Bivariate categorical data analysis using normal linear conditional multinomial probability model

Area of Science:

• Statistics
• Biostatistics
• Ophthalmology

Background:

• Bivariate multinomial data analysis often relies on complex joint probability or odds ratio models.
• Existing methods present challenges in parameter interpretation and correlation analysis between categorical variables.

Purpose of the Study:

• To develop a novel bivariate linear conditional multinomial probability model.
• To enhance the understanding of correlations between two categorical variables, using pre-specified marginal probabilities.

Main Methods:

• Development of a bivariate normal type linear conditional multinomial probability model.
• Consistent parameter estimation via optimal likelihood and generalized quasi-likelihood approaches.

Main Results:

• The proposed model facilitates a more straightforward interpretation of correlations between categorical variables.
• The model's efficacy was demonstrated through simulation studies and real-world data analysis.

Conclusions:

• The new bivariate model offers an effective alternative for analyzing categorical data, particularly in ophthalmological contexts.
• This approach provides improved interpretability of inter-variable correlations compared to traditional methods.