Q {pairwise}

Person Fit Index Q

Description

function for calculating the person fit index Q, which was proposed by Tarnai and Rost (1990).

Usage

Q(obj = NULL, data = NULL, threshold = NULL, ...)

Arguments

obj

an object of class "pers" or class "pair"as a result from function pers or pair respectively.

data

optional response data when object of class "pers" or class "pair" is not provided.

threshold

optional in case that object of class "pers" or class "pair" is not provided. Threshold values as matrix with row and columnnames !! – items as rows and thresholds as columns. Thresholds should be ordered from left to right, some items may have less thresholds than the others, in this case the respective row/column is filled with an NA value - see examples.

...

not used so far.

Details

The person Q-index proposed by Tarnai and Rost, (1990) is solely based on the empirical responses and the item parameters. Thus the computation of person parameters using the function pers is not required - see examples. But for convenience return objects of both functions are accepted in function Q.

Value

a vector holding the Q-index for every person.

References

Tarnai, C., & Rost, J. (1990). Identifying aberrant response patterns in the Rasch model: the Q index. Münster: ISF.

Examples

#######################
data(bfiN) # get some data
ip <- pair(daten = bfiN,m = 6) # item parameters according the partial credit model
Q(ip)

### with data an thresholds as external objects #####
threshold <- matrix(seq(-3,3,length.out = 9),ncol = 3)
dimnames(threshold) <- list(c("I1","I2","I3"),c("1","2","2"))
threshold
resp_vec <- c(3,0,2,1,2,2,2,2,1,3,0,NA,NA,0,2,3,NA,2,NA,2,1,2,NA,1,2,2,NA)
resp_emp <- matrix(resp_vec,ncol = 3,byrow = TRUE)
colnames(resp_emp) <- c("I1","I2","I3")
resp_emp
Qindex <- Q(data = resp_emp,threshold = threshold)
cbind(resp_emp,Qindex)

#### unequal number of thresholds ###################
threshold <- matrix(seq(-3,3,length.out = 9),ncol = 3)
dimnames(threshold) <- list(c("I1","I2","I3"),c("1","2","2"))
threshold[2,3] <- NA

resp_vec <- c(3,0,2,1,2,2,2,2,1,3,0,NA,NA,0,2,3,NA,2,NA,2,1,2,NA,1,2,2,NA)
resp_emp <- matrix(resp_vec,ncol = 3,byrow = TRUE)
colnames(resp_emp) <- c("I1","I2","I3")
resp_emp
Qindex <- Q(data = resp_emp,threshold = threshold)
cbind(resp_emp,Qindex)