I have zero-inflated exponentially-distributed continuous variables that I would like to use for a latent variable. If the data were discrete (counts), I would have used poisson or negative binomial regression methods, but that is not the case. Is there any other method in Mplus that would be appropriate for this data? For example, would the skew-t distribution be appropriate?
Note: the factor is the dependent variable in a model where there are four observed, normally-distributed predictor variables (w regression paths to the factor).
Alex R posted on Wednesday, June 20, 2018 - 9:19 pm
Thanks for the suggestion, Mr. Muthen. From what I've read the censored option uses tobit regression, which assumes that the uncensored variables are normally distributed. In my case, there is some censoring due to the piling up of 0s, however, it is not theoretically defensible to assume normality of the variables, as they represent extreme human behaviors. For lack of a more specific term, they are exponentially-distributed, resembling the upper tail of a normal distribution.
Is there an appropriate option in Mplus that would not assume normality?
Note that our censored-inflated option is different from regular tobit and provides quite a lot of flexibility when 0's are piling up. This is described fully in Chapter 7 of our RMA book. A mixture may also be used. But an explicit exponential distribution is not available.
After doing some more reading, I'd like to clarify that there is no censoring and the inflation part of the model is not too important (I'm mainly interested in the continuous aspect). Just to be clear, there no option in Mplus that would accommodate continuous response variables (for a latent factor) with this distribution, is there: https://imgur.com/knSS2lq
If I had to analyze such variables individually, I would probably end up using the gamma regression model.
You can try treating the indicators as ordered polytomous variables (ordinal).
Wall, M. M., Guo, J., & Amemiya, Y. (2012). Mixture factor analysis for approximating a nonnormally distributed continuous latent factor with continuous and dichotomous observed variables. Multivariate Behavioral Research, 47:2, 276-313. download paper contact first author show abstract