I know this has been already asked, but I am quite confused about the interpretation of logit regression estimates if I have interacted variables (continuous and binary ones).

I run the following regression:

`model <- glm(elected ~ treat + factor(School) + factor(Race) + treat*Treat.City, data = subset(df, Year == 2016), family = binomial(link = 'logit')) `

My dependent variable `elected`

is equal to 1 if a political candidate got elected, 0 otherwise. `treat`

equals 1 if the candidate belongs to a treatment group, 0 if belongs to the control group.

After controlling for schooling and race dummy variables, I have put the interaction `treat*Treat.City`

, in which `Treat.City`

is a continuous variables indicating the percentage of treatment candidates in relation to the total number of challengers inside candidate's i city.

Running the regression in `R`

, I have the following results:

`Call: glm(formula = elected ~ treat + factor(School) + factor(Race) + treat * Treat.City, family = binomial(link = "logit"), data = subset(df, Year == 2016)) Deviance Residuals: Min 1Q Median 3Q Max -1.875 -1.321 1.000 1.039 1.262 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) 0.42387 0.15196 2.789 0.005281 ** treat -0.22397 0.03879 -5.775 7.71e-09 *** factor(School)MÉDIO_INCOMPLETO 0.04055 0.03452 1.174 0.240227 factor(School)SUPERIOR_COMPLETO 0.11976 0.03221 3.718 0.000201 *** factor(School)SUPERIOR_INCOMPLETO 0.11576 0.02947 3.929 8.55e-05 *** factor(Race)BRANCA -0.12757 0.15054 -0.847 0.396742 factor(Race)INDÍGENA -0.57795 0.26393 -2.190 0.028542 * factor(Race)Preta_Parda -0.20933 0.15073 -1.389 0.164897 Treat.City 1.50083 0.61352 2.446 0.014435 * treat:Treat.City 2.80625 0.95484 2.939 0.003293 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 54123 on 39893 degrees of freedom Residual deviance: 54033 on 39884 degrees of freedom AIC: 54053 Number of Fisher Scoring iterations: 4 `

How can I interpret such coefficients? More specifically, how can I numerically make a statement about the effect of the treatment on the probability in getting elected?

Can I make any clear interpretation about this 'Intensity of treatment' variable that `Treat.City`

is?

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#### Best Answer

The odds of being elected when you are not treated increases by a factor $exp(1.50083)approx 4.49$ or $(4.49-1)times100%=349%$ if you move from a city with no one treated to a city where everyone is treated.

This effect of `Treat.City`

increases by a factor $exp(2.80625approx16.55)$ or $(16.55-1)times100%=1555%$ if one is treated. For more see: http://maartenbuis.nl/publications/interactions.html

Given the large size of the effect I will assume that `Treat.City`

is not a percentage but a proportion. The effects will be more realistic and easier to interpret when you turn `Treat.City`

into percentages.

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