Odds ratio over a fixed interval of an interval-scaled predictor

Source: Hedderich, Sachs and Reynarowych, Applied Statistics: Methods Using R, section 8.4.4, printed page 834, equation (8.63): log psi(a, b) = beta1 (b - a), so psi(a, b) = exp(beta1 (b - a)). The intercept cancels, so the odds ratio for moving the predictor from a to b depends on beta1 and the span alone.

Usage

Logor(beta1, a = 0, b = 1, se = NULL, level = 0.95)

Arguments

beta1

Logistic-regression slope on the logit scale.

a, b

Endpoints of the interval; the default gives exp(beta1).

se

Optional standard error of beta1; enables the Wald interval.

level

Confidence level, strictly inside (0, 1).

Value

list: or, logor, span, and with se also se_logor, ci_low, ci_high, level.

Details

A Wald interval is supplied when se is given: the log odds ratio is beta1 (b - a) with standard error abs(b - a) se(beta1), which is (8.56) transported through the same linear map.

Book worked example, same page: from the Challenger data the book estimates beta1 = -0.2322; a temperature rise of 10 degF gives psi(10) = exp(-2.322) = 0.098 and a drop of 10 degF gives psi(-10) = exp(2.322) = 10.2.

Examples

Logor(-0.2322, 0, 10)$or
#> [1] 0.09807723