Probit response models

Building Response Models in R

Kathrin Gruber

Assistant Professor of Econometrics Erasmus University Rotterdam

Probit response function

  • Purchase probabilities are latent propensities.
  • Assumes a regression for a continuous, unobservable response variable.

Building Response Models in R

A probit model for beer demand

probit.model <- glm(HOPPINESS ~ price.ratio,
                    family = binomial(link = probit), data  = choice.data)

coef(probit.model)

(Intercept)  price.ratio 
  -1.954092    -3.547546
Building Response Models in R

Logistic vs. probit

cbind(coef(logistic.model), coef(probit.model))

                 [,1]      [,2]
(Intercept) -3.572678 -1.954092
price.ratio -6.738768 -3.547546

Rescaling

coef(probit.model)*1.6

(Intercept)  price.ratio 
  -3.126547    -5.676073
Building Response Models in R

Average marginal effects

  • Logistic: interpretable log-odds
margins(logistic.model)

price.ratio
    -0.4585
  • Probit: uninterpretable z-values
margins(probit.model)

price.ratio
    -0.4503
Building Response Models in R

Let's practice!

Building Response Models in R

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