Hi all, I have a question that concerns how could I possibly use a correlation of fixed effects that comes standard with every (g)lmer call. I'll explain the situation I'm encountering briefly. - I used mixed effects models mostly for cross-national survey research. I have both individual-level fixed effects and country-level fixed effects. - My interest is mostly the country-level fixed effects. The individual-level stuff tends to be standard "controls" that reviewers want to see. - I'm not convinced the individual-level fixed effects are entirely necessary. My hunch is they just make for inefficient estimates of the country-level fixed effects that interest me. The individual-level variables just create missing data problems. However, they're stuff that reviewers insist on seeing absent any other information about what a mixed effects model is doing. I have a project (manuscript here: https://www.dropbox.com/s/harb6ylpcxdpalr/etst.pdf?dl=0 | appendix here: https://www.dropbox.com/s/pq8gmr7v1xvvu2h/etst-appendix.pdf?dl=0) that reviewers rejected because the country-level fixed effects were rendered statistically insignificant (i.e. not discernible from zero) upon the inclusion of the individual-level variables. They said that one individual-level attribute (which by itself contributes to listwise deletion of 30% of the data) somehow made the country-level fixed effects "spurious" to its inclusion. This already strikes me as a bold claim for theoretical and statistical reasons, but here's what I did to circumvent this claim: - Estimate just the country-level fixed effects. - Use multiple imputation to generate five full data sets and merge in the macro-level information after the imputation. The results for the country-level fixed effects were almost identical to the analyses with just the country-level fixed effects. - Omit the offending individual-level variables that contribute the most missingness. These results were consistent with the results from the other two estimation strategies. However, the reviewers just didn't buy it and torpedoed the manuscript. Is this something that the correlation of fixed effects could be useful in addressing? Here's the correlation of fixed effects (without the intercepts) for the analysis in question. In this analysis, the three variables at the bottom row (i.e. the two threat indices and the level of democracy) are the country-level variables for this cross-national survey analysis. The other variables are individual-level attributes. It's worth reiterating that every variable that is not binary is scaled by two standard deviations to create a meaningful zero. http://i.imgur.com/eIiZH9b.png Notice that the bottom-left quadrant is entirely white (i.e. the correlation of the individual-level fixed effects with the country-level fixed effects is basically zero). Is this telling me that the correlation for any one individual-level fixed effect and a country-level fixed effect is almost zero (i.e. they have almost no bearing on each other)? The most I've seen anyone discuss this correlation matrix is here: https://stat.ethz.ch/pipermail/r-sig-mixed-models/2009q1/001941.html It is an approximate correlation of the estimator of the fixed effects. (I include the word "approximate" because I should but in this case the approximation is very good.) I'm not sure how to explain it better than that. Suppose that you took an MCMC sample from the parameters in the model, then you would expect the sample of the fixed-effects parameters to display a correlation structure like this matrix. and here ( http://stats.stackexchange.com/questions/57240/how-do-i-interpret-the-correlations-of-fixed-effects-in-my-glmer-output ): The "correlation of fixed effects" output doesn't have the intuitive meaning that most would ascribe to it. Specifically, is not about the correlation of the variables (as OP notes). It is in fact about the expected correlation of the regression coefficients. Although this may speak to multicollinearity it does not necessarily. I should add that I've estimated hundreds of mixed effects models with individual-level and country-level variables and they all have fixed effects correlation matrices that resemble these. I have a strong hunch that individual-level variables don't meaningfully influence the parameter estimates for country-level variables beyond inefficiency introduced by missing data. In research projects where individual-level attributes don't concern the project, I'd like to ignore them for that reason. They just create estimation problems and slow down computation. I might be mistaken, which is why I ask here. I thank you for your time. - Steve
For what can I use a correlation of fixed effects from (g)lmer?
1 message · svm