.

0 (hodnocen0 x )

BK

Hoboken : John Wiley & Sons, c2010

xxxiii, 285 s. : il. ; 24 cm

ISBN 978-0-470-22839-5 (váz.)

Wiley series in probability and statistics

Obsahuje bibliografii na s. 266-278 a rejstříky

000251983

List of Figures xvii // List of Tables xxi // Acknowledgments xxxi // Acronyms xxxiii // PART I FUNDAMENTALS // 1 General Introduction 3 // 1.1 Overview 3 // 1.2 Conceptual foundation and brief history of the latent class model 4 // 1.2.1 LCA and other latent variable models 6 // 1.2.2 Some historical milestones in LCA 7 // 1.2.3 LCA as a person-oriented approach 8 // 1.3 Why select a categorical latent variable approach? 8 // 1.4 Scope of this book 9 // 1.5 Empirical example of LCA: Adolescent delinquency 10 // 1.6 Empirical example of LTA: Adolescent delinquency 14 // 1.7 About this book 17 // 1.7.1 Using this book 19 // 1.8 The examples in this book I9 // 1.8.1 Empirical data sets 20 // 1.9 Software // 1.10 Additional resources: The book’s web site // 111 Suggested supplemental readings 22 // 1.12 Points to remember 22 // 1.13 What’s next 99 // 2 The latent class model 23 // 2.1 Overview 23 // 2.2 Empirical example: Pubertal development 24 // 2.2.1 An initial look at the data 24 // 2.2.2 Why conduct LCA on the pubertal development data? 27 // 2.2.3 Latent classes in the pubertal development data 28 // 2.3 The role of item-response probabilities in interpreting latent classes 29 // 2.3.1 A hypothetical example 29 // 2.3.2 Interpreting the item-response probabilities to label the latent classes in the pubertal development example 30 // 2.3.3 Qualitative and quantitative differences among the pubertal development latent classes 34 // 2.4 Empirical example: Health risk behaviors 34 // 2.4.1 An initial look at the data 34 // 2.4.2 LCA of the health risk behavior data 35 // 2.5 LCA: Model and notation 39 // 2.5.1 Fundamental expressions 41 // 2.5.2 The local independence assumption 44 // 2.6 Suggested supplemental readings 46 // 2.7 Points to remember 47 // 2.8 What’s next ±1 // The relation between the latent variable and its indicators 49 // 3.1 Overview 49 //

3.2 The latent class measurement model 50 // 3.2.1 Parallels with factor analysis 50 // 3.2.2 Two criteria for evaluating item-response probabilities // for a single variable 50 // 3.2.3 Hypothetical and empirical examples of independence and weak relations 53 // 3.2.4 Hypothetical and empirical examples of strong relations 55 // 3.3 Homogeneity and latent class separation 56 // 3.3.1 Homogeneity 56 // 3.3.2 Latent class separation 57 // 3.3.3 Hypothetical examples of homogeneity and latent class // separation 58 // 3.3.4 How homogeneity and latent class separation are related 64 // 3.3.5 Homogeneity, latent class separation, and the number of response patterns observed 64 // 3.3.6 Homogeneity and latent class separation in empirical examples 65 // 3.4 The precision with which the observed variables measure the latent variable 67 // 3.4.1 Why posterior probabilities of latent class membership are of interest 67 // 3.4.2 Bayes’ theorem 68 // 3.4.3 What homogeneity and latent class separation imply about posterior probabilities and classification uncertainty 69 // 3.4.4 Posterior classification uncertainty even with a high degree of homogeneity and latent class separation 72 // 3.5 Expressing the degree of uncertainty: Mean posterior probabilities and entropy 73 // 3.6 Points to remember 75 // 3.7 What’s next 76 // 4 Parameter estimation and model selection 77 // 4.1 Overview 77 // 4.2 Maximum Likelihood estimation 78 // 4.2.1 Estimating model parameters 78 // 4.2.2 Options for treatment of individual parameters: // Parameter restrictions 79 // 4.2.3 Missing data and estimation 80 // 4.3 Model fit and model selection 81 // 4.3.1 Absolute model fit 82 // 4.3.2 The likelihood-ratio statistic and its degrees of // freedom 83 // 4.3.3 Relative model fit 86 // 4.3.4 Cross-validation 88 // 4.4 Finding the ML solution 89 //

4.4.1 Overview of model identification issues 89 // 4.4.2 Visualizing identification, underidentification, and unidentification 89 // 4.4.3 Identification and information 92 // 4.4.4 How to find the ML solution 92 // 4.4.5 Label switching 94 // 4.4.6 User-provided starting values 94 // 4.5 Empirical example of using many starting values 95 // 4.6 Empirical examples of selecting the number of latent classes 97 // 4.6.1 Positive health behaviors 97 // 4.6.2 Past-year delinquency 98 // 4.6.3 Female pubertal development 99 // 4.6.4 Health risk behaviors 100 // 4.7 More about parameter restrictions 102 // 4.7.1 Reasons for using parameter restrictions 102 // 4.7.2 Parameter restrictions and model fit 103 // 4.7.3 Using parameter restrictions to achieve positive degrees of freedom 103 // 4.8 Standard errors 106 // 4.9 Suggested supplemental readings 108 // 4.10 Points to remember 108 // 4.11 What’s next 110 // PART II ADVANCED LCA // Multiple-group LCA 113 // 5.1 Overview 113 // 5.2 Introduction 114 // 5.3 Multiple-group LCA: Model and notation 114 // 5.4 Computing the number of parameters estimated 116 // 5.5 Expressing group differences in the LCA model 116 // 5.6 Measurement invariance 117 // 5.7 Establishing whether the number of latent classes is identical across groups 119 // 5.7.1 Empirical example: Adolescent delinquency 120 // 5.8 Establishing invariance of item-response probabilities across groups 121 // 5.8.1 Specifying parameter restrictions 122 // 5.8.2 Test of measurement invariance in the delinquency example 125 // 5.9 Interpretation when measurement invariance does not hold 126 // 5.10 Strategies when measurement invariance does not hold 129 // 5.10.1 Partial measurement invariance 129 // 5.10.2 When measurement invariance holds in a subset of groups 131 // 5.11 Significant differences and important differences 131 //

5.11.1 Empirical example: Positive health behaviors 133 // 5.12 Testing equivalence of latent class prevalences across groups 139 // 5.12.1 Empirical example: Adolescent delinquency 140 // 5.12.2 Empirical example: Health risk behaviors 141 // 5.13 Suggested supplemental readings 147 // 5.14 Points to remember 147 // 5.15 Whats next 148 // LCA with Covariates 149 // 6.1 Overview 149 // 6.2 Empirical example: Positive health behaviors 150 // 6.3 Preparing to conduct LCA with covariates 151 // 6.3.1 Preparing variables for use as covariates 151 // 6.4 LCA with covariates: Model and notation 153 // 6.4.1 What is estimated 154 // 6.4.2 Treatment of item-response probabilities in LCA with // covariates 154 // 6.5 Hypothesis testing in LCA with covariates 154 // 6.6 Interpretation of the intercepts and regression coefficients 155 // 6.6.1 Understanding odds and odds ratios 155 // 6.6.2 The correspondence between regression coefficients and odds/odds ratios 157 // 6.7 Empirical examples of LCA with a single covariate 159 // 6.7.1 Results of logistic regression using gender as a covariate 159 // 6.7.2 Results of logistic regression using maternal education as a covariate 161 // 6.8 Empirical example of multiple covariates and interaction terms 163 // 6.8.1 Interpretation of the interaction between gender and maternal education 165 // 6.9 Multiple-group LCA with covariates: Model and notation 166 // 6.9.1 Empirical example: Positive health behaviors 167 // 6.10 Grouping variable or covariate? 167 // 6.10.1 How the multiple-group and covariate models are different 168 // 6.10.2 When the multiple-group and covariate models are mathematically equivalent 169 // 6.11 Use of a Bayesian prior to stabilize estimation 171 // 6.12 Binomial logistic regression 172 // 6.12.1 Empirical example: Positive health behaviors 173 //

6.12.2 Comparison of binomial multiple groups and covariate // models 176 // 6.13 Suggested supplemental readings 176 // 6.14 Points to remember 176 // 6.15 Whats next 177 // PART III LATENT CLASS MODELS FOR LONGITUDINAL DATA // 7 RMLCA and LTA 181 // 7.1 Overview 181 // 7.2 RMLCA 182 // 7.2.1 Adding a grouping variable 185 // 7.2.2 RMLCA and growth mixture modeling 186 // 7.3 LTA 187 // 7.3.1 Empirical example: Adolescent delinquency 187 // 7.3.2 Why conduct LTA on the adolescent delinquency data? 188 // 7.3.3 Estimation and assessing model fit 189 // 7.3.4 Model fit in the adolescent delinquency example 190 // 7.4 LTA model parameters 192 // 7.4.1 Latent status prevalences 192 // 7.4.2 Item-response probabilities 193 // 7.4.3 Transition probabilities 195 // 7.5 LTA: Model and notation 196 // 7.5.1 Fundamental expression 198 // 7.6 Degrees of freedom associated with latent transition models 199 // 7.6.1 Computing the number of latent status prevalences estimated 199 // 7.6.2 Computing the number of item-response probabilities estimated 200 // 7.6.3 Computing the number of transition probabilities estimated 200 // 7.7 Empirical example: Adolescent depression 201 // 7.7.1 Latent status prevalences 203 // 7.7.2 Item-response probabilities 204 // 7.7.3 Transition probabilities 205 // 7.8 Empirical example: Dating and sexual risk behavior 207 // 7.9 Interpreting what a latent transition model reveals about change 209 // 7.10 Parameter restrictions in LTA 211 // 7.11 Testing the hypothesis of measurement invariance across times 212 // 7.11.1 Empirical example: Adolescent depression 213 // 7.12 Testing hypotheses about change between times 214 // 7.13 Relation between RMLCA and LTA 217 // 7.13.1 Relation between RMLCA and LTA when there are two times 217 // 7.13.2 Relation between RMLCA and LTA when there are three or more times 218 //

7.13.3 When to use RMLCA versus LTA 220 // 7.14 Invariance of the transition probability matrix 221 // 7.15 Suggested supplemental readings 221 // 7.16 Points to remember 223 // 7.17 Whats next 224 // Multiple-Group LTA and LTA with Covariates 225 // 8.1 Overview 225 // 8.2 LTA with a grouping variable 226 // 8.2.1 Empirical example: Adolescent depression 226 // 8.3 Multiple-group LTA: Model and notation 226 // 8.4 Computing the number of parameters estimated in multiple- 228 // group latent transition models // 8.5 Hypothesis tests concerning group differences: General considerations 229 // 8.6 Overall hypothesis tests about group differences in LTA 230 // 8.6.1 Empirical example: Cohort differences in adolescent depression 230 // 8.6.2 Empirical example: Gender differences in adolescent depression 233 // 8.7 Testing the hypothesis of equality of latent status prevalences 235 // 8.7.1 Empirical example: Gender differences in adolescent depression 236 // 8.7.2 Empirical example: Gender differences in dating and sexual risk behavior 237 // 8.8 Testing the hypothesis of equality of transition probabilities 238 // 8.8.1 Empirical example: Gender differences in adolescent depression 240 // 8.9 Incorporating covariates in LTA 241 // 8.9.1 Missing data and preparing variables for use as // covariates 241 // 8.10 LTA with covariates: Model and notation 242 // 8.10.1 Predicting latent status membership 243 // 8.10.2 Predicting transitions between latent statuses 243 // 8.10.3 Hypothetical example of LTA with covariates 244 // 8.10.4 What is estimated 245 // 8.11 Hypothesis testing in LTA with covariates 246 // 8.11.1 Empirical example of predicting latent status membership at Time 1 : Adolescent depression 247 // 8.11.2 Empirical example of predicting latent status membership at Time 1 : Dating and sexual risk behavior 250 //

8.11.3 Empirical example of predicting transitions between latent statuses: Adolescent depression 252 // 8.11.4 Empirical example of predicting transitions between latent statuses: Dating and sexual risk behavior 256 // 8.12 Including both a grouping variable and a covariate in LTA 257 // 8.12.1 Empirical example: Dating and sexual risk behavior 258 // 8.13 Binomial logistic regression 258 // 8.13.1 Empirical example: Adolescent depression 259 // 8.13.2 Empirical example: Dating and sexual risk behavior 261 // 8.14 The relation between multiple-group LTA and LTA with a covariate 263 // 8.15 Suggested supplemental readings 263 // 8.16 Points to remember 264 // Topic Index 279 // Author Index 283