Regression modeling of ordinal data with nonzero baselines
Related Experiment Video
Updated: Aug 11, 2026

Probing the Limits of Egg Recognition Using Egg Rejection Experiments Along Phenotypic Gradients
Published on: August 22, 2018
1National Institute of Statistical Sciences, Research Triangle Park, North Carolina 27709, USA. mxie@stat.rutgers.edu
Abstract:
This paper develops regression models for ordinal data with nonzero control response probabilities. The models are especially useful in dose-response studies where the spontaneous or natural response rate is nonnegligible and the dosage is logarithmic. These models generalize Abbott's formula, which has been commonly used to model binary data with nonzero background observations. We describe a biologically plausible latent structure and develop an EM algorithm for fitting the models. The EM algorithm can be implemented using standard software for ordinal regression. A toxicology data set where the proposed model fits the data but a more conventional model fails is used to illustrate the methodology.
Related Concept Videos
Regression Toward the Mean
Ordinal Level of Measurement
Data measured using an ordinal scale are similar to nominal scale data, but there is one major difference. The ordinal scale data can be ordered. An example of ordinal scale data is a list of the top five national parks in the...
Nominal Level of Measurement
The data that cannot be measured but can be grouped into categories fall under the nominal level of measurement. Data that is measured using a nominal scale is...
Residuals and Least-Squares Property
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
Ranks
Friedman Two-way Analysis of Variance by Ranks

