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I am running logistic regression in Mplus using FIML. I would like to be able to generate some of the traditional model evaluation statistics that journal reviewers expect for logistic regression, to decrease the odds of my paper being rejected due to a reviewer's lack of familiarity with modelling in Mplus. To this end, I have two questions: 1) The Rsquare statistic in the output (presumably for Y*, per equation 15 of the first technical appendix) is helpful, but I would also like to provide the more commonly reported McFadden Rsquare. McFadden's pseudo Rsquare is a ratio of the estimated and null models' loglikelihoods, but the loglikelihood required is different from the one provided in Mplus' Model Fit section. Is there any way to obtain the loglikelihood statistic required for McFadden's Rsquare in the Mplus output? 2) I would also like to calculate the Hosmer & Lemeshow goodnessoffit statistic. For a model without missing data, I could calculate it from the parameter estimates. But this is a poor approach for a model with missingness on variables that strongly predict the outcome variable. Is there any way to generate predicted probabilities (or predicted Y* values for all observations in a dataset) using the Mplus model's FIMLbased estimates? Or would this be a violation of the assumptions required in an FIML modelling context? 


1) You can get the McFadden Rsquare using 2 runs, one with all the slopes fixed at zero. 2) It sounds like you have missingness on covariates  I don't know the best way to do get the predicted probs for that case. 


Thank you for the guidance. When I do the two runs to get McFadden's Rsquare, what values should I plug into the Rsquare equation? I tried using the Loglikelihood from the Model Fit section, but the resultant value was far from the true McFadden Rsquare I calculated based on running the same model in SAS: 0.014 from Mplus vs. 0.149 from SAS (all variables had complete data). Note: this was a simulation dataset, and the SAS value is inline with expectations. 


Show me the formula you use, the output section from Mplus where you pick up the LL values, and how you plug in the values. 


The formula I'm using is: R2v = 1  LLM / LL0 (LLM = LL of the estimation model; LL0 = LL of the null model) I've pulled the LL values from the Model Fit section of the output. For the estimation model:
MODEL FIT INFORMATION Number of Free Parameters 19 Loglikelihood H0 Value 6715.375
And for the null model:
MODEL FIT INFORMATION Number of Free Parameters 15 Loglikelihood H0 Value 6808.280
This results in: R2v = 1  6715.375 / 6808.280 = 0.0136 By contrast, the SAS output of the same estimation model includes:
Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 1251.175 1073.364 SC 1256.083 1097.903 2 Log L 1249.175 1063.364
R2v = 1  (1063.364/2) / (1249.175/2) = 0.1490 All parameter and variance estimates are equivalent across the two programs. 


The loglikelihood values are very different between what you report for SAS and Mplus, so something is off here. For instance, the LL for the Mplus H0 model is 6715.375 whereas the SAS number is 531.682, which is 10 times less. To sort this out, send your Mplus outputs and a pdf of the SAS output to Support. 


The reason the LLs are so different is that by mentioning their variances your Mplus runs bring the covariates into the model in the sense of estimating their parameters. That implies that you have not one but several DVs and therefore the LLs of the two programs are not on the same metric. Since you are doing regression you don't want to include the covariates in the model. Don't mention the variances of the covariates and you will get agreement. 


Thank you for the clarification. The example I sent you had complete data, for simplicity  I'm sorry that I neglected to mention this. Once I apply the model to a dataset with missing data, I will need to include the covariates in the model to invoke FIML. Based on your response, I take it that the LLs cannot be used to calculate McFadden's Rsquare for the logistic DV when the model utilizes FIML  is that correct? 


I don't know  that is a research question. Perhaps it is possible to do a run with only the covariates  justidentified modeling handling the missingness  and then subtract that LL value from each of the two LL's to eliminate the marginal covariate LL and thereby still consider "y  x" as in McFadden's approach. 


Dr. Muthen, would you still recommend subtracting the covariateonly model LL from the estimated model LL and null model LL to calculate McFadden's Rsquare? I have a similar situation where I'm including the covariates in order to use maximum likelihood but want to calculate a pseudo Rsquare for models with nominal DVs. 


I would do 2 runs, one with all covariate coefficients free and one with all of them fixed at zero. 


To clarify, if this is my model (DV has 3 categories): DV#1 on IV cov1 cov2 ; DV#2 on IV cov1 cov2 ; IV; cov1 ; cov2 ; I would compare the loglikelihood from the model above to the LL from the following model: DV#1 on IV@0 cov1@0 cov2@0 ; 


Right, but you would mention the X parameters in both models and I would do it this way: IV with cov1 cov2; cov1 with cov2 ; 

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