Zero inflation in ordinal data: Incorporating susceptibility to response through the use of a mixture model

Abstract

The aim of this paper is to produce a methodology that will allow users of ordinal scale data to more accurately model the distribution of ordinal outcomes in which some subjects are susceptible to exhibiting the response and some are not (i.e. the dependent variable exhibits zero inflation). This situation occurs with ordinal scales in which there is an anchor that represents the absence of the symptom or activity, such as 'none', 'never' or 'normal,' and is particularly common when measuring abnormal behavior, symptoms, and side effects. Due to the unusually large number of zeros, traditional statistical tests of association can be non-informative. We propose a mixture model for ordinal data with a built-in probability of non-response, which allows modeling of the range (e.g. severity) of the scale, while simultaneously modeling the presence/absence of the symptom. Simulations show that the model is well behaved and a likelihood ratio test can be used to choose between the zero-inflated and the traditional proportional odds model. The model, however, does have minor restrictions on the nature of the covariates that must be satisfied in order for the model to be identifiable. The method is particularly relevant for public health research such as large epidemiological surveys where more careful documentation of the reasons for response may be difficult.