Longitudinal Analysis Michael L. Berbaum Institute for Health Research and Policy University of Illinois at Chicago Course description: Longitudinal analysis is the study of short series of observations obtained from many respondents over time and is also referred to as panel analysis (of a cross-section of time series) or repeated measures or growth curve analysis (polynomials in time) or multilevel analysis (where one level is a sequence of observations from respondents). Longitudinal analysis is used for panel surveys, experiments and quasi-experiments in health and biomedicine, education and psychology, and the evaluation of prevention and treatment programs. This course treats the statistical basis and practical application of linear models for longitudinal normal data and generalized linear models for longitudinal binary, count, and ordinal data. The approach involves inclusion of random effects in linear models to reflect within-person cross-time correlation. Techniques for irregularly observed (unequally spaced) data will be covered. Other ICPSR courses focus on time series and structural equations approaches, including latent growth curve models, which are only briefly discussed in this course. The technical level will be at Track II, with interludes at Track III (matrix algebra, probability distributions). Examples and exercises will use both standard and special-purpose software. Participants should have a good understanding of linear regression or analysis of variance. Required text: Applied Longitudinal Analysis Fitzmaurice, Garrett M., Laird, Nan M., and Ware, James H. (2011). Applied longitudinal analysis (2nd ed.). Hoboken, NJ: John Wiley & Sons. [FLW] Recommended text: Generalized Linear Models Gill, Jeff (2001). Generalized linear models: A unified approach. Thousand Oaks, CA: Sage Publications. [Gill] Recommended texts: Random Effects or Mixed Models Approach Brown, Helen, and Prescott, Robin (2006). Applied mixed models in medicine (2nd ed.). Chichester, England: John Wiuley7 & Sons. Demidenko, Eugene (2004). Mixed models: Theory and applications. Hoboken, NJ: John Wiley & Sons, Inc. 1
Diggle, Peter J., Heagerty, P., Liang, Kung-Yee, and Zeger, Scott L. (2002). Analysis of longitudinal data (2nd ed.). Oxford, England: Oxford University Press. Fitzmaurice, Garrett, Davidian, Marie, Verbeke, Geert, and Molenberghs, Geert (Eds.)(2009). Longitudinal data analysis. Boca Raton, FL: Chapman & Hall/CRC, Taylor & Francis Group, LLC. Hedeker, Donald, and Gibbons, Robert D. (2006) Longitudinal data analysis. Hoboken, NJ: John Wiley & Sons. Note: New edition in preparation. Hedeker, Donald, and Gibbons, Robert D. (2011). SuperMix mixed effects models. Chicago, IL: Scientific Software International, Inc. Jiang, Jiming (2007). Linear and generalized linear mixed models and their applications. New York: Spring Science+Business Media. Littell, Ramon C., Milliken, George A., Stroup, Walter W., Wolfinger, Russell D., and Schabenberger, Oliver (2006). SAS system for mixed models (2nd ed.). Cary, NC: SAS Institute, Inc. McCulloch, Charles E., and Searle, Shayle R. (2001). Generalized, linear, and mixed models. New York: John Wiley & Sons. Molenberghs, Geert, and Verbeke Geert (2005). Models for discrete longitudinal data. New York: Springer Science+Media, Inc. [M&V] Pinheiro, Jose C., and Bates, Douglas M. (2000). Mixed effects models in S and S-PLUS. New York: Springer-Verlag. Stroup, Walter W. (2012) Generalized linear mixed models: Modern concepts, methods, and applications. Chapman & Hall/ CRC. Verbeke, Geert, and Molenberghs, Geert (2000). Linear mixed models for longitudinal data. New York: Springer-Verlag. [V&M] Willett, John B., and Singer, Judith D. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. New York: Oxford University Press. Recommended texts: Multilevel Models (forms of Mixed Models) de Leeuw, Jan, and Meijer, Erik (Eds.)(2010). Handbook of multilevel modeling. New York: Springer Science+Business Media, LLC. Finch, W. Holmes, Bolin, Jocelyn E., Kelley, K. (2014). Multilevel modeling using R. Chapman & Hall/CRC. 2
Hox, Joop J., and Roberts, J. Kyle (Eds.)(2011). Handbook of advanced multilevel analysis. New York: Routledge, Taylor & Francis Group, LLC. Luke, Douglas A (2004) Multilevel modeling. (Quantitative Applications in the Social Sciences). Sage Publications, Inc. Raudenbush, Stephen W., and Bryk, Anthony S. (2002). Hierarchical linear models: Applications and data analysis methods (2nd ed.). Thousand Oaks, CA: Sage Publications. Snijders, Tom A. B., and Roel Bosker (2011). Multilevel analysis: An introduction to basic and advanced multilevel modeling (2nd ed.). Sage Publications, Ltd. Recommended texts: Panel Econometrics Approach Allison, Paul (2005). Fixed effects regression methods for longitudinal data using SAS. Cary, NC: SAS Institute, Inc. Allison, Paul (2009). Fixed effects regression models. Thousand Oaks, CA: Sage Publications. [Allison] Arellano, Manuel (2003). Panel data econometrics. Oxford: Oxford University Press. Baltagi, Badi H. (2013). Econometric analysis of panel data (5th ed.) Hoboken, NJ: John Wiley & Sons. Baltagi, Badi H. (2009). A companion to Econometric analysis of panel data. Hoboken, NJ: John Wiley & Sons. (Corresponds to 4th edition) Baltagi, Badi H. (2013). e-study Guide for: A Companion to Econometric Analysis of Panel Data by Prof. Badi Baltagi. Cram101. (Corresponds to 5th edition; Kindle) Frees, Edward W. (2004). Longitudinal and panel data: Analysis and applications in the social sciences. New York, NY: Cambridge University Press. Hsiao, Cheng (2014). Analysis of panel data (3rd ed.). (Econometric Society Monographs). Cambridge: Cambridge University Press. Wooldridge, Jeffrey M. (2010). Econometric analysis of cross section and panel data (2nd ed.). Cambridge, MA: MIT Press. 3
Schedule of topics (approximate): Day 1 Introduction, course scope and organization, examples of longitudinal data, marginal and random-effects models for longitudinal data, models for longitudinal categorical data (binary, count, and ordinal responses), the diamond of models to be addressed. Read FLW, Ch. 1, Longitudinal and Clustered Data, and Ch. 2, Longitudinal Data: Basic Concepts. Day 2 Linear Model (LM) and Linear Mixed Model (LMM). Read FLW, Ch. 3, Overview of Linear Models for Longitudinal Data, and scan Ch. 8, Linear Mixed Effects Models. Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10 Day 11 Day 12 Continue discussion of LM and LMM models; the SAS MIXED procedure. FLW is brief about MIXED: Sections 5.9, 6.6, and 7.8. For more detail read V&M, Ch. 8, Fitting Linear Mixed Models with SAS. Chapters 1-5 of Littell cover the mixed model approach to common experimental designs, with examples in SAS. Maximum likelihood (ML) estimation and restricted maximum likelihood (REML). Read FLW, Ch. 4, Estimation and Statistical Inference. Modelling the mean. Read FLW, Ch. 5, Modeling the Mean: Analyzing Response Profiles, and Ch. 6, Modeling the Mean: Parametric Curves. Continue discussion of modelling the mean. For another account of this subject read V&M, Ch. 6, Inference for the Marginal Model. Modelling the covariance. Read FLW, Ch. 7, Modeling the Covariance. LMM. Read FLW, Ch. 8, Linear Mixed Effects Models. Continue LMM. Model diagnostics. Read FLW, Ch. 10, Residual Analyses and Diagnostics. (For further discussion of diagnostics, see John Fox s Sage monograph, Regression diagnostics.) Missing data. Read FLW, Ch. 17, Missing Data and Dropout: Overview of Concepts and Methods. (V&M devote Chapters 14-21 to this important topic. See Ch. 14, Exploring Incomplete Data, Ch. 15, Joint Modeling of Measurements and Missingness, and Ch. 16, Simple Missing Data Methods. ) Continue discussion of missing data. 4
Day 13 Day 14 Day 15 Power analysis for random effects models. Read FLW, Ch. 20, Sample Size and Power, and handouts provided in class. See also V&M, Ch. 23, Design Considerations, Generalized linear models (GLM) framework. Read FLW, Ch. 11, Review of Generalized Linear Models. For more on GLMs, read Gill. Generalized linear mixed model (GLMM). Read FLW, Ch. 14, Generalized Linear Mixed Effects Models. Day 16 Software for estimation of GLM and GLMM. Read FLW, Sections 11.6, 13.6, and 14.8. (Cf. V&M, Appendix A, Software, and Littell, et al. (2006), Generalized Linear Mixed Models. ) Day 17 Day 18 Day 19 Continue discussion of GLMM; examples of binary and count responses. Overdispersion. (Receive handouts for ordinal responses.) Mixed models for ordinal responses. Handouts on the SAS NLMIXED procedure) Multilevel or hierarchical models. Read FLW, Ch. 22, Multilevel Models.. Supplemental readings: The texts are thoroughly referenced. In addition, additional references will be provided as class handouts, including a bibliography on experimental design and analysis of variance, and another on GLM and GLMM. Software: The primary software package for this course is SAS. Some examples will employ the lme/nlme libraries in the S family of packages (S/S-Plus/R). Stata has comparable capabilities for certain problems. 5