Ideally, the observed data should have the sample mean equal to the sample variance (or close to one another except for randomness) in order for the Poisson Regression model to be appropriate for that data. If the observed count data for a sample has a variance that is larger than the sample mean, it is said to be over dispersed.

Question

Ideally, the observed data should have the sample mean equal to the sample variance (or close to one another except for randomness) in order for the Poisson Regression model to be appropriate for that data.  If the observed count data for a sample has a variance that is larger than the sample mean, it is said to be over dispersed.

BlackTom AI · Accepted Answer

The question discusses a property of Poisson regression and when it is appropriate to use this model. 
Option 1: True. In a Poisson distribution, the mean and the variance are equal (both equal to the rate parameter λ). Therefore, for Poisson regression to be appropriate, the observed data should exhibit roughly equal sample mean and sample variance, allowing for randomness. When the observed variance is larger than the mean, this is termed overdispersion, which suggests that the Poisson assumption (mean equals variance) is violated and alternative models (like negative binomial) may be more suitable. 
Option 2: False. If one assumes Poisson regression and observes overdispersion (variance greater than the mean), the statement that Poisson is appropriate is not supported. The presence of overdispersion indicates a mismatch between the data and the Poisson assumptions, making False an incorrect stance in this context. 
To summarize the core idea: the Poisson model implies mean equals variance, so equal or near-equal sample mean and variance is desirable; overdispersion (variance > mean) signals potential model misspecification for Poisson rather than suitability. Hence the true description is that observed overdispersion contradicts Poisson appropriateness, reinforcing why the True option aligns with the underlying theory.

类似问题

Poisson Regression uses a logistic transformation on Y so that a linear model can be used on the transformed data.

Poisson regression is a type of Generalized Linear Model.

A Poisson model is a good choice of regression model in which of the following situations:

Name the Supreme Court decision that removed financial constraints on PACs.

Political scientists Joshua Kalla and David Broockman find that senior policy makers made themselves available to _____ between three and four times more often than they did to constituents.

Name the political scientist who argues that parties are designed to serve the needs of ambitious politicians (namely candidates and officeholders).

Name the political scientist who said this famous quote about the problems of pluralism: “The flaw in the pluralist heaven is that the heavenly choir sings with a strong upper-class accent.”

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单