Preface 1. Introduction 2. The concept of risk 3. Overview of count response models 4. Methods of estimation and assessment 5. Assessment of count models 6. Poisson regression 7. Overdispersion 8. Negative binomial regression 9. Negative binomial regression: modeling 10. Alternative variance parameterizations 11. Problems with zero counts 12. Censored and truncated count models 13. Handling endogeneity and latent class models 14. Count panel models 15. Bayesian negative binomial models Appendix A. Constructing and interpreting interactions Appendix B. Data sets and Stata files References Index.

/pdf/negative-binomial-regression-29q4k5nu4u.pdf

Negative Binomial Regression

When data are collected via anonymous Internet surveys, particularly under conditions of obligatory participation (such as with student samples), data quality can be a concern. However, little guidance exists in the published literature regarding techniques for detecting careless responses. Previously several potential approaches have been suggested for identifying careless respondents via indices computed from the data, yet almost no prior work has examined the relationships among these indicators or the types of data patterns identified by each. In 2 studies, we examined several methods for identifying careless responses, including (a) special items designed to detect careless response, (b) response consistency indices formed from responses to typical survey items, (c) multivariate outlier analysis, (d) response time, and (e) self-reported diligence. Results indicated that there are two distinct patterns of careless response (random and nonrandom) and that different indices are needed to identify these different response patterns. We also found that approximately 10%–12% of undergraduates completing a lengthy survey for course credit were identified as careless responders. In Study 2, we simulated data with known random response patterns to determine the efficacy of several indicators of careless response. We found that the nature of the data strongly influenced the efficacy of the indices to identify careless responses. Recommendations include using identified rather than anonymous responses, incorporating instructed response items before data collection, as well as computing consistency indices and multivariate outlier analysis to ensure high-quality data.

http://ubc-emotionlab.ca/wp-content/uploads/2012/06/Meade-Craig-2012-Careless-Responding-in-Survey-Data.pdf

Identifying careless responses in survey data.

In recent years, there has been a growing interest among researchers in the use of latent class and growth mixture modeling techniques for applications in the social and psychological sciences, in part due to advances in and availability of computer software designed for this purpose (e.g., Mplus and SAS Proc Traj). Latent growth modeling approaches, such as latent class growth analysis (LCGA) and growth mixture modeling (GMM), have been increasingly recognized for their usefulness for identifying homogeneous subpopulations within the larger heterogeneous population and for the identification of meaningful groups or classes of individuals. The purpose of this paper is to provide an overview of LCGA and GMM, compare the different techniques of latent growth modeling, discuss current debates and issues, and provide readers with a practical guide for conducting LCGA and GMM using the Mplus software. Researchers in the fields of social and psychological sciences are often interested in modeling the longitudinal developmental trajectories of individuals, whether for the study of personality development or for better understanding how social behaviors unfold over time (whether it be days, months, or years). This usually requires an extensive dataset consisting of longitudinal, repeated measures of variables, sometimes including multiple cohorts, and analyzing this data using various longitudinal latent variable modeling techniques such as latent growth curve models (cf. MacCallum & Austin, 2000). The objective of these approaches is to capture information about interindividual differences in intraindividual change over time (Nesselroade, 1991). However, conventional growth modeling approaches assume that individuals come from a single population and that a single growth trajectory can adequately approximate an entire population. Also, it is assumed that covariates that affect the growth factors influence each individual in the same way. Yet, theoretical frameworks and existing studies often categorize individuals into distinct subpopulations (e.g., socioeconomic classes, age groups, at-risk populations). For example, in the field of alcohol research, theoretical literature suggests different classes

/pdf/an-introduction-to-latent-class-growth-analysis-and-growth-3yadg8aqzn.pdf

An introduction to latent class growth analysis and growth mixture modeling.

Group-based trajectory models are increasingly being applied in clinical research to map the developmental course of symptoms and assess heterogeneity in response to clinical interventions. In this review, we provide a nontechnical overview of group-based trajectory and growth mixture modeling alongside a sampling of how these models have been applied in clinical research. We discuss the challenges associated with the application of both types of group-based models and propose a set of preliminary guidelines for applied researchers to follow when reporting model results. Future directions in group-based modeling applications are discussed, including the use of trajectory models to facilitate causal inference when random assignment to treatment condition is not possible.

Group-Based Trajectory Modeling in Clinical Research

Negative binomial regression, 2nd ed.

Mixture modeling is a widely applied data analysis technique used to identify unobserved heterogeneity in a population. Despite mixture models' usefulness in practice, one unresolved issue in the application of mixture models is that there is not one commonly accepted statistical indicator for deciding on the number of classes in a study population. This article presents the results of a simulation study that examines the performance of likelihood-based tests and the traditionally used Information Criterion (ICs) used for determining the number of classes in mixture modeling. We look at the performance of these tests and indexes for 3 types of mixture models: latent class analysis (LCA), a factor mixture model (FMA), and a growth mixture models (GMM). We evaluate the ability of the tests and indexes to correctly identify the number of classes at three different sample sizes (n = 200, 500, 1,000). Whereas the Bayesian Information Criterion performed the best of the ICs, the bootstrap likelihood ratio test ...

Deciding on the Number of Classes in Latent Class Analysis and Growth Mixture Modeling: A Monte Carlo Simulation Study

This study uses latent class analysis (LCA) to empirically identify victimization groups during middle school. Approximately 2,000 urban, public middle school students (mean age in sixth grade = 11.57) reported on their peer victimization during the Fall and Spring semesters of their sixth, seventh, and eighth grades. Independent LCA analyses at each semester yielded 3 victim classes based on victimization degree rather than type (e.g., physical vs. relational). The most victimized class always represented the smallest proportion of the sample, decreasing from 20% in sixth grade to 6% by the end of eighth grade. This victimized class also always reported feeling less safe at school concurrently and more depressed than others 1 semester later, illustrating the validity of the LCA approach.

Subtypes, severity, and structural stability of peer victimization: what does latent class analysis say?

This paper is an advanced application of latent transition analysis (LTA). Examining the peer victimization experiences of approximately 1300 urban, public school students across the 3 middle school years, we extend the conventional LTA model to simultaneously include time varying covariates with time varying effects, second-order effects, a mover-stayer variable, and distal outcomes. We present five key modeling steps that can be used in the application of the LTA model. The analyses yielded three victim classes based on victimization degree (victimized, sometimes victimized, nonvictimized). LTA indicated that when students transitioned between victimization classes, they were most likely to transition from a more victimized group into one of the less victimized groups. Further, results indicated that students who experience any sort of victimization, compared to those who do not, felt less safe at school, more socially anxious, and more depressed during certain middle school years. We also found that students who were chronically victimized in middle school reported more physical health problems and more social worries once in high school. Stability and Instability 3 Stability and Instability of Peer Victimization during Middle School: Using Latent Transition Analysis with Covariates, Distal Outcomes, and Modeling Extensions Peer victimization is a known antecedent of a wide range of negative outcomes for youth, from psychological and social maladjustment to physical symptoms to problems in school functioning (Juvonen & Graham, 2001). Around sixth grade, peer victimization appears to reach its peak in frequency (Nansel et al., 2001), but the research pointing to this peak has been mainly cross sectional (e.g., Salmivalli, 2002). Less is known about what happens longitudinally and it is likely that peer victimization does not decrease for all youth. At the same time, while a host of research has identified antecedents, covariates, and consequences of peer victimization (Juvonen & Graham, 2001; Hawker & Boulton, 2000), less is known about the covariates (especially time varying covariates) that might predict victimization over time. There is also limited research about the extended consequences associated with different patterns of peer victimization (cf., chronically victimized, consistently nonvictimized) (Juvonen, Nishina, & Graham, 2000). The wider availability of different longitudinal models allows researchers to describe change and integrate important correlates and consequences of change into the models to understand development more completely. The present study outlines five important modeling steps for using latent transition analysis (LTA)—including key model extensions—to demonstrate the types developmental processes LTA can identify. Time invariant and time varying covariates, distal outcomes, and a mover-stayer second-order latent variable are explored in relation to peer victimization during early adolescence. A second-order transition effect is also used to describe longitudinal transitions into and out of peer victimization classes. The most common longitudinal models are the growth curve and the auto regressive models (Collins & Sayer, 2001). These models differ in the research questions they address. A Stability and Instability 4 growth model describes the general rate at which peer victimization changes during middle school, while an autoregressive model describes the probability of a student transitioning from one victimization state to another between grades. In growth modeling, dependent variables are correlated through the growth parameters while in autoregressive models the dependent variables are directly related to each other. In autoregressive models, change parameters are regression coefficients that describe the relationship between adjacent time points, implying that victim status from earlier school years directly affects status in later school years. For example, students’ peer victimization status in sixth grade should predict their victimization status in seventh grade. The latent variable can represent a continuous factor or a categorical latent

Stability and Instability of Peer Victimization during Middle School: Using Latent Transition Analysis with Covariates, Distal Outcomes, and Modeling Extensions

Karen L. Nylund

Papers

Deciding on the Number of Classes in Latent Class Analysis and Growth Mixture Modeling: A Monte Carlo Simulation Study

Subtypes, severity, and structural stability of peer victimization: what does latent class analysis say?

Stability and Instability of Peer Victimization during Middle School: Using Latent Transition Analysis with Covariates, Distal Outcomes, and Modeling Extensions