Regression Analysis for Longitudinal Survey Data with a Diverging Number of Covariates

Music City Center 

In economics and the social and health sciences, longitudinal sample surveys often exhibit complex sampling design features such as unequal selection probabilities, stratification and clustering of individuals. For data collected from some large-scale surveys, or from surveys linked to administrative data files, special methods are required for inference when exploring relationships between outcome variables and covariates.

Under the semiparametric modeling approach, the within-cluster correlation is unspecified. The quadratic inference function approach provides consistent and asymptotically normal estimators of model parameters when their number is finite. In this paper, we consider the case when the number of covariates grows to infinity as the number of clusters increases and we illustrate how the rate of divergence in the number of parameters affects the convergence rate of penalized estimators. The procedure simultaneously estimates parameters and selects important variables, accounting for both within-cluster correlation and the complex survey design features.

Complex sampling design

Diverging number of parameters

Longitudinal data

Model selection

Oracle property

Quadratic inference functions 

Survey Research Methods Section