Multilevel Modeling Techniques

Statistical Consequences of Nested Data

The general linear model, which subsumes both regression and ANOVA, assumes that errors are independent and normally distributed, with a mean of zero and a constant variance. Yet when the data are nested—for example, when the behaviors and attitudes of individuals within a team are affected by teammates—this assumption is violated. This is known as nonindependence, and its major consequence is that standard errors are smaller than they should be, which, in turn, contributes to inflated Type I errors. There are other, more subtle effects of non-independence that can cause problems with estimation of effect size and statistical significance; the Further Reading section contains links for more details.

Nonindependence is most frequently documented by the intraclass correlation coefficient. When non-independence exists, the use of HLM becomes problematic; however, we now have the tools to more directly model the data in such situations.

A Nontechnical Introduction to HLM

Many references to the technical details of HLM are provided in the Further Reading section. The purpose of this entry is only to introduce the concept, and this is done through the use of figures and an example. Figure 1 shows a simple example in which organizational climate is hypothesized to influence individual job satisfaction directly, as well as the relationship between satisfaction and pay. This hypothesis can be represented in terms of two levels. In the Level 1 model, job satisfaction can be regressed on pay. One would expect a positive relationship, such that higher pay is associated with more job satisfaction. However, what if multiple organizations were sampled and it was found there are mean differences in satisfaction across organizations, as well as differences in the relationship between pay and job satisfaction? Such a situation might occur when individuals within an organization share at least some common sources of influence, hence the nonindependence of their job satisfaction scores.

Figure 1 Graphical Example of Hierarchical Linear

The between-organization differences could be explained by organizational climate. Note that organizational climate would be considered a Level 2 predictor because the Level 1 scores are nested within organizations. Hence, one could determine whether organizational climate directly explains mean organizational differences in job satisfaction and whether the relationship between pay and satisfaction differs as a function of climate. The hypothesis might be that favorable climates enhance satisfaction and weaken the relationship between pay and satisfaction.

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