# GLMM with Gamma distribution vs. Gaussian distribution with log transformation

Is there really a difference in result if I use a GLMM with Gamma distribution vs. a model with a Gaussian distribution with log transformation? If so, how do I choose between the two methods?

See predict.merMod in R is acting strangely (poorly) when using new levels with glmer models for an issue with predicting values from a Gamma model that seems to be fixed using a log-transformed model.

Any thoughts?

GLMs generalize linear regression by allowing you to specify a link function and variance structure. A log link with Gaussian errors leads to one regression model. The natural link for Gamma regression is the inverse link, not the log. One can specify an inverse link, but the Gamma probability model for outcomes still has a different variance structure than normal probability models. See ?Gamma and the mean-variance relationship function variance definition is variance(mu) = mu^2. Also see ?glm, ?family, and here.