1. Multilevel Modeling Software Wayne Osgood Crime, Law & Justice Program Department of Sociology

2. What I’ll Cover What are multi-level models? Varieties of multi-level models Program features Descriptions of seven programs For more info: –Reviews by U of Bristol Center for Multilevel Modeling: http://www.mlwin.com/softrev/index.html

3. What are multi-level models? Multi-level data: nesting The statistical problem: dependence The basic model

4. The Basic Multilevel Model Hierarchical notation Composite/Mixed Model Notation

5. What are multi-level models? Multi-level data: nesting The statistical problem: dependence The basic model Results: –Regression coefficients –Variances (and covariances) for residuals These address dependence Key new assumption: –Variance components have multivariate normal distribution

6. Programs I’ll Discuss Yes: –Random effects multilevel regression –Stand alone and stat package No: –“Fixed effects” panel models –Latent growth models –Latent class trajectory models A note on terminology: I’m sorry!

7. Varieties of Multilevel Models Nature of nesting 2 level 3 level More than 3! Multivariate (dependent variable) Cross-nested

8. Varieties of Multilevel Models Linear/ Normal Non-linear/Generalized Linear Level 1 non-normal, higher levels normal –Dichotomous: logistic, probit –Ordinal: logistic –Multinomial: logisitic –Count: Poisson, negative binomial –Censored/limited continuous: Tobit

9. Features of Programs: Estimation Iterative generalized least squares Restricted maximum likelihood –Max likelihood variance, least sq coefs Full maximum likelihood Partially qualified likelihood (non-linear) Markov chain Monte Carlo Differences in estimates?

10. Features: Model Complexities Complex variance structures –Level 1 dependent on explanatory variables –Longitudinal structures Latent variable effects/mediation Unit specific vs. population average Robust standard errors –GEE / sandwich –Bootstrap

11. Features: Data Handling Stat package input Sample weights Multiply imputed datasets Automated centering Automated cross-level interactions

12. Features: Additional Information Wald tests Residual analysis Graphing Unit specific estimates –“OLS” –Fitted –Bayes/Shrinkage

13. Multilevel Modeling Programs MLM programs: General –HLM, MLwinN MLM programs: Specialized –aML, WINBUGS MLM in stat packages –STATA, SAS, SPSS Others I’ll skip –MIXed up suite, R, LIMDEP, M+, S+, SYSTAT

14. What’s in a user friendly MLM interface? Equation display with point-and-click modification Automated centering and cross-level interactions Ready access to: –Residual analysis and tests of assumptions –Multiple coefficient tests (Wald) –Estimation and iteration options

15. HLM Full featured, user friendly, continuing development Strengths: user interface, range of options and output Recommended: For anyone who expects to do a good deal of MLM Bryk, Raudenbush & Congdon –Scientific Software International, Chicago –$425, $100 each additional

16. MLwiN Fully featured, very powerful, continuing development Strengths: range of options, up to 10 levels, bootstrap & MCMC Recommended for more advanced users, special purposes Goldstein & colleagues –Centre for Multilevel Modeling, UK –$990, $360 additional user, $3600 50 users

17. aML Specializes in unusual models –Multiple equation selection models –Joint modeling of outcomes with different response functions (e.g., normal & Poisson) Strengths: Technical, flexible Weaknesses: Interface, slow Recommended: For economists and when it’s the only choice From Lillard & Panis –Now free to download

18. WINBUGS A Bayesian stat package Mainly of interest for MCMC estimation Much slower Recommended: For MCMC beyond MLwiN. Medical Research Council Biostat Unit, Cambridge UK –Free to download

19. STATA High level, broad, popular, user friendly, stat package Where to find multilevel: –“xt” commands (many) Strengths: data management, other features of STATA Weaknesses: range of MLM options Recommended: STATA users running random intercept models

20. SAS High level, broad, popular stat package Primary multilevel commands: –PROC MIXED & PROC NLMIXED –Quite general Strengths: other features of SAS, breadth of programs Weaknesses: interface & options Recommended: For PROC-aholics

21. SPSS Less advanced general statistical package Where to find MLM: –MIXED (mixed models) –VARCOMP (general linear model, variance components) Strengths: other features of SPSS Weaknesses: limited range of options, interface for MLM Recommended: for SPSS users running a few simple models