lmris posted on Monday, November 14, 2011 - 1:11 pm
Hello, I am Jin and have a quick question about the log-transformation method in Mplus.
My path model has a count variable as a DV. It has more than 90% of 0s and I fit the model with zero-inflated poisson model.
Given the log transformation is not available for 0, does Mplus log-transform this kind of DV after adding 1 by default? Or 0.1, 0.5 or any other value?
I need this info for calculation of meditational effect size according to Preacher & Kelley (2011)'s method. As the Mplus presents path coefficients based on log-transformation, I think I have to use variance and covariance with the log-transformed DV.
No transformation is made of the DV when it is specified as count. Zero-inflated Poisson is a model for the raw counts, not transformed counts. I don't think the Preacher-Kelley paper is applicable to counts because they talk about linear models for continuous outcomes.
Rather than focusing on effect size representation by standardization and other means, it is important to get the effect itself expressed in a meaningful way and that calls for the causally-defined approach to mediation for a count DV shown in the new paper
No, but I can see how you would think so. You don't first log transform Y and then do linear regression of that new DV on x's. Instead, you keep the original count and apply the Poisson model. The probability for a certain count (0, 1, 2, ...) is a function of exp(-mu), where mu is the mean of the count variable. It is the log of the mean that has a linear regression on x's. So the model is nonlinear. That doesn't mean that we have to transform the count into a new DV.
Perhaps it is easier to understand this in terms of logistic regression describing the probability of a 0/1 outcome. That is also a non-linear model. The "logit" has a linear regression on x. But that doesn't mean that we first transform the 0/1 DV into sample logits and then do linear regression (although in the old days that was how it was done).
lmris posted on Monday, November 14, 2011 - 5:50 pm
Now everything's crystal clear. Thanks so much for your help!