Supplemental Table: Fit Statistics for LCA Models

Parent Report
NonReferred only / -2LL / BIC / bootstrap p
1-Cluster (with age,sex) / -6291.7783 / 12643.3093 / <0.001
2-Cluster (with age,sex) / -5718.9971 / 11579.9069 / 0.008
3-Cluster (with age,sex) / -5663.6026 / 11551.2778 / 0.008
4-Cluster (with age,sex) / -5620.7073 / 11547.647 / 0.058
5-Cluster (with age,sex) / -5595.4858 / 11579.3639 / 0.076
4-Cluster (age only) / -5625.9464 / 11535.718 / 0.072
4-Cluster (sex only) / -5675.0766 / 11633.9783 / 0.338
4-Cluster (age, sad->underactive) / -5618.7109 / 11528.7161 / 0.05
4-Cluster (age, sad->underactive->enjoys little) / -5614.6253 / 11528.0139 / 0.094
Teacher Report
NonReferred only / -2LL / BIC / bootstrap p
1-Cluster (with age,sex) / -3211.4231 / 6482.5988 / <0.001
2-Cluster (with age,sex) / -2624.9118 / 5391.7362 / 0.016
3-Cluster (with age,sex) / -2577.4303 / 5378.9332 / 0.27
4-Cluster (with age,sex) / -2552.2703 / 5410.7731 / 0.254
5-Cluster (with age,sex) / -2538.5486 / 5465.4896 / 0.248
3-Cluster (age only) / -2577.9908 / 5365.1159 / 0.132
3-Cluster (sex only) / -2578.6872 / 5366.5088 / 0
3-Cluster (neither age nor sex) / -2579.1774 / 5352.5509 / 0
3-Cluster (age only, enjoyslittle->shy) / -2572.0876 / 5360.7787 / 0.144
Self Report
NonReferred only / -2LL / BIC / bootstrap p
1-Cluster (with age,sex) / -4958.3599 / 9976.4724 / <0.001
2-Cluster (with age,sex) / -4572.5125 / 9286.9376 / 0.01
3-Cluster (with age,sex) / -4544.6768 / 9313.4261 / 0.034
4-Cluster (with age,sex) / -4521.9859 / 9350.2043 / 0.022
5-Cluster (with age,sex) / -4503.3116 / 9395.0156 / 0.026
3-Cluster (age only) / -4550.2392 / 9309.6127 / 0.022
3-Cluster (sex only) / -4552.4056 / 9313.9455 / 0.034
3-Cluster (age only, won't talk->shy) / -4540.5234 / 9297.6502 / 0.018

Supplemental Table notes on model fitting:

For the parent report, we first fit 1-5 classes with age and sex as covariates. The 4 class solution had the lowest BIC, was 0.05 or greater on bootstrapping and had the fewest significant bivariate residuals. Dropping sex as a covariate did not worsen the BIC, but dropping age did. We then added in a direct effect between sad  underactive and the BIC improved while the model remained 0.05 or greater on bootstrapping. Adding another direct effect with enjoys little made little change in the BIC, so a 4-class solution with age only and with a direct effect sad  underactive was accepted as the best model (indicated in bold).

For the teacher report, we first fit 1-5 classes with age and sex as covariates. The 3 class solution had the lowest BIC, was 0.05 or greater on bootstrapping and had the fewest significant bivariate residuals. Dropping sex as a covariate did not worsen the BIC. Dropping age as a covariate also improved the BIC, but the models were <0.001 by bootstrapping, so age was retained. Adding in a direct effect between enjoys little  shy led to a lower BIC than age only and was still greater than 0.05 by bootstrapping. There were no further significant bivariate residuals, so a 3-class model with age only and with a direct effect between enjoys litte shy was accepted as the best model (indicated in bold).

For the self report, we first fit 1-5 classes with age and sex as covariates. There was no model that was 0.05 or greater on bootstrapping. While the 2-class solution had the lower BIC, the 3-class solution had only one significant bivariate residual. Thus, we decided to choose the 3-class solution as the best model. Dropping sex as a covariate did not worsen the BIC. Dropping age as a covariate made little difference in the BIC, but did make a difference when the one significant bivariate residual, won’t talk  shy, was included as a direct effect. With no particularly outstanding model, a 3-class model with age only and with a direct effect between won’t talk  shy was accepted as the best model (indicated in bold).