Suppressor Effects Effect Size CorrectionsSuppressor Effects in Linear ModelsDr. J. Kyle RobertsSouthern Methodist UniversitySimmons School of Education and Human DevelopmentDepartment of Teaching and LearningSuppressor Effects Effect Size CorrectionsThinking Graphically About Suppressors•A suppressor effect occurs when a variable has a non-zero βweight but a zero structure coefficient.•The inclusion of a suppressor in a regression equation removesthe unwanted variance from the predictor variable, thusenhancing the relationship between the other independentvariable and the dependent variable.!"#$"#%&''()**+(#Suppressor Effects Effect Size CorrectionsIllustrating Suppressors in R> library(MASS)> correlation <- matrix(c(1, 0.5, 0, 0.5, 1, 0.5,+ 0, 0.5, 1), ncol = 3, nrow = 3, dimnames = list(c("dv",+ "iv1", "iv2"), c("dv", "iv1", "iv2")))> correlationdv iv1 iv2dv 1.0 0.5 0.0iv1 0.5 1.0 0.5iv2 0.0 0.5 1.0> set.seed(12346)> suppressor.set <- data.frame(mvrnorm(n = 1000,+ rep(10, 3), correlation))Suppressor Effects Effect Size CorrectionsIllustration cont.> m1 <- lm(dv ~ iv1 + iv2, suppressor.set)> summary(m1)Call:lm(formula = dv ~ iv1 + iv2, data = suppressor.set)Residuals:Min 1Q Median 3Q Max-2.75190 -0.54804 0.03108 0.53789 2.93339Coefficients:Estimate Std. Error t value Pr(>|t|)(Intercept) 6.00115 0.29836 20.114 <2e-16iv1 0.67842 0.03044 22.285 <2e-16iv2 -0.28112 0.03015 -9.323 <2e-16Residual standard error: 0.8217 on 997 degrees of freedomMultiple R-squared: 0.3356, Adjusted R-squared: 0.3343F-statistic: 251.8 on 2 and 997 DF, p-value: < 2.2e-16Suppressor Effects Effect Size CorrectionsIllustration cont.> library(yhat)> regr(m1)$Beta_Weightsdviv1 0.673360iv2 -0.281694> regr(m1)$Structure_Coefficientsiv1 iv20.9096263 0.1178144> regr(m1)$Commonality_Data$CCCoefficient % TotalUnique to iv1 0.3310 98.61Unique to iv2 0.0579 17.26Common to iv1, and iv2 -0.0533 -15.87Total 0.3356 100.00Suppressor Effects Effect Size CorrectionsTypes of Effect Size CorrectionsWherry-1: = 1 −N − 1N − p − 1(1 − R2)Claudy3: = 1 −(N − 4)(1 − R2)N − p − 11 +2(1 − R2)N − p + 1Smith-1: = 1 −NN − p(1 − R2)Wherry-2: = 1 −N − 1N − p(1 − R2)Olkin&Pratt: = 1 −(N − 3)(1 − R2)N − p − 11 +2(1 − R2)N − p + 1Pratt: = 1 −(N − 3)(1 − R2)N − p − 11 +2(1 − R2)N − p − 2.3Suppressor Effects Effect Size CorrectionsYin and Fan, 2001•Yin and Fan (2002) showed how the multiple R2is really anupward bound for the actual R2in the population.•Perhaps most important, they noted that the Wherry formula(basis for the default adjusted R2in commonly used statisticalsoftware) has been found to be an ineffective analyticalformula when sample sizes are small.•What regr does is compute the multiple R2correction thathas the least amount of bias given the simulations done byYin and Fan (2002).Suppressor Effects Effect Size CorrectionsHomework•Find a journal article in a journal in your field that has usedmultiple regression.•Make sure that the one you identify has used both multipleregression and has the correlation matrix attached in a table.•Reproduce their results by simulating their dataset.•Try other competing models against their full model and see ifyou can find a different, better (or at least as good as) model.•Use the anova function to compare the models.> m0 <- lm(dv ~ iv1, suppressor.set)> anova(m0, m1)Analysis of Variance TableModel 1: dv ~ iv1Model 2: dv ~ iv1 + iv2Res.Df RSS Df Sum of Sq F Pr(>F)1 998 731.862 997 673.17 1 58.685 86.915 <