Jim Shaw posted on Wednesday, September 23, 2009 - 4:39 pm
I have a student who is interested in conducting a path analysis:
(1) Y1 = X (2) Y2 = Y1 + X (3) Y3 = Y1 + Y2 + X,
where Y1 and Y3 are nominal (polytomous) outcomes, Y2 is a dichotomous outcome, and X is a set of continuous exogenous variables. We are receiving error messages that suggest nominal outcome variables (e.g., Y1) cannot be treated as regressors when modeling other outcome variables (e.g., Y2 or Y3). Is there any way to get around this in M-Plus, or is our only option to collapse the nominal outcome (Y1) to 2 categories and treat it as categorical in the path analysis? Also, is there any way to calculate indirect effects when modeling nominal outcomes in a path analysis? If outcomes are categorical, then I believe one may calculate indirect effects by simply multiplying the appropriate probit coefficients.
I assume y1 and y3 are unordered polytomous variables. If they are ordered, you should using the CATEGORICAL option.
Unordered polytomous variables cannot be used as mediators. As predictors, they would be treated as continuous variables which would be incorrect as they have no order.
Jim Shaw posted on Thursday, September 24, 2009 - 5:15 am
Thanks for the information. That is what I suspected. So it seems our only real option is to collapse the problematic variable (Y1 in this case) to two categories and treat it as categorical in the analysis. This would be analogous to collapsing health insurance from four cats (public insurance, private insurance, both, or neither) to two cats (insured or uninsured).
Is there any way to calculate indirect effects when one of the outcomes is nominal? I believe Mplus uses numerical integration when fitting models to nominal outcomes and that this precludes use of the "model indirect" statement. Using the above example, and assuming Y1 was collapsed and treated as categorical, is there any way we could estimate the indirect effect of Y1 on Y3 via Y2? For instance, could we estimate (3) with and without adjustment for Y2 and then take the difference between the adjusted and unadjusted estimates for Y1 as estimates of the variable's indirect effects? There would be a separate indirect effect estimate for each (save one) category of Y3 since Y3 would be treated as nominal in the estimation.
I don't think mediation via a nominal mediator m has been studied methodologically - but correct me if I am wrong. One possible direction to go would be to create a latent class variable c where the nominal categories of c are the same as the observed nominal variable categories of m (this is done via logit thresholds). c on x is then a multinomial logistic regression and the influnce of c on y is captured by the means of y changing over the c categories (you don't say "y on c", but it has the same effect). This avoids the y on m regression which would treat m as continuous which would not make sense when m is nominal.
One can then explore if there is a need for direct effects y on x. But there isn't any guidance for how one should/could simply quantify how much of the x influence goes via m versus directly. Perhaps that isn't needed. This topic is a method research paper in itself - anyone?
is there a way to specify additional indirect effects in a SEM with a multinomial outcome, 5 binary coded and 2 continous predictor variables? The binary variables are considered to be mediated by the continous variables.
If you calculate by hand, you then have to calculate the standard errors by hand using the Delta method to obtain p-values. I would use MODEL CONSTRAINT where you will get the standard errors and p-values automatically.
I would like to estimate the following model: Y1 on X1 X2; Y2 on Y1 X1 X2; where Y1 is continuous and Y2 is a nominal variable. I am using TYPE=MIXTURE to have multiple groupings. I don't care about Mplus calculating indirect effects so I don't include the function MODEL INDIRECT.
When I try to estimate this model, Mplus tells me that it can only estimate this model with Monte Carlo integration. Could you please explain me why I can't estimate it with gaussian quadrature? I would prefer avoiding Montecarlo integration.
Following up on my previous message, I was wondering whether I could go around this requirement of using Monte Carlo integration by renaming variables Y1 to say Y3 when it is on the right hand side. My model would thus look like the following: Y1 on X1 X2; Y2 on Y3 X1 X2;
This way, Mplus wouldn't notice that there is a mediating variable and would not impose the requirement of using Monte Carlo integration. Given that I am not interested in Mplus calculating the indirect effect, would this work too? By this, would the coefficient on Y3 be unbiased?
The reason for Monte Carlo integration is probably because your mediator has missing data, so for some subjects it is a latent variable which together with a nominal/categorical outcome gives numerical integration. Because for some subjects it is missing and for others it is not, thereby varying the dimensionality of the integration, Monte Carlo integration is used. If you use listwise deletion you avoid this.
I don't understand why you use Type=Mixture when you specify Y2 as nominal.
I don't know how it would work having 2 copies of the mediator in the model.