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I am running glm on beetle counts data. My predictors are environmental variables and my response variable is the number of beetles.

I ran three glms:

  1. The response variable $Y_1$ is the total number of beetles.

  2. The response is a subset of $Y_1$ ($Y_2$).

  3. The response is also a subset of $Y_1$ ($Y_3=Y_1-Y_2$). In this $Y_3$, there are many zeros in my distribution, so the residual distribution is very far from normal.

How can I transform $Y_3$ to meet the assumption of normality? Does anyone have an equivalent robust non-parametric test?

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    $\begingroup$ If your outcome is a count is there any reason why you are avoiding Poisson regression? $\endgroup$
    – mdewey
    Commented May 29, 2018 at 10:56
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    $\begingroup$ Or negative binomial regression, etc... $\endgroup$
    – Glen_b
    Commented May 29, 2018 at 12:11
  • $\begingroup$ thanks for your answers. I log-transformed to normalize my response variable and diagnosed the model by checking for residuals normality... what is wrong. I will do a simple one glm(Y~X, family=poisson) and check for the goodness-of-fit the model. $\endgroup$
    – Noelline Tsafack
    Commented May 30, 2018 at 6:16

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You should use a Poisson regression (or in case of overdispersion, maybe negative binomial or quasi-Poisson regression). There is no assumption of normality in those models, so no need for transformations. See Normality requirements for GLM and GEE models

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