Hierarchical Linear Models For Longitudinal Data August 6-8, 2012

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1 Hierarchical Linear Models For Longitudinal Data August 6-8, 2012 Instructor: Aline G. Sayer, University of Massachusetts Amherst Course Description The hierarchical linear model (HLM) provides a conceptual framework and a flexible set of analytic tools to study a variety of social, political, and developmental processes. The workshop will consider the formulation of statistical models for repeated measures longitudinal data, where individuals, families, dyads, or organizations are followed over time. Interest centers on the shape of the average trajectory, the heterogeneity around the mean growth curve, and individual and contextual characteristics that predict differences in change. Topics include an introduction to the two-level model for polynomial growth functions, an introduction to discontinuous (piecewise) growth models that incorporate multiple growth segments, models for accelerated longitudinal designs, model comparison tests, multiparameter hypothesis testing, the incorporation of time-varying predictors, and the multivariate outcomes model for longitudinal dyads. Emphasis will be placed on checking model assumptions and considering a variety of alternative covariance structures that include compound symmetry, autoregressive structures, and heterogeneous level-1 variance. If time permits, we will consider the three-level model for growth in student achievement, where students are changing over time but are nested in schools. Participants will be exposed to a wide variety of examples, with emphasis on the interpretation of computer output and reporting of results. A basic understanding of statistical inference and skill in interpreting results from multiple regression are pre-requisites. Course Website: psych.umass.edu/people/alinesayer/longitudinal All handouts, selected readings, datasets, and lab annotated output are available for download from the course website. Recommended Texts Raudenbush, S. W. & Bryk, A. S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods. 2 nd edition. Newbury Park, CA: Sage. Raudenbush, S. W., Bryk, A. S.,Cheong, Y. F., & Congdon, R. T.(2004). HLM6: Hierarchical Linear and Nonlinear Modeling. Chicago: Scientific Software International. (This is the computer manual for HLM6. It is also on-line in the HELP section of the program). Singer, J. D., and Willett, J. W. (2003). Applied Longitudinal Data Analysis: Modeling Change and Event Occurence. Cambridge: Oxford University Press. 1

2 Sequence of Topics Monday August 6 I. An Introduction and Brief History * Methodological criticism of past treatment of hierarchical data -problems in the measurement of change -breakthroughs in statistical theory and computation Reading: Raudenbush & Bryk, Chapter 1 II. The 2-level hierarchical linear model illustrated by an application to the study of individual change over time: Chapman data (referenced in Willett, 1989; Singer, 1998). * Modeling change over time for one individual: The Level 1 model * Modeling change over time for J individuals: The Level 2 model Reading: Willett (1989) Singer (1998) II An Introduction to the HLM 7 Computer Program (we may do this in the lab) * Data input and creating the MDM file; modeling; graphing Reading: HLM7 Computer Manual IV. Applications to repeated measures: NYS data * Polynomial models * Studying correlates of growth * Model comparison tests using deviance statistics Reading: Raudenbush, & Bryk: Chapter 6 Willett & Sayer (1994) Tuesday August 7 I. Disaggregating within-person and between-person effects using a time-varying covariate (NYS data; Transition to Parenthood, KPS, 2008; general approach, CB, 2011) Reading: Curran & Bauer (2011) Keeton, Perry-Jenkins & Sayer (2008) Raudenbush & Bryk, Chapter 6 2

3 II. Accelerated longitudinal designs (Eccles data) Reading: Raudenbush and Chan (1993) Jacobs et al (2002) III. Assessing Model Fit * Proportional reduction of variance * Multiparameter parameter hypothesis testing * Assessing distributional assumptions via residual analysis - Level-1 assumptions: Creating and using the level-1 residual file - Level-2 assumptions: Creating and using the level-2 residual file Reading: Raudenbush, & Bryk: Chapters 3, 9 Wednesday August 8 I. Multivariate linear models for change as hierarchical models The multivariate approach to modeling longitudinal data: The unrestricted model Comparison of models for level-1 residual variance: homogeneous, heterogeneous, and a log-linear function of time Compound symmetry and models for autoregressive (AR1) residual variance Reading: Raudenbush & Bryk, Chapter 6 Suggested: Raudenbush (2001, 2002) Sayer & Willett (1998) Willett and Sayer (1994) II. Discontinuous (piecewise) growth models (Laws cortisol data) Reading: Cumsille, Sayer,& Graham (2000) Raudenbush & Bryk, Chapter 6 Svartberg, Seltzer, Stiles & Khoo (1995) II. Longitudinal models for dyads (Powers cortisol data) Reading: Lyons and Sayer (2005) Powers, Pietromonaco, Gunlicks & Sayer (2006) Raudenbush, Brennan, & Barnett (1995) Sayer & Klute (2005) 3

4 Selected References Organized by Topic Methodological Overview Collins, L. M. & Sayer, A. G. (2000). Modeling growth and change processes: Design, measurement, and analysis for research in social psychology. In Harry Reis and Charles Judd (Eds.), Handbook of research methods in social psychology (pp ). Cambridge: Cambridge University Press. Raudenbush, S.W. (2000). Hierarchical Models. In Kotz, S. (Ed.) Encyclopedia of Statistical Sciences (Volume 3). New York: John Wiley and Sons. Willett, J. B. (1989). Questions and answers in the measurement of change. In E. Z. Rothkopf (Ed.). Review of Research in Education, 15, (pp ). Washington DC: American Educational Research Association. Individual Growth Modeling Applications Hauser-Cram, P., Warfield, M. E., Shonkoff, J., Krauss, M. W., Upshur, C., & Sayer, A. (1999). Family influences on adaptive development in young children with down syndrome. Child Development, 70 (4), Hauser-Cram, P., Warfield, M., Shonkoff, J., Krauss, M., Sayer, A., & Upshur, C. (2001). Children with disabilities: A longitudinal study of child development and parent wellbeing. Monographs of the Society for Research in Child Development, 66 (3, Serial No. 266). Huttenlocher, J., Haight, W., Bryk, A., Seltzer, M., & Lyons, T. (1991). Early vocabulary growth: Relation to language input and gender. Developmental Psychology, 27, Singer, J. D. (1998). Using SAS Proc Mixed to fit multilevel models, hierarchical models, and individual growth models. Journal of Educational and Behavioral Statistics, 24, Svartberg, M., Seltzer, M., Stiles, T., & Khoo, S. T. (1995). Symptom improvement and its temporal course in short-term dynamic psychotherapy: A growth curve analysis. Journal of Nervous and Mental Disease, 183 (4), Time-varying covariates and compositional effects Curran, P. J. & Bauer, D. J. (2011). The disaggregation of within-person and betweenperson effects in longitudinal models of change. Annual Review of Psychology, 62,

5 Keeton, C. P., Perry-Jenkins, M., & Sayer, A. G. (2008). Sense of control predicts depressive and anxious symptoms across the transition to parenthood. Journal of Family Psychology, 22(2), Multivariate Hierarchical Growth Models Raudenbush, S. W. (2001). Toward a coherent framework for comparing trajectories of change. In Collins, L. M. & Sayer, A. G. (Eds). New methods for the analysis of change (pp ). Washington DC: APA. Raudenbush, S. W. (2002). Alternative covariance structures for polynomial models of individual growth and change. In D. Moskowitz & S. L. Hershberger (Eds.). Modeling intraindividual variability with repeated measures data (pp ). Mahwah NJ: Erlbaum. Sayer, A. G. & Willett, J. B. (1998). A cross-domain for growth in adolescent alcohol expectancies. Multivariate Behavioral Research, 33, Willett, J. B. & Sayer, A. G. (1994). Using covariance structure analysis to detect correlates and predictors of individual change over time. Psychological Bulletin, 116 (2), Hierarchical Models for Longitudinal Dyads Lyons, K. S., Zarit, S. H., Sayer, A. G., & Whitlach, C. J. (2002). Caregiving as a dyadic process: Perspectives from the caregiver and receiver. Journal of Gerontology, 57 (3), Lyons, K. & Sayer, A. G. (2005). Longitudinal dyad models in family research. Journal of Marriage and Family, 67, Powers, S. I., Pietromonaco, P., Gunlicks, M., & Sayer, A. (2006). Dating couples attachment styles and patterns of cortisol reactivity and recovery in response to a relationship conflict. Journal of Personality and Social Psychology, 90 (4), Raudenbush, S.W., Brennan, R.T., & Barnett, R.C. (1995). A multivariate hierarchical model for studying psychological change within married couples. Journal of Family Psychology, 9(2), Sayer, A. G. & Klute, M.M. (2005). Analyzing couples and families: Multilevel methods. In V. L. Bengston, A. C. Acock, K. R. Allen, P. Dilworth-Anderson, & D. M. Klein (Eds). Sourcebook of family theory and research (pp ). Thousand Oaks, CA: Sage. Accelerated Longitudinal Designs Raudenbush, S.W. and Chan,W.S. (1993). Application of a hierarchical linear model to the study of adolescent deviance in an overlapping cohort design. Journal of Consulting and Clinical Psychology, 61,

6 Jacobs, J. E., Lanza, S., Osgood, D.W., Eccles, J.S., & Wigfield, A.W. (2002) Changes in Children's Self-Competence and Values: Gender and Domain Differences across Grades One through Twelve. Child Development, 73, Discontinuous Growth Models Cumsille, P. E., Sayer, A. G., & Graham, J. W. (2000). Perceived exposure to peer and adult drinking as predictros of growth in positive alcohol expectancies during adolescence. Journal of Consulting and Clinical Psychology, 68 (3), Seltzer, M. (1994). Studying variation in program success: A multilevel modeling approach. Evaluation Review, 18, Three-Level Models with Growth at Level-1 Raudenbush, S.W. (1995). Hierarchical linear models to study the effects of social context on development. In Gottman, J.M. (Ed.) The Analysis of Change. Mahwah, NJ: Lawrence Erlbaum, Chapter 6,

Introduction to Hierarchical Linear Models ICPSR 2009

Introduction to Hierarchical Linear Models ICPSR 2009 Instructors: Aline G. Sayer, University of Massachusetts Amherst Natalya Verbitsky Savitz, Mathematica Policy Research Course Description The hierarchical