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Tetrachoric Correlation Matrix

tetrachoric2.Rd

This function estimates a tetrachoric correlation matrix according to the maximum likelihood estimation of Olsson (Olsson, 1979; method="Ol"), the Tucker method (Method 2 of Froemel, 1971; method="Tu") and Divgi (1979, method="Di"). In addition, an alternative non-iterative approximation of Bonett and Price (2005; method="Bo") is provided.

Usage

tetrachoric2(dat, method="Ol", delta=0.007, maxit=1000000, cor.smooth=TRUE,
   progress=TRUE)

Arguments

dat

A data frame of dichotomous response

method

Computation method for calculating the tetrachoric correlation. The ML method is method="Ol" (which is the default), the Tucker method is method="Tu", the Divgi method is method="Di" the method of Bonett and Price (2005) is method="Bo".

delta

The step parameter. It is set by default to \(2^{-7}\) which is approximately .007.

maxit

Maximum number of iterations.

cor.smooth

Should smoothing of the tetrachoric correlation matrix be performed to ensure positive definiteness? Choosing cor.smooth=TRUE, the function cor.smooth from the psych package is used for obtaining a positive definite tetrachoric correlation matrix.

progress

Display progress? Default is TRUE.

Value

A list with following entries

tau

Item thresholds

rho

Tetrachoric correlation matrix

References

Bonett, D. G., & Price, R. M. (2005). Inferential methods for the tetrachoric correlation coefficient. Journal of Educational and Behavioral Statistics, 30(2), 213-225. doi:10.3102/10769986030002213

Divgi, D. R. (1979). Calculation of the tetrachoric correlation coefficient. Psychometrika, 44(2), 169-172. doi:10.1007/BF02293968

Froemel, E. C. (1971). A comparison of computer routines for the calculation of the tetrachoric correlation coefficient. Psychometrika, 36(2), 165-174. doi:10.1007/BF02291396

Olsson, U. (1979). Maximum likelihood estimation of the polychoric correlation coefficient. Psychometrika, 44(4), 443-460. doi:10.1007/BF02296207

Author

Alexander Robitzsch

The code is adapted from an R script of Cengiz Zopluoglu. See http://sites.education.miami.edu/zopluoglu/software-programs/.

See also

See also the psych::tetrachoric function in the psych package and the function irtoys::tet in the irtoys package.

See polychoric2 for estimating polychoric correlations.

Examples

#############################################################################
# EXAMPLE 1: data.read
#############################################################################

data(data.read)

# tetrachoric correlation from psych package
library(psych)
t0 <- psych::tetrachoric( data.read )$rho
# Olsson method (maximum likelihood estimation)
t1 <- sirt::tetrachoric2( data.read )$rho
# Divgi method
t2 <- sirt::tetrachoric2( data.read, method="Di"  )$rho
# Tucker method
t3 <- sirt::tetrachoric2( data.read, method="Tu" )$rho
# Bonett method
t4 <- sirt::tetrachoric2( data.read, method="Bo" )$rho

# maximum absolute deviation ML method
max( abs( t0 - t1 ) )
  ##   [1] 0.008224986
# mean absolute deviation Divgi method
max( abs( t0 - t2 ) )
  ##   [1] 0.1766688
# mean absolute deviation Tucker method
max( abs( t0 - t3 ) )
  ##   [1] 0.1766292
# mean absolute deviation Bonett method
max( abs( t0 - t4 ) )
  ##   [1] 0.05695522