Academic journal article Canadian Journal of Public Health

An Introduction to Multilevel Regression Models

Academic journal article Canadian Journal of Public Health

An Introduction to Multilevel Regression Models

Article excerpt


Data in health research are frequently structured hierarchically. For example, data may consist of patients nested within physicians, who in turn may be nested in hospitals or geographic regions. Fitting regression models that ignore the hierarchical structure of the data can lead to false inferences being drawn from the data. Implementing a statistical analysis that takes into account the hierarchical structure of the data requires special methodologies.

In this paper, we introduce the concept of hierarchically structured data, and present an introduction to hierarchical regression models. We then compare the performance of a traditional regression model with that of a hierarchical regression model on a dataset relating test utilization at the annual health exam with patient and physician characteristics. In comparing the resultant models, we see that false inferences can be drawn by ignoring the structure of the data.


Dans le domaine de la recherche en sante, les donnees sont souvent structures de facon hierarchique. Par exemple, des donnees peuvent regrouper des patients relies des medecins, qui a leur tour sont relies a un hopital ou une region geographique. L'elaboration de modules de regression qui negligent cette structure hierarchique peut mener a des conclusions erronees. La realisation d'une analyse statistique qui bent compte de la hierarchie des donnees requiem des methodes specifiques.

Dans notre article, nous presentons le concept des structures hierarchisees de donnees et initions le lecteur aux modules de regression hierarchiques. Nous comparons ensuite les resultats d'un module de regression traditionnel a ceux d'un module hierarchique applique a un fichier qui etablit des liens entre l'utilisation de tests lots d'examens annuels de same et les caracteristiques des patients et des medecins en cause. La comparaison entre les deux modeles montre que l'on peut titer de fausses conclusions si l'on ne tient pas compte de la structure des donnees.

Data in health research frequently have a hierarchical structure, with variables measured at each level of the hierarchy. For example, in a study to determine patient and physician factors that influence the use of Pap tests, women would be clustered within physicians. Subjects within the same cluster are often more alike than two randomly chosen subjects, as they will likely have some correlation on important variables. For example, women seen by the same physician may be alike in sociodemographic characteristics. Traditional statistical methods ignore the correlation of outcomes within clusters and tend to underestimate standard errors.' This artificially increases the significance of hypothesis tests, increasing the risk of falsely concluding that significant associations exist. Additionally, they do not allow one to incorporate characteristics measured at different levels of the hierarchy. The purpose of this paper is to introduce the reader to hierarchical and multilevel regression techniques that allow one to explicitly incorporate the hierarchical nature of the data into the analyses, to incorporate variables measured at different levels of the hierarchy, and to examine how regression relationships vary across clusters.

If one is interested simply in making inferences regarding characteristics measured at the lowest level of the hierarchy, then one can analyze the data with sample survey techniques that incorporate the design effect into the analysis.2 Alternatively, if the number of groups is small, and one is not interested in the effect of cluster-level characteristics, then one can introduce a categorical group membership variable into the regression models.3 This approach is useful if the groups are distinct entities, and the researcher only wants to draw inferences about those groups, and not to generalize to a larger population of groups. This would occur if the groups denoted ethnic or religious identity. …

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