1. 1 G89.2229 Lect 9W Review of Coding Schemes for Categorical Data Example revisited Inclusion of Covariates Example extended Adjusting in Regression G89.2229 Multiple Regression Week 9 (Wednesday)

2. 2 G89.2229 Lect 9W Coding Schemes for k categories Dummy variables »Ideal when paired contrasts of interest »Must choose a reference group Unweighted effect codes »ANOVA approach »Means of categories are compared without taking into account possibly different n’s. »Each of (k-1) categories compared to mean of means Weighted effect codes »Like UEC but compares category means to weighted grand mean Special Contrasts

3. 3 G89.2229 Lect 9W Example Revisited: Depression in PR Youth *Compute dummy codes with 12 year group as reference. COMPUTE AGE18=0. COMPUTE AGE16=0. COMPUTE AGE14=0. IF AGE EQ 18 AGE18=1. IF AGE EQ 16 AGE16=1. IF AGE EQ 14 AGE14=1. *Computing unweighted effect codes. COMPUTE AGE18E=0. COMPUTE AGE16E=0. COMPUTE AGE14E=0. IF AGE EQ 18 AGE18E=1. IF AGE EQ 16 AGE16E=1. IF AGE EQ 14 AGE14E=1. IF AGE EQ 12 AGE18E=-1. IF AGE EQ 12 AGE16E=-1. IF AGE EQ 12 AGE14E=-1. FREQUENCIES VARIABLES=age /ORDER= ANALYSIS. *Compute weighted effect codes with 12 year group as reference. COMPUTE AGE18EW=0. COMPUTE AGE16EW=0. COMPUTE AGE14EW=0. IF AGE EQ 18 AGE18EW=1. IF AGE EQ 16 AGE16EW=1. IF AGE EQ 14 AGE14EW=1. IF AGE EQ 12 AGE18EW=-222/356. IF AGE EQ 12 AGE16EW=-380/356. IF AGE EQ 12 AGE14EW=-356/356.

4. 4 G89.2229 Lect 9W Inclusion of Covariates In MR we often add new variables into prediction/structural model In ANOVA quantitative variables added to model are called covariates »In experiments covariates can increase precision »In nonexperimental research, covariates are often used to adjust for selection effects Example: Adjust age groups for level of adaptive functioning

5. 5 G89.2229 Lect 9W Computing adjusted category means When no covariate is included, the Expected means (from the model) are identical to the sample means When a covariate is included, the expected means vary according to the covariate value »Relative group mean differences are not affected (unless there is interaction) »“Adjusted means” often reported for covariate set at its own mean »Adjusted means are particularly easy to compute for centered covariates.

6. 6 G89.2229 Lect 9W Adjusting for Selection Effects Often we wish to make causal inferences from group comparisons »Drug use vs. no drug use »Active vs. negligent parenting »Participation in training programs Without random assignment, group differences are difficult to interpret Covariates often used to adjust for alternative selection explanations This is a difficult area

7. 7 G89.2229 Lect 9W Some References Relevant to Selection Rosenbaum, Paul R. (2002) Observational studies (Second Edition). New York: Springer. Campbell, D.T. & Kenny, D. A. (1999) A primer on regression artifacts. New York: Guilford Lord, F. M. (1967) A paradox in the interpretation of group comparisons. Psychological Bulletin, 68, 304-305.

8. 8 G89.2229 Lect 9W "Lord's Paradox" (Lord, 1967) Consider »Weight change in two dorms, Sept-May »Is there an effect of food service? »Adjust for September Wt September Wt May Wt

9. 9 G89.2229 Lect 9W The groups differ when Sept weight is a covariate The regressed change analysis focuses on May Weight holding constant September weight »Suppose we found that women were more likely to be in Dorm B and men in Dorm A »When we compare a man and a woman who are the same weight in September, we expect the man to gain weight, and the woman to lose weight. »Even though it is reliable and valid, September weight is not a perfect proxy for selection effects

10. 10 G89.2229 Lect 9W When Does Adjustment Work? When samples are likely to differ only because of random assignment fluctuations When the covariate is a direct measure of selection effects »AND when the covariate is measured reliably »AND when the covariate does not capture transient state effects »AND when there is no interaction between covariate and group differences