Multilevel Modeling of a Clustered Continuous Outcome

Abstract

Multilevel models were designed to analyze data generated from a nested structure (e.g., nurses within hospitals) because conventional linear regression models underestimate standard errors and, in turn, overestimate test statistics. To introduce 2 types of multilevel models, the random intercept model and the random coefficient model, to describe the correlation among observations within a cluster, and to demonstrate how to identify the superior model. The conceptual and mathematical bases for the 2 multilevel model types are presented. Intraclass correlation is defined and assessment of model fit is detailed. An empirical example is presented in which average work hours per week and burnout are analyzed using data from 4,320 staff nurses clustered in 19 hospitals. Average work hours were positively associated with nurse burnout. The multilevel models corrected the problem of underestimated standard errors in conventional linear regression models. Graphs displaying the hospital-level differences illustrated the 2 multilevel model types. Although the multilevel models corrected the underestimation of standard errors, the results did not differ substantively for the conventional or the 2 multilevel models. The intraclass correlation coefficient was .044, indicating that the extent of shared variance among nurses in a hospital was low. The random intercept model fit the data better than did the random coefficient model. Multilevel models provide a more accurate and comprehensive description of relationships in clustered data than do conventional models, by correcting underestimated standard errors, by estimating components of variance at several levels, and by estimating cluster-specific intercepts and slopes.