# rank.wald: Rank Responses based on the Wald Test In RankResponse: Ranking Responses in a Single Response Question or a Multiple Response Question

 rank.wald 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 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').

### Details

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

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

If `ranktype` is 2, the rank of the ith response can be defined as

R_{i} = k - ∑_{j=1, j\ne i}^{k} I(π_{i} > π_{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.

`rankL2R`, `rankLN`, `rank.gs`

### 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)

```

RankResponse documentation built on May 11, 2022, 5:18 p.m.