Coding Multiple Category Variables for Inclusion in Multiple Regression• More kinds of predictors for our multiple regression models• Some review of interpreting binary variables• Coding Binary variables– Dummy coding– Effect Coding– Interpreting b weights of binary coded variables– Interpreting weights in a larger model– Interpreting r of binary coded variables• Coding multiple-category variables– Dummy coding– Effect coding– Interpreting b weights of coded multiple-category variables– Interpreting weights in a larger model– Interpreting r of coded multiple-category variables• Comparison codingUp until now we have limited the kinds of predictor variables in our models to quantitative and binary (usually coded 1 & 2). In this section we will add several new variable types to our repertoire…dummy & effect codes for binary qualitative variables-- different coding strategies allow us to test specific RH:dummy, effect & comparison coding for k-category variables-- lots of categorical or qualitative variables aren’t binary-- k-group variables can be important predictors – we have to be able to accommodate them in MR models-- different coding strategies allow us to test specific RH:The idea is NOT to replace ANOVA with MR, but to be able to incorporate any variable type into multiple regression models !!Non-linear relationships-- not all the interesting relationships are “linear” or “just linear”≠≠ ≠r = 0.0 for both Æ no linear relationship. But the plot on the left shows a strong relationship – just not a linear relationshipEach has a “linear component“But not the “same shape of relationship”2-way interactions - any mix of binary, k-group & quant predictor varspractice% correctexpertnovice# sessionsdepressionDrugsTalkControl3-way interactions - any mix of binary, k-group & quant predictor varspractice% correctexpert noviceunpaid paidnon-linear interactions – you can miss interactions if only look for linear interactionspractice% correctexpertnovice# sessionsdepressionDrugsTalkControlThings we’ve learned so far …• for interpreting multivariate b from quantitative & binary predictor variables in models• both can be interpreted as “expected change in y for a 1-unit change in the predictor”• both interpretations need to include the statement “when controlling for all other variables in the model”• with binary variables we are more likely to use language about the direction and size of criterion variable mean difference between the binary groups, after controlling for all other variables in the modelReview of interpreting unit-coded (1 vs. 2) binary predictors…Correlationr -- tells direction & strength of the predictor-criterion relationship-- tells which coded group has the larger mean criterion scores(significance test of r is test of mean difference)Bivariate Regressionb -- tells size & direction mean difference between the groups(t-test of b is significance test of mean differences)a -- the expected value of y if x = 0 which can’t happen – since the binary variable is coded 1-2 !!Multivariate Regressionb -- tells size & direction of mean difference between the groups, holding all other variables constant (controlling for)(t-test of b is test of group mean difference beyond that accounted for by other predictors -- ANCOVA)a -- the expected value of y if value of all predictors = 0which can’t happen – since the binary variable is coded 1-2 !!Dummy Coding for two-category variables• need 2 codes (since there is 1 BG df)• comparison or control condition/group gets coded “0”• the treatment or target group gets coded “1”“conceptually”...Group dc1 12* 0* = comparison groupFor several participants...Case group dc 1 1 1 2 1 1 3 2 0 4 2 0 Interpretations for dummy coded binary variablesBivariate Regression R² is effect size & F sig-test of group differencea -- mean of comparison/control condition/groupb -- tells size & direction of y mean difference between groups(t-test of b is significance test of mean differences)Multivariate Regression (including other variables)b -- tells size & direction of mean difference between the groups, holding all other variables constant (controlling for)(t-test of b is test of group mean difference beyond that accounted for by other predictors -- ANCOVA)a -- the expected value of y if value of all predictors = 0Correlationr -- tells direction & strength of the predictor-criterion relationship-- tells which coded group has the larger mean criterion scores(significance test of r is test of mean difference)Effects Coding for two-category variables• need 2 codes (since there is 1 BG df)• comparison or control condition/group gets coded “-1”• the treatment or target group gets coded “1”“conceptually”...Group ec1 12* -1* = comparison groupFor several participants...Case group ec 1 1 1 2 1 1 3 2 -14 2 -1Interpretations for effect coded binary variablesBivariate Regression R² is effect size & F sig-test of group differencea – grand mean of all participants/groupsb -- tells size & direction of y mean difference between target group & grand mean(t-test of b is significance test of that mean)Multivariate Regression (including other variables)b -- tells size & direction of mean difference between target group & grand mean, holding all other variables constant (t-test of b is test of that mean difference beyond that accounted for by other predictors -- ANCOVA)a -- the expected value of y if value of all predictors = 0Correlationr -- tells direction & strength of the predictor-criterion relationship-- tells which coded group has the larger mean criterion scores(significance test of r is test of mean difference)Dummy Coding for multiple-category variables• can’t use the 1=Tx1, 2=Tx2, 3=Cx values put into SPSS- conditions aren’t quantitatively different • need k-1 codes (one for each BG df)• comparison or control condition/group gets “0” for all codes• each other group gets “1” for one code and “0” for all others“conceptually”...Group dc1 dc21 1 02 0 13* 0 0* = comparison groupFor several participants...Case group dc1 dc21 1 1 02