q3 {pairwise}

Q3 Fit Statistic

Description

Calculation of Q3 fit statistic for the rasch model based on the residuals, which was proposed by Yen (1984).

Usage

q3(
  pers_obj,
  na_treat = 0,
  use = "complete.obs",
  res = "stdr",
  method = "pearson"
)

Arguments

pers_obj

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

na_treat

value to be assigned to residual cells which have missing data in the original response matrix. default is set to na_treat=0 to set the residuals to 0, which implys that they are imputed as 'fitting data', i.e., zero residuals. This can attenuate contrasts (see. http://www.rasch.org/rmt/rmt142m.htm). An option is to set it to na_treat=NA.

use

a character string as used in function cor or cov, giving a method for computing covariances or correlations in the presence of missing values. This must be (an abbreviation of) one of the strings "everything", "all.obs", "complete.obs", "na.or.complete", or "pairwise.complete.obs". The default is set to use="complete.obs" which will exclude cases by listwise deletion to keep the correlation matrix positive definit.

res

a character string defining which type of (rasch–) residual to analyze when computing the correlations. This must be (exactly) one of the strings "sr" for score residuals , "stdr" for standardised residuals, "srsq" for score residuals squared, or "stdrsq" for standardised residuals squared. The default is set to res="stdr" refering to Linacre (1998).

method

a character string as used in function cor, indicating which correlation coefficient is to be computed. One of "pearson" (default), "kendall", or "spearman", can be abbreviated. The default is set to method="pearson".

Details

The lower level letter 'q' was used (intead of 'Q') for naming the function because the name 'Q3' was already used in another IRT package – namly TAM. As perhaps some users like to use both packages simultaniously, an alternative naming convention was choosen for 'pairwise'. No other details in the moment.

Value

An object of class c("Q3","list").

References

Yen, W. M. (1984). Effects of Local Item Dependence on the Fit and Equating Performance of the Three-Parameter Logistic Model. Applied Psychological Measurement, 8(2), 125–145. https://doi.org/10.1177/014662168400800201

Examples

######################
########
data(bfiN) # loading reponse data
pers_obj <- pers(pair(bfiN))
result <- q3(pers_obj)
str(result) # to see whats in ;-)
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