Weighted Least Squares Estimation with Simultaneous Consideration of Variance and Sampling Weights

• Activity Number: 511
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Survey Research Methods Section
• Author(s): Hee-Choon Shin*+ and Jibum Kim
• Companies: NCHS and Sungkyunkwan University
• Keywords: Projection ; Regression ; Weights ; Least Squares ; Weighted Least Squares

Abstract

A set of unweighted normal equations for a least squares solution assumes 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 the response variable in some equations, we use weighted least squares (WLS) to give more weight to those equations. For an analysis of experimental or observational data, an inverse of variance is typically used for efficient estimates. For an analysis of survey data, sampling weights are typically used for unbiased and efficient estimates. There might be reasons for deviating from these weights - e.g., heteroscedasticity or extreme weights. Different weights can yield different point and interval estimates of the coefficients, affecting the interpretation of results. In other work, we considered the impact of different functional forms of weights on the WLS solutions. In the current work, we simultaneously consider sampling weights and inverses of variance for the WLS solutions, using data from the 2009-2010 National Health and Nutrition Examination Survey (NHANES), a periodic survey conducted by the National Center for Health Statistics (NCHS), Centers for Di