psych (version 1.0-90)

tetra: Tetrachoric correlations from various types of input

Description

The tetrachoric correlation is the estimate of a Pearson Correlation from a two x two table with the assumption of bivariate normality. Particularly important when doing Item Response Theory or converting comorbidity statistics normal theory correlations. Input may be a 2 x 2 table of cell frequencies, a vector of cell frequencies, or a data.frame or matrix of dichotomous data.

Usage

tetrachor(x,correct=TRUE)

Arguments

x

The input may be in one of four forms: a)a data frame or matrix of dichotmous data (e.g., the lsat6 from the bock data set)

b)a 2 x 2 table of cell counts or cell frequencies

c) a vector with elements corresponding to the four cell frequencies

d) a

correct

Correct for continuity in the case of zero entry cell

Value

• rho
  The (matrix) of tetrachoric correlations
• tau
  The normal equivalent of the cutpoints

Details

Tetrachoric correlations convert a two x two table of frequencies to a Pearson correlation with the assumption of bivariate normality. The estimation procedure is two stage ML. Cells with zero counts are replaced with .5 as a correction for continuity.

The tetrachoric correlation is used in a variety of contexts, one important one being in Item Response Theory (IRT) analyses of test scores, a second in the conversion of comorbity statistics to correlation coefficients. It is in this second context that examples of the sensitivity of the coefficient to the cell frequencies becomes apparent:

Consider the test data set from Kirk (1973) who reports the effectiveness of a ML algorithm for the tetrachoric correlation (see examples).

Examples include the lsat6 and lsat7 data sets in the bock data.

References

A. Gunther and M. Hofler. Different results on tetrachorical correlations in mplus and stata-stata announces modified procedure. Int J Methods Psychiatr Res, 15(3):157-66, 2006.

David Kirk (1973) On the numerical approximation of the bivariate normal (tetrachoric) correlation coefficient. Psychometrika, 38, 259-268.

See Also

See also the polychor function in the polycor package.

Examples

if(require(mvtnorm)) {
data(bock)
tetrachor(lsat6)
tetrachor(matrix(c(44268,193,14,0),2,2))  #MPLUS reports.24
tetrachor(matrix(c(61661,1610,85,20),2,2)) #Mplus reports .35
tetrachor(matrix(c(62503,105,768,0),2,2)) #Mplus reports -.10
tetrachor(matrix(c(24875,265,47,0),2,2)) #Mplus reports  0
tetrachor(c(0.02275000, 0.0227501320, 0.500000000))
tetrachor(c(0.0227501320, 0.0227501320, 0.500000000)) } else {message("Sorry, you must have mvtnorm installed")}