Weighted Least Squares Estimation with Sampling Weights

• Activity Number: 139
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Survey Research Methods Section
• Author(s): Hee-Choon Shin*+
• Companies: National Center for Health Statistics
• Keywords: Projection ; Regression ; Weighted Least Squares ; Weights

Abstract

A set of unweighted normal equations assume that the response variable of each equation is equally reliable and should be treated equally. When there is a reason to expect higher reliability in response variable in some equations, we use weighted least squares (WLS) to give more weights to those equations. For an analysis of a survey data, sampling weights, as a relative importance variable, should be used for unbiased and efficient estimates. We will briefly go over the least squares theory and related issues, and propose a specific form of "weight" variable when we apply the sampling weights to the normal equations. The National Health and Nutrition Examination Survey (NHANES), a periodic survey conducted by the National Center for Health Statistics (NCHS), Centers for Disease Control and Prevention (CDC) will be analyzed to demonstrate the proposed approach.