Regression model for a 2x3 mixed design with repeated measures? Edited: I have a mixed (2x3) design setup where the between-subjects factor is "gender"(2 levels) and the within-subjects factor is "group"(3 levels). The main IV of interest is gender, however I suspect there might be some interaction between gender and group which I want to incorporate into the model. I was wondering how to include repeated measures for each individual, and how to specify such a regression model? Would it be proper to include a random intercept term to account for the repeated measures for each individual?
In an Anova one can specify an error term for each individual, or using a mixed effects model, one can specify a random intercept for each individual but I am not sure if this is an efficient way to do it.
Thanks in advance!
 A: It isn't so much the restriction imposed on the range of values observed in your outcome than it is a lack of variation in your independent variable(s).

As the main IV of interest is dummy coded I cannot control for fixed effects by demeaning the data.

A fixed effects model will adjust for time-invariant variables with time-invariant effects. As a consequence, all time-constant covariates will be dropped from estimation. The gender variable is likely a time-invariant attribute of most individuals, assuming a person identifies with the same gender across all three waves in your panel.

However, I think that controlling for individual fixed effects might be proper (I expect the omitted variables are correlated with some of the independent variables).

If you suspect the omitted variables are correlated with your explanatory variable(s) of interest, then a fixed effects model is appropriate. If gender is the principal variable in your analysis, then the individual fixed effects already adjust for this.

However, then I would need to include individual dummy variables (the LSDV approach) for all individuals (300 in total) in the dataset. Can this be done, or is it better to use a random effects model?

You don't need to do this.
The least squares dummy variables (LSDV) estimator produces mathematically equivalent estimates to a model using deviations from the within-individual time means. If demeaning your equation results in gender being dropped from your model, then estimating a series of $N-1$ dummies for each individual doesn't offer any advantages. Again, a model incorporating individual-specific effects adjusts for all time-invariant confounders at the individual level, whether measured or unmeasured. I don't know how your data is organized, but if your data has a nested structure then you may wish to estimate a fixed effect at a higher level of aggregation.
It is difficult to offer further guidance without seeing your data. If the gender dummy is of substantive interest, then one approach is to multiply gender with a series of time indicators. The classic example is the investigation of the effect of gender on a person's wage. The main effect for gender cannot be identified, but the coefficients on your interactions should be. Another approach to consider is the one proposed by Mundlak (1978) for a fixed effect model with time-invariant variables.
Peruse this old post for a more in-depth appraisal of the recommendations I have made here.
