In regression, the scale of exogenous variables is not an issue. Covariates can be continuous or binary. In both cases, they are treated as continuous. Given that the censored variable is the exogenous variable, indirect effect can be computed as the product of the two linear regression coefficients. It will be treated as continuous.
Tracy Witte posted on Tuesday, August 26, 2014 - 7:38 am
I am running a mediation model in Mplus. The exogenous variable is continuous. However, the mediator and the final outcome both have severe floor effects. For the mediator, the scores range from 0-27 (M=1.39, SD = 3.83). However, 75% of the sample has a score of 0. For the outcome variable, scores range from 0-9 (M =0.22, SD =0.80) , and 87% of the sample has a score of 0. I have a few questions:
1) Is it appropriate to model these variables as censored, even though the questionnaires from which they are derived don't explicitly limit responses at a certain value? That is, is it appropriate to model something as censored merely because there are floor effects in a particular sample?
2) Assuming modeling these variables as censored is the way to go, is it necessary to fence in outliers? Doing so would remove some of the variability that we have. However, I'm worried about outliers unduly affecting the results.
3) Is it still possible to use BC bootstrapping in MPlus with censored mediator and outcome variables? And is MLR or WLSMV the best estimator?
4) Do you know of any published examples of this type of analysis that would serve as a good model?
That is a very strong floor effect which may suggest dichotomizing or polytomizing the mediator and outcome. See also,
Muthén, B. & Asparouhov T. (2014). Causal effects in mediation modeling: An introduction with applications to latent variables. Forthcoming in Structural Equation Modeling.
1) Yes, at least if the zero point has is substantively meaningful.
2) You can use Mplus detection of outliers.
3) I would use WLSMV. You can use bootstrapping with WLSMV.
4) No. Although, see
Xie, Y. (1989). Structural equation models for ordinal variables. Sociological Methods & Research, 17, 325-352.
Tracy Witte posted on Wednesday, August 27, 2014 - 9:20 am
Thank you very much for your helpful response! A few follow-up questions:
1) When I attempt to run the model with WLSMV and the model indirect command, I get the error message, "Indirect effects with censored variables are not allowed." The problem appears to be with having a censored variable as the outcome variable, as the model runs ok if the censored variables serve as the mediators, as long as the outcome variable isn't specified as censored. In order to test the significance of the indirect effects, would it be appropriate to use the model constraint command in Mplus (see below), if the mediator and the outcome are censored?
Model: Y on M (p1) X (p2); M on X (p3);
MODEL constraint: new (ind tot); ind=p1*p3; tot=ind + p2
2) You state that I should consider dichotomizing or polytomizing the mediator and outcome. What is the best way to determine whether this should be done? If the model runs ok with the variables specified as censored, does that mean that it is acceptable to interpret the results?
3) Regarding outliers, when I attempted to request those, I got the error message, "The OUTLIERS option is not available with bootstrap." At any rate, I take it from your response that it is important to consider outliers, even when modeling a variable as censored?
1) Yes, you can do it that way. Note, however, that you are then considering the y* variable as the relevant outcome, not y. Here, y* is the uncensored, underlying continuous latent response variable.
2) Censored modeling makes strong assumptions such as normality for y*. Categorizing is perhaps more innocuous.
Jian Wang posted on Wednesday, January 28, 2015 - 11:50 am
Dear Dr. Muthen & Muthen,
I am trying to perform a mediation analysis with binary outcome variable (not censored), continuous mediator (censored) and categorical initial variable (censored). I wonder if tobit mediation method in Mplus works for this scenario?
but the indirect effect estimation requires special consideration as explained in
Muthén, B. & Asparouhov, T. (2014). 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
and the references in it.
As explained in the Muthen (2011) paper referred to there, a reasonable simplification is offered by using the WLSMV estimator.