Maartje Boer

CHAPTER 2 44 the four- and five-class solutions, which diminishes the interpretability of the classes (Celeux & Soromenho, 1996). Hence, the two- and three-class solutions were considered more eligible. We selected the three-class solution, which showed a substantial improvement of model fit compared to the two-class solution ( Δ AIC = -492.53 and Δ BIC = -424.54). Table 2.3 Fit Indices and Class Proportions for Five Latent Class Solutions, n = 6,626 C. Par. AIC BIC LMR-LRT Entropy Class size p- value Class 1 Class 2 Class 3 Class 4 Class 5 1 9 51973.96 52035.14 100% 2 19 47073.14 47202.32 < 0.001 0.739 73.91% 26.09% 3 29 46580.61 46777.78 0.014 0.726 61.65% 34.75% 3.60% 4 39 46448.72 46713.87 < 0.001 0.660 57.39% 29.81% 11.79% 1.01% 5 49 46378.87 46712.00 0.122 0.674 57.39% 29.84% 3.53% 8.18% 1.06% Notes. C. = class solution; Par. = number of free parameters; AIC = Akaike Information Criterion; BIC = Bayesian Information Criterion; LMR-LRT = Lo-Mendell-Ruben adjusted Likelihood Ratio Test. A sensitivity analysis was conducted to investigate whether this model selection was robust to conditional dependence of the items. In the one- class solution, 32 out of all 36 possible item correlations were found to be conditionally dependent and specified as such. In the two-class solution, 15 item correlations were specified, and in both the three- and four-class solutions, three item correlations were specified. The LMR-LRT p- value of the four-class solution was not significant ( p = 0.74), and hence no additional classes were estimated. Furthermore, this non-significant finding indicated that the four-class solution did not improve model fit relative to the three- class solution. The three-class solution showed the highest Entropy (0.67), and better model fit in terms of the AIC, BIC, and LMR-LRT p- value than the one- and two-class solutions. Hence, the LCA with conditional dependence also favored the three-class solution. Furthermore, the correlation between adolescents’ class membership based on the three-class solution with conditional dependence and their class membership based on the three- class solution with conditional independence was 0.95, which suggest that the class assignments with and without the imposed assumption were almost identical. These results imply that the model selection is not biased by conditional dependence of the items. Figure 2.3 illustrates the proportions of positive scores on the nine criteria per class. In Class 1 (61.65% of the sample), for all nine criteria, the proportions