# Log-normal vs. log-linear vs. logging the response variable

I've been reading a lot of Wikipedia pages and StackExchange/CrossValidated posts, and I have come to a point where I realize I do not understand some of the terminology I have been using.

What's the difference between log-normal models, log-linear models, and linear models that log the response?

I have been running power simulations for reaction time data (RTs, which are not exactly log-normally distributed, but have definite skew), and testing the power of models that are regressed on the raw RTs (i.e. glm(RT ~ predictors, family="gaussian") in R) vs. models that are regressed on the logged RTs (i.e. glm(log(RT) ~ predictors, family="gaussian")).

I have been referring to the models regressed on log(RT) as log-normal models, as well as sometimes log-linear. After this made some people I talked to confused, I realized I was unsure. They seemed to suggest that log-normal (or possibly log-linear models) were multiplicative models (in that log(predictor_1) + log(predictor_2) = log(predictor_3)). I don't believe that's what is happening in my models, since I'm never logging the predictors (in the log(RT) model, I was conceptualizing it as the predictors having linear effects on the RTs in log space).

For example this link clarified to me that I'm not taking the log of the mean, but taking the mean of the log. Importantly, that suggests to me that I'm not changing the link function. However, I've heard what I'm doing basically the same thing. And then I've heard log-linear models aren't the same as Poisson regression, but Wikipedia seems to say otherwise.

What the heck is going on here?

• One of the problems you're having there is that the term "log-linear model" is used in different contexts (to mean somewhat similar things). – Glen_b Jul 14 '18 at 10:43