Dear Members,
Please, Can anyone here help me for explanations in below equations? In particular, if there is any symbol or the equations structure refer to (Fixed or random or pooled logistic) and extra discussions? Thanks
1) Y i,t = α + β1x1i,t-1 + β2x2i,t-1 + β3x3i,t-1 + β4x4i,t-1 + εi,t-1
Y (0, 1)
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2) P(y = 1∣X) = G(β0 + βX)
G is a probability distribution function and X is the vector of explanatory variables. In
the Logit model G is modeled as a logistic function and G is the standard normal cumulative
Distribution functions in case of the Probit model.
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3) P(yit = 1|xit) = Λ(δ Featurit + γlDistressit).
The dep variable (Yit) is a binary variable which assumes the value 1
and 0. On the side of the explanatory variables, Λ is the cumulative distribution function (cdf) of the logistic distribution. The vector of features is δ that affect the likelihood of give security.
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4) P (Yi,t = 1∣log (σ A i,t−1 ) , Xi,t−1) = G(α + αt + αc + βlog (σ A i,t−1 ) + γXi,t−1),
where Y (0,1) . while P (Yi,t = 1∣log (σ A i,t−1 ) , Xi,t−1) is the conditional probability that organization i give the security in question during time period t. log (σ A i,t−1 ) is the log-transformed measure of one of the variable, whereas Xi,t−1 is the vector of indep varibels described below. α is an intercept term. αt and αc denote time and country fixed effects, respectively.
G(.) is a probability distribution function which is given by the logistic function in the case of logit.
Thanks a lot in advance.