6.18 LR in R: Predicting Recidvism (2)

Estimate model: glm(y ~ x1 + x2, family = binomial, data = data.train)

fit <- glm(as.factor(is_recid) ~ age + priors_count, 
           family = binomial, 
           data = data.train)
cat(paste(capture.output(summary(fit))[11:14], collapse="\n"))

##               Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   1.101001   0.097597   11.28   <2e-16 ***
## age          -0.049831   0.002861  -17.42   <2e-16 ***
## priors_count  0.159982   0.008236   19.43   <2e-16 ***

R output shows log odds: e.g., a one-unit increase in age is associated with an increase in the log odds of is_recid by -0.05 units (annoying interpretation)
predict(): Predict values
- Once coefficients have been estimated, it is a simple matter to compute the probability of outcome for values of our predictors (James et al. 2013, 134)
- predict(fit, newdata = NULL, type = "response"): Predict probability for each unit
- predict(fit, newdata = data_predict, type = "response"): Predict probability for particular Xs (contained in data_predict)
- type="response": Output probabilities of form \(P(Y=1|X)\) (as opposed to other information such as the logit)

data_predict = data.frame(age = c(30, 30, 50), 
                 priors_count = c(2, 4, 2))
data_predict$Pr <- predict(fit, newdata = data_predict, type = "response")
data_predict

age	priors_count	Pr
30	2	0.4815163
30	4	0.5611905
50	2	0.2552909

Q: How would you interpret these values?

Source: James et al. (2013 Chap. 4.3.3, 4.6.2)

References

James, Gareth, Daniela Witten, Trevor Hastie, and Robert Tibshirani. 2013. An Introduction to Statistical Learning: With Applications in R. Springer Texts in Statistics. Springer.