title: How to use the Laplace distribution in a GLM model
body: <p>Good morning everyone! I am a PhD student and I am performing some statistical analysis on a behavioral dataset related to aggression of pied flycatchers males against other male intruders. The aggression variables I am using are &quot;males peck rate&quot; (M_PECKS_H) and &quot;males attack rate&quot; (M_ATTACKS_H) and both have a Poisson distribution (I have tried transforming them to reach normality, but with no result). The research question I want to answer is: does the male's aggression depend on his ornamental traits? To answer this question, using the R software, I tried running GLM models with the aggression variable as the dependent variable, and the variables describing the male's ornaments as the independent variables (I performed a model for each aggression variable, so a total of two models). Performing some preliminary analysis, I realized that the two aggression variables (males peck rate and males attack rate) are highly correlated (B = 0.257, p&lt;0.001), so it was suggested that I calculate the residuals of one variable for the other, and enter the residuals into the model as the dependent variable (I named the residual variable as &quot;males physical aggression&quot;). The problem is that this new variable is not normally distributed (I tried transforming it with common transformation methods, but to no avail). I used Statgraphics 19 software to figure out the closest distribution to its real distribution, and the result was &quot;Laplace distribution.&quot; So my final question is, how can I perform a GLM model having a variable with a Laplace distribution as the dependent variable? If not, could there be another solution?</p>
  <p>I also add the three variables involved, if they can help with an answer Thank you in advance to everyone who will answer me!</p>
  <pre><code> [1]  0.32763821 -0.94806221  0.42966113 -0.40705296  1.64623753 -0.40606605 -1.69628970
   [8] -0.18288893 -0.24489983 -0.44856501 -0.36268715 -0.38924716  0.20351015 -0.40340094
  [15] -0.24993494 -0.44856501 -0.13957284 -0.04492754 -0.44856501 -0.44856501  1.03867845
  [22] -0.22239376  0.21517449 -0.29628075  0.35389341 -0.41711847  0.08461163 -0.09946749
  [29] -0.44856501 -0.26643190 -0.44856501 -0.59306794 -0.07874262  0.65301432 -0.06027983
  [36]  0.17872541  0.45812268  1.79260136 -0.38160072 -0.42591568  0.44959796 -0.22706765
  [43]  0.23904110 -0.47172246 -0.33855633 -0.53399640  0.17416460  0.13808756 -0.38823318
  [50] -0.08711228  1.30076077 -0.44856501 -0.44856501 -0.05768553  2.01970970  0.16219602
  [57] -0.25543196 -0.16661012  0.52462825  2.55114656 -0.38777473  0.27825875 -0.10859473
  [64] -0.29182520```
  
  ``` M_ATTACKS_H
   [1] 1.04992280 0.72911392 1.27087576 0.05741627 3.12781955 0.09528851 4.18945312 0.29543420
   [9] 0.22116904 0.00000000 0.08587786 0.05931785 1.03394256 0.06246746 0.22338049 0.00000000
  [17] 0.37368626 0.60900265 0.00000000 0.00000000 1.71682289 0.22617124 0.81407035 0.15228426
  [25] 0.99122354 0.03144654 0.92912448 0.50713154 0.00000000 0.21638331 0.00000000 1.33806386
  [33] 0.38772213 1.22320962 1.30573248 0.64516129 1.46143437 3.13621964 0.06696429 0.05078290
  [41] 3.81947744 0.23797719 0.68760611 0.06015038 0.15215554 0.79107505 1.72962227 1.90779014
  [49] 0.06033182 0.37894737 2.86294416 0.00000000 0.00000000 0.39087948 3.21804511 0.61076103
  [57] 0.19313305 0.28195489 1.34604599 4.05882353 0.06079027 0.95642933 0.38980510 0.15673981```
  
  ```M_PECKS_H
   [1] 0.49408132 2.21772152 0.70875764 0.02870813 1.86466165 0.09528851 9.81445312 0.05371531
   [9] 0.03159558 0.00000000 0.00000000 0.00000000 0.68929504 0.03123373 0.04467610 0.00000000
  [17] 0.11677696 0.37069726 0.00000000 0.00000000 0.41440552 0.00000000 0.27135678 0.00000000
  [25] 0.34073309 0.00000000 0.71471114 0.28526149 0.00000000 0.06182380 0.00000000 2.67612772
  [33] 0.03231018 0.21955044 1.65605095 0.03225807 1.00135318 1.61562830 0.00000000 0.05078290
  [41] 5.27315915 0.02974715 0.00000000 0.15037594 0.07607777 1.58215010 1.99801193 2.38473768
  [49] 0.00000000 0.03157895 2.01015228 0.00000000 0.00000000 0.00000000 1.35338346 0.00000000
  [57] 0.00000000 0.00000000 0.67302299 1.91176471 0.00000000 0.41445271 0.08995502 0.00000000```
  </code></pre>