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Journal of Applied Mathematics and Computation

DOI：http://dx.doi.org/10.26855/jamc.2023.03.020

# Effects of Zero Observations on Modelling Categorical Data

Tong Wang*, Wentao Li, Jing Ruan

Wenzhou Polytechnic, Wenzhou, Zhejiang, China.

*Corresponding author: Tong Wang

Date: May 6,2023　Hits: 702

### Abstract

We study the maximum likelihood estimate by using the numerical method Newton Raphson under the Poisson sampling conditions. Log-linear model and logistic model are introduced here, where we both analyze the Independent model and Saturated model for the following studies. Two kinds of zero observations are considered when a model is fitting using MLE, they are sampling zeros and structure zeros. Take two-way contingency table for example, we obtain the correspondence from log-linear model to logistic model when zero entries a contingency table. Each term in a logistic regression model can correspond one term in log-linear model. We study the relationships between those terms through the standard errors in the presence of sampling zeros. We conclude that it is the numbers and positions of zeros that matters when it comes to the effects of zero observations. As for these problems, we analyze the reasons and proposed some useful suggestion to this.

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### Full-Text HTML

Effects of Zero Observations on Modelling Categorical Data

How to cite this paper: Tong Wang, Wentao Li, Jing Ruan. (2023) Effects of Zero Observations on Modelling Categorical Data. Journal of Applied Mathematics and Computation7(1), 177-187.

DOI: http://dx.doi.org/10.26855/jamc.2023.03.020