Multilevel Modeling

History and Advantages

Statistical analyses conducted within an MLM framework date back to the late 19th century and the work of George Airy in astronomy, but the basic specifications used today were greatly advanced in the 20th century by Ronald Fisher and Churchill Eisenhart's introduction of fixed-and random-effects modeling. MLM permits the analysis of interdependent data without violating the assumptions of standard multiple regression. A critical statistic for determining the degree of inter-relatedness in one's data is the intraclass correlation (ICC). The ICC is calculated as the ratio of between-group variance to between-subject variance, divided by total variance. The degree to which the ICC affects alpha levels is dependent on the size of a sample; small ICCs inflate alpha in large samples, whereas large ICCs will inflate alpha in small samples. A high ICC suggests that the assumption of independence is violated. When the ICC is high, using traditional methods such as multiple linear regression is problematic because ignoring the interdependence in the data will often yield biased results by artificially inflating the sample size in the analysis, which can lead to statistically significant findings that are not based on random sampling. In addition, it is important to account for the nested structure of the data—that is, nonindependence—to generate an accurate model of the variation in the data that is due to differences between groups and between subjects after accounting for within differences within groups and within subjects. Because variation within groups and within individuals usually accounts for most of the total variance, disregarding this information will bias these estimates.

In addition to its ability to handle nonindependent data, an advantage of MLM is that more traditional approaches for studying repeated measures, such as repeated measures analysis of variance (ANOVA), assume that data are completely balanced with, for example, the same number of students per classroom or equivalent measurements for each individual. Missing data or unbalanced designs cannot be accommodated with repeated measures ANOVA and are dropped from further analysis. MLM techniques were designed to use an iterative process of model estimation by which all data can be used in analysis; the two [Page 836]most common approaches are maximum and restricted maximum likelihood estimation (both of which are discussed later in this entry).

...