I tried to run following model and ended up with an identification problem as it seems. I my model all y Variables are categorical (ordinal or binary). I´m wondering about the hint “THE MODEL ESTIMATION TERMINATED NORMALLY” and the warning about some estimation problems. Did I forgot some nessecary restrictions? Or may it be that the weighting matrix for the WLS is the problem? Do I have too little information in my data?? Also confusing is that the model is estimated without any problems when the relation between Cb and Aad is left out. And the results do not change with using other estimators (WLSMV).
A second question: I want to estimate for different models and compare these models. Is it true that the chi²difference-test is possible for the WLS estimation but not for the WLSMV. So that for the comparison the models should be estimated with WLS and the final model should be re-estimated with WLSMV?
Thanks for helping.
TITLE: xx DATA: xx FORMAT IS free ;
TYPE IS individual ;
VARIABLE: NAMES ARE y1 y2 y3 y4 y5 y6 y7 y8 y9 y10 y11 y12 y13 y14 y15 y16 y17 ; USEVARIABLES ARE y1-y15 ; CATEGORICAL ARE y1-y15 ; WEIGHT is y16 ; USEOBSERVATIONS ARE y17==1 ; MISSING ARE ALL (-99.99) ;
MODEL: Cad by y1 ; Cb by y2 ; Aad by y3 y4 y5 ; Ab by y6 y7 y8 y9 y10 y11 y12 ; PI by y13 y14 y15 ; Aad on Cad; Cb on Aad ; Ab on Cb Aad ; PI on Ab ;
Paul Clear posted on Wednesday, December 07, 2005 - 4:20 pm
I am currently working on a model comparison for my dissertation research. My intention is to compare three alternative confirmatory factor models that have been discussed in the literature for an instrument developed to measure PTSD in children. The sample size is N = 124, there are fifteen items that are on an ordinal, four-category scale. All of the models converge and give interpretable results using the WLSMV estimator. However, the models are non-nested, and I would like to use the information criteria to select the best model. (Fit indices are relatively comparable and acceptable for all models run with WLSMV). As I understand the methodology, it is necessary to estimate parameters using maximumm likelihood to derive information criteria. In doing so (using the MLR estimator), I have been unable to obtain convergence for one of the models.
The model code is as follows: TITLE: Model 3 !Loadings accoring to Yule et al., entire sample-MLR.
DATA: FILE IS "H:\items1.txt";
VARIABLE: NAMES ARE ies1-ies15; USEVARIABLES ARE ies1-ies15; CATEGORICAL ARE ies1-ies15;
ANALYSIS: TYPE IS GENERAL ; ESTIMATOR IS MLR; ITERATIONS = 1000; CONVERGENCE = 0.00005;
MODEL: Int by ies1 ies4 ies5 ies6 ies10 ies11 ies12 ies14; Avo by ies2 ies3 ies7 ies9 ies13; Emo by ies8 ies15; Int with Avo; Int with Emo; Avo with Emo; Int@1Avo@1Emo@1;
OUTPUT: SAMPSTAT RESIDUAL STANDARDIZED CINTERVAL;
The input reading terminates normally, but I get an error message:
THE ESTIMATED COVARIANCE MATRIX COULD NOT BE INVERTED. COMPUTATION COULD NOT BE COMPLETED IN ITERATION 1. CHANGE YOUR MODEL AND/OR STARTING VALUES.
MODEL ESTIMATION DID NOT TERMINATE NNORMALLY DUE TO AN ERROR IN THE COMPUTATION. CHANGE YOUR MODEL AND/OR STARTING VALUES.
I have attempted to manipulate the number of STARTS, both initial and final in order to generate potentially better start values, but this has not worked.
Questions: 1) Is there a problem with identification in the context of this model type? 2) Is there a strategy I might use to obtain the BIC, AIC, etc.?
bmuthen posted on Wednesday, December 07, 2005 - 6:39 pm
Using MLR is a good approach to get BIC and compare models. Note that you should not fix the factor variances @1 because by default the first loading of each factor is already fixed @1.
I specified the following model in ESEM (WLSMV, Delta): 2 correlated common latent factors with 5 ordinal variables (variables loading on all factors), n = 514.
The model fit well the data (CFI =1.000; TLI = 1.006; RMSEA = 0.000; WRMR = 0.114; Chi-square = 0.641, df = 1; p = 0.4234), but only one variable loads significatively on the first factor, yet, with a standardized value greater than 1 associated with a negative error variance. 3 out 5 variables load significatively on the 2nd factor, without issue.
However, I realized that my model was actually structurally under-identified: # of non-duplicated variances and covariances: 5*6/2=15, number of parameters to estimate: 2 latent variances + 1 correlation bw latent + 8 factor loadings + 5 residuals = 16!
1. If the model is under-identified, how can Mplus find a converged solution? 2. Incidentally, how can there be 1 df, when it should be -1? Am I counting the # of parameters to identify correctly?
You are not computing the number of model parameters correctly. As you note, there are fifteen observed sample statistics (H1 parameters). You say that there are sixteen model parameters (H0 parameters). However, in this case the ESEM model is a regular EFA model and as such has ten factor loading parameters, three factor variance/covariance parameters and five residual variance parameters. This adds up to eighteen parameters from which you have to subtract four to take into account the m-squared EFA model restrictions. This gives fifteen minus fourteen, that is, one degree of freedom which is what Mplus prints. This is the case for both continuous and categorical factor indicators.
Note, however, that extracting two factors with only five factor indicators is at the border of what is recommended. See, for example,
Hayashi and Marcoulides (2006). Examining identification issues in factor analysis. SEM, 13, 631-645.
Note that non-identified models can give easy convergence but Mplus gives a warning that the model is not identified and does not print standard errors.