Collaborative Research: Nonparametric Models for Incomplete Clustered Data with Applications to the Social Sciences

Clustered data are very common in social sciences research and other fields. For example, in a study involving school children, school districts form clusters and schools form sub-clusters within each cluster. In this context, researchers want to explain a certain variable of interest (the response variable) in terms of certain categorical variables (factors) while adjusting for the presence of other incidental variables (covariates) which might influence the response. This project aims at developing statistical methods for analyzing such data. Though the classical statistical methods accommodate the lack of independence that is inherent to data arising from cluster sampling, they are very often unsuitable for data arising from social science research. This is because they require a set of restrictive assumptions (such as normality and homogeneity of the residuals, linearity, scale dependence) which are rarely satisfied in the social sciences. In addition, data in social sciences research are often incomplete (censored or missing) in which case inference based on the classical statistical models cannot be implemented. Alternative approaches developed to deal with these issues also rely on assumptions which may or may not be satisfied for any given application. The research for this project will focus on the development of statistical models and methods that are free of restrictive assumptions. Central components of the project is the application of these methods to questions regarding routine activities and deviant behavior, and to the question of whether there has been a secular rise in job instability among young adults over the past three decades using two cohorts from the National Longitudinal Survey (NLS). Programs for formal hypothesis testing, graphical summaries of effects and exploratory data analysis plots, will be made available on the web for use by the social sciences community. Correct statistical analysis is very important as it often forms the basis for policy and other decisions. The nonparametric formulation in this project is especially apt for many kinds of social science data where we have weak theories about functional forms and weak measurement procedures (e.g., with attitudes) that produce ordinal or only somewhat stronger (but typically not interval) scales. The violation of assumptions underlying a statistical approach can result in misuse of scarce data resources and ultimately misguided policy decisions.