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 Chelsea Jin posted on Thursday, March 01, 2012 - 9:19 pm
I've recently worked on a project involving correlated errors between a count and a continuous variables. For example, I have equations like:

y1 ON x1 - x5;
y2 ON x1 - x6;

Say, y1 is a count variable. It could be negative binomial or zero-inflated. y2 is approximately normally distributed. I want to do "y1 WITH y2", however, the statement doesn't apply to a count variable with a continuous one. So, I'm looking for a solution.

Many thanks!
 Linda K. Muthen posted on Friday, March 02, 2012 - 11:37 am
In your situation, each residual covariance requires one dimension of integration. You need to specify them using the BY option, for example,

f BY y1@1 y2;
f@1;
[f@0];

where the factor loading for y2 will contain the residual covariance parameter.
 Chelsea Jin posted on Friday, March 02, 2012 - 2:57 pm
Oh, thanks so much, Linda! But does it matter much if y1 is either negative binomial, poisson, or zero-inflated distributed?

In addition, what if I want to regress y2 on y1, say "y2 ON x1 - x6 y1", should I do further steps to take y1 as a count variable into account?

I would appreciate that you will reply me.
 Linda K. Muthen posted on Friday, March 02, 2012 - 4:26 pm
No, it does not matter what type of model you are estimating.

You cannot regress y2 on y1 if you have a residual covariance for y2 and y1. Both parameters cannot be identified.
 Chelsea Jin posted on Friday, March 02, 2012 - 4:35 pm
Oh, it's another question... I mean there's no residual covariance between y2 and y1 this time. It's just a continuous variable regressing on a count one. Maybe the count one is a outcome of another regression,like "y1 ON x1 - x5; y2 ON x1 - x6 y1;", so y1 is a mediator.

I think I read some notes saying in Mplus, if a count variable is a predictor, then it's being considered as a continuous variable. Even it's a mediator, it's still a continuous variable. Am I right? Is there any other situation to deal with the count variable as a mediator?

Many thanks.
 Linda K. Muthen posted on Friday, March 02, 2012 - 5:38 pm
When a count variable is a mediator, it is treated as a count variable when it is a dependent variable and a continuous variables when it is an independent variable.
 Chelsea Jin posted on Sunday, March 04, 2012 - 12:06 pm
Hi, I have questions still back to correlated residuals. Now, I have three regressions:

y1 ON x1 - x5;
y2 ON x1 - x6;
y3 ON x1 - x5;

Still, y1 is a count, and y2 is a continuous. y3 could be either count or continuous. What if I want three residuals mutually correlated, should I say:

if y3 is continuous:

f BY y1@1 y2 y3;
f@1;
[f@0];

if y3 is count:

f BY y1@1 y3@1 y2;
f@1;
[f@0];

or two factors have to be extracted, one from y1 and the other from y3,like:

f1 BY y1@1 y2;
f1@1;
[f1@0];
f2 BY y3@1 y2;
f2@1;
[f2@0];
f1 WITH f2;

I'm not sure which one should be correct...

Then for the first one, "f BY y1@1 y2 y3", I can get factor loadings on y2 and y3, but how can I know the correlation coefficient of the residuals between y2 and y3? The same question for the second situation.

Many thanks.
 Bengt O. Muthen posted on Sunday, March 04, 2012 - 6:08 pm
For each pair of residuals you need one factor.
 Chelsea Jin posted on Sunday, March 04, 2012 - 9:27 pm
Hmmm... but how to correlate two count variables' residuals, since the both factor loadings are 1...

Thanks~
 Linda K. Muthen posted on Monday, March 05, 2012 - 6:11 am
They are not both one:

f BY c1@1 c2;
f@1;
[f@0];

where the factor loading of c2 is the covariance.
 Chelsea Jin posted on Monday, March 05, 2012 - 8:23 am
But it's still confusing~ Mplus also estimates the correlations among the factors... How can I know the correlated factors are not the correlated residuals...?

I would appreciate your reply.
 Bengt O. Muthen posted on Monday, March 05, 2012 - 8:46 am
The factors should be uncorrelated:

f1 with f2@0 etc
 Nicholas Bishop posted on Monday, December 23, 2013 - 2:24 pm
Hello,
This is an interesting problem that my apply to a parallel process model I am running. If one growth process is continuous and the other process is specified with a Poisson distribution through the COUNT command, are the covariances between the latent intercepts of each process (would also apply to the slope) specified correctly by a simple WITH statement, or would I need to specify with the BY command as described above? Thank you for your advice.

Nick
 Bengt O. Muthen posted on Monday, December 23, 2013 - 4:59 pm
The WITH statement correlate the latent variables. You can use the BY approach to correlate observed outcomes beyond what the correlation among their latents can explain, so a residual correlation.
 Nicholas Bishop posted on Monday, December 23, 2013 - 8:01 pm
OK that helped, thank you.
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