Judith D. Singer

Applied Longitudinal Data Analysis

PART I 1. A framework for investigating change over time 2. Exploring Longitudinal Data on Change 3. Introducing the multilevel model for change 4. Doing data analysis with the multilevel mode for change 5. Treating TIME more flexibly 6. Modelling discontinuous and nonlinear change 7. Examining the multilevel models error covariance structure 8. Modelling change using covariance structure analysis PART II 9. A Framework for Investigating Event Occurrence 10. Describing discrete-time event occurrence data 11. Fitting basic Discrete-Time Hazard Models 12. Extending the Discrete-Time Hazard Model 13. Describing Continuous-Time Event Occurrence Data 14. Fitting Cox Regression Models 15. Extending the Cox Regression Model

Using SAS PROC MIXED to Fit Multilevel Models, Hierarchical Models, and Individual Growth Models

SAS PROC MIXED is a flexible program suitable for fitting multilevel models, hierarchical linear models, and individual growth models. Its position as an integrated program within the SAS statistical package makes it an ideal choice for empirical researchers and applied statisticians seeking to do data reduction, management, and analysis within a single statistical package. Because the program was developed from the perspective of a “mixed” statistical model with both random and fixed effects, its syntax and programming logic may appear unfamiliar to users in education and the social and behavioral sciences who tend to express these models as multilevel or hierarchical models. The purpose of this paper is to help users familiar with fitting multilevel models using other statistical packages (e.g., HLM, MLwiN, MIXREG) add SAS PROC MIXED to their array of analytic options. The paper is written as a step-by-step tutorial that shows how to fit the two most common multilevel models: (a) school effects models, designed for data on individuals nested within naturally occurring hierarchies (e.g., students within classes); and (b) individual growth models, designed for exploring longitudinal data (on individuals) over time. The conclusion discusses how these ideas can be extended straighforwardly to the case of three level models. An appendix presents general strategies for working with multilevel data in SAS and for creating data sets at several levels.

It's About Time: Using Discrete-Time Survival Analysis to Study Duration and the Timing of Events

Educational researchers frequently ask whether and, if so, when events occur. Until relatively recently, however, sound statistical methods for answering such questions have not been readily available. In this article, by empirical example and mathematical argument, we demonstrate how the methods of discrete-time survival analysis provide educational statisticians with an ideal framework for studying event occurrence. Using longitudinal data on the career paths of 3,941 special educators as a springboard, we derive maximum likelihood estimators for the parameters of a discrete-time hazard model, and we show how the model can befit using standard logistic regression software. We then distinguish among the several types of main effects and interactions that can be included as predictors in the model, offering data analytic advice for the practitioner. To aid educational statisticians interested in conducting discrete-time survival analysis, we provide illustrative computer code (SAS, 1989) for fitting discrete-time hazard models and for recapturing fitted hazard and survival functions.

Modeling the days of our lives: Using survival analysis when designing and analyzing longitudinal studies of duration and the timing of events.

Psychologists studying whether and when events occur face unique design and analytic difficulties. The fundamental problem is how to handle censored observations, the people for whom the target event does not occur before data collection ends. The methods of survival analysis overcome these difficulties and allow researchers to describe patterns of occurrence, compare these patterns among groups, and build statistical models of the risk of occurrence over time. This article presents a unified description of survival analysis that focuses on 2 topics: study design and data analysis

The design and analysis of longitudinal studies of development and psychopathology in context: Statistical models and methodological recommendations

The utility and flexibility of recent advances in statistical methods for the quantitative analysis of developmental data--in particular, the methods of individual growth modeling and survival analysis--are unquestioned by methodologists, but have yet to have a major impact on empirical research within the field of developmental psychopathology and elsewhere. In this paper, we show how these new methods provide developmental psychopathologists with powerful ways of answering their research questions about systematic changes over time in individual behavior and about the occurrence and timing of life events. In the first section, we present a descriptive overview of each method by illustrating the types of research questions that each method can address, introducing the statistical models, and commenting on methods of model fitting, estimation, and interpretation. In the following three sections, we offer six concrete recommendations for developmental psychopathologists hoping to use these methods. First, we recommend that when designing studies, investigators should increase the number of waves of data they collect and consider the use of accelerated longitudinal designs. Second, we recommend that when selecting measurement strategies, investigators should strive to collect equatable data prospectively on all time-varying measures and should never standardize their measures before analysis. Third, we recommend that when specifying statistical models, researchers should consider a variety of alternative specifications for the time predictor and should test for interactions among predictors, particularly interactions between substantive predictors and time. Our goal throughout is to show that these methods are essential tools for answering questions about life-span developmental processes in both normal and atypical populations and that their proper use will help developmental psychopathologists and others illuminate how important contextual variables contribute to various pathways of development.

From Whether to When: New Methods for Studying Student Dropout and Teacher Attrition

Educational researchers studying student dropout and teacher attrition typically ask whether specific events occur by particular points in time. In this article, we argue that a more powerful and informative way of framing such questions is to ask when the transitions occur. We believe that researchers avoid asking questions about time-to-event (“When?”) because of methodological difficulties introduced when members of the sample do not experience the target events during the data collection period. These people—the students who do not graduate or drop out, the teachers who do not quit—possess censored event times. Until recently, statistical techniques available for analyzing censored data were in their infancy. In this article, we show how the methods of survival analysis (also known as event history analysis) lend themselves naturally to the study of the timing of educational events. Drawing examples from the literature on teacher attrition and student dropout and graduation, we introduce a panoply of survival methods useful for describing the timing of educational transitions and for building statistical models of the risk of event occurrence over time. We hope that this nontechnical introduction to survival methods will help educational researchers articulate and explore important substantive questions that they have raised but have yet to answer.

Are Special Educators' Career Paths Special? Results from a 13-Year Longitudinal Study

A statistical methodology relatively new to education—survival analysis—is used to describe the career paths of over 6,600 special education teachers newly hired in Michigan and North Carolina between 1972 and 1983, following them for up to 13 years, or until they stopped teaching in the state. Beginning special educators in both states continue to teach for an average of 7 years. They are most likely to leave teaching during the first few years after hire; those who survive this initial “hazardous” period typically teach for many years to come. Young women are particularly likely to leave, as are those special educators who provide support services or teach students with speech, hearing, or vision disabilities. Teachers with high test scores are at greater risk of leaving as are teachers paid comparatively low salaries.

Ethnic differences in child care selection: the influence of family structure, parental practices, and home language ☆

Abstract Recent work reveals sharp disparities in which types of children participate in centers and preschools. Enrollment rates are especially low for Latino children, relative to Black and Anglo preschoolers, a gap that remains after taking into account maternal employment and family income. Early attempts to model parents’ likelihood of enrolling their youngster in a center have drawn heavily from the household-economics tradition, emphasizing the influence of cost and family income. Yet we show that, after controlling for household-economic factors, the household’s social structure and the mother’s language, child-rearing beliefs, and practices further help to predict the probability of selecting a center-based program. Children are more likely to be enrolled in a center when the mother defines child rearing as an explicit process that should impart school-related skills—reading to her youngster, frequenting the library, teaching cooperative skills, and speaking English. After taking these social factors into account, ethnic differences in center selection still operate: African American families continue to participate at higher rates for reasons that may not be solely attributable to family-level processes, such as greater access to Head Start centers or state preschools. In addition, the lower center selection rate for Latinos appears to be lodged primarily in those families which speak Spanish in the home, further pointing to how cultural preferences are diverse and interact with the local supply of centers. These findings stem from an analysis of whether, and at what age, a national sample of 3,624 children first entered a center, using discrete-time survival analysis. We discuss how center selection can be seen as one element of a broader parental agenda, linked to parents’ acculturation to middle-class Anglo commitments and involving the task of getting one’s child ready for school.

Job experiences over time, multiple roles, and women's mental health: A longitudinal study.

Are changes over time in the quality of a womans job associated with changes in her psychological distress? Do family roles moderate these relationships? We addressed these questions using longitudinal data from a 2-year 3-wave study of a stratified random sample of 403 employed women who varied in occupation, race, partnership, and parental status. After estimating individual rates of change for each woman on each of the predictors and the outcome, we modeled the relationships between family role occupancy and change in job-role quality on the one hand, and change in psychological distress on the other. Among single women and women without children, as job-role quality declined, levels of psychological distress increased. Among partnered women and women with children, change in job-role quality was unrelated to change in psychological distress.

Early child-care selection: variation by geographic location, maternal characteristics, and family structure.

More than half of all U.S. infants and toddlers spend at least 20 hr per week in the care of a nonparent adult. This article uses survival analysis to identify which families are most likely to place their child in care and the ages when these choices are made, using data from a national probability sample of 2,614 households. Median age at first placement is 33 months, but age varies by geographic region, mothers employment status during pregnancy, mothers education level, and family structure (1 vs. 2 parents, mothers age at 1st birth, and number of siblings). Controlling for these effects, differences by race and ethnicity are small. Implications for studies of child-care selection and evaluations of early childhood programs are discussed.