Tetrachoric Correlation is superior to the phi coefficient as a measure of the relation of an item pair. See Divgi, 1979; Olsson, 1979;Harris, 1988.
tetrachoric(x, y)
Returns a single numeric value of class "exametrika" representing the tetrachoric correlation coefficient between the two binary variables. The value ranges from -1 to 1, where:
1 indicates perfect positive correlation
-1 indicates perfect negative correlation
0 indicates no correlation
binary vector x
binary vector y
Divgi, D. R. (1979). Calculation of the tetrachoric correlation coefficient. Psychometrika, 44, 169–172.
Olsson, U. (1979). Maximum likelihood estimation of the polychoric correlation coefficient. Psychometrika,44, 443–460.
Harris, B. (1988). Tetrachoric correlation coefficient. In L. Kotz, & N. L. Johnson (Eds.), Encyclopedia of statistical sciences (Vol. 9, pp. 223–225). Wiley.