2013 - 9:03 am
You could try using only 1 factor for each of the 3 time points and let the different loadings capture the different sizes of the residual correlations among the 3 processes. So 3 dimensions instead of 9. Make sure the 3 factors are uncorrelated with each other.
 Jacqueline Homel posted on Saturday, February 02, 2013 - 11:55 am
Thanks very much - would the factors be defined like this?

f3 by cdc73@1 dep3 TDef3 TDer3 ;
f4 by cdc74@1 dep4 TDef4 TDer4 ;
f5 by cdc75@1 dep5 TDef5 TDer5 ;

f3@1 ; [f3@0] ;
f4@1 ; [f4@0] ;
f5@1 ; [f5@0] ;

f3 with f4@0 ;
f3 with f5@0 ;
f4 with f5@0 ;
 Bengt O. Muthen posted on Saturday, February 02, 2013 - 12:11 pm
Yes, but those 3 factors need to also be set uncorrelated with your 8 growth factors.
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