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I have a response variable that is non-normaly distributed (~Gamma). Due to the fact that I have a lot of "contamination", I would need to use a robust mixed-effects model method that is able to remove it. I was thinking on using the package robustlmm, however, I don't know if I can use it since my data don't follow a normal distribution.

Does anyone know something about that?

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Note that there is no requirement for your data to follow a normal distribution.

To perform certain inferences we would like the residuals to be approximately normally distributed. However this is not required if you are only interested in prediction.

rlmer:robustlmm does not fit generalized linear mixed models as far as I am aware, so the gamma distribution would not be available.

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  • $\begingroup$ Thanks @Robert Long, so, If I understood well, there is no restriction in my case to use robustlmm::rlmer(), right? I wonder what you mean distinguishing between inference and predictions. In my case, Y is a measure of activity (m.s⁻²) of an animal taken with one device (A), and X is the measure of the same thing (=activity) with another device (B) with more restricted settings and in a different position than device A. The advantage of dev B is that it allows to record longer time periods. Then Y is more accurate measure than X might be very useful in my field (ecology). $\endgroup$
    – Dekike
    Sep 23 '20 at 10:27
  • $\begingroup$ Thus, I want to assess the relationship among Y and X and discuss the suitability of using dev B. My idea was to stablish if the relationship is linear or exponential between variables and also to calculate R². What is my problem? The animal(s) moves little, meaning that I get a gamma distribution of activities. However, the biggest problem is that X measures sometimes go far from the general trend due to its settings and position, generating some extrange patterns in my plot of residuals vs predicted values. $\endgroup$
    – Dekike
    Sep 23 '20 at 10:32
  • $\begingroup$ I tried log-transforming variables, using "natural splines" or using robustlmm to remove the "contamination", which is not contamination. However, I couldn't remove completely my residual patterns. Now, I wonder if I could just run the models I though from the beginning (GLMM with a gamma distribution and a log link function), and then show the residuals patterns to finally say that more research should be done for using X instead of Y, because it is clear that some settings of X are doing that predictions are better or worst depending on X value. $\endgroup$
    – Dekike
    Sep 23 '20 at 10:39
  • $\begingroup$ Using GLMM I get a r2m of 80%, which means that X explains 80% of the variance of Y, however, given that I have residual patterns, I don't know what to do. Your comment about that normal distribution is (or not) required depending on if I make inferences or predictions, has made me think about all this. Could you give me your advice? I am a little bit lost. $\endgroup$
    – Dekike
    Sep 23 '20 at 10:39
  • $\begingroup$ OK. Are you interested in making predictions for new data, or investigating causal relations among your data ? What is your research question ? $\endgroup$ Sep 23 '20 at 13:02

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