Homework assignment due mardi, 1 dec

1. Exercise 9.7: Gain-score models: in the discussion of gain-score models in Section 9.3, we noted that if we include the pre-treatment measure of the outcome in a gain score model, the coefficient on the treatment indicator will be the same as if we had just run a standard regression of the outcome on the treatment indicator and the pre-treatment measure. Show why this is true.

2. Exercise 9.8: Assume that linear regression is appropriate for the regression of an outcome, y, on treatment indicator, T , and a single confounding covariate, x. Sketch hypothetical data (plotting y versus x, with treated and control units indicated by circles and dots, respectively) and regression lines (for treatment and control group) that represent each of the following situations:

(a) No treatment effect,

(b) Constant treatment effect,

(c) Treatment effect increasing with x.

3. Exercise 9.9: Consider a study with an outcome, y, a treatment indicator, T , and a single confounding covariate, x. Draw a scatterplot of treatment and control observations that demonstrates each of the following:

(a) A scenario where the difference in means estimate would not capture the true treatment effect but a regression of y on x and T would yield the correct estimate.

(b) A scenario where a linear regression would yield the wrong estimate but a nonlinear regression would yield the correct estimate.