Indirect effects PreviousNext
Mplus Discussion > Categorical Data Modeling >
Message/Author
 Jim Shaw posted on Monday, November 09, 2009 - 3:11 pm
I am trying to estimate the parameters of a path model where X (independent variable), Y (dependent variable), and Z (mediator) are all binary (ordered categorical) variables.

The MODEL INDIRECT statement can be used to estimate the indirect effect of X on Y via Z when a probit link function is specified in conjunction with the ULS, WLS, WLSM, or WLSMV estimator. I have observed that the WLSMV (and other LS) estimates for X and Z in the model for Y are not equivalent to the corresponding ML estimates. However, the WLSMV and ML estimates for X in the model for Z are the same. Why the discrepancy?

My preference would be to fit models for Y and Z using the ML estimator. However, indirect effects cannot be estimated when the ML estimator is used (due to the need for integration). It seems to me that I should be able to estimate the indirect effect as the product of (1) the estimate for X in the model for Z and (2) the estimate for Z in the model for Y regardless of whether a logit (ML) or probit (WLSMV) specification (estimator) is used.
 Bengt O. Muthen posted on Tuesday, November 10, 2009 - 9:07 am
There are 3 factors involved here: estimator, probit/logit model choice, and z vs z* model choice (z being your observed mediator). ML can do probit, but a remaining difference between the ML approach using probit and the WLSMV probit approach is the z vs z* difference, that is, the choice between the observed binary mediator or its underlying continuous latent response variable. This choice has no impact on the regression of z on x. In the regression of y on the mediator, however, ML uses z while WLSMV uses z*. With z you cannot multiply slopes due to different link functions.
 Jim Shaw posted on Thursday, November 12, 2009 - 11:18 am
Since my previous post, I have read that Mplus substitutes the probit model score variable for the observed categorical variable (Z) in the outcome (Y) equation.

In the context of MLE, the score is the derivative of the log-likelihood function with respect to the product of the regressors and estimated parameters. I am not sure how the score variable is derived following weighted least squares estimation, though I presume it has a similar interpretation.

This leads to two questions:

(1) If the first- and second-stage regressions were estimated using ML probit regression, could one still substitute the score variable from the first-stage regression for Z in the second-stage regression and derive consistent estimates for X (in eq. 1) and Z (in eq. 2) allowing for the computation of the indirect effect?

(2) If the approach discussed in (1) is valid, then could it be extended to nominal variables? Let N be a categorical variable that mediates the relationship between X and Y (as defined previously). Could one fit a ML multinomial probit model to N, generate score variables for each of N's categories (save 1), and then model Y as a function of X and the 3 score variables for N?
 Jim Shaw posted on Thursday, November 12, 2009 - 11:46 am
My comments regarding "N" may have been unclear. I meant to say that N is a nominal variable with 4 levels. Thus, 3 score variables would be generated after modeling of N via multinomial probit.
 Bengt O. Muthen posted on Friday, November 13, 2009 - 9:00 am
I don't know what you mean when you say

"that Mplus substitutes the probit model score variable for the observed categorical variable (Z) in the outcome (Y) equation."

See my previous post for what Mplus does with the mediator in the Y equation.
 Jim Shaw posted on Friday, November 13, 2009 - 11:42 am
In the chapter of his logistic regression text that discusses path analysis with logistic regression, Scott Menard notes that one approach to estimating path coefficients with categorical mediator and outcome variables is to "calculate probit or logit model scores for observed categorical variables and then use these scores as input" for the structural model. He attributes this approach to the chapter you authored in Testing Structural Equation Models.

I interpreted what Dr. Menard wrote as meaning that the score variable predicted from the probit regression of Z on X is substituted for Z in the probit regression of Y on Z and X. That is, Y is regressed on Z* and X instead of Z and X, where Z* is represented by the prediced score for Z from the first regression. With MLE, the score is the derivative of the LL function with respect to x'b.
 Nate Breznau posted on Monday, October 17, 2016 - 2:58 am
In specifying indirect effects using the Model Indirect command with WLSM/WLSMV estimation, does Mplus (I am using version 7) calculate these effects following Bengt's manuscript?:

Muthén, Bengt O. 2011. “Applications of Causally Defined Direct and Indirect Effects in Mediation Analysis Using SEM in Mplus.” Mplus Website https://www.statmodel.com/download/causalmediation.pdf.

And is that the same method as the one tested by Valeri and Vanderweele in this paper?:

Valeri, Linda and Tyler J. VanderWeele. 2013. “Mediation Analysis Allowing for Exposure–mediator Interactions and Causal Interpretation: Theoretical Assumptions and Implementation with SAS and SPSS Macros.” Psychological Methods 18(2):137–50.
 Bengt O. Muthen posted on Monday, October 17, 2016 - 4:34 pm
Q1: Yes, but with a categorical mediator WLSMV uses the latent response variables instead of the observed categorical mediator. I recommend using ML or Bayes.

Q2. Yes.

More information is given in our new book:

http://www.statmodel.com/Mplus_Book.shtml
 Wen-Hsu Lin posted on Friday, August 07, 2020 - 2:03 am
Hi, I also want to run similar model but with bootstrap for CI. However, when I ask estimator = ML, bootstrap cannot be used. So, no logit when asking bootstrap CI? Thank you
 Bengt O. Muthen posted on Saturday, August 08, 2020 - 4:27 pm
Bootstrap can be obtained by by saying ML, but not MLR.
 Wen-Hsu Lin posted on Sunday, August 09, 2020 - 5:38 pm
Thank you Dr. Bengt. But I did this and it said that it cannot go with algorithm=integration. My model is like this:
X: continuous
CX: a bunch of control variables
Z: mediating variable with two categories
Y: outcome with two categories
I wanted to estimate x-->z--->y and the mediating effect. Since I want to get odds, I specified ML (for logistic) but it cannot run bootstrap. Is anything wrong here? Thank you
 Bengt O. Muthen posted on Monday, August 10, 2020 - 3:03 pm
Bootstrap with algo=int is available in the current Mplus version.
 Gaye Ildeniz posted on Tuesday, August 11, 2020 - 6:30 am
Hi,

I am trying to estimate a model with one IV, 4 mediators and 2 DVs. For the IV, the indicators are binary, for the 4 mediators the indicators are ordinal and both the IV and the mediators have continuous latent variables. The two DVs are single observed items on a likert-type scale. I have the option to treat the DVs as continuous or categorical. I have been using WLSMV (because of the indicators in the measurement models) but treating the DVs as continuous thus getting linear regressions. would there be any particular pros or cons if I treated the DVs as ordinal beyond getting probit coefficients?
Thank you.
 Gaye Ildeniz posted on Tuesday, August 11, 2020 - 6:32 am
I am trying to estimate a model with one IV, 4 mediators and 2 DVs. For the IV, the indicators are binary, for the 4 mediators the indicators are ordinal and both the IV and the mediators have continuous latent variables. The two DVs are single observed items on a likert-type scale. I have the option to treat the DVs as continuous or categorical. I have been using WLSMV (because of the indicators in the measurement models) but treating the DVs as continuous thus getting linear regressions. would there be any particular pros or cons if I treated the DVs as ordinal beyond getting probit coefficients?

apologies forgot to add my actual question for this thread:

are there any particular pros or cons if I treated the DVs as ordinal when interpreting indirect effects? also would you recommend using STD or STDYX estimates for the indirect cases in the case above?

Thank you again.
 Bengt O. Muthen posted on Wednesday, August 12, 2020 - 5:43 pm
It sounds like your mediators are latent. Regarding the Likert-scale DV, you would treat it as categorical really only if you have strong floor or ceiling effects.
Back to top
Add Your Message Here
Post:
Username: Posting Information:
This is a private posting area. Only registered users and moderators may post messages here.
Password:
Options: Enable HTML code in message
Automatically activate URLs in message
Action: