Inference for the Analysis of Ordinal Data with Spatio-Temporal Models

Area of Science:

• Agricultural Science
• Epidemiology
• Statistical Modeling

Background:

• Understanding plant disease dissemination is crucial for crop management.
• Existing models may not fully capture spatio-temporal dynamics of ordinal disease observations.
• Previous studies highlight the need for robust prediction tools in plant pathology.

Purpose of the Study:

• To propose a new spatio-temporal Markovian-like model for ordinal plant disease data.
• To establish conditions for the existence, uniqueness, and statistical properties of the model's parameters.
• To develop methods for testing spatial and spat-temporal dependencies in disease spread.

Main Methods:

• Construction of a logistic distribution-based spatio-temporal model for ordinal data.
• Establishment of conditions for Maximum Likelihood Estimator (MLE) existence and uniqueness.
• Application of Partially Ordered Markov Models (POMMs) for MLE consistency and asymptotic normality.
• Development of hypothesis testing methods based on asymptotic normality.

Main Results:

• The proposed model effectively predicts disease spread in a grid of plants.
• Conditions for the statistical validity of the model parameters were established.
• The Maximum Likelihood Estimator (MLE) was shown to be consistent and normally asymptotic under specific conditions.
• New methods for testing spatial and spat-temporal dependencies were proposed.

Conclusions:

• The developed model provides a robust framework for analyzing and predicting ordinal plant disease spread.
• The statistical properties of the MLE ensure reliable parameter estimation and hypothesis testing.
• The prediction maps generated offer valuable insights into disease transmission patterns, aiding in agricultural management.