Epidemiology Research International

Research Article

Developing a Dynamic Microsimulation Model of the Australian Health System: A Means to Explore Impacts of Obesity over the Next 50 Years

Box 2

Generalised ordinal logistic regression model.
Model specification:
  𝑃 ( 𝑌 𝑖 > 𝑗 ) = 𝑔 ( 𝑋 𝛽 𝑗 ) = e x p ( 𝛼 𝑗 + 𝑋 𝑖 𝛽 𝑗 ) / ( 1 + [ e x p ( 𝛼 𝑗 + 𝑋 𝑖 𝛽 𝑗 ) ] ) , 𝑗 = 1 , 2 , … , 𝑀 − 1  
Probability equations for the five levels of health status:
  𝑃 ( 𝑌 𝑖 = Excellent Health ) = 𝑔 ( 𝑋 𝑖 𝛽 1 )                    
  𝑃 ( 𝑌 𝑖 = Very Good Health ) = 𝑔 ( 𝑋 𝑖 𝛽 1 ) − 𝑔 ( 𝑋 𝑖 𝛽 2 )                
  𝑃 ( 𝑌 𝑖 = Good Health ) = 𝑔 ( 𝑋 𝑖 𝛽 2 ) − 𝑔 ( 𝑋 𝑖 𝛽 3 )                   
  𝑃 ( 𝑌 𝑖 = Fair Health ) = 𝑔 ( 𝑋 𝑖 𝛽 3 ) − 𝑔 ( 𝑋 𝑖 𝛽 4 )
  𝑃 ( 𝑌 𝑖 = Poor Health) = 𝑔 ( 𝑋 𝑖 𝛽 4 )
Cumulative Distribution Function of Health Status:
 Cut Point(Excellent health) = 𝑃 ( 𝑌 𝑖 = Excellent Health )
 Cut Point(Very good health) = 𝑃 ( 𝑌 𝑖 = Excellent Health ) + 𝑃 ( 𝑌 𝑖 = Very Good Health )
 Cut Point(Good health) = 𝑃 ( 𝑌 𝑖 = Excellent Health ) + 𝑃 ( 𝑌 𝑖 = Very Good Health ) + 𝑃 ( 𝑌 𝑖 = Good Health )
 Cut Point(Fair health) = 𝑃 ( 𝑌 𝑖 = Excellent Health ) + 𝑃 ( 𝑌 𝑖 = Very Good Health ) + 𝑃 ( 𝑌 𝑖 = Good Health) + 𝑃 ( 𝑌 𝑖 = Fair Health)
See [47]