Demand Potential for Goat Meat in Southern States: Empirical Evidence from a Multi-State Goat Meat Consumer Survey

the probability that yi equals one, and (1-Pi) is the probability that yi equals zero. LPM
links yi with the explanatory variable set linearly (equation 2) and could be estimated
using OLS as traditional regression does. The flaws of LPM are inefficient estimators,

(2)         ^y_i = B1 ^xi 1 +∙∙∙ + Bk-1 xi, k-1 ⁺ Bk xi, k + ei
violation of 0≤ prediction of yi ≤ 1, and the dependence of variance on particular values
of independent variables. Probit and logit models avoid those problems by defining the
probability of the event, Pi, with nonlinear functions of a linear combination of variables
(equation 3). The probit model links I, the linear combination of independent variables,
with an accumulative distribution of a standardized normal variable defined in equation 4,

(3)           Ii = B1 xi ,1 +••• + Bk-1 xi, k-1 ⁺ Bk xi, k ⁺ ei

and the logit model links I with an accumulative distribution defined in equation 5.

^Ii 1

Pi =F(Ii)=∫    ¹ e

-∞

_eIi

Pi = F ( Ii) =----_τ

1 + e^Ii

In both equation (4) and (5), Pi is constrained between 0 and 1. Thus, probit and logit
models offer a solution to the dilemma in LPM. Both models find applications in
academic investigation. But the logit model was more extensively used because of much
easier interpretation of its parameters. The logit model works for both binary and multiple
outcomes (ordinal and nominal). Depending on response variables, the response function
could be either the cumulative logit or the general logit. The cumulative logit function is
used for ordinal response with multiple ordered levels. The generalized logit function fits
for nominal response with unordered multiple alternatives. In the case of the generalized
logit, each non-reference category is contrasted with a specified reference category.

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