Build Status AppVeyor Build Status

Codecov test coverage DOI Project Status: Active – The project has reached a stable, usable state and is being actively developed.

An R package for the congeneric normal-ogive model.


The congeneric normal-ogive model (McDonald, R. P., 1997) is a psychometric model for Likert data with one latent factor. This package has functions to estimate such models, calculate their ordinal reliabilities, and make predictions. It implements the concrete ordinal reliabilities of (Moss, 2020).


From inside R, use one of the following commands:



Estimate a congeneric normal-ogive model with congive, predict the value of the latent factor with predict, and calculate the reliability with ordinal_r.

extraversion = psychTools::bfi[c("E1", "E2", "E3", "E4", "E5")]
extraversion[, "E1"] = 7 - extraversion[, "E1"] # Reverse-coded item.
extraversion[, "E2"] = 7 - extraversion[, "E2"] # Reverse-coded item.

object = conogive(extraversion)

ordinal_r(object) # Observed reliability
#> [1] 0.7046056
theoretical_ordinal_r(object) # Theoretical reliability
#> [1] 0.8122607

hist(predict(object, extraversion)) # Plot distribution of predictions.


McDonald, R. P. (1997). Normal-ogive multidimensional model. In W. J. van der Linden & R. K. Hambleton (Eds.), Handbook of Modern Item Response Theory (pp. 257–269). Springer.

Moss, J. (2020). Please avoid the standardized alpha and the ordinal alpha.