Error variance for endogenous count v... PreviousNext
Mplus Discussion > Categorical Data Modeling >
 patrick sturgis posted on Wednesday, May 03, 2006 - 8:58 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,

 Bengt O. Muthen posted on Thursday, May 04, 2006 - 5:32 pm
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 - 7:16 pm
Thank you Bengt

do you have a reference for this approach?

 Bengt O. Muthen posted on Friday, May 05, 2006 - 3:04 am
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 - 6:48 am

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

 Bengt O. Muthen posted on Saturday, May 06, 2006 - 4:42 pm
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 - 9:38 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 - 2:54 pm
That's right.
 Jacqueline Homel posted on Friday, February 01, 2013 - 6:34 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 ;
Algorithm = integration ;
Integration =montecarlo(5000) ;
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 - 3:03 pm
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 - 5:55 pm
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 - 6:11 pm
Yes, but those 3 factors need to also be set uncorrelated with your 8 growth factors.
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