不懂就问：logistic regression的assumption

1. logistic regression is generalized regression, which means it does not have an explicit error term as linear regression. its error is is embedded in the randomness of the output. There will be similar assumptions as linear regression such as independence, etc.
2. linear regression assumes linear relation on the mean, logistic assumes linear relation on log odds.
3. checking the linear relation for numerical variables on the data is a trickier than regression where you can just do the simple scatter plot. for binary data you have to group the data so you can estimate the log odds, then plot it against the variable you want to check, similar to linear regression.

microsat 发表于 2022-2-15 12:03
我有个疑问。logistic regression是用来干什么的？  比如  weight~ age+sex+city

有人会用odd ratios来 ...

you need to define "importance" first.  
statistical significance is different from practical significance. Whether one is important can change depending on situation.
for example, assume sex=M has a high OR vs F, but in your target sample, it is only 1% of M. is it important? probably not. but if you are concerned with M, it probably is important.
There are many different "importance" measures. You really need to use them according your problem. Specifically some "importance measure" from variable selection may not be very meaningful to real problem.

linear regression 和 logistic regression都是GLM, 关于logistic regression 的 assumption和推导，我看过这个文章总结得比较细致：https://bit.ly/3Hb1ccC    也介绍了从glm角度比较两个模型。

看了这么多回复感觉有两点没有提。
1. 如果做LR是用来分析odd和参数的话，那么binary target不可以是linear separable或者接近。如果是的话那预测很容易，但参数估不出来或者不准。
2. LR的误差项是有分布假设的。LR是可以用discrete choice model从概率公式推导出来。基于的假设是residual符合Gumbell distribution。但这玩意没法观测也就没法验证。所以没人像OLR那样去检查LR residual的分布。说LR是GLM也没啥问题，因为GLM本身就是随便变形下target variable，不用像OLR那么严格。所以也不用说误差项是normal，因为对不对没人在乎。

microsat 发表于 2022-2-15 12:03
我有个疑问。logistic regression是用来干什么的？  比如  weight~ age+sex+city

有人会用odd ratios来 ...

这个问题可以参考GLM的内容来解释。

hea_bow0w 发表于 2022-2-14 20:08
我之前复习的时候参考的assumption，链接是 https://www.statisticssolutions.com/fre ...

make sense

非常谢谢大家！

Model a probability of having an event
Can be related to classification
Can be used as a prediction tool for new input