PSYC 612, SPRING 2010Moderation (cont.)Lecture Week: 3/23/2010Contents1 Preliminary Questions 12 Part I: Demonstrate another Moderation Analysis (30 minutes; 2 minute break) 12.1 Purpose: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Objectives: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.3 The Dat a and Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Part II: Beyond the readings (20 minutes; 2 minute break) 43.1 Purpose: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.2 Objectives: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.3 Partitioning of Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.4 Shared variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.5 Sums of Squares (SS) Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.5.1 Type I: Hierarchical partitioning - ordered or sequential . . . . . . . . . . . . 63.5.2 Type II: Partial hierarchical - non-ordered but hierarchical . . . . . . . . . . 83.5.3 Type III: Simultaneous - non-ordered . . . . . . . . . . . . . . . . . . . . . . 93.5.4 Others . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Part III: Introduction to Linear or Matrix Algebra (cont.) (20 minutes) 111 Preliminary Questions•Did you read the Iacobucci text?•Are you ready for module 2?2 Part I: Demonstrate another Moderation Analysis (30minutes; 2 minute break)12.1 Purpose:Solidify conceptual knowledge with an example2.2 Objectives:1. Describe data and model2. Run a moderation a nalysis3. Discuss results in detail2.3 The Data and ModelsThe following data come from the now tainted top 50 home run hitters of all time in Major LeagueBaseball (MLB). I say tainted because MLB underwent a substantial steroids scandal that likelybegan in the mid 1990s and continued until the r ecent crackdown last year. The data from the top50 home run hitters is relevant to our discussion because steroids provides a boost to power enablingthe player to hit more home runs. That boost ought to provide more home runs than would b eexpected by year for each player.yearsHR020406012345KalineSnider12345RipkenJrFoxx12345MusialMurphy12345NettlesYaz12345DawsonBaines12345BenchOtt12345JacksonMurrayBigCatKillebreMaysMcCoveWinfieldJCarterMcGriffRobinsonBanksMatthewsStargell0204060DwEvans0204060GonzalezGriffeyJrMantlePiazzaBWmsKingmanSchmidtLWalkerWilliamsBagwellSheffieldAaronDEvansThomas12345RamirezCanseco12345RuthPalmeiro12345GehrigThome12345ARodSosa12345McGwire0204060Bonds2Estimate Std. Error t value Pr(>|t|)(Intercept) 49.8131 7.1481 6.97 0.0000Year -1.7433 0.3876 -4.5 0 0.0000steroids 22.9092 9.0291 2.54 0.0118Year:st eroids -1.3175 0.5182 -2.54 0.0116Table 1: Linear model results for the first modelWhat do these results suggest? The results indicate that players on steroids performed differentlythan players not on steroids. How differently? Look at Figure 1 for the main effects and interaction.10 15 200 20 40 60YearHRAll DataSteroid Suspectsnon−Steroid SuspectsFigure 1: Interaction plot.Note that the steroid users appear to fall off more rapidly than the non-steroid users (umm, Imean suspects). To better understand the nature of this effect, we ought to decompose the effectsby hand. I will work out the simple slope and simple intercept on the board so you can follow eachstep.33 Part II: Beyond the readings (20 minutes; 2 minute break)3.1 Purpose:Moderation details - the ugly stuff3.2 Objectives:1. Introduce partitioning of variance and shared variance2. Discuss sums of squares (Types)3.3 Partitioning of VarianceConsider the problem of multicollinearity for a second. If you have two main effects and an in-teraction then the interaction must be collinear with the main effects. Of course we know this bywhy are interactions not treated as confounded effects just as collinear main effects? The answer isquite simple but requires a bit of information beyond the readings. Bear with me while I draw outvarious Venn Diagr ams on the board and talk about lions eating wild beats on the plains of Africa.3.4 Shared varianceRemember, The most important concept for you to understand and ap-preciate is variance. Shared variance is just how much variability onevariable has in common with another variableTo say that two variables share variance is essentially like saying that those two variables areassociated. The deviations about their respective means tends to be somewhat parallel. I understandthat this concept is somewhat abstract but a nice way of representing this abstract notion is throughthe use of Venn diagrams. During lecture, I will draw several Venn diagrams and describe whatthey represent a nd how they a re relevant to our discussion.Venn Diagrams3.5 Sums of Squares (SS) TypesOne o f the most confusing aspects of multiple regression is the concept of partitioning variance.Recall that sums of squares are cent r al to least squares estimation. Also recall that sums ofsquares are the sum of the squared deviations fro m the mean. We use sums of squares in leastsquares to get t he least summed squared deviation and hence, the least squares. For that procedureto make sense, we ought to work t hro ugh a problem.Go to the following web page for a nice visual display of sums of squares:http://www.dangoldstein.com/regression.html4The purpose of least squares estimation is to arrive at the best fit between the linear model andour data. The sums of squares also play another impo rt ant role and that is in hypothesis testing.We use the SS as estimates of variance. Recall also that those estimates, when divided by thedegrees of freedom, make up what we use in hypothesis tests (e.g., F and t value computation).So SS are essential for hypothesis testing and parameter estimation. We will leave the domain ofparameter estimation and shift our a tt ention to hypothesis testing for the rest of this discussion.Since NHST tends to be the gate-keeper of social science findings, you might find some comfortin knowing how the tests are computed. MRC (and the GLM in g eneral) uses hypothesis tests intwo stages - one global and the other specific. The global is what is oft en referred to as the omnibustest or overall model …