Software and literature

In addition to special purpose software such as HLM and Mlwin, routines for estimating multilevel models have now been incorporated into general purpose software packages for statistical analysis. In SAS, the Mixed procedure can estimate a variety of linear multilevel models. In SPSS, Linear Mixed Models allows the estimation of multilevel models with several levels. The routine is restricted to continuous dependent variables, however. In other words, all versions of multilevel logistic models (binary, multinomial, ordinal) cannot be estimated in SPSS. Heck, Thomas and Tabata (2010) have written an extended manual to show how multilevel models for cross-sectional and longitudinal data can be estimated in SPSS. Linear mixed models are generalizations of the linear OLS regression model to allow for correlated data and non-constant variability (heterocedasticity). These routines enable variances and covariances to be modelled, in addition to estimating the regression coefficients.

Stata has several routines for estimating linear (XTREG, XTMIXED) and logistic (XTLOGIT, XTMELOGIT) multilevel models in addition to the very powerful add-in program Gllamm (Rabe-Hesketh and Skrondal 2012). At present, Stata has the most complete routines for multilevel modelling besides the special purpose programs HLM and Mlwin. Rabe-Hesketh and Skrondal (2012) give examples of how the Stata routines can be used to estimate a variety of multilevel models.

The public domain program R is growing in popularity among advanced users. Routines for multilevel models have been developed for R. The web page developed in connection with Kreft and de Leeuw’s introductory book includes data sets from the book in formats for the most popular software packages.

Finally, some programs for Structural Equation Models (SEM) are able to estimate multilevel models with and without latent variables. Mplus and Lisrel are two widely used SEM programs with this capability.

In linear multilevel models, all programs generally produce almost identical results. In non-linear models, such as variations of multilevel logistic models, the results are more prone to differ due to differences in the estimation algorithms.

In this learning module, we will estimate all models in the general purpose statistical packages Stata and SPSS.

Introductory books on multilevel analysis

There are now a large number of introductory books on multilevel analysis. Below follows a short list of good introductory books, including the book by Rabe-Hesketh and Skrondal, which is better suited for the advanced user than for the novice. It is an excellent sourcebook, however, for Stata users working with multilevel models. I would recommend the novice to start with Hox’s book or the one by Kreft and Leeuw.

Goldstein, H. (1995), Multilevel Statistical Models, 2nd edition. London: Edward Arnold.

Hox, J. (2002), Multilevel Analysis. Techniques and Applications, 2nd edition. London: Lawrence Erlbaum.

Kreft, I. and Leeuw, J. de (2000), Introducing multilevel modelling. London: Sage

Rabe-Hesketh, Sophia and Anders Skrondal (2012), Multilevel and Longitudinal Modeling Using Stata. 3nd edition. Volume I: Continuous Responses. College Station, Texas: Stata Press.

Raudenbush, S.W. and Bryk, A.S. (2002), Hierarchical Linear Models. Applications and Data Analysis Methods, 2nd edition. Sage: Thousand Oaks.

Snijders, Tom A. B. and Roel J. Bosker (1999), Multilevel Analysis, London: Sage.

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