interpretation of logistic regression

[Sanjana Mon]

Hello,
I ran a logistic regression to find the correlation between stunting and mother's ownership of assets. However, I am having difficulty in interpreting it. I have seen some papers use odds ratio and then others use average marginal effect. The results from the logistic regression, after controlling other variables, are given below along with odds ratio and margins . It would be great if you could guide me with which would be the best way to interpret the final correlation:

	stunting
	Coeff	Odds ratio	dy/dx
Ownership of assets	-0.52832	0.5895975	-0.09958

[Erik Ruzek]

The dy/dx parameter estimate expresses how much of a probability decrease in the outcome going from 0 to 1 is associated with a a 1-unit change in the assets predictor, and is my personal favorite of these. Of course, depending on your field, it may be customary to report the odds ratio (more likely) or the logistic coefficient. You can certainly report both the OR and the dy/dx parameter estimates.

[Sanjana Mon]

Thank you for the explanation.

If I was to interpret the marginal effect and write it as "if the mother owns assets, it reduces the probability of child stunting by approx 10 percentage point compared to if she does not have ownership of any types of assets", could you please tell me if it would be correct or not?

[Erik Ruzek]

Yes, that is a correct interpretation.

[Sanjana Mon]

Thank you. I did a bit more research and since the paper I am working on is policy related, I think if I interpret the effects of women's empowerment indicators in term of marginal effects, it will be more suitable, however I will also add the odds ratio results along with it.

Another confusion I have is in the interpretations of interaction terms.

a. Could you please let me know how should I write down these results? I am working on 6 models with different women's empowerment indicators and the main model is a women's empowerment index. I added the results from the logistic regression below where the main independent variable is the women's empowerment index, however the dependent variable is a dummy variable. After finding the log odds results, I manually calculated the odds ratio which came out to be 0.243 so should I interpret it as "mother's empowerment reduces the odds of stunting for boys by 0.243, in comparison to a female child" ?

b. I will also repeat the same regression with the other independent variables that are dummy variables, it would be great if you could let me know if I should interpret all the models in the similar way?

stunting	Coef.	Std. Err.	z	P>z	[95% Conf.	Interval]
women_emp	-1.596628	.8446918	-1.89	0.059	-3.252194	.0589372
1.male	-.4204141	.794162	-0.53	0.597	-1.976943	1.136115
male#c.women_emp
1	.6066958	1.199011	0.51	0.613	-1.743322	2.956714

[Erik Ruzek]

I am not sure where you are getting the value of 0.243. However, to help you interpret this interaction, I would strongly suggest you go back to margins and utilize the excellent marginsplot command. For example:

logistic y c.women_emp##i.male

// i don't know the plausible values of women_emp, my code below makes it such that you get predictions for males and females at women_emp values of 0-50 at 5 unit intervals
margins male, at(women_emp=(0(5)50))
marginsplot

// you can also get the dy/dx marginal effect male estimate for the interaction if you like
magins , dydx(male) at(women_emp=(0(5)50))
marginsplot
// this shows the prediction for the male/female difference (dy/dx) at different values of women_emp

[Sanjana Mon]

I calculated the odds ratio by adding the coeff from women_emp+1.male+male#c.women_emp and took the exponential of the sum.

Thank you for the commands you gave. I used them and found the plot with the different probabilities for male and female.
If both of the variables are dummy variable and is it okay, if I use the same commands? I added them below:

logit stunting i.credit_decision_making##i.male
margins male, at ( credit_decision_making)

[Erik Ruzek]

If credit_decision_making is a categorical variable, then you should be able to do the following:

margins male#credit_decision_making
marginsplot

The at() option is mostly used when one of the interacting variables is continuous or near continuous.

[Sanjana Mon]

Got it! Thank you so much.