To facilitate construction of confidence intervals, it is common to transform parameters. Delta method can he used to derive the approximate variance in that case. Here is the general theory for logarithmic transformed parameters:
Similarly, other transformations can be used. Other than logarithms, complementary log-log also has some advantages.
Some of these popular transformations are implemented in R:
Similarly, other transformations can be used. Other than logarithms, complementary log-log also has some advantages.
Some of these popular transformations are implemented in R:
> N = 28 > x= 17 > p = x/N > library("binom") > binom.confint(x, N, conf.level=0.95, methods="agresti-coull") method x n mean lower upper 1 agresti-coull 17 28 0.6071429 0.4236592 0.7647744 > binom.confint(x, N, conf.level=0.95, methods="wilson") method x n mean lower upper 1 wilson 17 28 0.6071429 0.4240904 0.7643431 > binom.confint(x, N, conf.level=0.95, methods="bayes") method x n mean lower upper 1 bayes 17 28 0.6034483 0.4230935 0.7702817 > binom.bayes(x, N, conf.level=0.95) method x n shape1 shape2 mean lower upper sig 1 bayes 17 28 17.5 11.5 0.6034483 0.4230935 0.7702817 0.05 > binom.confint(x, N, conf.level=0.95, methods="logit") method x n mean lower upper 1 logit 17 28 0.6071429 0.4199214 0.7674079 > binom.confint(x, N, conf.level=0.95, methods="cloglog") method x n mean lower upper 1 cloglog 17 28 0.6071429 0.4038994 0.7598402 > binom.confint(x, N, conf.level=0.95, methods="probit") method x n mean lower upper 1 probit 17 28 0.6071429 0.4212743 0.7710758 > binom.confint(x, N, conf.level=0.95, methods="profile") method x n mean lower upper 1 profile 17 28 0.6071429 0.4227475 0.7727057 |
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