Modeling multiple‐response categorical data from complex surveys |
| |
Authors: | Christopher R Bilder Thomas M Loughin |
| |
Institution: | 1. Department of Statistics, University of Nebraska‐Lincoln, Lincoln, NE 68583, USA;2. Department of Statistics and Actuarial Science, Simon Fraser University Surrey, Surrey, BC, Canada V3T0A3 |
| |
Abstract: | Although “choose all that apply” questions are common in modern surveys, methods for analyzing associations among responses to such questions have only recently been developed. These methods are generally valid only for simple random sampling, but these types of questions often appear in surveys conducted under more complex sampling plans. The purpose of this article is to provide statistical analysis methods that can be applied to “choose all that apply” questions in complex survey sampling situations. Loglinear models are developed to incorporate the multiple responses inherent in these types of questions. Statistics to compare models and to measure association are proposed and their asymptotic distributions are derived. Monte Carlo simulations show that tests based on adjusted Pearson statistics generally hold their correct size when comparing models. These simulations also show that confidence intervals for odds ratios estimated from loglinear models have good coverage properties, while being shorter than those constructed using empirical estimates. Furthermore, the methods are shown to be applicable to more general problems of modeling associations between elements of two or more binary vectors. The proposed analysis methods are applied to data from the National Health and Nutrition Examination Survey. The Canadian Journal of Statistics © 2009 Statistical Society of Canada |
| |
Keywords: | Choose all that apply correlated binary data loglinear model NHANES Pearson statistic pick any/c Rao– Scott adjustments AMS subject classification: Primary 62D05 Secondary 62H17 |
|
|