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Spatial clustering based on geographically weighted multivariate generalized gamma regression.

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Summary
This summary is machine-generated.

This study introduces a new Geographically Weighted Multivariate Generalized Gamma Regression (GWMGGR) model to address spatial heterogeneity in data, overcoming the normality assumption of traditional GWR models.

Keywords:
Educational indicatorsGWMGGRGeographically Weighted Multivariate Generalized Gamma RegressionK-means clusterMaximum likelihood ratio testSpatial heterogeneity

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Area of Science:

  • Spatial statistics
  • Statistical modeling
  • Econometrics

Background:

  • Geographically Weighted Regression (GWR) models spatial heterogeneity but assumes normal errors.
  • Existing GWR models are limited for non-normally distributed data.
  • Multivariate continuous data often exhibit non-normal distributions.

Purpose of the Study:

  • Propose a novel Geographically Weighted Multivariate Generalized Gamma Regression (GWMGGR) model.
  • Extend GWR to handle multivariate generalized gamma distributed responses.
  • Overcome the normality assumption of errors in traditional GWR.

Main Methods:

  • Developed the GWMGGR model for generalized gamma distributed responses.
  • Employed Maximum Likelihood Estimation (MLE) with the BHHH algorithm for parameter estimation.
  • Utilized the Maximum Likelihood Ratio Test (MLRT) for hypothesis testing of spatial effects.
  • Applied k-means clustering for spatial interpretation of model parameters.

Main Results:

  • The GWMGGR model effectively captures spatial heterogeneity for non-normally distributed data.
  • The MLRT confirmed the significance of spatial effects in the proposed model.
  • Spatial clustering revealed distinct patterns in Central Java's educational indicators.

Conclusions:

  • The GWMGGR model offers a flexible alternative to standard GWR for non-normal data.
  • The method provides robust analysis of spatial heterogeneity in multivariate settings.
  • The study demonstrates the practical application of GWMGGR in analyzing regional educational disparities.