Clustering of log-linear models using LRT p-values to assess homogeneous regions relative to drought class transitions

Abstract

In this study, a statistical method is used aiming at finding if Alentejo, southern Portugal, could be considered a homogeneous region for drought management purposes. Time series of the standardized precipitation index (SPI) were obtained for 40 locations in the region using precipitation data for the period 1932–1999 (67 years). Contingency tables for the transitions between SPI drought classes were obtained for these time series. Log-linear models were fitted to these contingency tables to estimate the probabilities for drought class transitions. An approach of model clustering, where log-linear models were clustered using the asymptotic p-value of a likelihood ratio test (LRT) for the equality of parameters between pairs of models, was applied. Two types of LRT were performed: one considering all the parameters of the log-linear model of interest; another considering just some parameters of interest. Two p-value similarity matrices were computed to find similar models that could form clusters, however, the hypothesis of model clustering was not verified. No clustering was found, thus based on the presented technique, the Alentejo could be considered a homogeneous region relative to drought class transitions.

Keywords:

• log-linear models
• likelihood ratio test
• model clustering
• asymptotic p-value

AMS Subject Classification:

• 62F03
• 62F05
• 62H17
• 62H30
• 62H11
• 62P12

Acknowledgements

This work was partially supported by the research project PTDC/AGR-AAM/71649/2006 - Droughts Risk Management: Identification, Monitoring, Characterization, Prediction and Mitigation and by CMA/FCT/UNL under the project PEst-OE/MAT/UI0297/2011.