# Interpretation of interaction term in a probit estimation

I know this question may be duplicate but I don't find any answer that I could understand. I am running panel probit estimations. Estimations include interaction terms that I am able to interpret.

Here is the output of the regression :

Decision = -0.73* + 0.86***X1 - 0.46X2 - 1.47***X3 + 1.76***X2X3


where

X1= Financial incentives

X2= Context

X3= Gender (1 for Male)

I need help to interpret the coefficient of the interaction term. This can be interpreted regarding main effect variable. In the baseline condition : 0 financial incentives, no context, female, there is a significant negative effect. All thing equal, the higher the financial incentives, the higher the probability to take this decision. There is a negative and significant effect of the dummy Male meaning that Female are more prone to take this decision (holding constant the rest).

But I struggle to interpret the interaction term X2X3 : So -0.73 - 0.46 - 1.47 + 1.76 = -0.9. Does this mean that when Context and Male both apply the likelihood to take this decision is still lower than the Baseline condition (-0.9 < -0.73)?

Thank you !

• Try to write what would it be the equation for males and the equation for females. Comparing the two might help you understand what is going on. The interaction term can be interpreted as the response to $X_2$ being different between males and females. – Ertxiem - reinstate Monica Mar 23 '19 at 16:13
• Thank you for your answer. As I understand, the equation for males would be : -0.73 - 0.46X2 - 1.47X3 + 1.76 X2X3 = (- 0.46 + 1.76X3)X2 - 1.47X3 -0.73 = -0.9 while the equation for females would be : -0.73 - 0.46X2 = -1.19. – Marc Mar 23 '19 at 16:31

From your equations in the comments and since for males $$X_3=1$$ , we have that: $$Decision_{Males} = - 0.73 - 1.47 + 0.86 X_1 + (1.76 - 0.46) X_2$$ $$Decision_{Females} = - 0.73 \quad \quad \quad + 0.86 X_1 ~ \quad \quad \quad - 0.46 X_2$$
Regarding the interpretation, note that the effect of the financial incentives is the same for both sexes: higher incentives (assuming that higher values of $$X_1$$ mean higher incentives) will increase the odds of choosing the decision.
Looking at the effect of context, higher values of $$X_2$$ have different behaviours between the sexes: in males it increases the odds of choosing the decision while in females it decreases the odds.