APIM with count data and proportion data
Message/Author
 Biru Zhou posted on Thursday, October 10, 2013 - 2:21 pm
Hello, I am very new to SEM and Mplus. I have some questions regarding anlayzing proportion data or count data in actor partner interdependence models (APIM). My questions are as follows:
1) What are the appropriate estimators for count and proprotion data for APIM in the context of SEM?

2) APIM with count and proportion data can also be analyzed in the MLM approach using link functions = log and logit repectively (Loeys et al., 2013). What would the interpretation be like in SEM with the appropriate estimators? Would it be the same as in MLM, the results can be interpreted in terms of odds ratios?

Many thanks!
 Linda K. Muthen posted on Friday, October 11, 2013 - 5:27 pm
1. Maximum likelihood estimation is used for count variables. See the COUNT option in the user's guide to see the available models.

Proportion=Count / N ... you can then use offset modeling with a count variable – see the following post.

http://www.statmodel.com/discussion/messages/23/781.html

2. The results are in the log rate scale. When it is exponentiated, it is a mean.
 Biru Zhou posted on Wednesday, October 16, 2013 - 4:24 pm
Thank you for your reply, Linda. If I have two variables that are proportions (i.e., S2 and P2) and I want to run a simple APIM with S1 and P1 as IVs and S2, P2 as DVs, nS1 as the number of trails for S1 and nP1 as the number trials for P1, would the following syntax be correct:

VARIABLE: NAMES ARE id S1 S2 P1 P2 nS1 nP1;
USEVARIABLES ARE S1 S2 P1 P2 offset1 offset2;
COUNT = S2 P2;
DEFINE: offset1=log(nS1);
offset2=log(nP1)
ANALYSIS: Type = General;
Estimator = mlr;
MODEL: S2 ON offset1@1 S1;
S2 ON offset1@1 P1;
P2 ON offset2@1 S1;
P2 ON offset2@1 P1;

Many thanks!

Sincerely,

Biru
 Biru Zhou posted on Thursday, October 17, 2013 - 5:11 am
Hello, in my previous post, I realized that I missed one statement in the model:
P2 ON offset2@1 P1;
S2 WITH P2;

Since S2 and P2 are proportions, should I model is as:

offset1@1 WITH offset2@1 ?

Sincerely,

Biru
 Bengt O. Muthen posted on Thursday, October 17, 2013 - 6:20 am
WITH statements are not allowed with count DVs. Instead, a factor can be defined by the 2 DVs; this lets them correlate beyond what their predictors explain. You should not use WITH for the offsets.
 Catheryn Koss posted on Wednesday, February 03, 2016 - 7:54 am
I am analyzing dyadic data using the APIM model to predict 2 dichotomous outcome variables (1 for husbands, 1 for wives). The data are dyadically structured with one row per dyad. To account for correlations between the DVs, I defined a factor as suggested in an earlier post which seems to work well. However, several sources on APIM suggest to also estimate covariances among the predictor variables using WITH statements. When I do this, my model fails to converge. Are these WITH statements necessary, or does the Mplus default of allowing predictors to covary already account for the nonindependence of the IVs? Thanks in advance for any advice you can give.
 Bengt O. Muthen posted on Thursday, February 04, 2016 - 6:51 pm
Predictors (independent, x vbles) are correlated by default even though these correlations are not estimated for predictors.
 Catheryn Koss posted on Wednesday, February 10, 2016 - 6:53 am
Thank you for the confirmation. I have one more question about modeling an APIM with categorical variables. In order to account for the covariance of the two dichotomous outcome variables, I am following advice given earlier and creating one factor loading on my two outcome variables (adH and adW). I have been defining the factor as follows:
f1@1.0;

Does this seem correct? Thanks in advance.
 Bengt O. Muthen posted on Wednesday, February 10, 2016 - 1:17 pm
That's one way of doing it. It is ok because you achieve the goal of having a single parameter represent the residual covariance.
 Sarah Arpin posted on Saturday, February 24, 2018 - 10:41 am
Hello,

I am trying to estimate a path model wherein my dependent variable is a proportion (# of insomnia symptoms/# days of survey data). Values on this variable are between 0 and 1, and are zero-inflated. As this DV is not count, and includes non-integers, what is the appropriate way of modeling this dependent variable? I've read a bit about censored-inflated estimators. Is this an appropriate way to handle this data, or is there an alternative estimator/approach you would suggest?
 Bengt O. Muthen posted on Saturday, February 24, 2018 - 2:01 pm
You can do censored, censored-inflated, two-part etc. This is described in our Regression and Mediation book in Chapter 7. See also our YouTube video and handout for Short Course Topic 11 on our website.