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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) = xβ

Log Normal*

ln(cost)

Normal

Identity

1

E{ln(Y)} = xβ

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@ } = xβ

Gamma with log link

cost

Gamma

Log

μ 2

ln{E(Y)} = xβ

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@ = xβ

  1. * Transformation of dependent variable.
  2. Note: μ = E(y) and V(μ) is variance function.
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BMC Medical Research Methodology

ISSN: 1471-2288

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