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

jjj

jjj

ijijjjij

uZ

uZ

rXY

111101

001000

10

ijijjjijj

ijjij

rXuuXZ

XZY

1011

100100

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