I have a CFA - 4 facs, each measured by 3 to 5 items. Each factor reflects a type of support; e.g. from company, manager, colleague, family.
The question I want to answer is whether support differs by type i.e. the latent equivalent of a one-way within-subjects anova. I'm assuming that the way forward is to use a latent growth model type setup, but fix paths so that, rather than having intercept/slope/quadratic factors, the usual intercept/rate of change factors represent my preferred contrasts e.g.
msup BY msup1 msup2 msup3 msup4; orgsup BY osup1 osup2 osup3; socsup BY ssup1 ssup2 ssup3 ssup4; fsup BY fsup1 fsup2 fsup3 fsup4 fsup5;
Am I on the right track? Or is there an easier way (I suspect there is - this seems such an obvious analysis to want to do, the fact I can't find a reference suggests I have overlooked something really obvious)
The means of factors that measure different dimensions cannot be compared just as the means of different observed variables cannot be compared. In ANOVA, the same variable is compared for different groups. For repeated measures ANOVA, the same variable is compared over time. Once measurement invariance of a factor is established, the means can also be compared across groups or time.