

Log transformation of a count DV with 0s 

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lmris posted on Monday, November 14, 2011  7:11 am



Hello, I am Jin and have a quick question about the logtransformation 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 zeroinflated poisson model. Given the log transformation is not available for 0, does Mplus logtransform 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 logtransformation, I think I have to use variance and covariance with the logtransformed DV. Any tips would be really really appreciated. Best regards, Jin Lee 


No transformation is made of the DV when it is specified as count. Zeroinflated Poisson is a model for the raw counts, not transformed counts. I don't think the PreacherKelley 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 causallydefined approach to mediation for a count DV shown in the new paper http://www.statmodel.com/examples/penn.shtml#extendSEM 

lmris posted on Monday, November 14, 2011  10:38 am



Thanks much for your answer. Your paper will be really helpful for my further analyses. It was my misundersanding that the counts variables should be logtransformed for path estimation. With the path coefficients from a model whose variables were not logtransformed, does the X>Y coefficient indicate the amount of Y change followed by 1 unit change in x? Plus, could you recommend me any readings, materials, or web site about how the estimation can be made without log transformation for a model with a count outcome? 


Q1. No, that path coefficient indicates the expected change in the log mean of the count variable Y. To get at the expected change in Y, you will have to use the formulas in my paper. Q2. Look at our video and handout for Topic 2 on our web site, covering count regression. And also the book by Hilbe that we refer to there (second edition). 

lmris posted on Monday, November 14, 2011  11:17 am



Thanks again, Dr. Muthen. For clarification, doen't your answer in Q1 imply that the count Y was logtransformed? 


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 nonlinear 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  11:50 am



Now everything's crystal clear. Thanks so much for your help! 

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