Interpreting marginal effects in stata with logistic regression and interaction term

[Danny Wellens]

Hi community. So i am trying to interpret the results of my analysis but i am having a hard time doing so. For my research, i am interested in the relation between certain independent variables and one binary dependent variable (voluntary deductible yes/no).

The following independent variables are used:
Age (3 groups: 18- 39 years old, 40 - 64 years old, 65 +)
Gender (male and female)
Income (between 0 - 1666 euros, x, x, x) -> see picture for exact categories
Education (see picture for exact categories)
Proxy Health (Low / high)
Health insurance literacy (above / below)

The first picture represents the output of the logistic model. In the second picture i ran the 'margins' command, followed by all the independent variables.

My question is, how do i interpret these margins? for example: the age scale 18 - 39 years olf has a margin of 0.2425..., how do i interpret this?

Many thanks for helping me out, very much appriciated!

[Clyde Schechter]

In the -margins- output, the number appearing in the "Margin" column is the model-predicted probability (adjusted for all of the other variables in the model) of your outcome variable having value 1, conditional on the value of the variable to its left. So for example, if an person falls in the 18-39 year age group, his or her probability of outcome = 1 is 0.242507. If that person fell in the 40-64 year age group, his or her probability of outcome = 1 would be 0.1949592, etc. (Of course, do not take all of those decimal places seriously. The standard errors suggest that only 1 decimal place in your results is pinned down by the data.)

The z-statistics and p-values in this table should almost always be ignored. It is extremely rare that a test of the hypothesis that the outcome probability = 0 would be meaningful, or even make any sense at all. So just skip over those. The 95% confidence intervals, however, can be understood in the usual way. Be aware, however, that these are calculated with the delta method, and so the confidence bounds can extend outside the 0 to 1 interval.

[Danny Wellens]

Thanks Clyde for the big help! One more thing. I also want to include an interaction term. inclusing this term in the regression, and then typing the 'margins' command provides me the following output (see picture).

Can i still interpret the main effects of the two variables used in the interaction term HIL_above_below*Proxy_gezondheid (health)? Also, say the margins of the variable is is 0.223, can i multiply that number by 100% to get the actual chance for the outcome = 1?

Thank you very much once again Clyde

[Clyde Schechter]

What I can't tell from your post is whether you also modified the regression itself to include an interaction term. Either way, the following would be true:

1. The value in the margins column for a value of a main effect is still the model-predicted probability of outcome = 1, adjusted for all other model variables, for people in that level of the main effect.
2. The value in the margins column for a value of the interaction term is the model-predicted probability of outcome = 1, adjusted for all other model variables, for people in the combination of values of the two main effects specified in that row.

However, bear in mind what model-predicted means depends on the model; it differs according to whether the regression also includes an interaction term.

say the margins of the variable is is 0.223, can i multiply that number by 100% to get the actual chance for the outcome = 1?

The value of 0.223 already is the actual probability. If you multiply it by 100% you get the probability expressed as a percentage. Not sure what you mean by "actual chance" in this context.

[Daniel Schaefer]

Clyde Schechter

The standard errors suggest that only 1 decimal place in your results is pinned down by the data.

How can you tell based on the standard error?

[Clyde Schechter]

The standard errors shown are all <0.1; in fact they are all < 0.03. So the uncertainty in the results (measured as 1 SE) is somewhere in the second decimal place. Even the second decimal place does not have that much wiggle in it, given the SEs are all < 0.03. If I were writing up these results myself, I'd probably show them to 2 decimal places. Accompanied by their confidence intervals, also shown to 2 places, I would be comfortable that I was giving a fair presentation of the uncertainty in these results.

[Daniel Schaefer]

Ah, I see, thank you!

[Danny Wellens]

Thank for helping me out Clyde. So when i want to copy the marginal effects in my paper, i can just use the last table i sent? Can I just interpret the main effects while the interaction is also in the output?

[Clyde Schechter]

Can I just interpret the main effects while the interaction is also in the output?

If you are referring to -margins- output, the answer is yes. If you are referring to the output of a regression, the interpretations are different. Indeed, that is one of the main purposes of using -margins-: in an interaction model, the interpretation of -margins- output is simple and direct, whereas that of the underlying regression is not.