Measuring heterogeneous preferences for cattle traits among cattle-keeping households in East Africa.

where [x.sub.njt] is a vector of observed variables that includes the cattle traits and socioeconomic characteristics of cattle owners. Coefficient vector [beta] is unobserved for each n and varies in the population with density f([[beta].sub.n] | [theta]), where [theta] is a vector of parameters of a continuous population distribution, [[epsilon].sub.njt] is an unobserved random term that is assumed to be identically and independently distributed. The focus in mixed logit shifts from finding estimates of [[beta].sub.n] to finding the estimates of [theta], the population parameters (e.g., location and spread parameters), which determine the behavior of [[beta].sub.n]. Conditional on [[beta].sub.n] the probability that person n chooses alternative i, in choice situation t, is the conditional logit specification

(4) [ILLUSTRATION OMITTED]

Given that [[beta].sub.n] is unknown to the analyst, the unconditional probability is usually employed. The unconditional probability is the integral of the conditional probability over all possible values of [beta], which depends on the distribution of [beta]. This integral takes the form

(5) [P.sub.nit]([theta]) = [integral] [L.sub.nit]([[beta].sub.n])f([[beta].sub.n] | [theta])d[[beta].sub.n].

Although mixed logit accounts for preference heterogeneity by allowing taste parameters to vary randomly over individuals, it is not well suited to explaining the sources of heterogeneity (Boxall and Adamowicz 2002). These sources often relate to the socioeconomic characteristics and taste of the decision maker. Though it is possible to account for the socioeconomic characteristics of the decision maker by interacting key individual characteristics with the traits, this requires a priori selection of key limited individual-specific variables.

Latent class models are more suited in explaining the sources of heterogeneity, since individuals are intrinsically sorted into a number of latent classes. Each is characterized by homogenous preferences though heterogeneous across classes (Boxall and Adamowicz 2002). However, its limitation is the assumption of local independence, where the choice variables are assumed to be independent of each other, conditional on latent class membership. Assignment of individuals into classes is probabilistic based on their sociodemographic characteristics. In this article we use a mixed logit model to identify the existence of preference heterogeneity and latent class modeling to estimate segment or class-specific parameters.

In the latent class logit, the mixing distribution f([[beta].sub.n] | [theta]), is discrete, with [[beta].sub.n] taking a finite set of distinct values (Train 2003). In this case, it is assumed that individuals are intrinsically sorted into a number of classes based on their tastes. Members of each class have similar tastes. However, the classes are latent, not observable by the analyst. Within the class, the individual choices from one choice situation to the next are assumed to be independent and choice probabilities are assumed to be generated by the logit model (Greene 2002). For instance, the probability that individual n chooses alternative i in a given number of choice situation t, given that he belongs to latent class c is

(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [x.sub.nit] is a vector of observable traits associated with alternative i, and [[beta].sub.c] is a class-specific parameter vector; t denotes the number of choice situations for person n, while [[beta].sub.c] is used to capture heterogeneity in preferences across classes. Since the classes are not observable, class probabilities are specified by the multinomial logit form

(7) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [z.sub.t] is a set of observable characteristics that enter the model for class membership. The cth parameter vector is normalized to zero to ensure identification of the model. This model does not impose the independence of irrelevant alternatives on the observed probabilities. For a given individual n, the model's estimate for the probability of a specific choice is the expected value, over classes, of the class-specific probabilities. In our case, each person makes repeated choices for either eleven bull profiles or twelve cow profiles. The repeated choices permit an examination of how the levels of various traits influence individual utility and a comparison with a priori expectations.

Survey Design and Data Description

The choice experiment household surveys were conducted in Narok and Suba districts in Kenya and the Ghibe Valley in Ethiopia, representing different livestock production systems in trypanosomosis prevalent areas. The three areas were selected after spatial mappings of tsetse fly distribution and cattle densities in Kenya and Ethiopia were done to target areas with trypanosomosis challenge. A purposive random sampling procedure to identify cattle-keeping households was employed to select 172 households in three divisions of Narok district, 132 households in two divisions of Suba district, and 204 households in the lower and upper Ghibe Valley. Sampling was done along line transects within the lowest administrative unit in the two countries. The sample size was calculated as a proportion of the total number of households in the administrative unit. The survey was administered between September and December 2004 in Kenya and April to May 2005 in Ethiopia by locally trained enumerators.

In order to identify the relevant cattle traits to be included in the choice experiment, informal focus group meetings were held with cattle keepers in the study sites. Cattle keepers were asked to identify the cattle traits that they considered important in meeting their objectives, while taking into consideration their prevailing local and environmental conditions. Pair-wise ranking technique was then employed to select the relatively highly preferred traits. A total of seven preferred traits for cows and six for bulls, each with two to three levels were identified for inclusion in the design of the choice experiment. An additional monetary trait, purchase price, was included to capture the marginal willingness to pay for the traits. The different purchase price levels considered were based on the prevailing market prices of bulls and cows. Table 1 presents the traits included in the choice experiment and their levels.

The identified traits and their levels were then combined according to an experimental design to create choice sets. A full factorial design, which includes all possible combinations of the traits, would yield 864 ([2.sup.5] x [3.sup.3]) possible choice sets for cows and 432 ([2.sup.4] x [3.sup.3]) for bulls. Since it is not practically feasible to work with such a large number of choice sets, a randomized, partially orthogonal main effects only combinations was created using Choice-Based Conjoint (CBC) software, which resulted in twelve generic choice sets for cows and eleven for bulls. (2) These were then used to construct cards with pictorial profiles describing the differences in traits and the levels to demonstrate each choice set to survey respondents. The choice experiment was administered as part of a household-level questionnaire survey using in-person interviews in respondents' homes. The rest of the questionnaire covered socioeconomic aspects such as household and farm characteristics as well as market and resource access.

The administration of the choice experiment was conducted in the following manner: respondents were first introduced to the type of choice task and asked to indicate their preferences between cows and bulls for purchases. The respondents were then presented with choice tasks for either bulls or cows and shown two pictorial profiles based on each choice set. They were then asked to choose the most preferable animal profile to purchase for rearing. Each of them was presented with either twelve choice sets in the case of cows or eleven choice sets in the case of bulls. In each case, a "don't buy" option was also included for respondents who preferred neither of the two profiles presented. A total of 253 complete choice experiment interviews were carried out for bulls and another 253 for cows, yielding 2,783 completed choice sets for bulls and 3,036 for cows. Twenty-three choices (two interviews) were discarded due to incomplete information.

Table 2 presents a description of the choice experiment variables used in estimating the mixed logit and latent class models. To avoid confoundment with the grand mean, we employed effects coding for the choice experiment variables to measure nonlinear effects in the trait levels (Hensher, Rose, and Greene 2005). (3) Effects coding uses values for codes, which when summed over any given trait column, equal zero. From an a priori perspective, we expect that the trait levels of trypanotolerance, high fertility in bulls, high reproduction potential in cows, and high milk yield should increase an individual's utility, as should an increase in live weight. A high reproductive performance and high fertility are expected to have a positive impact on herd productivity and herd size, while trypanotolerance would increase the competitiveness of the cattle enterprise by reducing the costs associated with the treatment of trypanosomosis disease.