I wish to fit a model in which one latent variable is regressed on 2 other latent variables and their interaction (plus an observed covariate, gender). The indicators for each factor are measured on a 5 point, ordinal scale. I fitted the model treating the indicators as continuous using MLR. I then fitted the model treating the indicators as CATEGORICAL, also using MLR. Can you recommend any diagnostic procedures to determine which set of analysis is most appropriate?
If your variables are ordinal, the most appropriate way to treat them is as categorical variables. If your 5 point variables do not have strong floor or ceiling effects, you can probably treat them as continuous will little ill effect.
Guillermo posted on Friday, January 23, 2015 - 3:53 am
Dear Dr. Muthen:
I have a CFA with 4-point ordinal indicators (not strong floor or ceiling effects). When I treat them as categorical using WLSMV, I get the warning message 'THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE', and the results are somewhat incoherent. However, when I treat them as continuous using ML and MLM, the model runs perfectly and the results are as expected. Is it OK using ML or MLM in a case like this, or is there any way to deal with the non-positive definite matrix?
The data you analyze are different when you treat the variables as categorical versus continuous. A more accurate comparison would be to use the CATEGORICAL option and ML. I would want to understand why treating them most appropriately has a problem. If you want help with this, send the output and your license number to firstname.lastname@example.org.
Guillermo posted on Friday, January 23, 2015 - 6:37 am
I understand that when using ML with the CATEGORICAL option, ML estimation is applied to the polychoric correlation matrix. Is this correct? Would it be any better using MLM?
We have 6 ordinal items repeated across 4 time points and are aiming to fit a latent growth model.
Summing the items cross-sectionally we obtained skewed sum-scores in which the variance decreases across time.
However, if we fit a CFA model with full measurement invariance to the ordinal data (WLSMV and theta parametrisation) the variance of the latent variables actually INCREASES across time. This is the case even when fixing all of the factor loadings and thresholds within and across time to be equal and fixing all of the residual variances for the indicators to 1.
However, if we treat the ordinal indicators as continuous and estimate the model using ML, we see the variances of the latent variables decreasing across time as with the manifest total scores.
Is there a possible explanation for the changing pattern of variances when specifying indicators as categorical or continuous?
When you treat a categorical variable as continuous, the correlations among the variables are attenuated. As a result, the data being analyzed are not the same and the results will different depending on how much attenuation is involved.