R: Confidence intervals for proportions

svyciprop {survey} | R Documentation

## 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"), 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 `"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.

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.

### 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")

    ## 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")

[Package survey version 3.32-1 Index]