如何在GLM模型中使用拉普拉斯分布
大家早上好！我是一名博士生，我正在对与其他男性对其他男性入侵者的侵略性有关的行为数据集进行一些统计分析。我正在使用的侵略变量是“男性啄率”（M_PECKS_H）和“男性攻击率”（M_ATTACKS_H），并且都具有泊松分布（我尝试将它们转换为达到正常性，但没有结果）。我想回答的研究问题是：男性的侵略是否取决于他的观念特征？为了回答这个问题，使用R软件，我尝试运行以侵略性变量为因变量的GLM模型，以及将男性装饰品描述为自变量的变量（我为每个攻击变量执行了一个模型，因此总共有两个模型模型）。进行一些初步分析时，我意识到两个侵略变量（男性啄率和男性攻击率）高度相关（b = 0.257，p＆lt; 0.001），因此建议我计算另一个变量的残留物的另一个变量，并将残留物作为因变量输入模型（我将残差变量称为“男性物理攻击”）。问题在于，这个新变量不是正态分布的（我尝试使用常见的转换方法对其进行转换，但无济于事）。我使用StatGraphics 19软件来找出最接近其实际分布的分布，结果是“拉普拉斯分布”。因此，我的最后一个问题是，如何执行具有带有拉普拉斯分布的变量作为因变量的GLM模型？如果没有，可以还有另一个解决方案吗？
我还添加了所涉及的三个变量，如果他们可以帮助答案，请事先感谢您会回答我的所有人！
[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```
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 "males peck rate" (M_PECKS_H) and "males attack rate" (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<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 "males physical aggression"). 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 "Laplace distribution." 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?
I also add the three variables involved, if they can help with an answer Thank you in advance to everyone who will answer me!
[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```
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