3.14 The multivariate normal model for joint attribute distribution

The multivariate normal model is also referred to as unstructured tetrachoric model (Maris, 1999). This model assumes that attributes are generated from underlying continuous variables, which are usually assumed to be normally distributed.

Parameters in a multivariate normal model include \(K\) threshold parameters and \(\frac{K(K-1)}{2}\) tetrachoric correlation coefficients.

An example

What are the joint probabilities of two attributes in the following table under a multivariate normal model?

References

Maris, E. (1999). Estimating multiple classification latent class models. Psychometrika, 64(2), 187–212. https://doi.org/10.1007/bf02294535