
WEIGHTED LEAST SQUARES REGRESSION
A graduatelevel introduction and illustrated tutorial on weighted least squares regression (WLS) using SPSS, SAS, or Stata. WLS addresses the heteroscedasticity problem in OLS. In the face of heteroscedasticity, ordinary regression computes erroneous standard errors. This in turn makes significance tests incorrect.
Why we think it's important: Heteroscedasticity is a common regression problem which causes significance tests to be in error. Moreover, contrary to widely held belief, regression with robust standard errors does not substitute for WLS, which is rarely covered in general texts on multivariate analysis.
New in the 2013 edition:
Over twice as much depth (now 54 pp. compared to 19 in the 2012 edition)
The full content is now available from Statistical Associates Publishers. Click here.
Below is the unformatted table of contents.
WEIGHTED LEAST SQUARES Table of Contents Overview of WLS 5 What the researcher can expect if WLS regression is needed 6 Are robust standard errors a substitute for WLS? 6 Weighting with replicates 7 Weight estimation functions 8 Data example 9 Key Terms and Concepts 9 The homoscedasticity assumption in regression 9 Weighted cases 11 WLS in SPSS 11 SPSS overview 11 Testing for heteroscedasticity in SPSS 11 The graphical method 11 Statistical tests for heteroscedasticity 12 Park test 13 BreuschPagan test 15 White's test 16 GoldfeldQuandt test 16 Glejser test 17 Weighting cases in SPSS 17 Weight estimation input: Weighting with powers 17 Weight estimation output: The loglikelihood values table 19 Output from SPSS Weight Estimation 21 SPSS OLS regression on weighted cases 23 SPSS input 23 SPSS output 24 WLS in SAS 28 Overview 28 SAS input 29 SAS output 34 OLS output 34 WLS output 38 WLS in Stata 39 Stata overview 39 Stata input 39 Stata output 42 Unweighted linear regression 42 Weighted least squares regression 44 Assumptions 45 Proper specification 45 Proper weighting 46 Data level 46 Multivariate normality 46 Linearity 46 Independence 46 Predictable variance 47 Frequently Asked Questions 47 Is WLS regression something that could be used with regression models other than OLS? 47 What is SPSS syntax for WLS? 47 How can one get OLS regression with robust standard errors in SAS? 48 How does PROC ROBUSTREG in SAS work? 48 Heteroskedasticity or heteroscedasticity? 51 Acknowledgment 52 Bibliography 52 Pagecount: 54