### Table 2. Correlations of Latent Variables and Evidence for Discriminant Validity

"... In PAGE 7: ... For satisfactory discriminant validity, the square root of AVE from the construct should be greater than the variance shared between the construct and other constructs in the model [4]. These items also demonstrated satisfactory convergent and discriminant validity (see Table2 ). Having validated the measurement modeling, the next step was testing the hypothesized relationships among various latent constructs in the PLS structural model.... ..."

### 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 7: Properties of the Measurement Model Latent

"... In PAGE 25: ...ncluded 1.0, which supports the discriminant validity of the model (Anderson amp; Gerbing 1988). These above findings support the reliability and validity of the constructs and their indicators. The properties of the measurement model are summarized in Table7 in Appendix. 5.... ..."

### Table 6: Performance comparison for DLCMs with different numbers of latent classes.

2004

"... In PAGE 17: ... In this paper, we did not attempt the problem of estimating the optimal number of latent classes, which is definitely an important open research problem. Instead, we tried three different number of a51 and the performance comparison is tabulated in Table6 and revealed in Figure 9. Generally speaking,... ..."

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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 3b. Solution Statistics for Model 2 (Minimization)

1999

"... In PAGE 4: ...6 Table 2. Problem Statistics Model 1 Model 2 Pt Rows Cols 0/1 Vars Rows Cols 0/1 Vars 1 4398 4568 4568 4398 4568 170 2 4546 4738 4738 4546 4738 192 3 3030 3128 3128 3030 3128 98 4 2774 2921 2921 2774 2921 147 5 5732 5957 5957 5732 5957 225 6 5728 5978 5978 5728 5978 250 7 2538 2658 2658 2538 2658 120 8 3506 3695 3695 3506 3695 189 9 2616 2777 2777 2616 2777 161 10 1680 1758 1758 1680 1758 78 11 5628 5848 5848 5628 5848 220 12 3484 3644 3644 3484 3644 160 13 3700 3833 3833 3700 3833 133 14 4220 4436 4436 4220 4436 216 15 2234 2330 2330 2234 2330 96 16 3823 3949 3949 3823 3949 126 17 4222 4362 4362 4222 4362 140 18 2612 2747 2747 2612 2747 135 19 2400 2484 2484 2400 2484 84 20 2298 2406 2406 2298 2406 108 Table3 a. Solution Statistics for Model 1 (Maximization) Pt Initial First Heuristic Best Best LP Obj.... In PAGE 5: ...) list the elapsed time when the heuristic procedure is first called and the objective value corresponding to the feasible integer solution returned by the heuristic. For Table3 a, the columns Best LP Obj. and Best IP Obj.... In PAGE 5: ... report, respectively, the LP objective bound corresponding to the best node in the remaining branch-and-bound tree and the incumbent objective value corresponding to the best integer feasible solution upon termination of the solution process (10,000 CPU seconds). In Table3 b, the columns Optimal IP Obj., bb nodes, and Elapsed Time report, respectively, the optimal IP objective value, the total number of branch-and-bound tree nodes solved, and the total elapsed time for the solution process.... ..."

### 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 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 shows estimates of the logarithm of model likelihoods for all these models. We see that the RCM (column Q 6 =0, line K =1) is clearly prefered to all LCMs (column Q =0). Under the assumption of fixed brand by quadratic price interactions the optimal latent class model has seventeen classes. The optimal model out of all models under consideration is a general heterogeneity model with K =3.

"... In PAGE 5: ... Table1 : Left-hand side: estimates of the log L(y N jModel), (rel. std.... In PAGE 6: ... These evaluations serve as holdout data to compare our models through their capability to predict. We give the traditional measure mean squared error (MSE) in Table1 and illustrate the differences between predictive densities of selected models for one selected consumer in Figure 4. We include the estimates of individual OLS estimation.... ..."

### 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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