Hierarchical Linear Models II: Advanced Topics ICPSR 2008

Instructors Stephen W. Raudenbush, University of Chicago Aline Sayer, University of Massachusetts Amherst ___________________________________________________________________________

Course Description This is a second course in hierarchical linear models. Individuals who enroll should have taken the ICPSR course Hierarchical Linear Models I: Introduction or its equivalent. This course will consider several advanced topics. These include: 1) generalized hierarchical linear models, including nonlinear models for binary, binomial, count, ordinal, and multinomial outcomes; 2) multivariate models for longitudinal data, with consideration of a variety of alternative covariance structures including compound symmetry, autoregressive structures, and heterogeneous level-1 variance; 3) embedding IRT measurement models in HLM; 4) latent variable models, including random effects as latent variables and random coefficients as predictors; 5) models for cross-classified data; 6) hierarchical models for distinguishable dyads and 6) models for causal inference in multi-level research. Required Reading Raudenbush, S.W., & Bryk, A.S., (2002). Hierarchical Linear Models: Applications and Data Analysis Methods. Newbury Park, CA: Sage. 2nd edition. Raudenbush, S.W., Bryk, A.S., Cheong, Y.F., & Congdon, R.T. (2004) HLM6:Hierarchical Linear and Nonlinear Modeling. Chicago: Scientific Software International. Sequence of Topics Monday July 7 I. Generalized hierarchical linear models

• Binary outcomes (example from Thailand survey data) • A Bernoulli Model • A Binomial Model • Overdispersion at Level 1 • Counts (example from the National Youth Survey) • Unit-Specific versus Population-Average Models • Models for ordinal data (example from Teacher Commitment data) • Models for multinomial data (example from NELS on post-secondary education)

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Reading: HLM (2nd edition) Chapter 10 Suggested: Horney, Osgood, & Marshall (1995) Rumberger (1995)

Tuesday July 8 I. Multivariate linear models for change as hierarchical models

• Disaggregating within-person and between-person effects using a time-varying covariate: Compositional effects model (example from the National Youth Survey)

• The unrestricted model • Compound symmetry model • Autoregressive (AR1) models • Time-varying level-1 variance • A log-linear model for the level-1 variance

Reading: HLM (2nd edition): Chapter 6 Suggested: Raudenbush (2001, 2002) Sayer & Willett (1998) Willett & Sayer (1994)

II. Item response models at Level-1: HLM as a measurement model (example from Arnett data)

Reading: HLM (2nd edition): Chapter 11 Suggested: Cheong & Raudenbush (2000)

Doorenbos, Verbitsky, Given & Given (2005) Raudenbush, Johnson, & Sampson (2003)

Wednesday July 9 I. Latent Variable Models Within the Framework of HLM

• Estimating indirect and direct effects of latent variable ( example from PHDCN) • Random coefficients as predictors

Reading: HLM (2nd edition) Chapter 11 Suggested: Raudenbush & Sampson (1999, 2000)

II. Extending the multivariate outcomes model to dyads (cross-sectional & longitudinal) Reading: Sayer & Klute (2005)

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Raudenbush, Brennan, & Barnett (1995) Suggested: Lyons & Sayer (2005)

III. Cross-classified models within the framework of HLM

• Partitioning variance (example from Garner) • Random intercept models • Random coefficient models

Reading: HLM (2nd edition) Chapter 12 Suggested: Raudenbush (1993) Garner & Raudenbush (1991)

Thursday July 10 I. Causal inference for multilevel data: An introduction

• Introduction and brief overview • Rubin’s causal model • Causal effects of educational interventions: An application using grade retention • Multi-level randomized experiments: Naïve analysis of ECLS-K data • Selection bias and the propensity score • Logistic regression and hierarchical logistic regression • Propensity score estimation • Propensity stratification, causal analysis with propensity adjustment • Sensitivity analysis • Final remarks

Reading: Hong & Raudenbush (2005) Optional topics (if time permits):

• Optimal design for hierarchical models (power analysis) • Missing data models, multiple imputation within HLM, measurement error in

explanatory variables

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Selected References Organized by Topic

Generalized Linear Models with Random Effects Horney, J., Osgood, D.W. & Marshall, I.K. (1995). Criminal careers in the short term:

Intra-individual variability in crime and its relation to local life circumstances. American Sociological Review, 60, 655-673.

Raudenbush, S. W., Yang, M-L., Yosef, M. (2000). Maximum likelihood for generalized

linear models with random effects via high-order, multivariate Laplace approximation. Journal of Computational and Graphical Statistics, 9 (1), 141-157.

Rumberger, R.W. (1995). Dropping out of middle school: A multilevel analysis of students

and schools. American Educational Research Journal, 32(3), 583-562. Sampson, R.J., Raudenbush, S.W., & Earls, F. (1997). Neighborhoods and violent crime: A

multilevel study of collective efficacy. Science, 277, 918-924. 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. 33-64). 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. 25-58). Mahwah NJ: Erlbaum.

Sayer, A.G. & Willett, J.B. (1998). A cross-domain model for growth in adolescent alcohol

expectancies. Multivariate Behavioral Research, 33, 509-543. 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), 363-381.

Latent Variable and IRT Models Cheong, Y. F. & Raudenbush, S. W. (2000). Measurement and structural models for

children’s problem behaviors. Psychological Methods, 5(4), 477- 495.

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Doorenbos, A. Z., Verbitsky, N., Given, B., & Given, C. W. (2005). An analytic strategy for modeling multiple-item responses. Nursing Research, 54(4), 229-234.

Raudenbush, S. W. & Sampson, R. J. (1999). Ecometrics: Toward a science of assessing

ecological settings, with application to the systematic social observation of neighborhoods. Sociological Methodology, 29, 1- 41.

Raudenbush, S. W. & Sampson, R. (2000). Assessing direct and indirect associations in

multilevel designs with latent variables. Sociological Methods and Research, 28, 123-153.

Raudenbush, S.W., Johnson, C., & Sampson, R.J., (2003). A multivariate, multilevel Rasch

model for self-reported criminal behavior. Sociological Methodology, 33(1),169-211. Bayesian Methods for Hierarchical Models Seltzer, M.H., Wong, W.H., & Bryk, A.S. (1996). Bayesian analysis in hierarchical models:

Issues and methods. Journal of Educational and Behavioral Statistics, 2(2), 131-167. Cross-classified Models Garner, C. L. and Raudenbush, SW (1991). Neighborhood effects on educational attainment:

A multilevel analysis. Sociology of Education, 64, 251-262. Raudenbush, S.W. (1993). A crossed random effects model for unbalanced data with applications in cross-sectional and longitudinal research. Journal of Educational Statistics. 18(4), 321-349. Models for Causal Inference Hong, G.L. and Raudenbush, S.W. (2005). Effects of kindergarten retention policy on

children’s cognitive growth in reading and mathematics. Educational Evaluation and Policy Analysis, 27(3), 205-224.

Hierarchical Models for Cross-Sectional and Longitudinal Dyads 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), 161-174.

Lyons, K. & Sayer, A. G. (2005). Longitudinal dyad models in family research. Journal of

Marriage and Family, 67, 1048-1060.

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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), 613-628.

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. 289-313). Thousand Oaks, CA: Sage.

Models for Multivariate Outcomes Brennan, R., Kim, J., Wenz-Gross, M. & Siperstein, G. (2001). The relative equitability of

high-stakes testing versus teacher-assigned grades: An analysis of the Massachusetts Comprehensive Assessment System (MCAS). Harvard Educational Review, 71 (2), 173-216.

Kuo, M., Mohler, B., Raudenbush, S., & Earls, F. (2000). Assessing exposure to violence

using multiple informants: Application of hierarchical linear model. Journal of Child Psychology and Psychiatry, 41 (8), 1049-1056.

Supovitz, J. & Brennan, R. (1997). Mirror, mirror on the wall, which is the fairest test of all?

An examination of the equitability of portfolio assessment relative to standardized tests. Harvard Educational Review, 67 (3), 472-506.