multi-level models A set of closely related approaches to examining the links between macro- and micro-levels of social phenomena. Multi-level (also known as ‘contextual’ or ‘hierarchical’) models in sociology attempt to identify the effects of social context on individual-level outcomes.

The idea that individuals are affected by and respond to their social surroundings is fundamental to sociology as a discipline. Among the classic sociologists, Durkheim studied the impact of community structure on suicide rates, and Weber the impact of religious communities (such as the Protestant sects) on economic conduct. However, since the mid-1980s, new theories have been developed and new statistical techniques applied to a variety of sociological problems, and these represent a significant advance over earlier approaches.

There are a number of multi-level models, going under a variety of names, most of which are extensions of the ‘contextual regression analysis’ used in sociology since the 1960s. These include the hierarchical linear model, hierarchical linear regression, random coefficients model, hierarchical mixed linear model, and bayesian linear model. Numerous other types are being developed by sociologists of education, stratification, and criminology. These involve, among others, the extension of event-history and contingency table analysis to include multi-level effects. The essential feature that they have in common is that all make allowance for contextual effects; that is, for macro-processes that are presumed to have an impact on the individual actor, over and above the effects of any individual-level variables that may be operating. In this definition, an ‘individual’ is any unit of analysis that is micro relative to some other macro-level in the study, and contextual effects may be those associated with, for example, space (nation, community), time (history), or organizations (schools, corporations). Multiple contexts can apply to any given unit.

Multi-level models explain micro-level outcomes either by showing that the parameters of models specified at the micro-level (where micro-level outcomes are explained by micro–level covariates) are a function of context, or by showing that micro–macro relationships can be expressed in terms of characteristics of the context, in the form of macro-level variables. Thus, for example, researchers have used multi-level event-history models to specify community effects in outcomes such as the timing of marriage or fertility ( J. O. G. Billy and and D. E. Moore , ‘A Multi-level Analysis of Marital and Nonmarital Fertility in the U.S.’, Social Forces, 1992
). There is an extensive literature on school effects. Some research suggests that the effects of race are reduced in orderly schools, while those of class and academic background are reduced in smaller schools, as well as those where discipline procedures are effective and fair. Other studies have looked at the impact of local labour-market effects on decisions to remain at school (see, for example, the article by D. Raffe and and J. D. Willms , on ‘Schooling and the Discouraged Worker’, in the journal Sociology, 1989
). There have also been numerous multi-level analyses of the effects of organizational structure and labour-market segmentation on career outcomes, based on data collected at the individual, firm, and labour-market levels. For example, W. J. Villemez and and W. P. Bridges (‘When Bigger is Better: Differences in the Individual-Level Effect of Firm and Establishment Size’, American Sociological Review, 1988)
examined the impact of firm size and other organizational characteristics on individual earnings, and how this varied across occupations and the sexes.

Although multi-level models promise greater understanding of precisely what context means, and how it may affect individual outcomes in which sociologists are interested, the approach is not without its problems. Robust statistical estimates for model parameters can be hard to provide if models are too complicated. (Some studies have used five-level models having ten variables on each level.) Missing data may also bias statistical estimates.