sirt: tetrachoric2 – R documentation

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tetrachoric2

Tetrachoric Correlation Matrix

Description

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

Author(s)

Alexander Robitzsch

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

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

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

sirt

Supplementary Item Response Theory Models

v3.10-118

GPL (>= 2)

Authors

Alexander Robitzsch [aut,cre] (<https://orcid.org/0000-0002-8226-3132>)

Initial release

2021-09-22 17:45:34