Example of Models Including Quantitative and Coded Categorical Predictors The research question concerned depression differences between women (coded 2) and men (coded 1). An initial ANOVA revealed … Analyze à GLM à Univariate click “options” Select “Descriptive Statistics” & “Parameter estimates” GLM output Descriptive StatisticsDependent Variable: depression (BDI)7.05 5.992 1808.78 6.950 2258.01 6.590 405gendermalefemaleTotalMeanStd.Deviation N The mean difference is… 8.78 – 7.05 = 1.73 Tests of Between-Subjects EffectsDependent Variable: depression (BDI)298.522a1 298.522 6.975 .00925051.855 1 25051.855 585.356 .000298.522 1 298.522 6.975 .00917247.439 403 42.79843530.000 40517545.960 404SourceCorrected ModelInterceptgenderErrorTotalCorrected TotalType III Sumof Squares df Mean Square F Sig.R Squared = .017 (Adjusted R Squared = .015)a. Things to notice: F = t² they both test H0: GML uses a dummy code with the highest coded group as the control group, so … a = mean of control group (females) b = male – female = -1.73 Parameter EstimatesDependent Variable: depression (BDI)8.778 .436 20.126 .000 7.920 9.635-1.728 .654 -2.641 .009 -3.014 -.4420a. . . . .ParameterIntercept[gender=1][gender=2]B Std. Error t Sig. Lower Bound Upper Bound95% Confidence IntervalThis parameter is set to zero because it is redundant.a.To get the same results using Multiple Regression, we first need to dummy code gender. We will use female (2) as the comparison group (same as GLM). Analyze à Regression à Linear Regression output Model Summary.130a.017 .015 6.542Model1R R SquareAdjustedR SquareStd. Error ofthe EstimatePredictors: (Constant), gendca. ANOVAb298.522 1 298.522 6.975 .009a17247.44 403 42.79817545.96 404RegressionResidualTotalModel1Sum ofSquares df Mean Square F Sig.Predictors: (Constant), gendca. Dependent Variable: depression (BDI)b. All the results and interpretations are the same as the GLM Coefficientsa8.778 .436 20.126 .000-1.728 .654 -.130 -2.641 .009(Constant)gendcModel1B Std. ErrorUnstandardizedCoefficientsBetaStandardizedCoefficientst Sig.Dependent Variable: depression (BDI)a.Considering that there may be more to the story, a model including other variables related to depression was examined. Analyze à GLM à Univariate “Covariates” can be any quantitative, binary or coded variable. Adding variables to the “Fixed Factors” window will create an factorial design, whereas adding them to the “Covariates” will create a “main effects model” Moving the “IV” into the “Display Means for” wi ndow will give use the “corrected mean” for each condition of the variable. GLM outtput Descriptive StatisticsDependent Variable: depression (BDI)7.055.9921808.78 6.950 2258.01 6.590 405gendermalefemaleTotalMeanStd.Deviation N Descriptive Statistics28.48 10.88537.21 11.3775.6233 1.18204agelonelinesstotal social supportMeanStd.Deviation Tests of Between-Subjects EffectsDependent Variable: depression (BDI)6281.245a4 1570.311 55.760 .00040.821 1 40.821 1.450 .229930.640 1 930.640 33.046 .0002982.872 1 2982.872 105.919 .00074.807 1 74.807 2.656 .104580.881 1 580.881 20.627 .00011264.715 400 28.16243530.000 40517545.960 404SourceCorrected ModelInterceptagerulstssgenderErrorTotalCorrected TotalType III Sumof Squares df Mean Square F Sig.R Squared = .358 (Adjusted R Squared = .352)a.genderDependent Variable: depression (BDI)6.642a.400 5.855 7.4299.104a.357 8.402 9.806gendermalefemaleMean Std. Error Lower Bound Upper Bound95% Confidence IntervalCovariates appearing in the model are evaluated at thefollowing values: age = 28.48, loneliness = 37.21, totalsocial support = 5.6233.a. Parameter EstimatesDependent Variable: depression (BDI)4.340 2.633 1.649 .100 -.835 9.515-.145 .025 -5.749 .000 -.195 -.096.311 .030 10.292 .000 .251 .370-.473 .290 -1.630 .104 -1.043 .097-2.462 .542 -4.542 .000 -3.528 -1.3960a. . . . .ParameterInterceptagerulstss[gender=1][gender=2]B Std. Error t Sig. Lower Bound Upper Bound95% Confidence IntervalThis parameter is set to zero because it is redundant.a. Notice that the regression weight for gender is the same as the corrected mean difference. Notice that this is the mean difference “holding the value of all other variables constant at their mean” Notice that the F-tests and the t-tests of the regression weights all agree – two versions of the same H0: testsHere are the results from a Multiple Regression Analysis including the same variables Model Summary.598a.358 .352 5.307Model1R R SquareAdjustedR SquareStd. Error ofthe EstimatePredictors: (Constant), total social support, gendc,age, lonelinessa. ANOVAb6281.245 4 1570.311 55.760 .000a11264.72 400 28.16217545.96 404RegressionResidualTotalModel1Sum ofSquares df Mean Square F Sig.Predictors: (Constant), total social support, gendc, age, lonelinessa. Dependent Variable: depression (BDI)b. Again, all the results parallel those from the GLM. Coefficientsa4.340 2.633 1.649 .100-2.462 .542 -.186 -4.542 .000-.145 .025 -.240 -5.749 .000.311 .030 .536 10.292 .000-.473 .290 -.085 -1.630 .104(Constant)gendcagelonelinesstotal social supportModel1B Std. ErrorUnstandardizedCoefficientsBetaStandardizedCoefficientst Sig.Dependent Variable: depression (BDI)a. One thing to be careful about when comparing the regression and GLM results is whether the same “comparison” group was used in the dummy codes of the two models. Had we used males as the comparison group in the multiple regression, the gender weight would have the same value, as the GLM, but would have the opposite sign.Here’s an example of the same analysis involving a 3-group variable, via GLM and regression. If we put more than one variable into the “Fixed Factors” window, we will obtain a factorial analysis. If we do not want a factorial analysis, we can do two different things… 1) Any 2-group variable can be put in to the covariates (unit- or dummy -coded) 2) We can specify that we want a “main effects model”, as shown below Either way, we would want to get the descriptive stats, corrected means and regression parameters. GLM output Descriptive StatisticsDependent Variable: depression (BDI)7.25 5.673 1226.11 6.699 478.91 6.188 117.05 5.992 18010.04 8.110 1206.89 4.571 748.39 5.800 318.78 6.950 2258.63 7.113 2426.59 5.483 1218.52 5.832 428.01 6.590