Mplus Users Guide v6.. - Muthén & Muthén

CHAPTER 12MONTE CARLO OUTPUTChi-Square Test of Model FitThe default output for the MONTECARLO command includes a listingof the input setup, a summary of the analysis specifications, samplestatistics from the first replication, the analysis results summarized overreplications, and TECH1 which shows the free parameters in the modeland the starting values. Following is an example of the output for testsof model fit for the chi-square test statistic. The same format is usedwith other fit statistics.Degrees of freedom 8Mean 8.245Std Dev 3.933Number of successful computations 500ProportionsPercentilesExpected Observed Expected Observed0.990 0.994 1.646 1.9270.980 0.984 2.032 2.1760.950 0.954 2.733 2.7840.900 0.926 3.490 3.8710.800 0.836 4.594 4.8920.700 0.722 5.527 5.6330.500 0.534 7.344 8.0000.300 0.314 9.524 9.7380.200 0.206 11.030 11.1350.100 0.108 13.362 13.5890.050 0.058 15.507 15.9570.020 0.016 18.168 17.7060.010 0.010 20.090 19.524The mean and standard deviation of the chi-square test statistic over thereplications of the Monte Carlo analysis are given. The column labeledProportions Expected (column 1) should be understood in conjunctionwith the column labeled Percentiles Expected (column 3). Each value incolumn 1 gives the probability of observing a chi-square value greaterthan the corresponding value in column 3. The column 3 percentilevalues are determined from a chi-square distribution with the degrees offreedom given by the model, in this case 8. In this output, the column 1value of 0.05 gives the probability that the chi-square value exceeds thecolumn 3 percentile value (the critical value of the chi-squaredistribution) of 15.507. Columns 2 and 4 give the corresponding valuesobserved in the Monte Carlo replications. Column 2 gives theproportion of replications for which the critical value is exceeded, which362