An odds ratio compares the odds of an event under one condition with its odds under another. Odds themselves divide the probability of success by the probability of failure, while log odds are the natural logarithm of those odds. section 14.6.2
From probability to odds and back
If a flight has a 70% probability of departing on time, its odds are 0.70 / 0.30 = 2.33. The log odds are ln(2.33) = 0.846; exp(0.85) returns an odds ratio of about 2.34, and 2.34 / 3.34 returns a probability of about 0.70. section 14.6.2
Logistic regression estimates log odds for a binary outcome, so converting its coefficients makes model effects easier to interpret as probabilities. For the NBA playoff model, plogis(-1.72) gives about 0.15 for a one-unit value of the standardized offensive-points predictor; the analysis reports roughly a 15% probability change. section 14.6.2
fit3 <- glm(playoffs2 ~ z_o_pts, family = "binomial", data = train) summary(fit3) ## ## Call: ## glm(formula = playoffs2 ~ z_o_pts, family = "binomial", data = train) ## ## Deviance Residuals: ## Min 1Q Median 3Q Max ## -2.17428 -0.77250 -0.01473 0.76694 2.13669 ## ## Coefficients: ## Estimate Std. Error z value Pr(>|z|) ## (Intercept) 0.1998 0.1727 1.157 0.247 ## z_o_pts -1.7210 0.2317 -7.428 0.00000000000011 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## (Dispersion parameter for binomial family taken to be 1) ## ## Null deviance: 304.98 on 219 degrees of freedom ## Residual deviance: 210.91 on 218 degrees of freedom ## AIC: 214.91 ## ## Number of Fisher Scoring iterations: 5
Use the fitted NBA logistic regression and its output to connect a coefficient on the log-odds scale with probability calculations and model evaluation. section 14.6.2
