解释glm的输出以进行Poisson回归 [英] Interpreting the output of glm for Poisson regression

问题描述

请考虑以下内容:

foo = 1:10
bar = 2 * foo
glm(bar ~ foo, family=poisson)

我得到结果

Coefficients:
(Intercept)          foo  
     1.1878       0.1929  

Degrees of Freedom: 9 Total (i.e. Null);  8 Residual
Null Deviance:      33.29 
Residual Deviance: 2.399    AIC: 47.06 

根据此页面上的说明，似乎foo的系数应为log(2)，但不是.

From the explanation on this page, it seems like the coefficient of foo should be log(2), but it's not.

更一般地说，我认为此输出应该表示lambda = 1.187 + .1929 * foo，其中lambda是泊松分布的参数，但似乎与数据不符.

More generally, I thought the output of this is supposed to mean that lambda = 1.187 + .1929 * foo where lambda is the parameter for the Poisson distribution, but that doesn't seem to fit with the data.

我应该如何解释此回归的输出?

How should I interpret the output of this regression?

推荐答案

泊松模型具有可乘性.这是说，由于某种平均过程的结果，阶次增加1(foo预测变量的增量)将与seq(2，20范围内的相邻偶数整数的比率)相关联. ，乘以2)即exp(0.1929).我认为预测不是很好，但是当您查看可能的值时，还不错.

Poisson models are multiplicative. What this is saying is that as a result of some sort of averaging process that an increase of 1 in the order (increments in the foo predictor), will be associated with ratio of adjacent even integers in the range seq( 2, 20, by 2) that is exp(0.1929). I don't think the prediction is very good but when you look at the possible values, not bad.

> exp(0.1929)
[1] 1.212762

> seq(4,20,by=2)/seq(2,18,by=2) 
[1] 2.000000 1.500000 1.333333 1.250000 1.200000 1.166667 1.142857 1.125000 1.111111 
> mean( (2:11)/(1:10) )
[1] 1.292897

这篇关于解释glm的输出以进行Poisson回归的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！