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I have data with an explanatory variable $X$ (I think I can treat this as continuous, as scores 1-100 on a certain test) and a response variable $Y$ (continuous variable, never lower than 0). Both are NOT normally distributed ($X$ is close to, $Y$ is not at all).

I wanted to do a regression, using glm() in R. However, I cannot decide what family/link function to use.

I found that it does not really matter that my $X$ is not normally distributed. However, it does that my $Y$ is not. There are many 0 observations, i.e. skewed right. Doing a log transformation of this variable makes it more difficult to interpret the results, so I found that using family = Gamma would be appropriate. However, I do not know / understand how to choose a link function. Should it be inverse, log or identity? How can I choose?

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  • $\begingroup$ The link function describes the relationship between the predictor and the response variable, so a good choice will really depend on the nature of the variables. Can you describe $X$ and $Y$? $\endgroup$ – Ous Jun 28 at 9:44
  • $\begingroup$ X is a score of a soccer player on a certain cognitive test, ranging from 0-100. Y is a continuous variable, his market value. $\endgroup$ – Pannie Jun 28 at 9:56
  • $\begingroup$ I thought using the link = log was the best option, but I got an error. I thought this was because log(0) is not possible, so I gave the players with a market value of 0 a 'symbolical' value of 1 for the glm to be able to do the math with these players as well. This also did not work. What should I do? $\endgroup$ – Pannie Jun 28 at 10:00
  • $\begingroup$ Also, X is in fact normally distributed. $\endgroup$ – Pannie Jun 28 at 10:01
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    $\begingroup$ you should look at regression models with a zero inflated continuous response (a number of posts already on site discuss zero-inflated gamma or similar models) $\endgroup$ – Glen_b Jun 29 at 8:45

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