How to interpret coefficient on interaction term between 2 dummy variables

Question

Using logistic regression, I am attempting to model the marginal effect of being female and earning below the poverty threshold (both binary variables) on predicting probability of developing hypertension. I created an interaction term (poverty_FEMALE) to attempt to model this, but am unsure if my interpretation of the coefficients is correct.

Is it correct to say that the:

• marginal effect of being below the threshold and male is: .067 - .055
• the marginal effect of being female and not in poverty is: .041 - .055
• the marginal effect of being female and in poverty is -.055?

If so, why would it make sense that those in poverty and female are at lower risk, when the coefficients of those two variables on their own our positive values?

pov_FEMALE=(df$BELOW_100_POVERTY*(df$FEMALE))

Marginal Effects:
                       dF/dx  Std. Err.       z     P>|z|    
BELOW_100_POVERTY  0.0670417  0.0243266  2.7559 0.0058531 **  
FEMALE             0.0410705  0.0172280  2.3839 0.0171283 *  
pov_FEMALE        -0.0553485  0.0160284 -3.4531 0.0005541 ***

Answer 1

Assuming that dF/dx shown there is the type of marginal effect you want,

• marginal effect of being below the threshold (0.067) and male (0) is: .067

• the marginal effect of being female (0.041) and not in poverty (0) is: 0.041

• the marginal effect of being female (0.041) and in poverty (0.067) and the joint condition (-0.055) is: 0.041 + 0.067 -.055

Think about the meaning of partial derivatives. The direct effect and interaction effect are additive as you take partial derivative of the estimating equation with respect to variable x.

Assuming that the variables you describe are indicators (1 or 0 in values), the marginal effects of the base (value 0, say "male") is not identified separately from the intercept. One can only interpret the result as the baseline probability plus marginal effects where the baseline in this case is defined for being male and non-poor.