Chapter 7 Multilevel Models
Multilevel models, also known as hierarchical models, are a statistical technique designed for the analysis of data with a hierarchical structure, such as those from household surveys, where the observation units are not independent of each other. Individuals belong to households, households are located in specific geographic areas (PSUs) and these, in turn, are part of broader territorial units (strata or domains). As a consequence, observations that share the same context tend to present characteristics that are more similar to each other than those belonging to different contexts. This dependence structure violates one of the fundamental assumptions of conventional regression models and can lead to inefficient estimates and incorrect inferences.
Unlike conventional regression models, multilevel models recognize that observations can be grouped at different levels and that each of them can contribute to explaining the observed variability. Consequently, they allow the effects associated with the characteristics of the units of analysis and those derived from the environment or context in which they are located to be simultaneously represented. This formulation is especially useful when seeking to study phenomena determined both by individual factors and by characteristics of households, communities, or geographic areas.
Another important feature of multilevel models is that they make it possible to quantify the proportion of variability associated with each level of grouping present in the data. While fixed effects summarize the average relationship between the response variable and the covariates included in the model, random effects represent systematic differences between groups that are not explained by these covariates. Thanks to this structure, it is possible to explicitly model the dependence between observations belonging to the same group and obtain more appropriate inferences when the data have a hierarchical organization.
The theoretical and methodological development of multilevel models has been widely documented in the sampling literature. Among the most influential references are the works of Goldstein (2011), Gelman & Hill (2006), and Rabe-Hesketh & Skrondal (2012), which present the conceptual foundations, estimation strategies, and various applications of these models in social and demographic contexts. In addition, Browne & Draper (2006) compare different estimation approaches for hierarchical models, evaluating the differences between methods based on maximum likelihood and Bayesian approaches. In the field of social epidemiology, Merlo et al. (2006) emphasize the usefulness of multilevel models for studying contextual phenomena, showing how factors associated with the environment can contribute to explaining inequalities in health and other outcomes of population interest.