Mokken scale analysis uses an automated bottom-up stepwise item selection procedure that suffers from two problems. First, when selected during the procedure items satisfy the scaling conditions but they may fail to do so after the scale has been completed. Second, the procedure is approximate...

We propose a new method to test conditional independence of two real random variables $Y$ and $Z$ conditionally on an arbitrary third random variable $X$. The partial copula is introduced, defined as the joint distribution of $U=F_{Y|X}(Y|X)$ and $V=F_{Z|X}(Z|X)$. We call this transformation of...

A package accompanying the book Marginal Models for Dependent, Clustered, and Longitudinal Categorical Data by Bergsma, Croon, & Hagenaars, 2009. It’s purpose is fitting and testing of marginal models.

The standard two-variable chi-square test is typically consistent for all alternatives to independence, but effectively treats the data as nominal which may lead to loss of power for ordinal data. Alternatively, a test based on Kendall's tau does take ordinality into account, but only has power...

A possible drawback of the ordinary correlation coefficient p for two real random variables X and Y is that zero correlation does not imply independence. In this paper we introduce a new correlation coefficient p* which assumes values between zero and one, equalling zero iff the two variables...

This article discusses how several hypotheses about change in discrete variables can be tested on data obtained in a longitudinal study. A first class of hypotheses pertain to the invariance of certain characteristics of marginal distributions. A second class of hypotheses derive from...