A joint model of correlated ordinal and continuous variables

TL;DR

This paper introduces a joint modeling approach for binary, ordinal, and continuous data types using multivariate normal errors, with estimation via composite likelihood and practical implementation in an R package, demonstrated through risk management case studies.

Contribution

It develops a novel joint model for mixed response types with estimation methods and provides an R package for practical application, advancing analysis of correlated mixed data.

Findings

Effective modeling of mixed response data in risk management.

Implementation of composite likelihood for parameter estimation.

Availability of an R package for practical use.

Abstract

In this paper we build a joint model which can accommodate for binary, ordinal and continuous responses, by assuming that the errors of the continuous variables and the errors underlying the ordinal and binary outcomes follow a multivariate normal distribution. We employ composite likelihood methods to estimate the model parameters and use composite likelihood inference for model comparison and uncertainty quantification. The complimentary R package mvordnorm implements estimation of this model using composite likelihood methods and is available for download from Github. We present two use-cases in the area of risk management to illustrate our approach.