Return to Revisions

(This started out as a comment but seemed to be getting too long.)

• This question may be getting less attention than it would otherwise deserve because it is very broad (among other things, you've asked 5 separate questions here). A few answers:

• Conditional and marginal residuals just mean different things, I'm not sure there is a "right answer" here -- you would just be asking about different kinds of outlierishness/leverage. In general it would seem that conditional residuals (i.e. re.form=NULL, or the default, in lme4) would make more sense.

• Note that many of the influence measures you get (e.g. by hatvalues.merMod(), see below) will be conditional on the estimated variance-covariance matrices of the random effects; this is different from the question of whether you're conditioning on conditional modes/BLUPs or not. If you don't want to condition on these estimates, you'll either have to (1) assume multivariate Normality of the estimates of the variance-covariance parameters (ugh) or (2) do some kind of parametric bootstrapping (double-ugh).

• Many of the standard influence measures are more difficult for (G)LMMs if they involve inverting large matrices -- that's not always practical. The influence.ME package does a lot of its work by a semi-brute force method:

the influence() function iteratively modifies the mixed effects model to neutralize the effect a grouped set of data has on the parameters, and which returns returns [sic] the fixed parameters of these iteratively modified models. Note also the difference between influential observations and influential groups, either of which might be of interest.

• The lme4 package does provide a hat matrix (or its diagonal) via ?hatvalues.merMod, you could use these to compute some standard influence measures.
• As far as marginal Q-Q plots for the BLUPs/conditional modes go: if the BLUPs/conditional modes are multivariate Normal, then the univariate distributions will be too. The contrapositive holds (if the univariate distributions are bad, then the multivariate distribution is bad), but not necessarily the converse (if the univariate distributions look good, the multivariate distribution might still be bad), but IMO you'd have to work pretty hard to construct such an example.
• There are formal tests for the misspecification of random effects, e.g. Abad et al. Biostatistics 2010 (see full citation below). Don't know offhand where it has been implemented.

Abad, Ariel Alonso, Saskia Litière, and Geert Molenberghs. “Testing for Misspecification in Generalized Linear Mixed Models.” Biostatistics 11, no. 4 (October 1, 2010): 771–86. doi:10.1093/biostatistics/kxq019.