负二项式回归:系数解释 [英] Negative Binomial Regression: coefficient interpretation

问题描述

如何在负二项式回归模型中解释系数(截距，分类变量，连续变量)?回归背后的基本公式是什么(例如对于Poisson回归，它是$ \ ln(\ mu)= \ beta_0 + \ beta_1 x_1 + \ dots $)?

How should coefficients (intercept, categorical variable, continuous variable) in a negative binomial regression model be interpreted? What is the base formula behind the regression (such as for Poisson regression, it is $\ln(\mu)=\beta_0+\beta_1 x_1 + \dots$)?

下面是我要解释的特定模型的输出示例，其中seizure.rate是计数变量，并且是分类治疗(安慰剂与非安慰剂).

Below I have an example output from my specific model that I want to interpret, where seizure.rate is a count variable and treatment categorical (placebo vs. non-placebo).

Call:
glm.nb(formula = seizure.rate2 ~ treatment2, data = epilepsy2, 
    init.theta = 1.499060952, link = log)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.3504  -0.8814  -0.4627   0.4279   1.8897  

Coefficients:
                    Estimate Std. Error z value Pr(>|z|)    
(Intercept)           2.0750     0.1683  12.332   <2e-16 ***
treatment2Progabide  -0.4994     0.2397  -2.084   0.0372 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for Negative Binomial(1.4991) family taken to be 1)

    Null deviance: 71.220  on 57  degrees of freedom
Residual deviance: 66.879  on 56  degrees of freedom
AIC: 339.12

Number of Fisher Scoring iterations: 1


              Theta:  1.499 
          Std. Err.:  0.362 

 2 x log-likelihood:  -333.120 

推荐答案

这是系数总和的指数: seizure.rate2 = exp(2.0750-0.4994 * treatment2Proabide) = exp(2.075)* exp(-0.4994 * treatment2Proabide)

It's the exponential of the sum of the coefficients: seizure.rate2= exp(2.0750-0.4994*treatment2Proabide) =exp(2.075)*exp(-0.4994*treatment2Proabide)

或者您可以使用代码 名称(您的型号名称) 该代码将为您提供名称的输出，您可以查看 fitted.values 来获得预测值.我偶尔会做一次仔细检查，以查看是否正确写出了公式.

or you can use the code names(YourModelname) This code will give you output of the names and you can look at fitted.values to give you the predicted values. I occasionally do this as a double check to see if I wrote out my formula correctly.

这篇关于负二项式回归:系数解释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！