[R-lang] weights in empirical logit analyses

[João Veríssimo]

Dear all,

I'm conducting an analysis in which responses fall into one of three
possible categories and the main predictors are between-item.

I've followed this post here (by Jaeger: http://is.gd/3VHHmx ), where it
is considered "an acceptable solution" to conduct analyses "over
empirical logit transformed proportions (when cases are weighted
inversely to the variance of the cell mean)".

(I could have used (mixed-effects) logistic regression, but bear with
me... I'm interested in how far this type of analysis can be taken)

So, for each item, I have first transformed proportions of responses
into empirical logits and computed the appropriate case weights
(according to the formulas in Barr, 2008) and then analysed these with
linear methods (linear regression, anovas, t-tests).

When performing between-item analyses, it is straightforward to conduct
the weighting of the cases, by simply passing them as an argument to
lm() or aov().

However...

1. How can cases be weighted appropriately in repeated measures
analyses? (for example, comparing average proportions, across items, for
two different subject groups)

I have considered using aov(), but the help explicitly says "Weights can
be specified by a weights argument, but should not be used with an Error
term".

2. How can different weights be considered in multivariate regression?

I have fitted three regressions, using a one-vs-rest analysis (i.e.,
three lm() models for each of the three categories of responses), but a
reviewer suggested a multinomial analysis.

In order to obtain the multivariate statistics, I have used
lm(cbind(R1.logit, R2.logit, R3.logit) ~ ... ) and then Anova().
But can (or should?) the 3 weight vectors be considered??

3. Should regression assumptions regarding residuals (normality, etc.)
be applied to resid(lm(...)) or to the *weighted* residuals?

Thank you for your help!
João