Probit or Logit in Generalized Linear Model [duplicate]

Question

I'm trying to apply GLMs on a dataset in which dependent variable Y is dichotomous. I applied either logit and probit models, and probit fitted better than logit model. How do I justify the choice of the probit on the logit model?

#use of link=logit
Call:
glm(formula = DANNO ~ OCCUPAZIONE + PERCPIANTE, family = binomial(link = logit), 
    data = data)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.6908  -0.1688  -0.1321   0.1012   2.3223  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)  -4.7370     0.7624  -6.214 5.18e-10 ***
OCCUPAZIONE   7.3862     1.2981   5.690 1.27e-08 ***
PERCPIANTE    3.0168     1.5783   1.911    0.056 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 308.294  on 227  degrees of freedom
Residual deviance:  77.096  on 225  degrees of freedom
AIC: 83.096

Number of Fisher Scoring iterations: 7


#Use of link=probit
Call:
glm(formula = DANNO ~ OCCUPAZIONE + PERCPIANTE, family = binomial(link = probit), 
    data = data)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-2.57471  -0.13749  -0.09375   0.08136   2.28999  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)  -2.6209     0.3606  -7.267 3.66e-13 ***
OCCUPAZIONE   4.0762     0.6434   6.335 2.37e-10 ***
PERCPIANTE    1.4687     0.7271   2.020   0.0434 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 308.29  on 227  degrees of freedom
Residual deviance:  75.95  on 225  degrees of freedom
AIC: 81.95

Number of Fisher Scoring iterations: 7

Answer 1

There shouldn't really be any justification needed. The two models are essentially equivalent in predictive performance, except, as the linked-to answer discusses below, in the tails. The logit link function is used more widely because it is computationally cheaper (thought this is pretty negligible at this point, mattered a lot more in the 1940s) and easier to work with mathematically. Edit: and log odds interpretation of logistic regression can be useful, as discussed in answer to earlier question linked below.

Both models assume that a binary outcome random variable is driven by a latent random variable (probability) that ranges from 0-1. Probit just uses the cumulative distribution function of the normal distribution to enforce that assumption, while logit uses the sigmoid or logit function.

Edit: Also what this person said: Difference between logit and probit models