# Person Fit Index Q function for calculating the person fit index Q, which was proposed by Tarnai and Rost (1990). ```r 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. ## Returns a vector holding the Q-index for every person. ## 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`. ## Examples ```r ####################### 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) ``` ## References Tarnai, C., & Rost, J. (1990). **Identifying aberrant response patterns in the Rasch model: the Q index**. Münster: ISF.