Analyzing Group Level Effects with Clustered Data Using Taylor Series Linearization

Clustered data (e.g., students within schools) are often analyzed in educational research where data are naturally nested. As a consequence, multilevel modeling (MLM) has commonly been used to study the contextual or group-level (e.g., school) effects on individual outcomes. The current study investigates the use of an alternative procedure to MLM: regression using Taylor series linearization (TSL) variance estimation. Despite the name, regressions using TSL are straightforward to conduct, can yield consistent and unbiased estimates and standard errors (given the appropriate conditions), and can be performed using a variety of commercially- and freely-available statistical software. I analyze a subsample of the High School and Beyond (HSB) dataset using MLM, regression using TSL, and ordinary least squares regression and compare results. In addition, 12,000 random samples are drawn from the HSB dataset of varying level-one and level-two sample sizes in order to compute biases in standard errors based on the different conditions. Sample R and SAS syntax showing how to run regressions using TSL are provide