Part I Using the GSS from the years 2004 until 2010 and multinomial logistic regression, a researcher wanted to answer the following question: What determines which religion people will belong to? The options are: Protestant, Catholic, Jewish or no religion. (He excluded all other religions from the analysis.) As predictors, he includes: an index of the respondent's family's overall socioeconomic status (SES) when s/he was growing up, Pr SES, with a mean of approximately O and a standard deviation of about 0.8; whether the respondent was African-American or not, Black (yes=1, no=0); and whether the respondent's age is greater than 55 (Older=1) or not (Older=O). Just for your reference, a little more about Pr SES: The researcher wanted to make an index to capture a hypothesized latent variable of parental socioeconomic status (SES), so he calculated the Cronbach's alpha of three standardized variables: Father's education (Paeduc), mother's highest degree (Madeg), and the relative ranking of family income when the respondent was age 16 (Incom16). He gets a Chronach's alpha=0.668.

The output is in the following table.

1. Interpret both the logit and the relative risk ratio on Older for the category of "None" from Model 1 and Model 3 in Table 1; note statistical significance. What substantive conclusion do you draw from those coefficients?

2. The researcher hypothesized that because Protestantism was the dominant religion in the United States for the earlier part of the 20th century, and especially for the elites, that the older someone was and the more affluent there family was, the more likely they would be Protestant vs. being some other religion. Looking at the interactions in Model 2 in Table 1, does that theory find support? Speak to this in general and then also specifically by interpreting the relevant interactions and main effects.

3. There is a potential issue with interpreting interactions in the context of logit models, especially if we try to provide predicted probabilities or as odds-ratios or relative-risk ratios. Explain what the issue is of getting predicted probabilities or converting to odds-ratios or relative-risk ratios from interactions in logit models, like the multinomial one above.