A generalised linear space–time autoregressive model with space–time autoregressive disturbances

Abstract

We present a solution to problems where the response variable is a count, a rate or binary using a generalised linear space–time autoregressive model with space–time autoregressive disturbances (GLSTARAR). The possibility to test the fixed effect specification against the random effect specification of the panel data model is extended to include space–time error autocorrelation or a space–time lagged dependent variable. Space-time generalised estimating equations are used to estimate the spatio-temporal parameters in the model. We also present a measure of goodness of fit, and show the pseudo-best linear unbiased predictor for prediction purposes. Additionally, we propose a joint space–time modelling of mean and dispersion to give a solution when the variance is not constant. In the application, we use social, economic, geographic and state presence variables for 32 Colombian departments in order to analyse the relationship between the number of armed actions (AAs) per 1000 km${}^2$ committed by the guerrillas of the FARC-EP and ELN during the years 2003–2009, and a set of covariates given by attention rate to victims of violence, forced displacement-households expelled, forced displacement-households received, total armed confrontations per year, number of AAs by military forces and percentage of people living in urban area.

Keywords:

• armed actions
• generalised linear space–time autoregressive model
• space–time autoregressive disturbances model
• space–time generalised estimating equations
• fixedeffect parameters
• random effect parameters

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Work partially funded and supported by the Spanish Ministry of Science and Education under Grants MTM2013-43917-P and PROMETEOII/2014/062; Carolina Foundation; Applied Statistics in Experimental Research, Industry and Biotechnology (Universidad Nacional de Colombia); and Core Spatial Data Research (Faculty of Engineering, Universidad Distrital Francisco José de Caldas).