Calculate the change in the probability of having the two types of insurance as well as being uninsured

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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: 

N = 615; LR Chisquare, df (10): 42.99; Pseudo R-Squared: 0.0387 

Insurance Type   Coefficient    Standard Error 

Prepaid          

Age               -.011745        0.0062

Male              .561693         0.2027

Nonwhite      .9747768        0.2363

Site2             .1130359        0.2101

Site3             -.587988        0.2279

Constant       .2697127        0.3284

Uninsured

Age               -.0077961       0.0114

Male              .4518496        0.3675

Nonwhite      .2170589        0.4256

Site2             -1.211563       0.4705

Site3             -.2078123       0.3663

Constant       -1.286943       0.5923

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: 31.75 years; Modal Male: 1; Modal Site2: 1; Modal Site3: 0 

d) Calculate the probability of being uninsured for a 40 year-old female who is non-white and from Site 2.

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