The odds ratio is provided only if you select the logit link function for a model with a binary response. In this case, the odds ratio is useful in interpreting the relationship between a predictor and a response.
The odds ratio (τ) can be any nonnegative number. The odds ratio = 1 serves as the baseline for comparison. If τ = 1, no association exists between the response and predictor. If τ < 1, the odds of the event are higher for the reference level of the factor (or for lower levels of a continuous predictor). If τ > 1, the odds of the event are less for the reference level of the factor (or for lower levels of a continuous predictor). Values farther from 1 represent stronger degrees of association.
For the binary logistic regression model with one covariate or factor, the estimated odds of success are:
The exponential relationship provides an interpretation for β: The odds increase multiplicatively by eβ1 for every one-unit increase in x. The odds ratio is equivalent to exp(β1).
For example, if β is .75, the odd ratio is exp(.75), which is 2.11. This indicates that there is a 111% increase in the odds of success for every one unit increase in x.
| ||the estimated probability of a success for the ith row in the data|
|the estimated intercept coefficient|
|the estimated coefficient for predictor x|
|the data point for the ith row|