Локальная регрессия для вероятности.

my.seed <- 1
data(Boston)
attach(Boston)

fit_logit <- glm(I(crim > 30) ~ poly(nox, 3), data = Boston, family="gaussian")
fit_logit
## 
## Call:  glm(formula = I(crim > 30) ~ poly(nox, 3), family = "gaussian", 
##     data = Boston)
## 
## Coefficients:
##   (Intercept)  poly(nox, 3)1  poly(nox, 3)2  poly(nox, 3)3  
##       0.01581        0.36883       -0.18344       -0.35363  
## 
## Degrees of Freedom: 505 Total (i.e. Null);  502 Residual
## Null Deviance:       7.874 
## Residual Deviance: 7.579     AIC: -679.8
gam.lr <- gam(I(crim > 30) ~  s(nox, df = 5) , 
              family = 'binomial', data = Boston)
gam.lr
## Call:
## gam(formula = I(crim > 30) ~ s(nox, df = 5), family = "binomial", 
##     data = Boston)
## 
## Degrees of Freedom: 505 total; 500.0002 Residual
## Residual Deviance: 40.825
plot(gam.lr, se = T, col = 'green')

summary(gam.lr)
## 
## Call: gam(formula = I(crim > 30) ~ s(nox, df = 5), family = "binomial", 
##     data = Boston)
## Deviance Residuals:
##        Min         1Q     Median         3Q        Max 
## -8.176e-01 -5.027e-02 -2.790e-05 -2.107e-08  2.382e+00 
## 
## (Dispersion Parameter for binomial family taken to be 1)
## 
##     Null Deviance: 82.2264 on 505 degrees of freedom
## Residual Deviance: 40.825 on 500.0002 degrees of freedom
## AIC: 52.8245 
## 
## Number of Local Scoring Iterations: 30 
## 
## Anova for Parametric Effects
##                 Df Sum Sq Mean Sq F value    Pr(>F)    
## s(nox, df = 5)   1  4.626  4.6258  45.534 4.164e-11 ***
## Residuals      500 50.795  0.1016                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Anova for Nonparametric Effects
##                Npar Df Npar Chisq  P(Chi)  
## (Intercept)                                
## s(nox, df = 5)       4     9.2476 0.05519 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1