rfa {pairwise}

Rasch Residual Factor Analysis

Description

Calculation of the rasch residual factor analysis proposed by Wright (1996) and further discussed by Linacre (1998) to detect multidimensionality.

Usage

rfa(
  pers_obj,
  na_treat = 0,
  tr = FALSE,
  use = "complete.obs",
  res = "stdr",
  method = "pearson",
  cor = TRUE
)

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.

tr

a logical value indicating whether the data (the residual matrix) is transposed prior to calculation. This would perform a person analysis rather than a item analysis. The default is set to item analysis.

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 covariances or 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 or cov, indicating which correlation coefficient (or covariance) is to be computed. One of "pearson" (default), "kendall", or "spearman", can be abbreviated. The default is set to method="pearson".

cor

a logical value indicating whether the calculation should use the correlation matrix or the covariance matrix.The default is set to cor=TRUE to use the correlation matrix.

Details

no details in the moment.

Value

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

References

Wright, B. D. (1996). Comparing Rasch measurement and factor analysis. Structural Equation Modeling: A Multidisciplinary Journal, 3(1), 3–24.

Linacre, J. M. (1998). Detecting multidimensionality: which residual data-type works best? Journal of outcome measurement, 2, 266–283.

Examples

######################
########
data(bfiN) # loading reponse data
pers_obj <- pers(pair(bfiN))
result <- rfa(pers_obj)
summary(result)
plot(result)
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