rank.wald {RankResponse} | R Documentation |
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 |
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'). |
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})
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.
Author(s)
Hsiuying Wang wang@stat.nycu.edu.tw , Wan-Ting Huang wthuang.sc09@nycu.edu.tw , Yu-Chun Lin restart79610@hotmail.com
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
Examples
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)