Question 1:

Let’s say you have data on the type of health insurance available to 616 psychologically depressed subjects in the U.S. (Tarlov et al. 1989). The insurance is categorized as being either an indemnity plan (i.e., regular fee-for-service insurance which may have a deductible or coinsurance rate) or a prepaid plan (a fixed up-front payment allowing subsequent unlimited use as provided, for instance, by an HMO). The third possibility is that the subject has no insurance whatsoever. The dependent variable is coded 1 = Prepaid Plan, 2 = Uninsured, and 3 = Indemnity Plan. You wish to explore the demographic factors [(a) Age: continuous; (b) Gender: Male = 1; (c) Race: Nonwhite = 1] associated with each subject’s insurance choice, while controlling for the site of the study (the study was conducted in three sites, so you use two dummies one each for Site2 and Site3). Appropriately, you estimate a multinomial logit model using the Indemnity type insurance as the reference category and obtain the following results:

- a) Assess model fit and statistical significance of coefficients.
- b) Calculate odds (relative risk) ratios for all variables and interpret them.
- c) Calculate the change in the probability of having the two types of insurance as well as being uninsured for a discrete change in the variable Nonwhite. Assume the following mean/modal values for other independent variables: Mean Age: 25years; Modal Male: 1; Modal Site2: 1; Modal Site3: 0
- d) Calculate the probability of being Prepaid for a 40 years-old female who is non-white and from Site 2.

Question 2:

The Stata dataset for this question contains the 1978 repair records of 69 foreign and domestic cars. The variable that indicates the repair record (Rep78) takes on values 1=poor, 2=fair, 3=average, 4=good, and 5=excellent. Other variables in the dataset include each car’s Length (continuous), MPG (miles per gallon, continuous) and an indicator Foreign coded as 1 if it’s a foreign car and 0 if domestic. Analyze the repair record as a function of Length, MPG, and Foreign using the appropriate statistical model. Present a complete write-up of your analysis that addresses assessment of model fit, test of appropriate assumptions, and interpretation of parameter estimates. In addition, calculate the probability of each category of the dependent variable for foreign and domestic cars.

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