I have conducted a CFA to proof the structure of an questionnaire with 3 dimensions (DA, DB and DC). All 3 dimensions should build a global factor KSI. Because items with 6-point-likert-scales are used I took the WLSMV-estimator for my analysis. If I choose listwise on deletion I have a sample size of 187 persons. If I use the FIML approach as default (TYPE is MISSING), I have a sample size of 203 persons. This is my model card:
DA BY A1@1 A2 A3 A4 A5 A6 A7 A8 A9; DB BY B1@1 B2 B3 B4 B5 B6 B7 B8 B9; DC BY C1@1 C2 B3 C4 C5 C6 C7 C8 C9; KSI BY DA@1 DB DC;
I'm not sure, if the sample size is large enough to use FIML. Do you have some recommendations on this?
My variables are a bit skewed (SPSS results ranging between -1.11 and -0.30). Is the WLSMV-estimator appropriate in this case?
Just one point of clarification -- if you use TYPE=MISSING with WLSMV, the missing data technique is pairwise present.
In my opinion, your sample is small for any estimator given the size of your model. If you do not have floor or ceiling effects, a piling up at either end of the scale, I would treat the variables as continuous and use MLR. Skewness is really not relevant for categorical outcomes. If you have floor or ceiling effects, you should treat the variables as categorical.
Thanks a lot for your prompt reply. Graphically, there are no floor or ceiling effects (no piling up at either end of the scale). The percentage of scoring the extreme response catergory is nearly always less than 5% compared to the other categories.
So I will use MLR estimator for my analysis.
The aim of my analysis is to reduce the questionnaire, so that I have four items per dimension at the end. I did that already and found a nice solution with 4 items for each of the 3 dimensions and one global factor (Results with MLR: p=0.88, RMSEA=0.00 versus Results with WLSMV: p=0.24, RMSEA=0.03).
I agree with you that my sample size is really small for the model with 27 observables.
Do you think, it would be better to confirm the reduction of the questionnaire doing a CFA for each dimension (DA, DB and DC) seperately and showing that the dimensions could be reduced to four items showing uni-dimensionality. And if I done so, putting all 12 observables in one modell (with three first order factors and one second order factor) and showing that the reduced model has an excellent fit?
Do you have some references for the adequate sample size using MRL estimator? I only found Flora & Curran (2004) which showed that the WLSMV-estimator shows adequate statistics even for small sample sizes (min. 100 persons).
I don't think it matters whether you do all factors together or apart. I would probably go for together. You may not have a lot of power given the size of the model and sample size but this is what you have to work with.
I don't think sample size rules of thumb are usually very trustworthy. To truly get close to the sample size you need, you need to do a Monte Carlo study based on your particular data and model. See the following paper which is available on the website:
Muthén, L.K. & Muthén, B.O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, 4, 599-620.