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UT Knoxville STAT 201 - 8) sld_interaction_nominal

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INTERPRETING INTERACTIONSBETWEEN QUANTITATIVE & NOMINAL VARIABLESInteraction b/w Quantitative & Nominal -Association between DV and quantitative variable changes in direction and/or magnitude across levels of the nominal variable. That is, the slope of the quantitative variable is different across the levels of the nominal variableAND-Pattern of differences among the levels of the nominal variable on the DVchanges across values of the quantitative variable.e.g., males may score higher on the DV than do females at low levels ofNuances of Nominal Variables-G-level nominal variable requires G-1 predictors for regression-Predictors can be formed via dummy, effects, or contrast coding-With an interaction in the model, the interpretation of the betas for the g-1 predictors AND the beta for the quantitative predictor and product terms change across coding systems.Organization of Today’s DiscussionHow to:(1) Form an interaction b/w a nominal & quantitative variable(2) Interpret betas for lower order and higher order effects across dummy, effects, and contrast coding(3) Decompose the interactionAn Example & Bogus Data-Pretend we have the post-treatment depression scores and ratings of perceived social support for 26 depressed patients who received either smiling therapy, exercise therapy, or no-therapy.-We are interested in whether the efficacy of smiling and exercise therapy change depending on the patients perceived level of social support.-That is, do therapy and social support interact to predict post-treatment depression?An Example & Bogus Data-Assume depression & social support were assessed on valid and reliable scales that range from 1 – 7, with higher #’s indicating higher degrees of the measured construct.Forming the Interaction-Need to code the 3-level therapy variable for regression-Form 2 predictors with dummy, effects or contrast codingForming Therapy x Support Interaction(1) Center Continuous predictor (i.e., support)(2) Form necessary product termsT1*Support & T2*Support(3) Partial all lower order constituent effectsDepress = B0 + B1T1 + B2T2 + B3Support + B4T1*Support + B5T2*Support-B4 and B5 comprise the set that represents Therapy x SupportTesting Therapy x Support Interaction-Model comparisonDepress = B0 + B1T1 + B2T2 + B3Support + B4T1*Support + B5T2*SupportvsDepress = B0 + B1T1 + B2T2 + B3SupportHow To Interpret the B’s from Full ModelDepress = B0 + B1T1 + B2T2 + B3Support + B4T1*Support + B5T2*SupportContext of Dummy CodingDepress = B0 + B1T1 + B2T2 + B3Support + B4T1*Support + B5T2*SupportB0: mean level of depression in no-therapy (reference group)B1: amount by which mean of smiling differs from mean of no-therapyB2: amount by which mean of exercise differs from mean of no-therapyB3: support slope in no-therapy B4: amount support slope in smil differs from support slope in no-therapy B5: amount support slope in exer differs from support slope in no-therapyContext of Effects CodingDepress = B0 + B1T1 + B2T2 + B3Support + B4T1*Support + B5T2*SupportB0: unweighted depression mean across 3 levels of therapy B1: amount smiling mean differs from unweighted mean of all 3 groups B2: amount exercise mean differs from unweighted mean of all 3 groupsB3: unweighted mean of the support slopes across 3 levels of therapy B4: amount support slope in smil differs from unweighted mean of support slopes across all 3 groupsB5: amount support slope in exer differs from unweighted mean of supportslopes across all 3 groupsContext of Contrast CodingDepress = B0 + B1T1 + B2T2 + B3Support + B4T1*Support + B5T2*SupportB0: unweighted depression mean across 3 levels of therapy B1: amount no-ther mean differs from unweighted mean of smil & exer B2: amount smil mean differs from exercise mean B3: unweighted mean of the support slopes across 3 levels of therapy B4: amount support slope in no-ther differs from unweighted mean of support slopes across smiling and exerciseB5: amount support slope in smile differs from support slope in exerciseSpecial Case of a 2-level Nominal Variablee.g., Smiling therapy and no-therapy-Need to form only 1 predictor variable-contrast is effects coding & both differ from dummy codingContrast/effects: No-ther = -1, Smile = 1 Dummy: No-ther = 0, Smile = 1Depression = B0 + B1T1 + B2Support + B3T1*SupportSpecial Case of a 2-level Nominal VariableDepression = B0 + B1T1 + B2Support + B3T1*Support -Dummy CodingB0: mean level of depression in no-therapy (reference group)B1: amount by which mean of smiling differs from mean of no-therapyB2: support slope in no-therapy B3: amount support slope in smil differs from support slope in no-therapy -Contrast/effects CodingB0: unweighted depression mean across 2 levels of therapyB1: amount smiling mean differs from unweighted mean of both groupsB2: unweighted mean of the support slopes across both levels of therapyB3: amount support slope in smil differs from unweighted mean of supportslopes across both groupsDecomposing a Quant x NominalInteraction-Dummy Coding-Contrast CodingDecomposing with Dummy CodingCheck Cor. Among Predictors-A more formal check of multi-collinearity is to examine the tolerance of each predictor (i.e., 1-R2, in which R2 is from models in which each predictor is regressed on the others). Tolerance values < .10 are troublesome and suggest that < 10% of variability in predictor is unique from the others. In SAS, use “/ tol” option at end of the model statementTest the Interactionproc reg;model depress = de ds support de_sup ds_sup;model depress = de ds support;run;25.12)1526()8413.1()35()6469.8413(.)1()1()()(22Re2FFullRFstrictedFullknRkkRRFTherapy x Support is significant, F(2, 20) = 12.25, p < .05Decompose in Context of the Full ModelDecompose Therapy x SupportDepression = 6.25 –2.23De –2.58Ds + 0.07Support –1.03De*Support –0.97Ds*Support-Effect of therapy changes across values of support & effect of support changes across levels of therapy-Test dummy-coded predictors at high and low value of supportor-Test simple support slope in each therapy groupTest Dummies at High & Low Support-Dummies @ high support-Re-center centered support so it is centered 1 SD above mean-form necessary product terms (i.e. recentered support X dummies)-conduct regression in SASDepress = B0 + B1T1 + B2T2 + B3SupHigh + B4T1*SupHigh + B5T2*SupHighB0 = depression mean of no-therapy at high supportB1 = diff b/w smile and no-therapy


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UT Knoxville STAT 201 - 8) sld_interaction_nominal

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