John Mathew posted on Wednesday, March 19, 2008 - 11:08 am
Dear Prof Muthen,
We are fitting various models on a particular data set. For each model, we are running MLR and WLSMV to see consistencies across estimated coefficients. Surprisingly, for almost each model, the results from two different estimators are significantly different. In fact, the differences are so pronounced that I find it quite difficult to accept both results simultaneously.
Could you kindly explain to us the possible reasons behind such discrepancies in estimated coefficients.
It sounds like you have categorical outcomes. With MLR, you obtain logistic regression coefficients. With WLSMV, you obtain probit regression coefficients. They are in a different metric. The logisitic coefficient is approximately equal to 1.81 times the probit coefficient.
John Mathew posted on Monday, March 24, 2008 - 10:40 pm
I ran "ESTIMATOR=MLR; LINK=PROBIT;" and "ESTIMATOR=WLSMV;".
You guessed it correctly; we have a binary dependent variable (Y). In fact, we are interested in that ratio of the intercept/threshold associated with Y and coefficient associated with one of the explanatory variable.
The ratio is significantly different across these two estimators.
I'm not sure exactly what ratio you are referring to and how you determine that they are significantly different across the two estimators. If you are referring to the ratio of the parameter estimate to its standard error, they can be different because maximum likelihood likely has smaller standard errors than weighted least squares.
John Mathew posted on Wednesday, March 26, 2008 - 10:55 am
One of the various models that I ran on my dataset is the following;
Y1 = f(X1, X2, Y2); Y2 = g(X3);
where Y1 is binary and Y2 is ordinal variable, X2 and X3 are vector of explanatory variables with some unique elements. X1 is a bounded continuous variable (the maximum value of X1 is 2.75) and present only in Y1 equation.
We need to calculate the ratio of threshold associated with Y1 and beta1 (coefficient for X1). The ratio of Y1 threshold and beta1 should never cross the upper limit of X1.
I am facing two situations that I could not explain to myself;
1. MLR with Link =probit and WLSMV are giving substantially different results. 2. in some models, including the one I mentioned above, the ratio of Y1 threshold and beta 1 goes above 2.75
1. They will be different because y2 is treated as a continuous variable with maximum likelihood and a underlying latent response variable with weighted least squares. 2. I am not sure why you believe this ratio should not go above 2.75.
I want to examine a categorical variable as a mediator of several covariates on a continuous, non-normal outcome. I would like to use the MLR estimator in order to get parameter estimates that are robust to non-normality. However, it is my understanding that I need to use WLSMV in order to test the indirect effect, and am therefore unable to use MLR. Are the parameter estimates for continuous outcomes when using WLSMV also robust to non-normality? How do the parameter estimates using WLSMV when predicting continuous outcomes differ from those using MLR?
Currently, you would need to use WLSMV for an indirect effect with a categorical mediator. WLSMV is not robust to non-normality. The parameter estimates will be the same. It is the standard errors that may differ. You can use the BOOTSTRAP option to obtain bootstrapped standard errors.
Muthén, B. & Asparouhov T. (2015). Causal effects in mediation modeling: An introduction with applications to latent variables. Structural Equation Modeling: A Multidisciplinary Journal, 22(1), 12-23. DOI:10.1080/10705511.2014.935843