英文:

Using Vuong Test for SEM with MLM;MLR (robust estimator) / under non normality

问题

我有两个严格的非嵌套模型，我想进行比较。然而，正态分布假设被违反，因此模型是用鲁棒估计器（MLR）计算的。

英文:

I have two strict non-nested models that I would like to compare. However, the normal distribution assumption is violated, so the models were calculated with a robust estimator (MLR).

答案1

得分: 0

Your original post didn't contain a question, but from your comment:

this isn't not allowed for the MLR

原始帖子没有提出问题，但从您的评论中可以看出：

这在MLR中是不允许的

Robust ML estimation is a bit of a misnomer. 鲁棒的最大似然估计有点不恰当。 The point estimates are still obtained via maximum (multivariate-normal) likelihood, and only the SEs and test statistic are corrected for the (estimated) excess kurtosis that impacts them. 点估计仍然是通过最大（多变量正态）似然获得的，只有SE和检验统计量是根据影响它们的（估计的）过量峰度进行校正的。 Vuong's test is a function of casewise (log-)likelihoods, which are still multivariate-normal probability densities when using so-called MLR or MLM. 因此，Vuong的检验是基于案例的（对数）似然的函数，当使用所谓的MLR或MLM时，它们仍然是多变量正态概率密度。 Thus, Vuong's test is not robust to nonnormality. 因此，Vuong的检验对非正态性不鲁棒。 It would be if you were to use a likelihood that allowed for more kurtosis, such as the generalized multivariate skewed t distribution, but I've only seen that implemented in Bayesian programs, in which case there are other more appropriate model-comparison approaches you could use. 如果您使用允许更多峰度的似然，例如广义多变量倾斜t分布，那么它将是鲁棒的，但我只在贝叶斯程序中看到过这种实现，在这种情况下，您可以使用其他更合适的模型比较方法。

Is there a possibility to compare the models with another package and/or test?

有没有可能使用其他包或测试来比较模型？ You could use Vuong's test if you use standard ML estimation just for the purpose of obtaining the (identical) likelihoods. 如果您仅出于获得（相同的）似然值的目的使用标准ML估计，那么您可以使用Vuong的检验。 But I'm not sure how robust Vuong's test is to violations of normality. 但我不确定Vuong的检验在违反正态性时有多鲁棒。

英文:

Your original post didn't contain a question, but from your comment:

> this isn't not allowed for the MLR

Robust ML estimation is a bit of a misnomer. The point estimates are still obtained via maximum (multivariate-normal) likelihood, and only the SEs and test statistic are corrected for the (estimated) excess kurtosis that impacts them. Vuong's test is a function of casewise (log-)likelihoods, which are still multivariate-normal probability densities when using so-called MLR or MLM. Thus, Vuong's test is not robust to nonnormality. It would be if you were to use a likelihood that allowed for more kurtosis, such as the generalized multivariate skewed t distribution, but I've only seen that implemented in Bayesian programs, in which case there are other more appropriate model-comparison approaches you could use.

> Is there a possibility to compare the models with another package and/or test?

You could use Vuong's test if you use standard ML estimation just for the purpose of obtaining the (identical) likelihoods. But I'm not sure how robust Vuong's test is to violations of normality.