What model to use with repeated measures of count data with a factor and a covariate? My design involves three dependent variables. They are count data: frequencies of certain words used in a 20-min conversation. They're also repeated measure: the same subjects engaged in three 20-min conversations on three different topics and the use of certain words were counted alongside other variables. There is a factor of 2 levels and a covariate (IQ). My sample size is small (25) and there is an unequal number of subjects between the levels (13 and 12).
I've done a ton of online search and gone through a dozen of stats books but didn't find an appropriate model (I probably have missed something in my search). I think I am looking for a mixed design ANCOVA for count data (mixed effects negative binomial regression perhaps?). Any suggestions?  
 A: This sounds like a repeated measures version of shared frailty models. From what you, say, mixed effects negative binomial or mixed effects Poisson models sound like they would be very reasonable. I.e. you would at a minimum have a random subject effect, a random outcome effect (for the type of thing you are measuring) that would not yet reflect whether two records are from the same conversation, which you could do by numbering conversations across subjects and adding a random conversation effect. To use the notation of the lme4  R package: glmer(count ~ (1|subject)+(1|outcome)+(1|conversation) + factor(something) + IQ, family=poisson(link = "log")).
A: Correct, you wouldn't find much on models with multiple dependent variables based on "count data."  However, let's slice and dice what you are doing to break it down to a simpler idea, and then see if your goal can be accomplished.
I commonly only use the term count data when I have categorical data, such as what is used in a chi-squared test.  For an IQ example, this would be like a 2-by-2 table with 2 columns (low IQ, high IQ), and 2 rows (treated, control) with the counts representing the number of subjects (mice, patients) with the given characteristics in the four categories.  This type of analysis would be done if you said, "there is only count data for the 4 categories, and there are no averages and standard deviations of anything."  
While you do have count data, couldn't you still consider more counts as a better (worse) outcome, and treat it like a Poisson or normally-distributed outcome?  What do the histograms of each of the dependent variables look like for all records combined (independent of each experimental unit -- patient, mouse)?  Also, you are not saying you have 12 and 14 levels (groups) for your categories?  If so, you won't have a lot of data ($n=26$), since some counts will be sparse -- leading to an "ill-conditioned," or "over-parametrized" problem.  This is also called the "curse of dimensionality," i.e., to many dimensions or degrees of freedom for your model.  
Let's keep forging ahead however.  A trick we sometimes use is to assign ranks to measurement values when they are highly skewed, that is, we sometimes (rarely) replace values with the rank of the observation across the research subjects (within a variable).  Then, we input those ranks into a lot of different methods that usually require continuously-scaled data, like ANOVA and regression.  We have done this on smaller sample size mouse data, and when submitting to journals the stat reviewers know we ran into trouble with skewness and outliers in the original data, and transformed to ranks -- so no problem.  We describe that it's not perfect, since ranks are rectangularly-distributed, but there's no problem and the papers get published.  
Now if you look at your counts, don't they look a little like ranks?  If that's true, then probably run a panel-data (longitudinal) model such as GEE (generalized estimating equations) in Stata using a Poisson link for the count data, while clustering on subject ID.  Setting up panel-data regression models requires specification of the ID variable for each subject (mouse, patient, student), so the model can see the repeated measures for each object.  All the large packages (SAS, SPSS, Stata) have panel-data regression models for repeated measurements that allow specification of a link function, and they allow time to be used as a predictor as well.  For Stata, there's not a categorical (count) link function but there is one for SAS. You could use the Poisson link in Stata however.   In R, I am sure panel-data regression models with link functions are available.  If a categorical link is not used, then maybe the Poisson link would be appropriate.  Every package has a Binomial link, but that's used if your outcomes were binomial (y/n, 0/1) during each repeated measurement.  But Poisson can take on count values of $0,1,2,3,4,5,\ldots,\infty$ 
A: Implicitly, you are suggesting that there is one effect of your predictors on your responses, and that your responses really are "only" three different ways to measure this effect. If you want to throw them together, and if they additionally seem to derive from different distributions, I can only think of a hierarchical (Bayesian) approach:
Option 1: model each response separately, but state that the model coefficients (with the exception of the intercept) are identical in all three models. In this way, you can control the distribution of each response, make one normal, the other neg.binom. etc.
Option 2: a single model of a latent response, which is a linear combination of the three measured responses. 
Fundamentally, these two approaches should converge on the same statement: the effect of your predictors on a combination of responses.
To the best of my knowledge, either approach will take you to specialised software (e.g. JAGS, STAN, Win/OpenBUGS), as SEM-packages typically do not offer the flexibility of different distributions in the latent variable. (No-one said it would be easy.)
