RankResponse (version 4.0.0)

rank.wald: Rank Responses based on the Wald Test

Description

Rank responses of a single response question or a multiple response question by the wald test procedure.

Usage

rank.wald(data, alpha = 0.05, ranktype = 1)

Arguments

data

A m by n matrix \(d_{ij}\), where \(d_{ij}\) = 0 or 1. If the ith respondent selects the jth response, then \(d_{ij}\) = 1, otherwise \(d_{ij}\) = 0.

alpha

The significance level is used to control the type I error rate. The default is 0.05.

ranktype

A numerical value specifies which type of ranking method is used. The default is 1 (see 'Details').

Value

rank.wald returns a table contains the estimated probabilities of the responses being selected in the first line and the ranks of the responses in the second line.

Details

Suppose that the question has k responses. Let \(\pi_{j}\) denote the probability that the jth response is selected. Using the survey data, \(\pi_{j}\) can be estimated.

If ranktype is 1, the ranking rule is the following steps. Let \(\pi_{(j)}\) denote the order statistic. If the hypothesis \(\pi_{(k)}\) = \(\pi_{(k-1)}\) is rejected, we rank the response corresponding to \(\pi_{(k)}\) first. If it is not rejected, we compare \(\pi_{(k)}\) with \(\pi_{(j)}\) , \(j \le k-2\) sequentially.

If ranktype is 2, the rank of the ith response can be defined as $$ R_{i} = k - \sum_{j=1, j\ne i}^{k} I(\pi_{i} > \pi_{j}) $$

References

Wang, H. (2008). Ranking Responses in Multiple-Choice Questions. Journal of Applied Statistics, 35, 465-474.

Wang, H. and Huang, W. H. (2014). Bayesian Ranking Responses in Multiple Response Questions. Journal of the Royal Statistical Society: Series A (Statistics in Society), 177, 191-208.

See Also

rankL2R, rankLN, rank.gs

Examples

# NOT RUN {
set.seed(12345)
# This is an example to rank k responses in a multiple response question
# when the number of respondents is 1000.
# In this example, we do not use a real data, but generate data in the first six lines.
k <- 5
data <- matrix(NA, nrow = 1000, ncol = k)
for(i in 1:k){
  p <- runif(1)
  data[, i] <- sample(c(0, 1), 1000, p = c(p, 1-p), replace = TRUE)
}
## or upload the true data
rank.wald(data)

# }