Wald statistic and confidence interval for logistic-regression coefficients

Source: Hedderich, Sachs and Reynarowych, Applied Statistics: Methods Using R, section 8.4, printed pages 829-830, equations (8.56) and (8.57): beta_i +/- z_{1-alpha/2} se(beta_i) and W = beta_i / se(beta_i). W is asymptotically standard normal under H0: beta_i = 0, so the two-sided p-value is 2 (1 - Phi(abs(W))).

Usage

Lrwald(beta, se, level = 0.95, alpha = 0.05)

Arguments

beta: Estimated coefficients.
se: Their standard errors; positive, same length as beta.
level: Confidence level for the interval (8.56).
alpha: Significance level for the per-coefficient decision.

Value

list: beta, se, z, pvalue, ci_low, ci_high, reject, level, alpha.

Details

BOOK ERRATUM, confirmed by re-running the fit: the R input block printed on page 829 lists t and d vectors that do not pair up – fitting the printed vectors gives beta0 = 23.775, beta1 = -0.3667, not the values in the printed output. The printed output on the same page is nevertheless the correct Challenger O-ring logistic fit (beta0 = 15.0429, se 7.3786, z 2.039; beta1 = -0.2322, se 0.1082, z -2.145, p 0.0415 / 0.0320). The printed output is used as the anchor; the printed input vectors are not.

Examples

Lrwald(c(15.0429, -0.2322), c(7.3786, 0.1082))$z
#> [1]  2.038720 -2.146026