Nonlinear and Multilevel Longitudinal and Panel Data

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

Models of longitudinal and panel data are widely used by researchers in the social sciences. This project addresses two features that are commonly ignored by analysts. First, this research will introduce statistical models and methods to handle data characteristics that are motivated by studies of insurance claims. Specifically, the focus is on data that (i) are likely to be large (sometimes referred to as long-tailed), (ii) may be a combination of zeros (for no claims) and positive values (two-part data) or (iii) may only be available when they exceed a large deductible (or threshold). Regardless of these tendencies to be non-normal, longitudinal data still appear as repeated observations over time and hence tend to be clustered. This project will use copula-based methods for handling this clustering. Copulas are a tool for understanding relationships among multivariate outcomes that were introduced in 1959 in the context of probabilistic metric spaces but now are being used in more statistical contexts, including the insurance and actuarial science literatures. Second, the research will consider multilevel data, motivated by studies of school effectiveness within the educational sciences. The project will introduce robust estimators and tests of certain types of omitted variables that may arise in multilevel modeling. Procedures that use subject-specific dummy variables will be initially explored and developed. Further, because this type of procedure can obscure higher level model information, the research will focus on augmented or instrumental variable procedures that retain higher level model information. Although motivated by insurance and educational sciences, the project will develop models and methods that can be used in a wide variety of social science disciplines. To illustrate, economists study wage distributions that may have long tails, health researchers examine health quality indicators that have two-part distributions, flood analysts consider high threshold data, and organizational scientists examine multilevel models. The project also will provide statistical software and, whenever feasible, illustrative data for other researchers to use. Longitudinal modeling can be linked to insurance credibility theory and, for insurance analysts, the appealing aspect of the copula-based approach is that it links credibility theory to the study of (long-tailed) loss distributions. Currently, both credibility theory and loss distributions are core topics in actuarial education syllabi, without any linkage. Results of this study should generate substantial industry interest. Moreover, particularly in the educational sciences, multilevel modeling is becoming a standard tool for addressing complex testing situations such as in studies of school effectiveness. In longitudinal studies of school effectiveness, as with all observational studies, questions of omitted variables are common. This research will provide educational researchers with some new important tools that can be used to address questions of the effects of school variables on education outcomes such as student achievement, teacher effectiveness, and per-pupil expenditures. This award was supported as part of the Fiscal Year 2004 Mathematical Sciences priority area special competition on Mathematical Social and Behavioral Sciences (MSBS).