Interaction term significant; main terms significant but with an opposite sign

[amira elshal]

Dear colleagues,

I am studying the effect of hospital efficiency on absorbing the negative impact of health shocks on mortality rates. The coefficient of the interaction term is significant and has the correct sign. However, the sign of the main effect of hospital_efficiency is wrong (and significant). Is this okay? How can I interpret this counter-intuitive sign, please? Thank you in advance.

[Clyde Schechter]

You are probably misunderstanding this output. The coefficient of "hospital_efficiency" in this interaction model is not the effect of hospital_efficiency. In fact, in interaction models, there is no such thing as the effect of hospital efficiency. Rather there are two effects of hospital efficiency, one when health_shock = 0, and the other when health_shock = 1. To see those two effects, you can calculate them from the coefficients. One (when health_shock = 0) is the hospital_efficiency coefficient, and the other is the sum of that plus the interaction coefficient. But it is easier to have the -margins- command do that:

// RUN THIS IMMEDIATELY AFTER YOUR REGRESSION RUNS
margins health_shock, dydx(hospital_efficiency).

You will then find that when health_shock = 0, the marginal effect of hospital efficiency is a small positive number (0.023) and that when health_shock = 1, it is a much larger negative number, -0.76.

And, reading from the regression output, the correct interpretation of the interaction term itself is that the presence of a health shock is associated with a 0.096 decrease in the effect of hospital efficiency on mortality.

[amira elshal]

Many thanks for the elaboration. I was thinking of interpreting the coefficient on the interaction term the other way round. I would like to provide evidence that if hospitals are operating efficiently, hospital efficiency can mitigate (absorb) the negative impact of a health shock on mortality. Is that possible? Thanks again.

[Clyde Schechter]

Yes, that is equally valid, though expressing it is a bit more complicated because hospital_efficiency is a continuous variable. So what you would say is that each unit increase in hospital_efficiency is associated with a 0.096 decrement in the effect of a health shock on mortality.

[amira elshal]

I was afraid I could not say that as the signs of the coefficients on the two main variables are positive. Many thanks for your help!

[Clyde Schechter]

Well, rest assured, you can.

The term "main variable," though deeply entrenched in usage, is really unfortunate because it misleads people into thinking incorrect things like that. The "main variables" don't in fact really represent main effects in interaction models. They represent effects conditional on the other interacting variables all being zero--they are contingent effects, and often the zero values on which they are contingent are unrealistic or even impossible in principle.

[amira elshal]

Thanks for the clarification. Have a great day!

[Joro Kolev]

The marginal effect of efficiency on mortality is d(Mortality|X)/d(efficiency)=0.023 - 0.096*healthshock.

I agree with everything that Clyde says, and the interpretation that Original Poster looks for in #3 that " if hospitals are operating efficiently, hospital efficiency can mitigate (absorb) the negative impact of a health shock on mortality" is correct.

Still there is the disturbing result that the more efficient is the hostpial, the higher the mortality rate if there is no health shock, and the effect is borderline significant. Somehow the whole thread without saying anything wrong, somehow concluded that this is not a problem. I think it is a problem that needs further investigation. The result is counterintuitive.

[amira elshal]

Joro Kolev Thanks for the clarification and for raising an important point. My interpretation, as a health economist, is that when there is a health disaster in the broad sense in a country, and this country allocates funding for hospitals to act more efficiently (in the way it deals with the disaster), the funding is worth it. But when no health disaster occurs in a decade, let's say, but this country still invests money in hospital efficiency to be prepared to deal with potential disasters, the money does not pay off, and is actually diverted from direct interventions on child mortality. I hope this makes sense.