Latent category predicting observed v... PreviousNext
Mplus Discussion > Categorical Data Modeling >
 Jim Prisciandaro posted on Saturday, December 10, 2005 - 11:37 am
Hi Drs. Muthen,

I have been having trouble with an analysis involving a latent categorical variable (c) predicting a dichotomous observed variable ("attach1"). The input statement is:


TITLE: NCS depression EFA

FILE IS "C:\Documents and Settings\Jim\Desktop\fullattach2.dat";

NAMES ARE weight str cluster dep hypins fatigue retard agit conc indeci
death watedec wateinc insom anhed guilt lworth suic attach1 attach2 attach3;
USEVARIABLES ARE weight str cluster dep attach1;
CATEGORICAL ARE dep attach1;
CLASSES = c (2);
MISSING ARE attach1 (9);
WEIGHT = weight;
STRAT = str;
CLUSTER = cluster;





The latent categorical variable is simply an adjustment on a binary variable to remove some measurement error (by setting the thresholds). In this input sample I have left out the prediction statement entirely. I have tried many things revolving around "attach1 ON c#1 c#2;" (e.g., attach1 ON c#1 c#2 in the OVERALL statement; attach1 ON c#1 in the %c#1%
statement; attach1 ON c#2 in the %c#2% statement, and all combinations of these). I repeatedly get errors very similar to this:

*** WARNING in Model command
All variables are uncorrelated with all other variables within class.
Check that this is what is intended.
The following MODEL statements are ignored:
* Statements in the OVERALL class:
* Statements in Class 1:
[ DEP$1 ]
* Statements in Class 2:
[ DEP$1 ]

I have tried running these statements with and without "ALGORITHM = INTEGRATION". Again, all I am trying to do is regress the outcome (attach1) on to the latent class. This is probably a fairly obvious one, but I am new to latent categorical modeling. Any help would be appreciated.

 Linda K. Muthen posted on Sunday, December 11, 2005 - 9:28 am
The ON option is not used for the regression of a distal outcome on the categorical latent variable. See Example 8.6. The parameters of interest are the thresholds of the distal outcomes.
 Jim Prisciandaro posted on Sunday, December 11, 2005 - 12:09 pm
Thank you for your reply. When I include the outcome, I notice the thresholds for the outcome are printed separately for each latent cateogry (and are also printed in "probability scale"). I also notice some portion of results titled "ODDS RATIO RESULTS Latent Class 1 Compared to Latent Class 2," but I am not sure how this is interpreted. Is there any portion of the output that would speak to the question of "what is the expected change in the outcome when we move from latent class 1 to latent class 2?" What I was hoping for with this analysis was to regress outcomes (one at a time) onto a categorical diagnostic variable (e.g., 0 = no disorder; 1 = disorder) that was error free (or reduced). In other words, I was looking for a regression coefficient for the path from the latent categorical predictor to the outcome of interest (some are binary, others ordinal, others continuous), and an r-square value for each outcome variable. Is this mixture approach not a good way to do what I am looking to? Is there a good way to do what I am looking to in Mplus (or anywhere for that matter?)

 Linda K. Muthen posted on Monday, December 12, 2005 - 8:54 am
I think you are getting what you want. It just isn't in the format that you expect. With binary independent variables, the intercept is the estimate for individuals with value 0 and the slope is the shift in going from 0 to 1. So for the group with value 1 for the binary independent variable, you have an intercept that is equal to a + b.

When you regress a dichotomous distal outcome on an unordered categorical latent variable, it is the same as regressing it on a set of dummy binary variables. You obtain a threshold for all but the last class which is a reference class where the threshold is zero. These thresholds are analagous to the intercepts that I mentioned in the first paragraph.
 Jim Prisciandaro posted on Thursday, December 15, 2005 - 7:15 am
Thank you Linda for your help, I think I understand what you are describing. Can I obtain an r-square value for the outcome variable of interest in this framework (either printed by the program or hand calculated)?

 Linda K. Muthen posted on Thursday, December 15, 2005 - 9:24 am
Mplus does not provide an r-square in this case. You would need to compute it by hand. I don't know the formula off hand and I am not sure you would even have the information necessary to do it. I suggest looking in Snijders and Boskers multilevel book. It is the r-square for a logistic regression with dummy variables. Remember it is an r-square for u* not u in this case. I personally would not bother.
 Jim Prisciandaro posted on Friday, December 16, 2005 - 8:55 am
Thank you for your response. Is there any way for me to obtain standardized regression coeffients in this framework, either using the program or by hand (I've noticed that requesting "OUTPUT = STANDARDIZED" does not provide standardized regression coefficients, or thresholds in this case)?

 bmuthen posted on Friday, December 16, 2005 - 10:07 am
You are interested in the relationship between a distal categorical outcome u and a categorical latent variable c. In this case I would recommend not trying to standardize. First, the predictor c is a categorical variable and it does not make sense to talk about a standard deviation change in such a variable (just like you wouldn't want to standardize a slope for gender). Second, the dependent variable u is categorical in which case you have to use a standardization with respect to u*, the underlying continuous response variable. Instead, I think it is best to describe the results in terms of parameter estimate sign, significance, and then complement with presenting the estimated probabilities for the u for different c classes.
 Annonymous posted on Tuesday, February 07, 2006 - 12:54 pm
In a structural equation model with a dichotomous dependent variable 'D', r square values were provided. however i have read that with a binary outcome, the only r-square option is a pseudo r square. is that what is generated by MPlus? The estimator in the model is WLSMV, the model type is meanstructure.
 bmuthen posted on Tuesday, February 07, 2006 - 6:30 pm
Mplus uses the R_square of Zavoina & McKelvey (1975) Math Soc, also discussed in the multilevel book by Snijder & Boskers. It is the R-square for a hypothesized underlying continuous latent response variable.
 Annonymous posted on Wednesday, February 08, 2006 - 6:37 am
To clarify then - it is not appropriate to interpret the R-square provided for an observed dependent variable (as it is not a 'hypothesized underlying continuous latent response variable')?
 bmuthen posted on Wednesday, February 08, 2006 - 7:15 am
An R-square for a categorical dependent variable is a bit controversial. Using this R-square for a latent response variable instead of the categorical dependent variable is accepted in the literature. Nevertheless, a researcher may not find it compelling for a categorical outcome. If so, another option is to test the joint significance of the slopes of sets of covariates and this can be done by running Mplus with and without those slopes fixed at zero.
Back to top
Add Your Message Here
Username: Posting Information:
This is a private posting area. Only registered users and moderators may post messages here.
Options: Enable HTML code in message
Automatically activate URLs in message