I am fitting a binary response two level model to measure student performance (say pass and fail) using
lme4. There are a number of covariates. Covariate 5 in the table below is the method of assessment. I wish to apply weights to this model so that the data are matched between a treatment and control on covariate 5. The weights have been derived from a matching process using
quickmatch. The dataset is large and therefore this is the most appropriate matching method computationally. The weights from
quickmatch sum to 1 for the treatment and 1 for the control. When applying the weights in
glmer the standard errors are large but the parameter estimates are sensible*. To make the standard errors sensible, given the size of the dataset, I thought it might be appropriate to scale the weights to reflect the size of the dataset. I rerun the model and sure enough the standard errors are smaller but the parameter estimates have also changed. They still seem sensisble but I don't understand why changing weights by a scalar value should change the parameter estimates.
Quickmatch weight Scaled weight Estimate Std. Error Estimate Std. Error Intercept 0.92216 3.61177 0.96941 0.02972 Covariate1 0.09363 3.99407 0.10846 0.03004 Covariate2 2.27514 3.32276 2.42744 0.02508 Covariate3 -0.03241 2.02241 -0.03927 0.01899 Covariate4 -0.43783 5.90232 -0.48611 0.04424 Covariate5 -0.27863 3.99966 -0.28036 0.03127
I have used weights with linear multilevel models before and have not encountered this issue. Any help would be appreciated.
*Where I use the term sensible, I mean in line with my expectations given other analyses I have performed on the data.