Determining the Nesting Structure for Hierarchical Models Fitted to Education Data

• Activity Number: 605
• Type: Contributed
• Date/Time: Wednesday, August 3, 2016 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Education
• Author(s): Ulrike Genschel* and Jillian Downey and Mark Kaiser
• Companies: Iowa State University and Iowa State University and Iowa State University
• Keywords: hierarchical models ; nesting structure ; education data ; covariance structure

Abstract

In hierarchical models the nesting structure is often determined by the nature of the data. However, instances exist in which the nesting structure is not prescribed. Consider student assessment data for multiple schools, semesters, and instructors. Is semester nested within instructor more appropriate or vice versa? We present a data driven method to determine if one nesting structure is more suited than the other. Because the covariance structure of a hierarchical model depends on the nesting formulation, this can be done by comparing the two competing covariance matrices. We used method of moment type estimators to estimate the elements of the respective covariance matrices. We then performed a simulation study, in which data were simulated from one nesting structure. Then, the simulated data were used to estimate the covariance matrix under each nesting structure. Our results showed that under the incorrect nesting structure variance estimates at the highest level of the hierarchy assumed values less than zero where the exact percentage varied between 75% and 96% of the simulated data sets depending on size of the data and relative sizes of variances components.