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Thread: Model equation Binary probit model

  1. #1
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    Model equation Binary probit model


    the model equation for a binary probit model looks like that:

    Prob(Y=1|X) = Φ(Xβ)

    I just want to know if my vector X includes covariates varying on an individual level (Zi) and covariates varying on a country level (Uc) if i can also write the model as:

    Prob(Y=1|Zi,Uc) = Φ(Ziβ, Ucβ)

    Do I have to change the β?

    Thanks a lot.

  2. #2
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    Re: Model equation Binary probit model

    It makes sense to include variables varying on county level such that x'_i = (z'_i,u'_{c(i)})
    \Phi(x'_i\beta) = \Phi(z'_i\beta_1 + u'_{c(i)}\beta_2) where \beta = (\beta_1',\beta'_2)'
    here assuming that each individual is member of on and only one county such that county index c(.) is function of individual index i

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