Independent variable | Ordinary least squares estimation | Spatial* lag model—Maximum likelihood estimation | Spatial* error model—Maximum likelihood estimation | ||||||

R-squared: 0.529 Akaike info: 2093.5 Jarque-Bera prob: 0.000 | R-squared: 0.541 Akaike info: 2089.7 Breusch-Pagan test: 0.000 | R-squared: 0.537 Akaike info: 2090.43 Breusch-Pagan test: 0.000 | |||||||

Coeff. | t-stat. | P value | Coeff. | z-value | P value | Coeff. | z-value | P value | |

No central heating | −32.188 | −3.827 | 0.000 | −30.778 | −3.749 | 0.000 | −31.776 | −3.875 | 0.000 |

Unemployment | 39.025 | 5.561 | 0.000 | 37.957 | 5.526 | 0.000 | 39.568 | 5.71 | 0.000 |

WPS recipients – Veterans | 21.492 | 2.594 | 0.01 | 18.506 | 2.283 | 0.022 | 18.31 | 2.236 | 0.025 |

SIMD | 13.248 | 1.911 | 0.057 | 13.136 | 1.947 | 0.052 | 12.984 | 1.872 | 0.061 |

AFCS recipients – Veterans | 7.389 | 1.242 | 0.215 | 6.794 | 1.172 | 0.241 | 6.99 | 1.208 | 0.227 |

No qualifications | −8.976 | −1.095 | 0.275 | −9.342 | −1.171 | 0.242 | −9.837 | −1.207 | 0.227 |

AFPS recipients – Veterans | 10.607 | 1.08 | 0.281 | 15.126 | 1.564 | 0.118 | 14.674 | 1.5 | 0.134 |

Alcohol | −7.212 | −1.05 | 0.295 | −7.134 | −1.067 | 0.286 | −8.736 | −1.27 | 0.204 |

Spatial lag | --- | --- | --- | 0.372 | 2.672 | 0.008 | --- | --- | --- |

Lambda | --- | --- | --- | --- | --- | --- | 0.450 | 2.224 | 0.026 |

Breusch-Pagan: tests whether the variance of the spatial errors from a regression is dependent on the values of the independent variables.

Spatial lag and the spatially correlated errors (λ) reflect the spatial dependence inherent, measuring the average influence on observations by their neighbouring observations. Both coefficients have a positive effect and are highly significant. As a result, the general model fit improved. The effects of other independent variables remain virtually the same.

*Spatial distance weights: (a) Bandwidth: 162 km; (b) Min neighbours: 1; (c) Max neighbours: 203; (d) Mean neighbours: 130.

AFCS, Armed Forces Compensation Scheme; SIMD, Scottish Index of Multiple Deprivation; WPS, War Pension Scheme.