Logit model: how to interpret negative AMEs?

[Antonia Noerthemann]

Dear Statalist,

I am using Stata 15.1 with Windows 10. I have a logit model on cross-border deals in Private Equity, the dependent variable being CrossBorder (binary, 1 if a deal is a cross-border deal and zero if the deals is a domestic deal). My main variable of interest is the logarithmic variable "Involvement" (variable name: log_InvolveC) which reflects the support and monitoring intensity of the PE fund in an investment, which I interacted with the variale log_NationalDeals_pa (logarithmic variable, number of deals in the target market in the investment year the deal took place. log_NationalDeals_pa is a proxy for target market attractiveness). The full logit model includes several controls.

I am using the logit command with robust standard errors and fund names clustered.
In the regression output log_InvolveC, log_NationalDeals_pa and the interaction term c.log_InvolveC##c.log_NationalDeals_pa are significant with p> |z| 0,001.

To interpret the values I ran margins dydx command and marginsplot afterwards to illustrate the results.

Code:

logit CrossBorder c.log_InvolveC##c.log_NationalDeals_pa log_IntExperience log_DomeExperience log_DryPowder log_AgeofFund LEADInv Syndication SynSize SynMultinat i.FundStage_C i.IndustryFE i.InvestmentYear, robust cluster (FundName)
margins, at(log_NationalDeals_pa=(0 (1) 15)) dydx(log_InvolveC) vsquish level(95)
marginsplot

Plot:

The plot I created shows the average marginal effects of log_NationalDeals_pa on the probability of log_InvolveC for CrossBorder==1.
I interpret these results as negative influence of log_NationalDeals_pa on the probability of log_InvolveC for CrossBorder==1. Am I right?
According to my previous understanding average mariginal effects can only take values between 0 and 1.


How can negative values be interpreted here?

Thank you very much for your help!
Best regards
Antonia

[Maarten Buis]

A probability can only be between 0 and 1. However, you are not looking a probability, but at an effect on a probability, i.e. the slope. A slope can be positive (the probability of Crossborder == 1 increases when log_involveC increases for a given value of log_NationalDeals_pa) or negative (the probability of Crossborder == 1 decreases when log_involveC increases for a given value of log_NationalDeals_pa). Since marginal effects are derivatives they are not even bound to [-1,1].

[Antonia Noerthemann]

Thank you very much for your helpful answer!
At this point I have one more fundamental question.
How should I proceed, if AMEs are significant for all given values but the coefficient of the interaction term in the regression output is not?
In some post I read that p-values are omitted from the regression output and one should not give too much weight to p-values. Others only concentrate on the significance of the p-values of the coefficients, although in logit models they are difficult to interpret.
Should I reject the interaction?

Best regards,
Antonia

[Maarten Buis]

The confidence intervals in the graph test a different null hypothesis than the p-values for the interaction effects. The interaction effects tell us whether is the effect of log_involveC on the probability CrossBorder == 1 change when log_NationalDeals_pa changes, while the confidence intervals in your marginsplot tells you whether the effect of log_involveC on the probability CrossBorder == 1 is different from 0. Those are completely different hypotheses, so it is no surprise that one hypothesis has more support than another. That is not informative, they just cannot be compared.

[Antonia Noerthemann]

A slope can be positive (the probability of Crossborder == 1 increases when log_involveC increases for a given value of log_NationalDeals_pa) or negative (the probability of Crossborder == 1 decreases when log_involveC increases for a given value of log_NationalDeals_pa)

The interaction effects tell us whether is the effect of log_involveC on the probability CrossBorder == 1 change when log_NationalDeals_pa changes

I really apologize, but I can see no difference between those two statements. The first quote is about the interpretation of the marginsplot and the second quote belongs to the interpretation of the coefficient in the regression output.

Could you emphasize the difference once again? I am really sorry that I am at a loss.

[Maarten Buis]

The first is the effect at a given value of log_NationalDeals_pa, the second is the change in effect when log_NationalDeals_pa changes.