MultinomCI: Confidence Intervals for Multinomial Proportions

Description

Confidence intervals for multinomial proportions are often approximated by single binomial confidence intervals, which might in practice often yield satisfying results, but is properly speaking not correct. This function calculates simultaneous confidence intervals for multinomial proportions either according to the method of Sison and Glaz or according to Goodman's method.

Usage

MultinomCI(x, conf.level = 0.95, method = c("sisonglaz", "cplus1", "goodman"))

Arguments

A vector of positive integers representing the number of occurrences of each class. The total number of samples equals the sum of such elements.

conf.level

confidence level, defaults to 0.95.

method

character string specifing which method to use; can be one out of "sisonglaz", "cplus1", "goodman". Method can be abbreviated. See details. Defaults to "sisonglaz".

Value

A matrix with 3 columns:
estestimate
lwr.cilower bound of the confidence interval
upr.ciupper bound of the confidence interval
The number of rows correspond to the dimension of x.

Details

Given a vector of observations with the number of samples falling in each class of a multinomial distribution, builds the simultaneous confidence intervals for the multinomial probabilities according to the method proposed by Sison and Glaz (1995). The R code has been translated from the SAS code written by May and Johnson (2000).

References

Sison, C.P and Glaz, J. (1995) Simultaneous confidence intervals and sample size determination for multinomial proportions. Journal of the American Statistical Association, 90:366-369. http://tx.liberal.ntu.edu.tw/~purplewoo/Literature/!Methodology/!Distribution_SampleSize/SimultConfidIntervJASA.pdf Glaz, J., Sison, C.P. (1999) Simultaneous confidence intervals for multinomial proportions. Journal of Statistical Planning and Inference 82:251-262. May, W.L., Johnson, W.D.(2000) Constructing two-sided simultaneous confidence intervals for multinomial proportions for small counts in a large number of cells. Journal of Statistical Software 5(6) . Paper and code available at http://www.jstatsoft.org/v05/i06. Goodman, L. A. (1965) On Simultaneous Confidence Intervals for Multinomial Proportions Technometrics, 7, 247-254.

Examples

Run this code

# Multinomial distribution with 3 classes, from which a sample of 79 elements 
# were drawn: 23 of them belong to the first class, 12 to the 
# second class and 44 to the third class. Punctual estimations 
# of the probabilities from this sample would be 23/79, 12/79 
# and 44/79 but we want to build 95% simultaneous confidence intervals 
# for the true probabilities

MultinomCI(c(23, 12, 44), conf.level=0.95)


x <- c(35, 74, 22, 69)

MultinomCI(x, method="goodman")
MultinomCI(x, method="sisonglaz")
MultinomCI(x, method="cplus1")

# compare to
BinomCI(x, n=sum(x))

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