

Monte Carlo Numerical Integration 

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Mary Chmelka posted on Wednesday, October 05, 2016  2:26 pm



I have a question regarding Monte Carlo numerical integration and its impact on latent variables in SEM. The dependent variable is a 4indicator latent factor that yielded strong loadings (all indicators >= 0.7) in a SEM without a latent interaction effect. Adding the latent interaction effect, it was necessary to invoke Monte Carlo numerical integration. After that point, the dependent LV’s reference indicator loading dropped to 0.1, while the remaining 3 indicators continued to load strongly. The same pattern appears even when that particular indicator is removed from the latent variable. Loadings for other latent variables in the model (1 exogenous, 2 mediators) did not change after invoking Monte Carlo numerical integration. The sample size is over 6900 cases. Does anyone have an explanation for this change in dependent, latent variable loadings, and is there a recommendation for handing this situation? Thank you in advance. 


The decrease in the loading may be due to the factor variance changing. Version 7.4 has a standardized solution with XWITH. 


I have a model with a binary outcome that requires numerical integration to estimate.In the manual it mentions I should look out for large negative values in the estimation history (tech8). I was wondering if you could give any guidance on how large is "large" here? My model initially shows big reductions in loglikelihood (e.g., 1204.22, 185.79, 52.32) but then as estimation continues I get more negative values, including some slightly larger ones (e.g., 14.07). Are these negative abs change values large enough to be concerned with? Thanks for your help. 


Tech8 is useful to show problems of negative values in the ABS CHANGE column, that is, the likelihood gets lower rather than higher in some iterations. This may be due to low numerical precision. This can be resolved by using more integration points. With more numerical precision it is also possible to sharpen the convergence criterion which can avoid premature convergence and information matrix (SE computation) problems. By default this is Mconvergence=0.0001. A sharper criterion is obtained by e.g. Mconvergence=0.000001. A large negative ABS value can cause the final likelihood value to not be the highest achieved during the iterations. 

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