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I am relatively new to statistical analysis and so please forgive me for any cumbersome language/explanations.

I'm interested in how sex and race interact to affect the experience of discrimination in low income health care settings. I have two focal independent variables (sex and race/ethnicity) and I would like to create interaction terms for use in binary logistic regression in SPSS. Sex is a 0/1 dummy variable and race/ethnicity has 5 categories: non-Hispanic white, non-Hispanic black, non-Hispanic Asian, non-Hispanic "other" and Hispanic. So I would want interaction terms (in dummy variable form?) for each possible combination: white men, white women, Black men, Black women, Asian men....and so on. How should I best go about doing this? I've already constructed a single categorical variable "sex_race" but am not sure how to properly use it in logistic regression.

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  • $\begingroup$ I don't understand, why don't you estimate the interaction between sex and race/ethnicity directly through your model, rather than creating dummy variables yourself? What are you trying to achieve here? Also, what is your dependent variable and what type is it? $\endgroup$ – user2974951 Jul 12 '19 at 6:04
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You won't want to use a binary logistic regression. This type of model would be used to find the probability of an event given a value of your dependent variable(s). Use multiple linear regression to test these hypotheses. I am assuming your dependent variable is health care costs or something of that form? The "interaction terms" in this sense are just a set of terms, for which only one will be a nonzero value for any given observation. Because all possible values of these variables are {0,1}, they basically just act as conditional intercept terms. You will want 5 (races) x 2 (genders) = 10 - 2 terms, with one (say black and woman) of each category as the control variable. Be wary that having this many parameters will penalize your Adj R^2. The interpretation will be as follows:

Say that you have a term δ(wh*m), where wh = white, m = male, and δ is the coefficient. If δ=-250, this means that, if the observation is white AND male, ceteris peribus, the dependent variable (cost of hc?) will be 250 less than that of someone that is black OR a woman.

Depending on the data, you will likely also have non-conditional terms such as δ(wh) and δ(m) that are significant. If the coefficient of δ(wh) is -150, that means that regardless of gender, the y-hat is 150 less if you are white, than if you are black. The difference between δ(wh) + δ(m), and δ(wh*m) is due to the fact that the affect of (wh ∩ m) is different than (wh ∪ m). In other words, there is an extra benefit of being white AND male.

One last tip; make the control variable something that, for your research and motive, you want to be compared to. If you are looking at how each race/sex compare to a white male, use white and male as the controls to make the coefficients more useful and applicable.

If you want a simpler model that preserves some DFs, then you could make your races white and nonwhite. This would, however, limit analysis between groups inside "non-white".

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