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Very similar to this; How are the standard errors computed for the fitted values from a logistic regression? Although after manual calculation of se.fit with glm family = binomial rather than default?

Model fit and example;

> summary(logistic.model)

Call:
glm(formula = LossIncurred ~ ExposureYear + Quo_AmountFinanced + 
    LVR + Loan_VedaScore + ResidualPercentage + AssetAge + PropertyOwned + 
    RatingScore, family = "binomial", data = Default_data.train)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-0.6256  -0.0822  -0.0525  -0.0346   3.8582  

Coefficients:
                          Estimate Std. Error z value Pr(>|z|)    
(Intercept)             -7.400e+00  5.609e-01 -13.192  < 2e-16 ***
ExposureYear             7.039e-01  5.730e-02  12.283  < 2e-16 ***
Quo_AmountFinanced       3.763e-06  1.771e-06   2.124 0.033660 *  
LVR                      1.554e+00  4.804e-01   3.234 0.001221 ** 
Loan_VedaScoreAverage   -6.589e-01  1.921e-01  -3.430 0.000604 ***
Loan_VedaScoreGood      -1.575e+00  2.016e-01  -7.811 5.69e-15 ***
Loan_VedaScoreVery Good -2.522e+00  2.637e-01  -9.566  < 2e-16 ***
Loan_VedaScoreExcellent -3.255e+00  5.246e-01  -6.205 5.46e-10 ***
ResidualPercentage       8.173e-01  5.034e-01   1.624 0.104469    
AssetAge                 9.256e-02  2.464e-02   3.757 0.000172 ***
PropertyOwned           -5.768e-01  1.650e-01  -3.495 0.000475 ***
RatingScore             -1.314e-01  3.778e-02  -3.477 0.000506 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 2661.4  on 57163  degrees of freedom
Residual deviance: 2304.7  on 57152  degrees of freedom
  (355 observations deleted due to missingness)
AIC: 2328.7

Number of Fisher Scoring iterations: 10

Essentially needing to manually calculate the below value

predictTest <- predict(logistic.model, newdata = Default_data.test, type = "response", se.fit = TRUE)

> predictTest$se.fit[1]
           1 
0.0006774337
Josh
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  • Note that if you need the standard deviation for building a confidence interval, you should compute it on the link scale (log odds scale, logit scale) and then transform with *plogis*. Otherwise the confidence interval will extent beyond the range [0,1]. – cdalitz Feb 18 '22 at 13:17

0 Answers0