Holdings: Latent class and latent transition analysis

Latent class and latent transition analysis: with applications in the social, behavioral, and health sciences

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Bibliographic Details
Main Authors:	Collins, Linda M. 1955- (Author), Lanza, Stephanie T. 1969- (Author)
Format:	Book
Language:	English
Published:	Hoboken, NJ Wiley 2010
Series:	Wiley series in probability and statistics
Subjects:	Statistik Latent structure analysis Latent variables Statistics Latent-Class-Analyse Latente Variable
Online Access:	Inhaltsverzeichnis
Physical Description:	XXXIII, 285 S. graph. Darst.
ISBN:	9780470228395 0470228393

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245	1	0	\|a Latent class and latent transition analysis \|b with applications in the social, behavioral, and health sciences \|c Linda M. Collins ; Stephanie T. Lanza
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adam_text	CONTENTS List of Figures xvii List of Tables xxi Acknowledgments xxxi Acronyms xxxiii PART І FUNDAMENTALS 1 General Introduction 3 1.1 Overview 3 1.2 Conceptual foundatìoa and brief history of the lăţeai class model 4 1.2.1 LC A aná other latent variable models 6 1.2.2 Some historical milestones in LCA 7 1.2.3 LCA as a person-oriented approach S 1.3 Why select a categorical latent variable approach? 8 1.4 Scope of Ms book 9 1.5 Empirical example of LCÂ: Adolescent delinquency 10 1.6 Empirical example of LTA: Adolescent delinquency 14 1.7 About this book I? vii VÎH CONTENTS 1.7.1 Using this book 19 1.8 The examples in this book 19 1.8.1 Empirical data sets 20 1.9 Software 21 1.10 Additional resources: The book s web site 21 1.11 Suggested supplemental readings 22 1.12 Points to remember 22 1.13 What s next 22 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 poberta! 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 47 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 Paraléis with factor analysis 50 3.2.2 Two criteria for evaluating item-response probabilities for a single variable 50 CONTENTS ІХ 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 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 teatmeat of individual parameters: Parameter restrictions 79 4.2.3 Missing data and estimation g§ 4.3 Model it mă model selection 81 4.3.1 Absolute mode! it 82 CONTENTS 4.3.2 The Hkelihood-ratío statistic G2 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 il ADVANCED LCA Muliiple-group LCA 113 5Л Overview Ш 5.2 Introduction 114 5.3 Multiple-group LCA: Model and notatie» 114 5.4 Computing the number of parameters estimated 116 5.5 Expressing group differences in the LCA model ł Î6 5.6 Measurement iavariance Î 17 5.7 Estabishlag whether the raraber of latent classes is identical across poops 1 19 CONTENTS ХІ 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 What s next 148 LCA with Covariaies 149 6.1 Overview 149 6.2 Empirical example: Positive health behaviors 150 6.3 Preparing to conduct LCA with covariates 1 51 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 iteiB-respoase probabilities in LCA with covariates 154 6.5 - Hypothesis testing in LCA with covariates 154 6.6 InterpretatìOB of die intercepts and regression coefficients 155 6.6.1 Understanding odds and odds ratios 155 6.6.2 The correspondence between regression coeficiente and odds/odds ratios 157 6.7 Efflpiîieaî examples of LCA with a stagïe eovariate 159 6.7Л Resalte of logistic regression asiag grader asa covariate 159 6.7.2 Resalís of logistic regression iising materaal education as a covariate 161 ХИ CONTENTS 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 What s 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 it in the adolescent delinquency example 190 7.4 LTA model parameters 192 7.4.1 Latent states prevalences 192 7.4.2 Item-response probabilities 193 7.4.3 Transition probabilities Í95 7.5 LTA: Model and notation 196 7.5.1 Fundamental expression 198 7.6 .Degrees of freedom associated with latent transition models 199 CONTENTS ХІІІ 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 mere 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 What s next 224 8 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 notations 226 8.4 Computing the namber of parameters estimatei in multiple- group latent transition models 228 8.5 Hypothesis tests concerning group differeaees; Generai considerations 229 8.6 Överalt hypothesis tests about groep differences ia LTA 230 XIV CONTENTS 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 states 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 Inctodiag both a grouping variable and a covariate ír 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 mă sexaal risk behavior 261 8.14 The relation between, maltíple-groap LTA and LTA with a covariate 263 8.15 Suggested supplemental readiags 263 8.16 Points to remember 264 CONTENTS XV Topic Index 279 Author Index 283 List of Figures ł . 1 Latent variable with three observed variables as indicators. 5 1.2 Adolescent delinquency latent class membership probabilities (Add Health public-Hse data, Wave I; ¿V = 2,087). Note that the four probabilities sam to L 13 1.3 ftobabffîty of a Yes response to each delinquency item conditional on latent class membership (Add Health public-use data, Wave I; N = 2,087). Ï4 1.4 Probability of a Yes response to each delinquency Item conditional on latent statos membership (Add Health publie-Hse data, Waves Ï and H; N = 2,087), 16 2.1 Lateat ciass prevalences in pubertà! development example (Aie Health piłblic-ase date, Wave I; N - 469). 28 2.2 Item-response probabilities for measurement of Delayed Pubertai Onset latent class (Add Health public-use data» Wave I; N ~ 469), Respea.se category tobéis appear in Table 2.5» -32 xvii XVÜi LIST OF FIGURES 2.3 Item-response probabilities for measurement of Biologically Mature latent class (Add Health public-use data, Wave I; N = 469). Response category labels appear in Table 2.5. 32 2.4 Item-response probabilities for measurement of Visibly Mature latent class (Add Health public-use data, Wave I; N = 469). Response category labels appear in Table 2.5. 33 2.5 Item-response probabilities for measurement of Mature latent class (Add Health public-use data, Wave I; JV = 469). Response category labels appear in Table 2.5. 33 2.6 Probability of endorsing aicohol and tobacco use items conditional on latent class membership (Youth Risk Behavior Survey, 2005; N = 13,840). 36 2.7 Probability of endorsing other drag use items conditional on latent class membership (Youth Risk Behavior Survey, 2005; N = 13,840). 37 2.8 Probability of endorsing sexual behavior items conditional on latent class membership (Youtìi Risk Behavior Survey, 2005; N= 13,840). 37 2.9 Prevalence of health risk behavior latent classes (Youth Risk Behavior Survey, 2005; JVr = 13,840). 38 2.10 Figure 1.1, repeated here for convenience. Latent variable with three observed variables as indicators. This figure illustrates local independence. There are arrows connecting observed variables Xi, X2, and X3 to the latent variable but no other arrows connecting any components of the observed variables to each other. This signifies that the three observed variables are related only through the latent variable. 44 2.1 1 Latent variable with three observed variables as indicators. This figure illustrates a violation of local independence. Observed variables X% and X$ are related to each other not only through the latest variable, bat also throagh their error components (e s). 45 3. ł Probability of endorsing tobaeco ase behavior items conditional on latent class membership. Hypothetical data from Table 3.5 exhibit high homogeneity and high latent class separation. 59 LIST OF FIGURES ХІХ 3.2 Probability of endorsing tobacco use behavior items conditional on latent class membership. Hypothetical data from Table 3.6 exhibit high homogeneity overall and low separation between the Regular I and Π latent classes. 61 3.3 Probability of endorsing tobacco use behavior items conditional on latent class membership. Hypothetical data from Table 3.7 exhibit low homogeneity and low latent class separation. 63 4.1 Unimodal likelihood function for a single parameter Θ, indicative of good identification. 90 4.2 Multimodal likelihood function for a single parameter Q, indicative of underidentification. 9 1 4.3 Likelihood function for a single parameter Θ. This function has a flat region, which suggests that the model being fit is unidentified. 9 í 4.4 Distribution of log-likelihood values for five-latent-class model of positive health behaviors based on 100 random sets of starting values (Monitoring the Future data, 2004; Лг = 2,065). 96 4.5 G2, AIC, and BIC for models of positive health behaviors (Monitoring the Future data, 2004; Лг = 2,065). 98 4.6 G2, AIC, and BIC for models of female poberta! development (Add Health pablic-use data, Wave I; N - 469), 1ÖI 4.7 G2, AIC, and BIC for models of health risk behaviors (Youth Risk Behavior Survey, 2005; N = 13,840). І02 5. 1 Prevalence of latent classes of positive health behaviors by gender (Monitoring the Fatare data, 2004; N - 2,065). 139 5.2 Prevalence of health risk behavior latent classes tor each grade (Youth Risk Behavior Survey, 2005; N = 13,840). 144 6.1 Overall effect of one-stanđarđ-deviation increase ia maternal edecation ia positive health behavior example (Monitoring the Fatare data, 2004; Ar = 2,065). The Typical latent class is the reference group. 162 6.2 Effect of ene-staađarđ-đeviatioB increase in maternal eđaeatioa for males and females in positive health behavior example (Monitoring the Риже data, 2004; N - 2,065). 165 XX LIST OF FIGURES 6.3 Effect of one-standard-deviation increase in maternal education on odds of membership in Healthy latent class as compared to membership in other latent classes combined, by gender (Monitoring the Future data, 2004; N = 2,065). 175 7.1 Patterns of heavy drinking across four developmental periods, corresponding to the latent classes in Table 7.2 (from Lanza and Collins, 2006). Note that more precise values for item-response probabilities appear in Table 7.1. 184 7.2 G2, AIC, and BIC for latent transition models of adolescent delinquency (Add Health public-use data, Waves I and II; N~ 2,087). 191 7.3 G2, AIC, and BIC for latent transition models of adolescent depression (Add Health public-use data, Waves I and II; N = 2,061 ).2O3 7.4 Transition probabilities for latent transition model of adolescent depression (Add Health public -иѕе data, Waves I and II; N = 2,061).206 8.1 Prevalences of latent statuses of adolescent depression at Time 1 by gender (Add Health public-use data. Waves I and II; N = 2,061).237 8.2 Odds ratios associated with carrent cigarette use and lifetime marijuana use. Although not estimated, the odds ratio of 1 associated with the reference latent states, Not Depressed, is shown here for comparison purposes (Add Health public-use data, Waves I and II; N = 2,061). 250 List of Tables 1.1 FourDifferentLatentVariableModels 7 1.2 Proportion of Adolescents Responding Yes to Questioas About Delinquent Behaviors (Add Health Pabîic-Use Data, Wave I; .¥ = 2,087) 1Í 13 Foiir-Lateot-Class Model of Past-Year Delinquency (Add Health Public-Use Date, Wave І; Лг = 2,087) 12 1.4 Five-Latent-Stetas Model of Past-Year Delinquency (Add Health Public-Use Data, Waves I and Η; Ν - 2,087) 15 2.1 Marginal Respome Proportions for Female Pabertal Development Variables (Add Health PabBc-Use Data, Wave І; N = 469) 24 2.2 Response Patterns and Frequencies for Add Health Pabertal Development Data (Add Health Pubic-Use Data» Wave I; N = 469) 26 2.3 Item-Eesponse Probabilities for a Hypotìieticaì TWe-Lateat-CIass Model 30 2.4 Item-Response Probabilities for a Hypothetical Three-Latent- Clâss Model 3§ xxi XXÍI UST OF TABLES 2.5 Four-Latent-Class Model of Female Pubertal Development in Seventh Grade (Add Health Public-Use Data, Wave I; N = 469) 31 2.6 Proportion of Students Reporting Each Health Risk Behavior (Youth Risk Behavior Survey, 2005; JV = 13,840) 35 2.7 Five-Latent-Class Model of Health Risk Behaviors (Youth Risk Behavior Surveillance System Data; N = 13,840) 39 2.8 Hypothetical Example with Two Latent Classes and Two Observed Variables 42 2.9 Response Pattern Probabilities for Hypothetical Example in Table 2.8 44 3.1 Item-Response Probabilities from Four-Latent-Class Model of Female Pubertal Development (Add Health Pablic-Use-Data, Wave I; N = 469. From Table 2.5; repeated here for convenience) 52 3.2 Hypothetical Item-Response Probabilities Reiecting Independence of Observed Variables and Latent Variable 53 3.3 Item-Response Probabilities from Five-Latent-Class Model of Health Risk Behaviors (Youth Risk Behavior Survey, 2005; JV = 13,840. From Table 2.7; repeated here for convenience) 54 3.4 Item-Response Probabilities for a Hypothetical Three-Latent- Ciass Model 55 3.5 Item-Response Probabilities for a Hypothetical Three-Latent- Class Model with High Homogeneity and High Latent Class Separation 58 3.6 Item-Response Probabilities for a Hypothetical Three-Latent- Class Model with High Homogeneity and Low Latent Class Separation 60 3.7 Item-Response Probabilities for a Hypothetical Three-Latent- Class Model with Low Homogeneity and Low Latent Class Separation 62 4. 1 Marginal Response Proportions for Indicators of Positive Health Behavior {Monitoring Ése Future Data, 2004; iV = 2,065) 95 4.2 Summary of Information for Selecting Number of Latent Classes of Positive Health Behaviors (Monitoring the Fatare Data» 2004; iV = 2,065) 97 UST OF TABLES ХХІІІ 4.3 Summary of Information for Selecting Namber of Latent Classes of Past-Year Delinquency (Add Health Public-Use Data, Wave I; iV = 2,087) 99 4.4 Summary of Information for Selecting Number of Latent Classes of Female Pubertal Development (Add Health Public-Use Data, Wave I; N = 469) 100 4.5 Summary of Information for Selecting Number of Latent Classes of Health Risk Behaviors (Youth Risk Behavior Survey, 2005; N = 13,840) ЮІ 4.6 Item-Response Probabilities for a Hypothetical Three-Latetit- Class Model (Table 3.4 repeated for convenience) 104 4.7 Type A and Type В Errors for Hypothetical Three-Latent-Class Model in Table 4.6 105 5.1 Four-Latent-Class Model of Past-Year Delinquency (Add Health Public-Use Data, Wave I; N = 2,087; Table 1.3 repeated for convenience) 115 5.2 Selecting Number of Latent Classes in Multiple-Group Delinquency Example (Add Health Public-Use Data, Wave I; N = 2,087) 121 5.3 Parameter Restrictions Specifying Item-Response Probabilities Are Equal Across Grades in Adolescent Delinquency Example 123 5.4 Parameter Restrictions for Testing Measurement Invariance When Other Parameter Résiliations Are Present 124 5.5 Fit Statistics for Test of Measurement Invariance for Adolescent Delinquency Example (Add Health Public-Use Data, Wave Ï; N = 2,087) 125 5.6 Hypothetical Item-Response Probabilities for Delinquency Example Illustrating Pronounced Group Differences їй Measurement 127 5.7 Hypothetical Itero-RespoHse Probabilities for Defiaęueney Example Illustrating Moderate Gioiip Differences in Меаѕнгеигаи І28 5.8 Parameter Restrictions Constraining Most» But Mot AH, iiem- Response Probabilities to Be Equal Across Cohorts in Adolescent Delinquency Example 130 XXIV UST OF TABLES 5.9 Parameter Restrictions Constraining Item-Response Probabilities to Be Eqaal Across Cohorts for a Subset of Variables in Adolescent Delinquency Example 130 5.10 Parameter Restrictions Constraining Item-Response Probabilities to Be Equal Across Only Grades 10 and 11 in a Hypothetical Adolescent Delinquency Example with Three Grades 132 5.11 Five Latent Classes of Positive Health Behaviors (Monitoring the Future Data, 2004; N = 2,065) 134 5.12 Fit Statistics for Test of Measurement Invariance Across Genders for Latent Class Model of Positive Health Behaviors (Monitoring the Future Data, 2004; N = 2,065) 135 5.13 Latent Class Prevalences for Model of Positive Health Behaviors with Item-Response Probabilities Allowed to Vary Across Genders (Monitoring the Future Data, 2004; N = 2,065) 135 5.14 Item-Response Probabilities Allowed to Vary Across Genders for Model of Positive Health Behaviors (Monitoring the Future Data, 2004; N = 2,065) 136 5.15 Latent Class Model of Positive Health Behaviors with Item- Response Probabilities Constrained Equal Across Genders (Monitoring the Future Data, 2004; iV = 2,065) 137 5.16 Fit -Statistics for Test of Gender Differences in Latent Class Prevalences for Latent Class Model of Positive Health Behaviors (Monitoring the Future Data, 2004; N = 2,065) 138 5.17 Latent Class Prevalences Across Cohorts in Four-Latent-Class Model of Past-Year Delinquency (Add Health Public-Use Data, Wave I; JV = 2,087) 140 5.18 Parameter Restrictions Constraining Latent Class Prevalences to Be Equal Across Cohorts ia the Adolescent Delinquency Example (Äad Health Public-Use Data, Wave I; N = 2,087) 141 5.19 Fit Statistics for Test of Cohort Differences їв Latent Class Prevaleaces for Adolescent Delinquency Example (Add Health Ptibiîc-Use Data, Wave I; N = 2t0S7) 141 5.20 Proportion of Students In Each Cohort Reporting Each Health Risk Behavior (Youth Risk Behavior Survey, 2005; ]V = 13,840) 142 LIST OF TABLES XXV 5.21 Latent Class Prevalences Across Grades in Five-Latent-Class Model of Health Risk Behaviors (Youth Risk Behavior Sarvey, 2005; N = 13,840) 143 5.22 Freely Estimated and Restricted Latent Class Prevalences for Models of Health Risk Behaviors (Youth Risk Behavior Survey, 2005; N = 13,840) 145 5.23 Examination of the Impact of Parameter Restrictions on Model Fit for Model of Health Risk Behaviors (Youth Risk Behavior Survey, 2005; JV = 13,840) 146 5.24 Hypothesis Tests of Equality of Latent Class Prevalences Across Grades in Health Risk Behavior Example (Youth Risk Behavior Survey, 2005; N = 13,840) 147 6.1 Latent Class Prevalences and Log-Likelihoods from Previously Fit Models of Positive Heaftn Behaviors (Monitoring me Future Data, 2004; N = 2,065) 150 6.2 Example Coding Scheme to Represent a Covariate with Three Response Categories 152 6.3 Gender as a Predictor of Membership in Latent Classes of Positive Health Behaviors (Monitoring the Future Data, 2004; N = 2,065) 159 6.4 Maternal Education as a Predictor of Membership in Latent Classes of Positive Health Behaviors (Monitoring the Fatare Data, 2004; N = 2,065) 162 6.5 Gender and Maternal Education as Predictors of Membership in Latent Classes of Positive Health Behaviors (Monitoring the Future Data, 2004; N = 2,065) 164 6.6 Hypothesis Tests for Gender, Maternal Education» and Their Interaction for Model of Positive Health Behaviors Reported in Table 6,5 (Monitoring the Fatare Data, 2004; N ~ 2,065} 164 6.7 Maternal Education as a Predictor of Membership in Latent Classes of Posiive Health Behaviors, with Gender as a Groeping Variable (Monitoring the Futóié Data» 2004; N - 2,065) 168 6.8 Вшита! Logistic Regression with Gender as a Covâriató in Model of Positive Health Behaviors (Monitoring the Fatare Data, 2004; N = 2,065) Í73 XXVI LIST OF TABLES 6.9 Binomial Logistic Regression Model with Gender and Maternal Education as Covariates (Monitoring the Future Data, 2004; ,¥ = 2,065) 174 6.10 Hypothesis Tests for Gender, Maternal Education, and Their Interaction for Model in Table 6.9 (Monitoring the Future Data, 2004; N = 2,065) 174 6.11 Binomial Logistic Regression with Gender as a Grouping Variable and Maternal Education as a Covariate in Model of Positive Health Behavior (Monitoring the Future Data, 2004; N = 2,065) 175 7.1 Eight-Latent-Class Model of Heavy Drinking at Six Different Ages (NLSY; N = 1,265) (from Lanza and Collins, 2006) 183 7.2 Patterns of Heavy Drinking over Time Corresponding to Eight Latent Classes (NLSY; N = 1,265) (from Lanza and Coffins, 2006) 185 7.3 Prevalences of Latent Classes Representing Patterns of Heavy Drinking over Time for Those Enrolled in College and Those Not Enroled in College (NLSY; N = 1,265) (from Lanza and Coffins, 2006) 186 7.4 Prevalence of Heavy Drinking at Each Developmental Period for Those Enrolled in College and Those Not Enrolled in College (NLSY; N = 1,265) (from Lanza and Collins, 2006) 186 7.5 Marginal Response Proportions for Past-Year Delinquency Questionnaire Items (Add Health Public-Use Data, Waves I and П;і¥ = 2,087) 188 7.6 Summary of Information for Selecting Number of Latent Statuses of Adolescent Delinquency at Two Times (Add Health Public-Use Data, Waves I and П, Лг = 2,087) 191 7.7 Five-Latent-Status Model of Past-Year Delinquency (Add Health Public-Use Data, Waves I and H; JV = 2,087; Table 1.4 repeated for convenience) 193 7.8 Marginal Response Proportions for Adolescent Past-Week Depression Qeestionnaire Items (Add Health Pablic-Use Data, Waves I amili; IV = 2,061) 201 7.9 Summary of Information for Selecting Member of Latent Statuses of Adolescent Depression (Add Health Pablo-Use Data, Waves I and її; Ж 5=2,061) 203 UST OF TABLES XXVÜ 7.10 Five-Latent-Status Model of Adolescent Depression (Add Health Public-Use Data, Waves I and Π; Ν = 2,061) 204 7.11 Summary ofinformation for Selecting Number of Latent Statuses of Dating and Sexual Risk Behavior (NLSY, Rounds 2-4, N = 2,937) 207 7.12 Five-Latent-Status Model of Dating and Sexual Risk Behavior (NLSY, Rounds 2-4, JV = 2,937) 208 7.13 Parameter Restrictions Constraining Item-Response Probabilities to Be Equal Across Times for Adolescent Depression Example 214 7.14 Fit Statistics for Test of Measurement Invariance Across Times for Adolescent Depression Example (Add Health Public-Use Data, Waves I and П; JV = 2,061) 214 7.15 Fixed Transition Probability Parameter Values Expressing a Model of No Change in the Five-Latent-States Model of Adolescent Depression 215 7.16 Fit Statistics for Test of Hypothesis That Latent Stålas Membership Is Identical at Times 1 and 2 for Adolescent Depression Example (Add Health Public-Use Data, Waves I and II; N = 2,061) 216 7.17 Fixed Transition Probability Parameter Values Expressing a Model in Which There Is No Movement Between Sad and Disliked in the Five-Latent-Status Model of Adolescent Depression 216 7.18 Fixed Transition Probability Parameter Values Expressing a Model in Which There Is Only Increasing Depression Across Time in the Five-Latent-Status Model of Adolescent Depression 217 7.19 Parameter Eesttietions Constraining Transition Probabilities to Be Equal Across Three Times in a Hypothetical Five-Latettt-Status Model of Adolescent Depression 222 7.20 Five-Latent-Statas Modei of Datißg and Sexaal Risk Behavior with Transition Probability Matrices Constrained Equal Across Three Times (MLSY, Rounds 2-4, N - 2,937) 222 7.21 Fit Statistics for Test of Invariance of Transition Probability Matrices in rae Bating and Sexual Risk Behavior Example CNLSY, Rounds 2-4, AT = 2,937) 223 XXVIII LIST OF TABLES 8.1 Latent Status Prevalences and Transition Probabilities for Five-Latent-Status Model of Adolescent Depression, by Cohort (Add Health Public-Use Data, Waves I and II; N = 2,061) 227 8.2 Varying Types of Equivalence Across Groups in Latent Transition Models 229 8.3 Parameter Restrictions Constraining Latent Status Prevalences and Transition Probabilities to Be Equal Across Cohorts in Adolescent Depression Example 231 8.4 Latent Status Prevalences and Transition Probabilities Constrained Equal Across Cohorts for Five-Latent-Status Model of Adolescent Depression (Add Health Public-Use Data, Waves I and H;JV = 2,061) 232 8.5 Fit Statistics for Test of Cohort Differences in Latent States Prevalences and Transition Probabilities for Adolescent Depression Example (Add Health РнЬИс -Use Data, Waves I and її; Ж = 2,061) . 233 8.6 Latent States Prevalences and Transition Probabilities for Five-Latent-Status Model of Adolescent Depression, by Gender (Add Health Public-Use Data, Waves I and II; N = 2,061) 234 8.7 Kt Statistics for Test of Gender Differences in Latent States Prevalences and Transition Probabilities for Adolescent Depression Example (Add Health Public-Use Data, Waves I and II; JV = 2,061) 234 8.8 Fit Statistics for Two Approaches to Test of Gender Differences in Latent Status Prevalences for Adolescent Depression Example (Add Health Public-Use Data, Waves I and II; N = 2,061) 236 8.9 Fit Statistics for Test of Gender Differences in Latent States Prevalences Across Gender for Dating aad Sexual Risk Behavior Example (NLSY, Rounds 2-4; 2V = 2,937) 238 8.IÖ Latent States Prevalences and Transition Probabilities for Pive-Latent-States Model of Dating and Sexual Risk Behavior, by Gender (MLSY, Eoœds 2-4; Ν = 2,937) 239 8. і I Fit Statistics for Two Approaches to Tesi of Gender Differences in Transition Probabilities for Adolescent Depression Example (Add Health Fable-Use Data, Waves I and П; JV - 2,061) 240 LIST OF TABLES XXÍX 8.12 Hypothetical Example of Covariate (GPA) Predicting Latent Status Membership at Time 1 and Transitions Between Latent Statuses 245 8.13 Substance-Use Predictors of Membership in Time 1 Latent Statuses of Adolescent Depression (Add Health Public-Use Data, Waves I and П;І Г = 2,061) 248 8.14 Hypothesis Tests for Predictors of Membership in Latent Statuses of Adolescent Depression for Model Reported in Table 8.13 250 8.15 Substance-Use Predictors of Membership in Time 1 Latent Statuses of Dating and Sexual Risk Behavior (NLSY, Rounds 2-4; JV = 2,937) 251 8.16 Hypothesis Tests for Predictors of Membership in Latent Statuses of Dating and Sexual Risk Behavior for Model Reported in Table 8.15 252 8.17 Logistic Regression Parameters (/? s) for Substance-Use Predictors of Transitions Between Latent Statuses of Depression (Add Health Public-Use Data, Waves I and II; Лг = 2,061) 253 8.18 Odds Ratios for Substance-Use Predictors of Transitions Between Latent Statuses of Depression (Add Health Public-Use Data, Waves I and It АГ = 2,061) 254 8.19 Hypothesis Tests for Predictors of Transitions Between Latent Statuses of Adolescent Depression for Model Reported in Tables 8.17 and 8.18 256 8.20 Logistic Regression Parameters (jS s) and Odds Ratios for Drunkenness Predicting Transitions Between Latent Statuses of Dating and Sexual Risk Behavior (NLSY, Rounds 2-4; N = 2,937) 257 8.21 Substance-Use Predictors of Membership io Tíme 1 Latent Statuses of Dating and Sexual Misk Behavior by Gender (NLSY, Rounds 2-4; N - 2,937) 259 8.22 .Effect of Substance-Use Predictors on Probability of Transition to Depressed Latent Status Relative to Ail Other Latent Statoses Conditional oa Tíme 1 Latent States (Add Health Publie-Use Data, Waves I and II; N = 2,061) 26І 8.23 Hypothesis Teste for Predictors of Membership in Latent Statuses of Adolescent Depression at Time 1 and Transition to Depressed Latest Status for Model Reportei in Table 8.22 262 XXX LIST OF TABLES 8.24 Effect of Past-Year Drunkenness on Probability of Transition to Miiltipartner Exposed Latent Status at Time 2 Conditional on Time 1 Latent Status (NLSY, Rounds 2-4; N = 2,937) 262
any_adam_object	1
author	Collins, Linda M. 1955- Lanza, Stephanie T. 1969-
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dewey-search	519.5/35
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format	Book
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id	DE-604.BV036036249
illustrated	Illustrated
indexdate	2024-07-09T22:09:54Z
institution	BVB
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language	English
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physical	XXXIII, 285 S. graph. Darst.
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spelling	Collins, Linda M. 1955- Verfasser (DE-588)1028211910 aut Latent class and latent transition analysis with applications in the social, behavioral, and health sciences Linda M. Collins ; Stephanie T. Lanza Hoboken, NJ Wiley 2010 XXXIII, 285 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Statistik Latent structure analysis Latent variables Statistics Latent-Class-Analyse (DE-588)4166857-1 gnd rswk-swf Latente Variable (DE-588)4166860-1 gnd rswk-swf Latent-Class-Analyse (DE-588)4166857-1 s Latente Variable (DE-588)4166860-1 s DE-604 Lanza, Stephanie T. 1969- Verfasser (DE-588)142626376 aut Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018928222&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Collins, Linda M. 1955- Lanza, Stephanie T. 1969- Latent class and latent transition analysis with applications in the social, behavioral, and health sciences Statistik Latent structure analysis Latent variables Statistics Latent-Class-Analyse (DE-588)4166857-1 gnd Latente Variable (DE-588)4166860-1 gnd
subject_GND	(DE-588)4166857-1 (DE-588)4166860-1
title	Latent class and latent transition analysis with applications in the social, behavioral, and health sciences
title_auth	Latent class and latent transition analysis with applications in the social, behavioral, and health sciences
title_exact_search	Latent class and latent transition analysis with applications in the social, behavioral, and health sciences
title_full	Latent class and latent transition analysis with applications in the social, behavioral, and health sciences Linda M. Collins ; Stephanie T. Lanza
title_fullStr	Latent class and latent transition analysis with applications in the social, behavioral, and health sciences Linda M. Collins ; Stephanie T. Lanza
title_full_unstemmed	Latent class and latent transition analysis with applications in the social, behavioral, and health sciences Linda M. Collins ; Stephanie T. Lanza
title_short	Latent class and latent transition analysis
title_sort	latent class and latent transition analysis with applications in the social behavioral and health sciences
title_sub	with applications in the social, behavioral, and health sciences
topic	Statistik Latent structure analysis Latent variables Statistics Latent-Class-Analyse (DE-588)4166857-1 gnd Latente Variable (DE-588)4166860-1 gnd
topic_facet	Statistik Latent structure analysis Latent variables Statistics Latent-Class-Analyse Latente Variable
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018928222&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT collinslindam latentclassandlatenttransitionanalysiswithapplicationsinthesocialbehavioralandhealthsciences AT lanzastephaniet latentclassandlatenttransitionanalysiswithapplicationsinthesocialbehavioralandhealthsciences

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