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| WLSMV Montecarlo - comparing Theta an... |
 
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When running a Montecarlo simulation to compare WLSMV estimation under the Delta and Theta parameterisations, the WLSMV data has to be generated under the Theta parameterisation with the residual variances fixed to 1 for the factor loadings to be comparable:
MONTECARLO:
NAMES = Y1-Y3;
NOBSERVATIONS = 500000;
NREPS = 1;
SEED = 2020;
GENERATE = Y1-Y3 (3 p);
CATEGORICAL = Y1-Y3;
MODEL POPULATION:
F1 BY Y1-Y3*.7;
F1@1;
[Y1$1-Y3$1*-1.25 Y1$2-Y3$2*0 Y1$3-Y3$3*1.25];
Y1-Y3@1;
ANALYSIS:
PROCESS = 4;
ESTIMATOR = WLSMV;
PARAM = THETA;
However, when generating data under the Theta parameterisation like this, the reported polychoric correlations do not match those generated under the Delta parameterisation unless the residual variance is fixed to the same value (0.51). But when I do this, the factor loadings & thresholds are no longer consistent.
Is this to be expected? Should I make some other adjustments in order for the factor loadings, thresholds, and polychoric correlations to all be consistent? |
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| Sorry, posted this before thinking it through properly. The Theta and Delta loadings are in different scales, so I shouldn't expect them to be the same |
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| That's right. |
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