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Table 1 Model's description

From: Performance of statistical models to predict mental health and substance abuse cost

Model Name Dependent Variable Model Specification
   Family Link v(μ) Equation
Normal with identity link (OLS) cost Normal Identity 1 E(Y) =
Log Normal* ln(cost) Normal Identity 1 E{ln(Y)} =
Sqrt Normal* c o s t MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaGcaaqaaGqaciab=ngaJjab=9gaVjab=nhaZjabdsha0bWcbeaaaaa@325C@ Normal Identity 1 E{ Y MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaGcaaqaaiabdMfazbWcbeaaaaa@2E02@ } =
Gamma with log link cost Gamma Log μ 2 ln{E(Y)} =
Gamma with square-root link cost Gamma Square Root μ 2 E ( Y ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaadaGcaaqaaiabdweafjabcIcaOiabdMfazjabcMcaPaWcbeaaaaa@30C7@ =
  1. * Transformation of dependent variable.
  2. Note: μ = E(y) and V(μ) is variance function.