### Table 5 With Income as an active covariate:

2003

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### Table 3: Means by Group: Cluster and Latent Class Analysis

2005

"... In PAGE 9: ...this information.5 We interpreted the model using the estimated response probabilities (Table 2) and mean responses across groups ( Table3 ). We examined both ranking of mean responses within a group and comparison of mean responses across groups.... In PAGE 9: ... This is a reasonable thing to do since the conditional membership probabilities were 95% or higher for 93% of the sample. Table3 reports the actual means to the attitudinal question for each class. The data in this table tells a similar story to that of the response probabilities both when comparing statistically signiflcant means across classes 5Other demographic difierences such as education level also seemed important.... In PAGE 11: ... Cluster analysis supports the results from the latent-class model and indicates that the three groups difier in their sensitivity.7 Ranking of the means in Table3 within groups and comparision of means across groups shows that the characterization of the three groups is essentially the same. The primary difierence between the two methods is that for cluster analysis, the ranked means within a group are signiflcantly difierent from each other a smaller share of the time.... ..."

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### Table 2b: Test results for simultaneous LCA with heterogeneous class sizes and homogeneous conditional probabilities. The Monte Carlo distribution for 6 latent classes is not derived because the model with 5 latent classes could not be rejected, and the distribution for one latent class is not derived because it was clear in advance that it would clearly be rejected.

"... In PAGE 5: ... Because six extreme forms of anti-social behaviour were excluded, the interpretation of the results of the analyses will necessarily be in terms of relatively more common types of anti-social behaviour. In Table2 , the Monte Carlo distributions of the G2-statistic is shown, which can be compared with the G2-value that is obtained in our sample of 2918 youngsters. Monte Carlo distributions are derived from 50 parametric bootstrap samples.... In PAGE 5: ... For each analysis the Monte Carlo G2-values are ordered according to their value, and in order to give a rough idea about their distribution the first, second, fifth, twentieth, thirtieth, forty-fifth, forty-nineth and fiftieth values are given. For example, the second column of Table2 a shows the solution for one latent class (LC = 1), 18 independent parameters are fitted, the G2-value for the sample is 3958, the smallest (i.e.... In PAGE 5: ... We started with ordinary LCA, ignoring the possible grouping of the 2918 youngsters by age and gender. Table2 a shows that the latent class models with one, two or three latent classes clearly have to be rejected, because the sample G2-value is higher than the Monte Carlo distribution, indicating that it is very unlikely that these models have generated the data. Given the parametric bootstrap procedure, we cannot reject the model with four latent classes.... In PAGE 5: ...1 lt;p lt;.4 1 671 1733 1581 1615 2 696 1759 1602 1634 5 707 1802 1722 1667 20 757 1935 1798 1763 30 807 1997 1856 1833 45 829 2115 1967 1951 49 853 2148 1996 1982 50 875 2184 2001 2016 Table2 a: Test results for unrestricted LCA. The Monte Carlo distribution for 5 latent classes is not derived because the model with 4 latent classes could not be rejected.... In PAGE 6: ... Table2 c: Test results for simultaneous LCA with heterogeneous class sizes and heterogeneous conditional probabilities. In the first columns we find the results for the latent class model with one and with two classes.... In PAGE 7: ...which is .012 for variable 1. Therefore we turned to the simultaneous LC model with both heterogeneous class sizes and heterogeneous conditional probabilities. This model with two latent classes fitted very well for each of the eight age-gender groups (see Table2 c). Although this leads to an enormous increase of independent parameters fitted (namely from 139 for the 5 latent class model in Table 2b to 303 independent parameters for the 2 latent class model in Table 2c),... In PAGE 7: ... This model with two latent classes fitted very well for each of the eight age-gender groups (see Table 2c). Although this leads to an enormous increase of independent parameters fitted (namely from 139 for the 5 latent class model in Table2 b to 303 independent parameters for the 2 latent class model in Table 2c),... In PAGE 8: ... So, although the class structures are different, the latent class structures are conceptually identical. We now interpret the parameter estimates of the partly heterogeneous simultaneous latent class model with five latent classes in Table2 b and the completely heterogeneous simultaneous latent class model with two latent classes in Table 2c. In Table 3 we find the solution for simultaneous LCA with five latent classes, with heterogeneous class size estimates at the top and homogeneous conditional probabilities at the bottom.... In PAGE 8: ... So, although the class structures are different, the latent class structures are conceptually identical. We now interpret the parameter estimates of the partly heterogeneous simultaneous latent class model with five latent classes in Table 2b and the completely heterogeneous simultaneous latent class model with two latent classes in Table2 c. In Table 3 we find the solution for simultaneous LCA with five latent classes, with heterogeneous class size estimates at the top and homogeneous conditional probabilities at the bottom.... In PAGE 12: ... In doing this, we have conditioned on the sample size of each of the groups. This yields 8 Monte Carlo distributions of G2 (see the right part of Table2 c). We have created the Monte Carlo distribution of the overall model (i.... ..."

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### Table 2: Comparison of Heterogeneity Specifications: Discrete Latent Class vs. HB Random Parameters

"... In PAGE 19: ...1. Demand Model Results Table2 lists DIC results for the normal mixture model and BIC results for the discrete mixture and homogeneous cases as well as classical log-likelihood values for reference. The latent class model identified by BIC consists of seven segments, while the mixture model with a diagonally- restricted covariance matrix identified by DIC has three mixing components, and the full- covariance mixture model has two.... In PAGE 22: ... Because the discrete mixture model is natively supported in many statistical packages, it might prove convenient for line optimization. Though fit statistics ( Table2 ) alone argue that the discrete mixture model is dramatically inferior to the normal mixture specification, this does not necessarily mean that, conditional on the resulting estimates, the resulting optimal line will be similarly inferior. Table 3 lists a comparison between the resulting profitability (evaluated post hoc with the full normal mixture model) of the best locally- optimal solutions found using the discrete and continuous mixture demand models over ten multi- start runs with random starting points for each value of J.... ..."

### Table 2a: Test results for unrestricted LCA. The Monte Carlo distribution for 5 latent classes is not derived because the model with 4 latent classes could not be rejected.

"... In PAGE 5: ... Because six extreme forms of anti-social behaviour were excluded, the interpretation of the results of the analyses will necessarily be in terms of relatively more common types of anti-social behaviour. In Table2 , the Monte Carlo distributions of the G2-statistic is shown, which can be compared with the G2-value that is obtained in our sample of 2918 youngsters. Monte Carlo distributions are derived from 50 parametric bootstrap samples.... In PAGE 5: ... For each analysis the Monte Carlo G2-values are ordered according to their value, and in order to give a rough idea about their distribution the first, second, fifth, twentieth, thirtieth, forty-fifth, forty-nineth and fiftieth values are given. For example, the second column of Table2 a shows the solution for one latent class (LC = 1), 18 independent parameters are fitted, the G2-value for the sample is 3958, the smallest (i.e.... In PAGE 5: ... We started with ordinary LCA, ignoring the possible grouping of the 2918 youngsters by age and gender. Table2 a shows that the latent class models with one, two or three latent classes clearly have to be rejected, because the sample G2-value is higher than the Monte Carlo distribution, indicating that it is very unlikely that these models have generated the data. Given the parametric bootstrap procedure, we cannot reject the model with four latent classes.... In PAGE 6: ...04 lt;p lt;.06 1 3416 3244 3108 3032 2 3475 3270 3138 3087 5 3637 3321 3235 3131 20 3742 3507 3336 3244 30 3834 3580 3440 3326 45 3987 3737 3581 3531 49 4077 3817 3724 3599 50 4084 3842 3749 3669 Table2 b: Test results for simultaneous LCA with heterogeneous class sizes and homogeneous conditional probabilities. The Monte Carlo distribution for 6 latent classes is not derived because the model with 5 latent classes could not be rejected, and the distribution for one latent class is not derived because it was clear in advance that it would clearly be rejected.... In PAGE 6: ...16 lt;p lt;.18 3418 Table2 c: Test results for simultaneous LCA with heterogeneous class sizes and heterogeneous conditional probabilities. In the first columns we find the results for the latent class model with one and with two classes.... In PAGE 7: ...which is .012 for variable 1. Therefore we turned to the simultaneous LC model with both heterogeneous class sizes and heterogeneous conditional probabilities. This model with two latent classes fitted very well for each of the eight age-gender groups (see Table2 c). Although this leads to an enormous increase of independent parameters fitted (namely from 139 for the 5 latent class model in Table 2b to 303 independent parameters for the 2 latent class model in Table 2c),... In PAGE 7: ... This model with two latent classes fitted very well for each of the eight age-gender groups (see Table 2c). Although this leads to an enormous increase of independent parameters fitted (namely from 139 for the 5 latent class model in Table2 b to 303 independent parameters for the 2 latent class model in Table 2c),... In PAGE 8: ... So, although the class structures are different, the latent class structures are conceptually identical. We now interpret the parameter estimates of the partly heterogeneous simultaneous latent class model with five latent classes in Table2 b and the completely heterogeneous simultaneous latent class model with two latent classes in Table 2c. In Table 3 we find the solution for simultaneous LCA with five latent classes, with heterogeneous class size estimates at the top and homogeneous conditional probabilities at the bottom.... In PAGE 8: ... So, although the class structures are different, the latent class structures are conceptually identical. We now interpret the parameter estimates of the partly heterogeneous simultaneous latent class model with five latent classes in Table 2b and the completely heterogeneous simultaneous latent class model with two latent classes in Table2 c. In Table 3 we find the solution for simultaneous LCA with five latent classes, with heterogeneous class size estimates at the top and homogeneous conditional probabilities at the bottom.... In PAGE 12: ... In doing this, we have conditioned on the sample size of each of the groups. This yields 8 Monte Carlo distributions of G2 (see the right part of Table2 c). We have created the Monte Carlo distribution of the overall model (i.... ..."

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### Table 1: Goodness of Fit Measures for Latent Class Model Pearson Read-Cressie

2005

"... In PAGE 8: ...data well should have a bootstrapped p-value larger than 0:05. As is shown in Table1 , based on the bootstrapping technique, the one- and two-class models did not flt the data well while the three-class model did. The small p-value of the Read-Cressie statistic suggests that the one- and two-class models should be rejected.... In PAGE 8: ... Information criteria are often used alone without making use of the Pearson and Read-Cressie statistics. Table1 reports the ln likelihood value and information criteria for the one-, two-, and three- class models. The three-class model is also considered the best model using the information criteria.... ..."

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### Table 6 Goodness of Fit Statistics for Latent Means Analyses

"... In PAGE 19: ... This involved estimating the hypothesized models across the samples whilst constraining the intercept (means) of the observed items on the latent factors and the latent means of the factors to be zero as well as the observed factor loadings. Goodness of fit statistics for the analysis of the first and second-order CFA models are provided in Table6 . Neither model constraining the item intercepts exhibited acceptable fit with these data (M1 and M3) and the model fit significantly decreased with the inclusion of invariant latent means (M2 and M4).... ..."

### Table 1: Parameter estimates for the Latent Class CBC model parameter s1 s2 s3

### TABLE A4 ANALYSIS 1: A LATENT CLASS MODEL FOR A WITHIN-SUBJECTS DESIGN

### Table 1: 5 most probable movies for each latent class (type II).

"... In PAGE 8: ... 5.2 Model of type II Table1 shows 5 most probable movies for each class (grid point), i.e.... ..."

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