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 Jan Ivanouw posted on Monday, November 23, 2009 - 1:29 am
I am sorry for my ignorance, I am not quite sure about scale units in CFA-models when the dependent variables are count variables:

When setting the loading for one indicator = 1 (the default), what scale are
1) the intercepts?
2) the loadings?
3) the factor scores?
4) the residuals?

When setting the variance for the factor to one, what scale are
5) the intercepts?
6) the loadings?
7) the factor scores?
8) the residuals?
 Bengt O. Muthen posted on Monday, November 23, 2009 - 2:29 pm
The dependent variables, which are your factor indicators, are in the metric of elog rates in line with regression with count DVs. Here, rate is what governs the mean of the Poisson distribution for counts. See our regression pages in the Topic 2 handout. Using the default of the first loading fixed at 1, your factors are in the metric of that indicator, that is, the log rate of that indicator.
 Jan Ivanouw posted on Monday, November 30, 2009 - 3:28 am
Thank you for your answer. I am still struggling with my understanding. Could you help me whith this problem:

I have a latent variable M with 10 count indicators M1-M10 with the default loading 1 of the first indicator M1
The observed mean of M1 is 0.742 (variance = 0.668)
If I model an ordinary CFA, the intercept for M1 is as expected 0.742
But if I model the CFA with the indicators as count variables, the intercept for M1 is -0.427.
As the intercepts for a count model is in log units, I would expect to calculate the indicator mean as exp(-0.427) = 0.652. But this is lower than the observed mean of 0.742.

Calculating the means from the intercepts of the 9 other indicators also gives lower than expected means.

Where am I wrong?
 Bengt O. Muthen posted on Monday, November 30, 2009 - 9:33 am
The "observed means" that you mention are probably computed by treating the count variable as a continuous variable, not a count variable. Because of the long right tail, this value would be higher than the log rate that you computed from the count model.
 Yves Dejaeghere posted on Tuesday, December 08, 2009 - 12:12 pm

I am using MPlus4 and estimated a path model with a count variable (number of political activities) as dependent and one mediating variable that is continuous. Chapter three of the user guide says this is possible and I succesfully ran my model. I have a number of variables that go straight to the count variable but also go through the continuous variable. What is my interpretation of the indirect effect? I mainly want to see whether the mediator (an attitude) has some remaining effect on the behaviour (the count variable) or if the effect is spurious once I control for a number of other variables. I know for the Poisson I use the antilog of the coefficient but how do I work this out with a coefficient that first goes to a continuous mediator variable? I do not find any examples for this...I just did it because I saw MPlus could handle it and it was exactly what I needed...

My syntax is like this:
Missing are ALL(99);
Count is var1
var1 on var2 var3 var4 var5 var6;
var2 on var3 var4 var6;

So what is my effect for example for var3 through var2 on var1 (taken that all are significant)?

Thank you very much for looking at this problem. I might actually be obvious, but I can't find an example.
 Bengt O. Muthen posted on Tuesday, December 08, 2009 - 6:21 pm
Say you use the Model command labeling (for instance):

var1 on var2 (p1);
var2 on var3 (p2);

where p1 is a log rate regression slope and p2 a linear reg slope. Then the model says that the indirect effect is p1*p2, which is also a log rate slope. You get the effect estimate and SE via

Model constraint:
indir = p1*p2;
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