No. They aren't nested in groups unless you are generalising to a large/infinite population of groups (and even so n=2 is not sufficient sample so generalise). Group looks like a fixed effect.

If this is a balanced design I think this is just a 2x4 RM ANOVA. The question of mean entering is about whether you want to separate out the effect of group into different components - I'm not sure what the rationale for that would be here. Possibly you want to model the random slope for group? Then a multilevel model might be of interest and then you can decompose that effect into between and within person components (which sum to the total random effect of group).

Unless it is unbalanced or you have time varying covariates or want to look at random slopes I think ANOVA is sufficient.

I am reminded of the statistician's lament: Why wasn't I called at the design stage? Statisticians are often of more use then than after data collection. Remember the song, "And Fisher can always allow for it" was only sung about Fisher. Good luck, D. Booth

For me it is a two level multivariate multilevel model with products (level 1) nested within respondents, unless there are repeated measures of the products , that is occasion (level 1)nested within product (2) nested within respondents (3). The groups are a fixed effect measured at the respondent level, unless they can change groups.

For multivariate model see structures

http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#mlmbkgrd

and http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#multipleresp

It will also depend how the response has been measured, if you are not turning the multiple response on each product into some sort of scale, then it is another level below product.