# Handout11 - Lecture 11 1 Adjusting stratication regression...

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Lecture 11 1. Adjusting: stratifcation, regression 2. How do LSmeans adjust? 3. Non-estimable LSmeans 1 Comparing groups while adjusting or controlling a covariate Rat liver enzymes: we want to compare the eFFects oF diets, adjusting For livers oF diFFerent weights. Response y j From individuals in two or more groups ( A ) with additional covariate (predictor) x j measured on each individual. Adjusting the comparison oF groups A For X means comparing groups using individuals with equal X . Controlling For X means comparing groups using individuals with X held constant. Adjusting = controlling 2

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Adjusting 1: Strata To adjust comparison of groups A for X : compare levels of A using individuals with equal or nearly-equal X . • Cut X into categories = strata or blocks , creating a new variable B where individuals have similar values of x . This gives ANOVA adjustment. • Match individuals drawn from different groups on their values of X . 3 StratiFed or matched analysis: 1. Calculate difference between levels of A within each stratum or matched set 2. Test whether A differences vary with levels of B : interaction ; draw interaction plot ( LSmeans A*B ). 3. If no interaction, combine the A differences across X : LSmeans A 4. If there’s an interaction, explain how it works. 4
Adjusting 2: Regression To adjust comparison of groups A for X : compare levels of A using individuals with equal or nearly-equal X . Regression adjustment : 1. Regress response y on X for each treatment group (parallel or separate lines) 2. At selected value of X (default: overall mean ¯ x ), compute predicted mean ˆ y j

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Handout11 - Lecture 11 1 Adjusting stratication regression...

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