this paper we review some of the more important software programs and packages that can are designed for, or can be used for, multilevel analysis. These programs differ in many respects. Some are part of major statistics packages such as SAS or BMDP. Others are written in the macro language of a

Key Words methods, contextual effects, random effects, social epidemiology, ecologic s Abstract Over the past few years there has been growing interest in considering factors defined at multiple levels in public health research. Multilevel analysis has emerged as one analytical strategy that may

A multilevel analysis

Traditional study designs, such as individual-level studies and ecological studies, are unable to simultaneously examine the effects of individual-level and group-level factors on risk of disease. Multilevel analysis overcomes this limitation by allowing the simultaneous investigation of factors

Currently a comprehensive multilevel multiple group modeling framework is not well established and well defined. This is particularly true when the group variable is defined on the individual level. Consider the following simple example where students are nested within classrooms/teachers and are

This paper reports on a statewide study that examined the extent to which a safe school influences individual student achievement. The study used a two-level hierarchical model that included student characteristics and school conditions used in prior research. The statewide analysis was based on 46

The aim of this paper is to analyze, using a hierarchical linear model, the degree to which a system of choice, as the one implemented in Chile since the beginning of the 80’s, can promote student achievement and equity in the social distribution of achievement. Using data from a standardized achievement test, which includes the entire population of 4th grade students and schools of the country, we investigate the association between students’ socioeconomic status and achievement, within and between schools. We also investigate up to what extent different categories of schools enjoy advantages in educating low-income students. These are important issues because unlike the limited vouchers programs in the US, Chile has had a nationwide school choice program for more than 20 years.

er: problems with one may be solved by tinkering with one of the other aspects, and model misspecification in one respect may lead to consequences in other respects. E.g., unrecognized level-one heteroscedasticity may lead to a significant random slope variance, which then disappears if the heteroscedasticity is taken into account; non-linear effects of some variables in X , when unrecognized, may show up as heteroscedasticity at level 1 or as a random slope; and non-zero expected residuals sometimes can be dealt with by transformations of variables in X . This presentation of diagnostic techniques starts with techniques that can be represented as model checks remaining within the framework of the HLM. This is followed by a section on model checking based on various types of residuals. An important type of misspecification can reside in non-linearity of the effects of explanatory variables. The last part of the chapter presents methods to identify such misspecifications and estimate t

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hospital data. The paper has also benefited from the helpful comments from colleagues at the Cancer Registry. Some of the data have been extracted from the Municipality Data Base operated by the