Contribution of Economics to Design of Sustainable Cattle Breeding Programs in Eastern Africa: A Choice Experiment Approach

Where αni is the intercept or individual n’s intrinsic preference for choice i, sn contains the
socio-economic characteristics of the individual, and the coefficient λj captures the systematic
heterogeneity among the individuals in the sample. Xnj is a vector of the attributes and βn the
coefficients of the attributes. Maximum likelihood estimates for the parameter vector can be
obtained by maximizing the likelihood function. The limitation of the multinomial logit
model lies in its assumption of constant variance, which results in the independence of
irrelevant alternatives (IIA) property and the assumption of fixed taste parameters in the
population, which is rather limiting if taste actually varies in the population. This is a rather
restrictive assumption since cattle keepers face varying sets of constraints and incentives, and
are likely to exhibit different preference patterns. To relax this restrictive assumption, mixed
logit model has been employed in this study, making it possible to account for unobserved
taste variation.

In mixed logit, the taste parameters β, are allowed to vary in the population with
density g(β_n | θ), where θ are the parameters of the population distribution. Each
individual’s coefficient βn, differ from the population mean β, by some unobserved amount,
constituting an additional source of randomness (Ben-Akiva and Lerman, 1985). The
estimates for the location and spread parameter of the specified population distributions can
also be obtained by maximizing the likelihood function in Equation 2. The value is simulated
from random parameter draws from the postulated distribution g(β!θ). In the case of repeated
choices per respondent as in our case, the same random draw is used across all the choices
made by the same respondent in order to account for correlation across repeated responses
(Train and Revelt, 1998; Garrod et al., 2002). The joint probability of a set of t repeated
choices by respondent n and conditional on the drawn value for β is a product of logits;

L_n = ∏exp(x_{n(t) j}β).∑exp(x_{n(t) j}β)                                                       (3)

tj

The unconditional probability for the sequence of the choices for the nth individual is:

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