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Mplus Discussion > Categorical Data Modeling >
 Damon posted on Sunday, May 16, 2004 - 10:45 am
I'm a mplus novice and have a simple question. Under the categorical outcome analyses examples on your website, you have a path analysis example. In the analysis command, you don't specify "logistic". How then do I interpret the regression coefficients in this model. For example, for y8 on y5, the estimate is .246. I assume that this in not in logodds. Could I use the ouput to determine what the coefficient would be in logodds? Thank you.
 Linda K. Muthen posted on Sunday, May 16, 2004 - 10:52 am
With weighted least squares estimation and categorical outcomes, the regression coefficient is a probit regression coefficient. With maximum likelihood estimation and categorical outcomes, the regression coefficient is a logistic regression coefficient or a log odds. Version 3 allows both estimators with categorical outcomes.
 Peggy Tonkin posted on Friday, January 21, 2005 - 11:22 am
I am running mediational models using path analysis with continuous and binary predictors and continuous and binary outcomes. The estimates are WLSMV using the THETA matrix. I am also using the TYPE=GENERAL COMPLEX because I need to use the CLUSTER function (I am looking at students within schools). Which estimates are appropriate to report?--the StdYX? I am assuming the two binary outcomes are probit estimates?

Thank You,
Peggy Tonkin
 BMuthen posted on Saturday, January 22, 2005 - 3:34 pm
The regression coefficients for binary dependent variables with WLSMV are probit regression coefficients. In line with regular regression, I would report raw coefficients as well as StdYX coefficients except when binary covariates are involved.
 Peter Martin posted on Wednesday, September 28, 2005 - 4:59 am
Hello there,

Within a path model, how do I interpret the coefficient of a path where X is ordinal (but not binary) to a Y that may be either binary, ordinal, or continuous?

(I'm using WLSMV.)

 Linda K. Muthen posted on Wednesday, September 28, 2005 - 10:22 am
The scale of y determines the type of regression that is estimated. The scale of the exogenous x variable is not as issue in estimation. x variables can be either binary or continuous. With a binary or ordinal y variable, WLSMV estimates probit regresison coefficients. With a continuous y variable, WLSMV estimates a simple linear regression coefficent.
 Peter Martin posted on Thursday, September 29, 2005 - 1:55 am
Thanks, Linda. So does this mean that an ordinal X is treated as if it was on interval scale? E.g. in a linear regression, the coefficient would state the increase in Y given an increase of 1 rank in X?

Or does the procedure use the latent variable that underlies X (this latent variable would be estimated, because the X has also paths leading to it)?

Or am I missing the point?
 Linda K. Muthen posted on Thursday, September 29, 2005 - 8:12 am
 Peter Martin posted on Thursday, September 29, 2005 - 8:33 am
Sorry to be tenacious - yes to what?
 Linda K. Muthen posted on Thursday, September 29, 2005 - 8:35 am
The question in your first paragraph. Sorry.
 melissa posted on Thursday, July 12, 2007 - 8:30 am
I am running a SEM in which:

One endogenous latent variable is indicated by three dichotomous variables.

Another endogenous latent variable is indicated by two continuous and one dichotomous variable.

I have specified the categorical variables in the input and am using the wlsmv estimator.

Here are my questions:
1. Are the estimates related to the first mentioned latent variable (with all three dichotomous indicators) interpreted as probit estimates?
2. How are coefficients related to the second latent variable interpreted?
3. I am currently reporting both B's and StdYX's in my tables. I have the standardized coefficients labeled as Beta's. Is this inappropriate given the above mentioned latent variables? (I have other latent variables that do indeed include only continuous indicators).

Many advance thanks-
 Linda K. Muthen posted on Thursday, July 12, 2007 - 9:11 am
The scale of the dependent variable determines the type of regression coefficient. For categorical factor indicators and WLSMV, probit regression coefficients are estimated. For continuous indicators and WLSMV, linear regression coefficients are estimated.

The labels don't depend on the variables being categorical or continuous. In both cases, the parameter estimates are regression coefficients.
 Preeti posted on Saturday, December 13, 2008 - 2:29 pm
Hello. I am running an SEM model with a categorical outcome using the probit function. I have both latent and observed predictors. The reviewers would like effect sizes on my parameters. Could you please advise me on what would be the appropriate effect size to use and how to calculate it?
 Bengt O. Muthen posted on Saturday, December 13, 2008 - 5:07 pm
You have to decide what effect size is relevant here. Effect size is typically a difference in means under 2 different covariate conditions such a treatment/control, divided by the SD.
 Sarah Ryan posted on Tuesday, September 20, 2011 - 3:08 pm
My model involves:
4 binary and 1 continuous control covariate (x1-x5)
2 observed exogenous predictors (z1-z2)
3 latent exogenous predictors (L1-L3)
1 latent mediator (LM1)
1 observed ordinal outcome (y)

I have a few questions related to coeff. interpretation.

1) I read elsewhere that the interp. of stdzd. probit is not as straightforward as with linear coeff.- Is this simply due to awareness of when to use STDYX and STDY, as well as how there is a diff b/w a unit change in continuous x versus a change in category (binary x)?

2) One of my controls shares a large and large and signif assoc w/ my mediator such that in the full model the expected large and signif assoc b/w the control and the outcome is negative and signif. Can I interpret that to mean that once one controls for the rel. b/w the control and LM1, the remaining variance in the control no longer shares the formerly assumed relationship with y?

3) With an ordinal outcome, does a positive beta indicate that an increase in x is associated with an increase in the probability of moving from one category to the next?
 Bengt O. Muthen posted on Wednesday, September 21, 2011 - 6:40 am
1) Standardizing probit/logit with respect to the covariate variance is no different from linear regression with continuous outcomes. For instance, you don't want to do it for a binary covariate. As for the DV, you don't really need to standardize wrt the binary outcome (or rather its latent response variable counterpart).

2) I'm unclear about this question. Did the control->y relationship go from positive to negative once the mediator LM1 was introduced?

3) Think of it as the latent response variable increasing and when it does the probability of a lower category goes down and a higher category goes up. However, a middle category probability first goes up but with further covariate increase then goes down, favoring a higher category. It is easiest to see the effect in a graph.
 Sarah Ryan posted on Wednesday, September 21, 2011 - 8:29 am
Regarding 2) above:
Yes, you understand correctly. LM1->control is strong and positive, y->LM1 is strong and positive, y->control is small to moderate and negative.

Further, if I model the paths between this control and the two indicators of the latent mediator with which the control shares a direct relationship (indicated by M.I.'s), the sign of the control/indicator relationship is also negative and the standardized y->LM1 now just over 1; y->control remains neg, but grows in magnitude.

I've been doing some reading on suppression effects, but I am not sure that is what is going on. I've also done all the things I can think of to do to assess multicollinearity effects. Collinearity diagnostics with all of the measured varbs. in the model were okay. All of the latent variable correlations are below .6 except for that b/w the mediator and outcome. None of the bivariate correlations are above .5, and most are quite a bit less. Because I'm using three waves of data, it is not logistically possible for the predictors, mediator, and outcome to be measuring the same thing (nor is it theoretically possible). My standard errors range from .01 to .07 (however, the sample size is about 5000- when I run the baseline with the second group (N=1000), the SE's are larger (.03-.14))

 Bengt O. Muthen posted on Thursday, September 22, 2011 - 10:09 am
Sounds like a task for SEMNET.
 Sarah  posted on Wednesday, April 30, 2014 - 1:47 am
I am running a multiple mediation using wlsmv. I understand that for continuous outcomes linear regression coefficients are estimated and for categorical outcomes probit regression coefficients are estimated. I have a couple of questions however.

1. When the outcome is a latent variable consisting of entirely categorical indicators are the path estimates relating to the latent variable linear regression coefficients seeing as the latent variable is continuous?

2. I have two dummy predictor variables, 5 continuous mediator variables and 4 latent outcome variables. How are the coefficients for the direct and indirect effects interpreted? As the latent variables are continuous, does this mean that both the direct effects from the predictors and the indirect effects via the mediators to the latent outcomes are linear regression coefficients?

I hope my questions are clear.

Many thanks for your help.
 Linda K. Muthen posted on Wednesday, April 30, 2014 - 12:33 pm
1. All latent variables are continuous. The scale of the indicators is not an issue. When a latent variable is a dependent variable in a regression, a linear regression is estimated.

2. With all continuous mediators and all continuous outcomes, all coefficients are linear.
 Sarah  posted on Thursday, May 01, 2014 - 6:52 am
Many thanks for your help.
 Evelyn Hall posted on Friday, March 25, 2016 - 1:24 pm

I have a serial mediation model, with two mediators, one latent mediator has categorical indicators.

My variables are non-normal and so I am using WLSMV.

If I am interpreting M1 on X, whereby M1 is a latent variable with categorical indicators and X is a latent variable with continuous indicators. Is the estimator linear??

Also if M1 is a factor from a larger 4-factor solution. Can I account for other factors in the CFA solution using the WITH command?

F1 by X1 X2;
F2 by X3 X4;
F3 by X5 X6;

F1 ON X !

M1 with F2 F3;

Many thanks.
 Linda K. Muthen posted on Friday, March 25, 2016 - 6:07 pm
If m1 is a latent variable, any regression where m1 is a dependent variable is a linear regression.

Exogenous variables are correlated as the default.
 Salmi Md Zahid posted on Wednesday, March 28, 2018 - 1:30 am

Im quite confuse on how to interpret the 'Odds ratio' of my partial proportional odds model.

My DV is categorical (1 to 5): lower to higher benchmark.

My IV is gender (1-Female; 2-Male)

Let say the odds ratio for "category 1 versus higher category" is 0.741. Is it means, male has less probability to obtain higher benchmark compared to female? Or otherwise?

Thank you.
 Bengt O. Muthen posted on Wednesday, March 28, 2018 - 11:54 am
The best way to understand this is to do the computations yourself. From the model estimates you can compute the odds for females and the odds for males and then divide to get the odds ratio.
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