Estimation of parameters and hypothesis testing of multivariate spatial autoregressive model

Area of Science:

• Spatial statistics
• Epidemiology
• Environmental science
• Biostatistics

Background:

• Multivariate response variables are common in epidemiology and environmental studies.
• Existing spatial regression models (e.g., SAR) are limited to univariate responses.
• There's a need for models that capture spatial dependence in multiple response variables simultaneously.

Purpose of the Study:

• To introduce and validate a Multivariate Spatial Autoregressive (MSAR) model for multivariate spatial data.
• To address the limitations of existing models in handling multiple spatially dependent responses.
• To implement robust statistical significance testing for MSAR model parameters.

Main Methods:

• Developed a Multivariate Spatial Autoregressive (MSAR) model.
• Employed Maximum Likelihood Estimation (MLE) with a concentrated log-likelihood approach.
• Utilized the Maximum Likelihood Ratio Test (MLRT) and Wald Test for parameter significance assessment.

Main Results:

• The MSAR model provides unbiased and consistent parameter estimates.
• Significance tests identified key predictors for toddler pneumonia and diarrhea.
• The model demonstrated effectiveness with an R-squared of 60% and RMSE of 5.

Conclusions:

• The developed MSAR model effectively captures spatial dependencies in multivariate settings.
• Formal hypothesis testing enhances the reliability of parameter interpretations.
• The model is applicable to real-world spatial health data, as shown in the Indonesian study.