Lecture Using Proc RSQUARE

# Lecture Using Proc RSQUARE - PROC ROBUSTRET &amp;...

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I OWA S TATE U NIVERSITY Department of Animal Science PROC ROBUSTRET & Evaluating Regression analyses With The Help of PROC RSQUARE Animal Science 500 Lecture No. 10 October 5, 2010

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I OWA S TATE U NIVERSITY Department of Animal Science PROC ROBUSTREG The purpose of robust regression is to detect outliers and provide stable results in the presence of outliers. In order to achieve this stability, robust regression limits the influence of outliers. Outliers can be classified as: Problems with outliers in the y -direction (response direction) Problems with multivariate outliers in the x -space (i.e., outliers in the covariate space, which are also referred to as leverage points) Problems with outliers in both the y -direction and the x -space
I OWA S TATE U NIVERSITY Department of Animal Science PROC ROBUSTREG Two types of estimations methods M Estimation - is the method for outlier detection and robust regression when contamination is mainly in the response direction (y) LTS Estimation - the method used when data contamination occurs in the x space.

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I OWA S TATE U NIVERSITY Department of Animal Science PROC ROBUSTREG M-estimation The following ROBUSTREG statements analyze the data: Proc Robustreg data=stack; model y = x1 x2 x3 / diagnostics leverage; id x1; test x3; run; quit;
I OWA S TATE U NIVERSITY Department of Animal Science PROC ROBUSTREG M-estimation Proc Robustreg data=stack; model y = x1 x2 x3 / diagnostics leverage; id x1; test x3; run; quit; The procedure does M estimation with the bisquare weight function (default), and it uses the median method for estimating the scale parameter. The MODEL statement specifies the covariate effects. The DIAGNOSTICS option requests a table for outlier diagnostics, The LEVERAGE option adds leverage point diagnostic results to this table for continuous covariate effects. The ID statement specifies that variable x1 is used to identify each observation in this table. If the ID statement is missing, the observation number is used to identify the observations (might even be better this way in some cases). Tests of significance for the covariate effects are obtained using the test line with a variable(s) listed with the test term. http://support.sas.com/onlinedoc/913/getDoc/en/statug.hlp/rreg_sect3.htm

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I OWA S TATE U NIVERSITY Department of Animal Science PROC ROBUSTREG example output M-estimation The ROBUSTREG Procedure Model Information Data Set WORK.STACK Dependent Variable y Number of Covariates 3 Number of Observations 21 Method M Estimation Summary Statistics Variable Q1 Median Q3 Mean Standard MAD Deviation x1 53.0000 58.0000 62.0000 60.4286 9.1683 5.9304 x2 18.0000 20.0000 24.0000 21.0952 3.1608 2.9652 x3 82.0000 87.0000 89.5000 86.2857 5.3586 4.4478 y 10.0000 15.0000 19.5000 17.5238 10.1716 5.9304 http://support.sas.com/onlinedoc/913/getDoc/en/statug.hlp/rreg_sect3.htm
I OWA S TATE U NIVERSITY Department of Animal Science PROC ROBUSTREG example output Parameter Estimates Parameter DF Estimate Standard Error 95% Confidence Limits Chi-Square Pr > ChiSq Intercept 1 -42.2854 9.5045 -60.9138 -23.6569 19.79 <.0001 x1 1 0.9276 0.1077 0.7164 1.1387 74.11 <.0001 x2 1 0.6507 0.2940 0.0744 1.2270 4.90 0.0269 x3 1 -0.1123 0.1249 -0.3571 0.1324 0.81 0.3683 Scale 1 2.2819 http://support.sas.com/onlinedoc/913/getDoc/en/statug.hlp/rreg_sect3.htm

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Lecture Using Proc RSQUARE - PROC ROBUSTRET &amp;...

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