svyciprop: Confidence intervals for proportions

In survey: Analysis of Complex Survey Samples

Confidence intervals for proportions

Description

Computes confidence intervals for proportions using methods that may be more accurate near 0 and 1 than simply using confint(svymean()).

Usage

svyciprop(formula, design, 
  method = c("logit", "likelihood", "asin", "beta","mean","xlogit","wilson"), 
  level = 0.95, df=degf(design),...)

Arguments

formula	Model formula specifying a single binary variable
design	survey design object
method	See Details below. Partial matching is done on the argument.
level	Confidence level for interval
df	denominator degrees of freedom, for all methods except "beta". Use Inf for confidence intervals based on a Normal distribution, and for "likelihood" and "logit" use NULL for the default method in glms (currently degf(design)-1, but this may be improved in the future)
...	For "mean" and "asin", this is passed to confint.svystat

Details

The "logit" method fits a logistic regression model and computes a Wald-type interval on the log-odds scale, which is then transformed to the probability scale.

The "likelihood" method uses the (Rao-Scott) scaled chi-squared distribution for the loglikelihood from a binomial distribution.

The "asin" method uses the variance-stabilising transformation for the binomial distribution, the arcsine square root, and then back-transforms the interval to the probability scale

The "beta" method uses the incomplete beta function as in binom.test, with an effective sample size based on the estimated variance of the proportion. (Korn and Graubard, 1998)

The "xlogit" method uses a logit transformation of the mean and then back-transforms to the probablity scale. This appears to be the method used by SUDAAN and SPSS COMPLEX SAMPLES.

The "wilson" method is the Wilson score interval, which inverts the coverage probability statement using the true probability rather than the estimated probability, which results in a quadratic equation for the estimated probability. This interval is contained in [0,1].

The "mean" method is a Wald-type interval on the probability scale, the same as confint(svymean())

All methods undercover for probabilities close enough to zero or one, but "beta", "likelihood", "logit", and "logit" are noticeably better than the other two. None of the methods will work when the observed proportion is exactly 0 or 1.

The confint method extracts the confidence interval; the vcov and SE methods just report the variance or standard error of the mean.

Value

The point estimate of the proportion, with the confidence interval as an attribute

References

Rao, JNK, Scott, AJ (1984) "On Chi-squared Tests For Multiway Contingency Tables with Proportions Estimated From Survey Data" Annals of Statistics 12:46-60. https://doi.org/10.1214/AOS/1176346391

Korn EL, Graubard BI. (1998) Confidence Intervals For Proportions With Small Expected Number of Positive Counts Estimated From Survey Data. Survey Methodology 23:193-201. https://www150.statcan.gc.ca/n1/pub/12-001-x/1998002/article/4356-eng.pdf

Dean, N., and Pagano, M. (2015) Evaluating Confidence Interval Methods for Binomial Proportions in Clustered Surveys. Journal of Survey Statistics and Methodology, 3 (4), 484-503. https://doi.org/10.1093/jssam/smv024

See Also

svymean, yrbs

Examples

data(api)
dclus1<-svydesign(id=~dnum, fpc=~fpc, data=apiclus1)

svyciprop(~I(ell==0), dclus1, method="li")
svyciprop(~I(ell==0), dclus1, method="lo")
svyciprop(~I(ell==0), dclus1, method="as")
svyciprop(~I(ell==0), dclus1, method="be")
svyciprop(~I(ell==0), dclus1, method="me")
svyciprop(~I(ell==0), dclus1, method="xl")
svyciprop(~I(ell==0), dclus1, method="wi")

## reproduces Stata svy: mean
svyciprop(~I(ell==0), dclus1, method="me", df=degf(dclus1))
## reproduces Stata svy: prop
svyciprop(~I(ell==0), dclus1, method="lo", df=degf(dclus1))

rclus1<-as.svrepdesign(dclus1)
svyciprop(~I(emer==0), rclus1, method="li")
svyciprop(~I(emer==0), rclus1, method="lo")
svyciprop(~I(emer==0), rclus1, method="as")
svyciprop(~I(emer==0), rclus1, method="be")
svyciprop(~I(emer==0), rclus1, method="me")
svyciprop(~I(emer==0), rclus1, method="wi")

survey documentation built on Aug. 28, 2024, 3 a.m.