A data-science team is building a credit-default classifier. Extremely high or low default probabilities (<1 % or >99 %) are virtually nonexistent, and the domain experts believe the latent "propensity to default" can be viewed as a continuous, unobserved variable disturbed by a symmetric, thin-tailed error term. To honor these assumptions, the team chooses a probit regression instead of a logit model.
Which characteristic of the probit link most directly supports this decision?
It minimizes mean absolute error instead of maximum-likelihood loss, providing robustness to small residuals.
It yields the same predicted probabilities as a logit model but with odds ratios that are simpler to interpret.
It constrains every coefficient to lie between 0 and 1, preventing multicollinearity effects.
It transforms the linear predictor through the cumulative standard normal distribution, whose lighter tails dampen extreme probability estimates when errors are assumed normal.
The probit link applies the inverse cumulative distribution function of a standard normal distribution to the linear predictor. Because the normal distribution has lighter tails than the logistic distribution, it yields more conservative probability estimates at the extremes. When a problem involves rare outcomes and a theoretical justification for normally distributed latent errors, this thin-tailed assumption makes probit a better fit. The other statements are incorrect: probit still maximizes a likelihood (not mean absolute error), does not restrict coefficients to any specific interval, and does not produce identical probabilities or easier-to-interpret odds ratios than logit.
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What is a probit regression?
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How does the probit link differ from the logit link?