Multilevel Modeling Software Wayne Osgood Crime, Law & Justice Program Department of Sociology
Jan 03, 2016
Multilevel Modeling Software
Wayne Osgood
Crime, Law & Justice Program
Department of Sociology
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
What are multi-level models?
• Multi-level data: nesting• The statistical problem: dependence• The basic model
The Basic Multilevel Model
• Hierarchical notation
• Composite/Mixed Model Notation
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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
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!
Varieties of Multilevel Models
Nature of nesting
• 2 level
• 3 level
• More than 3!
• Multivariate (dependent variable)
• Cross-nested
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
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?
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
Features: Data Handling
• Stat package input
• Sample weights
• Multiply imputed datasets
• Automated centering
• Automated cross-level interactions
Features: Additional Information
• Wald tests
• Residual analysis
• Graphing
• Unit specific estimates– “OLS”– Fitted– Bayes/Shrinkage
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
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
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
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
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
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
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
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
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