Confidence intervals for misskappa coefficients

Wald or exact-delete-one jackknife confidence intervals for a `misskappa_estimate`. Wald intervals use the estimator covariance and a normal critical value. Jackknife intervals transform every complete-data leave-one-subject-out estimate directly, use the ordinary delete-one jackknife standard error, and use a Student t critical value with `n - 1` degrees of freedom.

Besides the natural and Fisher scales, `transform = "log_complement"` uses the upper-bound-only transform `-log(1 - theta)`. It remains defined for alpha values below -1. At an exact kappa boundary, a degenerate transformed jackknife is replaced by a one-sided hybrid: a Clopper–Pearson upper limit for the probability of any item disagreement is divided by a delete-one t lower limit for chance disagreement. Alpha has no corresponding binomial item event, so an exact-boundary alpha interval is returned as `NA`.

Usage

# S3 method for class 'misskappa_estimate'
confint(
  object,
  parm = NULL,
  level = 0.95,
  method = c("wald", "jackknife"),
  transform = c("none", "fisher", "log_complement"),
  ...
)

Arguments

object

A `misskappa_estimate` object.

parm

Optional subset of coefficients (names or indices), defaults to all.

level

Confidence level.

method

Either `"wald"` or `"jackknife"`. Exact delete-one summaries are attached automatically to supported complete-data kappa and alpha fits with at least three subjects.

transform

One of `"none"`, `"fisher"`, or `"log_complement"`. Wald uses a delta-method standard error on the selected scale; jackknife transforms the exact delete-one estimates directly.

...

Unused, present for S3 generic conformance.

Value

A two-column numeric matrix of lower and upper limits, one row per coefficient.

References

Efron, B., and Tibshirani, R. J. (1993). *An Introduction to the Bootstrap*. Chapman and Hall, Chapter 11.

Clopper, C. J., and Pearson, E. S. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. *Biometrika*, 26(4), 404–413. doi:10.1093/biomet/26.4.404 .

Examples

fit <- kappa(dat.gwet2014, estimator = "ipw")
#> Warning: rater pair(s) rater4-rater5 co-observed by only one subject; the corresponding pairwise covariance is degenerate and the standard error unreliable.
confint(fit)                       # natural-scale Wald interval
#>                      2.5 %    97.5 %
#> Conger           0.2040066 0.6426036
#> Fleiss           0.1966366 0.6399174
#> Brennan-Prediger 0.2045079 0.6797335
#> attr(,"method")
#> [1] "wald"
#> attr(,"transform")
#> [1] "none"
#> attr(,"boundary_fallback")
#>           Conger           Fleiss Brennan-Prediger 
#>            FALSE            FALSE            FALSE 
confint(fit, transform = "fisher") # Fisher z interval, always within (-1, 1)
#>                      2.5 %    97.5 %
#> Conger           0.1824728 0.6162177
#> Fleiss           0.1751369 0.6133302
#> Brennan-Prediger 0.1776159 0.6470501
#> attr(,"method")
#> [1] "wald"
#> attr(,"transform")
#> [1] "fisher"
#> attr(,"boundary_fallback")
#>           Conger           Fleiss Brennan-Prediger 
#>            FALSE            FALSE            FALSE 
complete_fit <- kappa_counts(dat.fleiss1971)
confint(complete_fit, method = "jackknife", transform = "fisher")
#>                      2.5 %    97.5 %
#> Fleiss           0.3117814 0.5355365
#> Brennan-Prediger 0.3255388 0.5495116
#> attr(,"method")
#> [1] "jackknife"
#> attr(,"transform")
#> [1] "fisher"
#> attr(,"boundary_fallback")
#>           Fleiss Brennan-Prediger 
#>            FALSE            FALSE