How is the observed coefficient tested in a mixed model?
The observed coefficient is tested against the generated empirical distribution. Since the distributions of coefficients are only approximately asymptotical, two or more of the above are generally done to confirm results of tests that are inconclusive.
How are mixed models different from Ols parameters?
Mixed model parameters do not have nice asymptotic distributions to test against. This is in contrast to OLS parameters, and to some extent GLM parameters, which asymptotically converge to known distributions. This complicates the inferences which can be made from mixed models.
How is a test of zero valid in a mixed model?
Since the variance must be greater than or equal to zero, a test of zero is on the border of the parameter space. Tests of parameters are valid only on the interior of their space and not on the border. The correlation structure within the data complicates using bootstrap procedures to test these statistics which do not have known distributions.
Is there a Wald test for linear mixed models?
For linear mixed models with little correlation among predictors, a Wald test using the approach of Kenward and Rogers (1997) will be quite similar to LRT test results. The SSCC does not recommend the use of Wald tests for generalized models.
Is there another way to tell which model is more predictive?
It was suggested that I use a likelihood ratio test, but as far as I can tell, there isn’t a function in R that can be applied to 2 linear mixed effects models. Is there another way to tell which model is more predictive? You just use an ANOVA test for this like Stéphane and the help file of the package suggest!
Why is correlation important in a mixed model?
Correlation between the tested predictor and the other model predictors, can cause the estimate made from the model including the parameter to be different from a model which holds the parameter to zero. The LRT requires the formal estimation of a model which restricts the parameter to zero and therefore accounts for correlation in its test.
Can a generalized mixed model have an asymptotic distribution?
The variance parameter of a generalized mixed models does not have a known asymptotic distribution. The LRT for these variance parameters at times can be poor estimates. We recommend treating these p-values with caution. The LRT test of a variance parameter equalling zero will be conservative (larger p-value).
How is the significance of a variance parameter tested?
Another source of complications is testing the significance of a variance parameter, θ. Since the variance must be greater than or equal to zero, a test of zero is on the border of the parameter space. Tests of parameters are valid only on the interior of their space and not on the border.
Can a random effect model be used for inference?
Models with random effects do not have classic asymptotic theory which one can appeal to for inference. There currently is debate among good statisticians as to what statistical tools are appropriate to evaluate these models and to use for inference.