Generating ordinal data

In the recent years, a great interest has been devoted by researchers to categorical data and the related statistical methods employed for their joint analysis. Specifically in explorative analysis, the robustness and performance of these techniques can be assessed almost exclusively through simulation studies, which require to generate a huge number of datasets, according to some experimental conditions. A general method for obtaining data with a desired pattern is proposed by Cario and Nelson (1997) and it is called NORTA (NORmal To Anything). This method produces random vectors with fixed marginal distributions and correlation matrix starting from a standard multivariate normal. This method has been extended by Stanhope (2004), trying to overcome some practical drawbacks. With regard, more properly, to ordinal data, Demirtas (2009) proposes a method for generating multivariate ordinal data given marginal distribution and correlation matrix RORD . His technique first generates binary data by collapsing the corresponding ordinal categories and then, through an iterative procedure, finds a proper binary correlation matrix RBIN, which assures for the ordinal data the desired correlation structure. Even if very flexible, this method presents some limits. In this paper the focus is on ordinal variables and a simple procedure to obtain multivariate ordinal variables with specified marginal distributions and correlation structure, no longer impaired by previous drawbacks, is proposed and its performance is investigated through a simulation study and two applications