03-16-2012 06:42 AM
Are you sure that your metric variables are really metric? If so, are they merely interval or are they ratio?
A very, very common convienient assumption about agreement scales with semantic anchors (such as likert scales) is that they meet the criteria for interval measures. If you think carefully about, maybe they don't.
My point? Maybe ALL your variables are ordinal. That may not be as bad as you fear. Item measures only really have to be additive, as in those that meet Rasch Measurement Model criteria, not gaussian distributed.
Does this help if you are wanting to use the measures in path analysis, say wtih PROC CALIS?
I'd say go ahead and try, and see how far apart your most non-controversial (safest) model's error distribution looks from a gaussian distribution. You can always bootstrap your model to quantify the impact of your ordinal items on your model parameters without relying on standard assumptions.
11-01-2012 10:34 PM
Start wtih the number of measurement items, double that. (two parameters per measurement item, a factor loading, and an error variance). E.g. if you have 7 latent factors with 3 measurement items each you have 21 measurement items each with 2 parameters = 42.
Add the 'triangular number' ((n x (n-1))/2) associated wtih the number (n) of latent factors (and/or manifest structural items if you have a non-standard SEM). E.g. if you have 7 latent factors, (7 x 6)/2 = 21. This is the number of covariances amongst your 7 latent factors you will need to specify for the initial measurement model.
subtotal = 42 + 21 = 63.
Multiply this by 10 = 630. This is your recommended sample size.