Table 3 Random effects estimates from the joint spatial model of childhood fever, diarrhoea and pneumo nia morbidity in Malawi, 2000.

Random effects

Spatial structured

(Σ₁₁, Σ₂₂, Σ₃₃)

Spatial unstructured

(Ω₁₁, Ω₂₂, Ω₃₃)

Proportion of structured

spatial variation

(p₁₁, p₂₂, p₃₃)

Correlation structured

Fever

$r_{12}=\frac{{\Sigma }_{12}}{\sqrt{{\Sigma }_{11}{\Sigma }_{22}}},r_{13}=\frac{{\Sigma }_{13}}{\sqrt{{\Sigma }_{11}{\Sigma }_{33}}}$

Diarrhoea

$r_{23}=\frac{{\Sigma }_{23}}{\sqrt{{\Sigma }_{22}{\Sigma }_{33}}}$

Pneumonia

Correlation unstructured

Fever

$q_{12}=\frac{{\Omega }_{12}}{\sqrt{{\Omega }_{11}{\Omega }_{22}}},q_{13}=\frac{{\Omega }_{13}}{\sqrt{{\Omega }_{11}{\Omega }_{33}}}$

Diarrhoea

$q_{23}=\frac{{\Omega }_{23}}{\sqrt{{\Omega }_2{\Omega }_{33}}}$

Pneumonia

Total correlation (q + r)

Fever

Diarrhoea

Pneumonia