ols的时候，如果只是 control variables 不是正态分布，还有必要调整至正态分布吗？

如题。。谢谢！！

不用。自变量不必服从正态分布。

OLS不要求任何变量要正态分布,去看伍德里奇的<计量经济学导论>看两章你就明白OLS该怎么用了.OK.,

soccy 发表于 2010-2-21 09:42
不用。自变量不必服从正态分布。

唉。。。。

为什么唉声叹气？

soccy 发表于 2010-2-21 23:55
为什么唉声叹气？

找不到详细的解释的资料，总觉得雾里看花一样的。。郁闷。

呵呵, 回归的意思就是知道一些变量与另一些变量之间的关系,
这里控制变量就是自变量,因变量需要正态,其实到了后来就是有只要是指数分布族就可以了

爱萌 发表于 2010-2-27 22:41
呵呵, 回归的意思就是知道一些变量与另一些变量之间的关系,
这里控制变量就是自变量,因变量需要正态,其实到了后来就是有只要是指数分布族就可以了

It is a BIG blunderer.

Where do you see the 因变量需要正态 (need to be normally distributed) in a regression model? The error term in a regression model is only assumed its first and second moments. There is no 'shape'  (normality) needed.  

"其实到了后来就是有只要是指数分布族就可以了" if y does not belong to exponanial family, what will it happen. Regression model will be invalid???

8# bobguy

For ols, we really do not need the error terms to be normal. But if you want to take statistical inference of betas or responses, we always assume that the error terms be normal. Because we have so many statistical tools from normal, like F-test, chi-sq test. And luckly, the Maximum Likelihood estimators (assuming that responses are normal) are same as OLS.

Generalized Linear Models (different from General Linear Models) are used to deal with exponential distribution. The coresponding methods is weighted least sqare with ML method.

Sometime, we might normalize or standardlize the covariates for the units. If your models contains covariates length, volume, speed, or weight with various units, you'd better standardlize the data.

zj_ocean 发表于 2010-2-28 13:23
8# bobguy

For ols, we really do not need the error terms to be normal. But if you want to take statistical inference of betas or responses, we always assume that the error terms be normal. Because we have so many statistical tools from normal, like F-test, chi-sq test. And luckly, the Maximum Likelihood estimators (assuming that responses are normal) are same as OLS.

Generalized Linear Models (different from General Linear Models) are used to deal with exponential distribution. The coresponding methods is weighted least sqare with ML method.

Sometime, we might normalize or standardlize the covariates for the units. If your models contains covariates length, volume, speed, or weight with various units, you'd better standardlize the data.

"But if you want to take statistical inference of betas or responses, wealways assume that the error terms be normal. Because we have so manystatistical tools from normal, like F-test, chi-sq test."   ---  Agree ! For a small sample size, the normality is necessary for statistic inference. This assumption can be relaxed under a large sample size.

"And luckly, the Maximum Likelihood estimators"  OLS is almost the same as ML under normality assumption. But variance estimation is biased and need to be adjusted by DF in ML. Both are equivelant under a large sample size. OLS was used by Gauss and others before the normal distribution was introduced by Gauss several years later. And ML was invented by Fisher many years later. I believe he got some idea from Laplace.

"Sometime, we might normalize or standardlize the covariates for theunits. If your models contains covariates length, volume, speed, orweight with various units, you'd better standardlize the data. " When you want to contrast the coefs, the normalization of the covariates makes sense. But it is not necessary.