Hi, I'm trying to fit a second-order and a bifactor model on a 14-item scale with 2 underlying (first-order) factors. A unidimensional and correlated 2-factor model run fine, but the second-order and bifactor model are both producing an error. For instance the second order model:
TITLE: Second-order factor analysis TVS DATA: FILE IS TVS.dat; VARIABLE: NAMES ARE y1-y16; CATEGORICAL ARE y1-y16; ANALYSIS: ESTIMATOR = WLSMV; MODEL: f1 BY y1-y10; f2 BY y11-y16; f3 BY f1-f2;
gives the follwong error: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL. PROBLEM INVOLVING PARAMETER 80.
The bifactor model produces a similar parameter model.
Do you know what the problem is with these models and how I could run these anyway?
We are testing a bifactor model for an empirically supported traditional 3 factor model due to high correlations between the factors in the 3 factor CFA. Generally, the correlations between the 3 factors range from .6-.8.
We hypothesized, based on theory, that there would be one general factor (with 10 indicators) and three specific factors (2 factors with 3 indicators and 1 factor with 4 indicators); all continuous; variable correlations set to 0. However, our models with the three specific factors and one general factor would not converge. I have tried different starting values as well as setting the covariance to 0 for one of the specific factors as some of the other exploratory analyses I did suggested that that factors had a negative covariance.
Due to the nonconvergence, I tested a model combining two of the specific factors. This collapsing of the factors was also based on theory as well as a .76 correlation between these two factors in the three factor CFA. Is this an accepted solution (to combine the two factors?). Doing this yielded better fit statistics for the bifactor model compared to the three factor CFA.
For us to diagnose the problem, you would have to send input, output, data, and license number to firstname.lastname@example.org.
The EFA version of bi-factor analyais can be very helpful in these situations, so getting V7 might be worth your while if you do a lot of bi-factor modeling.
JOEL WONG posted on Thursday, August 01, 2013 - 1:40 am
I've been reading the works of Steven Reise on bifactor models, and I've 3 questions on the test of bifactor models in Mplus:
1. In a bifactor CFA, why is it important to specify that the specific factors are uncorrelated with each other, i.e., f1 WITH f2@0? Would it be a problem if we know from a regular CFA that the specific factors are in fact strongly correlated with each other?
2. Based on a bifactor model, Reise computes a coefficient omega hierarchical (omegaH), which is how much variance in summed scores can be attributed to a single general factor. Can Mplus compute OmegaH or is information available in the output to compute OmegaH?
3. Reise also computes an explained common variance (ECV) index in bifactor models (common variance explained by the general factor divided by (common variance explained by general factor + common variance explained by specific factors). In the Mplus output under "Model Results," there is a section on variances for the general factor and each of the specific factors. Are these the same as the common variance Reise referred to? If so, could I use these to compute the ECV?
Thanks a lot.
Reise, S. P., Moore, T. M., & Haviland, M. G. (2010). Bifactor models and rotations: Exploring the extent to which multidimensional data yield univocal scale scores. Journal of personality assessment, 92(6), 544-559.