The study used the random utility maximization theory framework, which is particularly relevant for understanding how beekeepers choose specific market outlets, considering the inherent uncertainty in how beekeepers perceive these outlets. The fundamental assumption is that beekeepers select a particular outlet/outlets based on its utility or benefit. Following this theory, the decision to choose an outlet/outlets is determined by random factors (McFadden, 1973).

Unlike the standard discrete choice setting that assumes mutually exclusive alternatives, this study conceptualizes market outlet engagement as a set of non-mutually exclusive participation decisions. Beekeepers may sell honey through more than one outlet within a production period, implying that the decision to participate in one outlet does not impede participation in others.

The latent utility that beekeeper i derives from participating in market outlet j is specified as:

where U_ij represents the unobserved net utility associated with participation in outlet j; X_i is a vector of beekeeper-specific, institutional, and market-related characteristics; βj′ is a vector of outlet-specific parameters; and ε_ij is a stochastic error term capturing unobserved factors affecting participation (Green, 2012).

The observed participation decision is linked to this latent utility through a binary indicator defined as:

where Y_ij = 1 denotes participation by beekeeper i in outlet j, and Y_ij = 0 indicates non-participation. This formulation implies that participation occurs when the perceived net utility from engaging in a specific outlet is positive, independent of participation decisions in other outlets.

The study was conducted in Baringo County, one of the 47 Counties in Kenya, in the Rift Valley region. The County lies between longitudes 35⁰30′ and 36⁰30′ East and latitudes 0⁰10′South and 1⁰40′ It borders Turkana and Samburu Counties to the North, Uasin Gishu to the South West, Laikipia to the East, Nakuru to the South, and Elgeyo-Marakwet and West Pokot to the West. The main crops grown in the County are maize, pigeon peas, beans, Irish potatoes, sweet potatoes, sorghum, cassava, and finger millet. In contrast, the cash crops are coffee, cotton, macadamia, and pyrethrum. Livestock products include honey, beef, mutton, hides, and skin. However, little value addition is done to these products (Safari and Wambua, 2024). Baringo South Sub-County was chosen because of its significance in honey production, with an area of 1678Km² out of which 215Km² constitutes arable land (Baringo County Government, 2018). The area's estimated population is 89,210; furthermore, the area has four administrative wards: Marigat, Ilchamus, Mochongoi and Mukutani (KNBS, 2019). Figure 1 represents a map of the study.

The study used a cross-sectional research design, which is helpful because much information is obtained quickly. It allows data collection from different groups of respondents at one point in time. Moreover, this design also collects data, enabling measurement of the prevalence of all factors under investigation (Kumar, 2014).

A multi-stage sampling procedure was used to select the sample for the study. First, Baringo County was chosen because beekeeping is a priority value chain in its annual strategic plan. Baringo South Sub-County was also selected purposively since it is the leading Sub-County in honey production. Marigat, Ilchamus, Mochongoi, and Mukutani wards in the Sub-County were all selected because they have the highest concentration of beehives. Respondents were selected using simple random sampling.

The target population comprises beekeepers in Baringo South Sub-County. According to data from the Sub-County Agricultural Office, there are 5,416 registered beekeepers in the four wards. As Yamane (1967) suggested, since the population size is known with certainty, the following formula is appropriate to determine the sample size.

Kothari (2004) accepts an error of less than 10 percent thus, this study used an error of 0.07, which is precise, hence a smaller sample size that could fit the budget.

Where:

n= Sample size,

N= Total population of interest,

e= The allowable margin of error ranges from 0.05 to 0.1.

When confronted with several potential marketing outlets, beekeepers may sell through multiple outlets to maximize profits. Therefore, in conjunction with using a specific market outlet, a beekeeper can select other outlets. The decision might have been informed by prior use of a particular outlet, which could help inform future decisions.

Multinomial Probit model could be used however, it assumes that decision-makers select a single option from a set of mutually exclusive alternatives, implying a ranked preference structure across choices. In contrast, the Multivariate Probit (MVP) model estimates a system of correlated binary participation decisions, allowing producers to engage in multiple market outlets simultaneously (Shah and Alharthi, 2024; Wang et al., 2023). In the context of honey marketing, beekeepers often sell through more than one outlet within a production period, making outlet participation non-mutually exclusive. The MVP framework is therefore appropriate, as it captures both the determinants of participation in each outlet and the potential correlation across outlet decisions arising from unobserved factors.

Therefore, the study adopted a multivariate probit (MVP) econometric model, which evaluates the influence of the set of explanatory variables on each market outlet while allowing unobserved components to be flexibly linked. The source of correlation might be positive and negative correlations between different market outlet options (Mengstu et al., 2023). In this study, the dependent variables are four dummy variables —Wholesalers, retailers, individual consumers, and middlemen —that equal 1 if the beekeeper chooses the outlet option and 0 otherwise. The model can be defined empirically as shown in Equation 5:

Where Yik* denotes a latent variable that captures the observed and unobserved characteristics associated with k^th market outlet, while Y_ik is the binary dependent variable and (k = 1, …., m) denotes the different market outlets beekeepers use. The ability of beekeepers to use a market outlet option to take value 1 and 0 otherwise, X_ik is a vector of independent variables that represent household demographic characteristics and institutional factors. β_k and ε_k represent the parameter to be estimated and the error term, respectively. A positive correlation among market outlets indicates complementarity, whereas a negative correlation indicates substitutability. The error term follows a multivariate normal distribution, with zero mean, variance normalized to unity and a n×n covariance matrix. The covariance matrix is shown in Equation 6;

Parts (ρ₂₁, ρ₁₂, ρ₃₁, ρ₁₃, ρ₄₁ and ρ₁₄) in the variance-covariance matrix represent the correlation between the stochastic components of different market outlets. Equation 7 provides a multivariate probit model that jointly depicts decisions to select a particular market outlet under the premise of the unobserved correlation between the stochastic component of the k^thand m^th outlet options. Correlation between the error terms of several latent equations, which represent unobserved qualities that influence the choice of different adaptation strategies, is made possible by this specification's non-zero off-diagonal elements.

The explanatory variables used in this study (Table 1) were obtained from past studies on the choice of honey market outlets (Adgo and Seyoum, 2018; Borena et al., 2023; Kaygisiz, 2023; Tadesse et al., 2021; Tarekegn et al., 2017).

Based on the variance inflation factor (VIF) results in Table 5, there is no evidence of multicollinearity among the explanatory variables used in the MVP model. All VIF values are below the commonly accepted threshold of 5, indicating that the regression coefficient estimates are stable and reliable.

Table 6 presents the results of the heteroscedasticity using White's test.

Heteroscedasticity is one of the violations of the linear regression model, in which the variance across observations is not constant (Green, 2012). The Breusch-Pagan test is specifically designed to assess the linear form of Heteroscedasticity. In contrast, the White test allows the independent variable to have a nonlinear and interactive effect on the error variance. The white test is more potent than Breusch Pagan since it can detect a more general form of Heteroscedasticity (Wooldridge, 2004). The results showed that there was no major problem with Heteroscedasticity, as the p-value for the chi-square test was 0.3881, which is greater than 0.05; therefore, we failed to reject the null hypothesis.

Table 7 presents the overall fit statistics, predicted probabilities, joint probabilities, and the estimated correlation matrix of market outlet participation based on the Multivariate Probit (MVP) model. The predicted probabilities indicate that participation is most likely in the individual consumer outlet, with an estimated probability of 0.733. This is followed by middlemen (0.430), wholesalers (0.403), and retailers (0.066). These results imply that, conditional on observed characteristics, beekeepers have a higher likelihood of participating in individual consumer markets, while participation in retail outlets is comparatively less likely.

The joint probabilities of success (all outlets chosen simultaneously) and failure (no outlet chosen) are both 0.0203. These low values imply that the simultaneous choice of all market outlets is uncommon, highlighting the distinctiveness of each outlet.

The estimated correlation matrix reveals important relationships between the unobserved factors influencing these market outlet choices. Notably, there is a significant negative correlation between retailers and wholesalers (-0.495) and between retailers and middlemen (-0.189), both statistically significant at the 1% level. This indicates that factors increasing the likelihood of choosing retailers tend to decrease the likelihood of selecting wholesalers or middlemen, and vice versa. The correlation between middlemen and individual consumers is positive and significant at the 5% level (0.156), suggesting some shared unobserved influences. Other correlations, such as between wholesalers, middlemen, wholesalers, and individual consumers, were not statistically significant.

The likelihood ratio test strongly rejects the null hypothesis that all correlation coefficients are zero (χ²(6) = 73.64, p < 0.001), confirming that accounting for correlations among the choices significantly improves the model fit. This justifies the use of the MVP approach over separate univariate models. Furthermore, the Wald test statistic (X²(56) = 140.77, p < 0.001) and the log-likelihood value of−438.95 indicate that the model fits the data well. The analysis is based on 197 observations, and five simulation draws were used for estimation.

Age was positively and statistically associated with participation in the wholesale market outlet at the 5% (Table 8), indicating that older beekeepers are more likely to engage in bulk selling. This could be due to greater experience, trust networks, and risk tolerance when dealing with larger transactions. Similar trends were observed by Mwembe et al. (2021), who reported that older farmers often have more market knowledge and contacts, which enable them to negotiate better terms.

Gender was negatively and statistically associated with participation in individual consumer and middlemen market outlets at the 10% significance level. This implies that Male beekeepers were less likely to sell through these channels than female beekeepers. This could reflect gender-based roles in marketing activities, where women are often more involved in informal and local market transactions. From a behavioral perspective, this association may also relate to substitutability between informal channels and more formal market options, with male beekeepers potentially substituting away from individual consumer and middlemen outlets toward alternative channels. However, Arumugam et al. (2022) report that male farmers are more likely than their female counterparts to participate in middlemen and wholesaler outlets, which they associate with differences in bargaining capacity, negotiation practices, and contract enforcement.

The education level of respondents was positively and statistically associated with participation in the wholesale market outlet at the 5% significance level. The findings imply that educated beekeepers were much more aware of the profitability of selling at higher returns market outlets. The finding aligns with Anthony et al. (2021), who found that higher education levels increase the chance of farm product producers integrating into high-value chain markets.

Access to extension services was positively and statistically associated with participation in the retailer outlet at the 1% significance level. This association may reflect greater exposure to market information, quality requirements, and marketing practices among beekeepers with extension contact, which is often linked to engagement with more structured market channels. Similar associations between extension access and market participation are reported by Ermias (2021) and Ozkan et al. (2022). In contrast, access to extension services was negatively associated with participation in the middlemen outlet at the 10% significance level. This pattern may indicate that beekeepers with extension support are less likely to rely on informal intermediaries and instead engage with alternative outlets or collective marketing arrangements. This finding differs from Chelanga et al. (2021), who report a positive association between extension access and middlemen participation.

Training was positively and statistically associated with participation in both wholesaler and middlemen market outlets, at the 5% and 1% significance levels, respectively. This association could be indicative of the greater range of skills and information that is generally delivered in training programs, such as that of honey production, handling, quality control, packaging and the basic marketing procedures. From a behavioral perspective, training may be associated with complementary engagement in formal and informal channels, where trained beekeepers meet observable requirements for bulk buyers such as wholesalers while retaining flexibility to transact with middlemen when transaction costs, liquidity needs, or market conditions make informal channels more suitable. These results are in line with those of Mizero et al. (2024), who show positive relationships between training and participation in honey market outlets.

Access to credit was negatively and statistically associated with participation in both retailer and middlemen outlets at the 1% significance level. This pattern may reflect substitutability between these outlets and alternative market channels, whereby beekeepers with access to credit are less reliant on outlets that prioritize immediacy of payment or minimal quality and packaging requirements. Credit access may be associated with greater flexibility in covering harvesting, packaging, and transport costs, enabling engagement with other market outlets. This finding is similar to that of Mwembe et al. (2021), who concluded that producers are more likely to opt for high-value market outlets with higher prices rather than sell at farm-gate prices.

Distance to market was negatively and statistically associated with participation in the retailer outlet at the 1% significance level and positively associated with participation in the wholesaler outlet at the 10% significance level. This pattern may reflect substitutability between retailer and wholesaler channels in the presence of spatial transaction costs. Beekeepers located farther from markets may be more frequently observed engaging with wholesalers, who are better positioned to accommodate bulk transactions and transportation logistics, while proximity to markets is more compatible with retailer participation. The finding is consistent with Ngeno et al. (2024), who found that distance played an important role in determining carrot farmers' choice of market outlet.

Beekeeping experience was negatively and statistically associated with participation in the retailer outlet at the 1% significance level. This association may reflect differences in marketing orientation between more and less experienced producers, with more experienced beekeepers potentially engaging in alternative outlets that better align with their scale of operation or accumulated market relationships. The study corroborates Tarekegn et al. (2017), who found that farming experience significantly influenced honey producers' market outlet choices.

The quantity of honey produced was positively and statistically associated with participation in the wholesaler outlet at the 1% significance level. This association is consistent with the volume requirements typically associated with wholesaler transactions, as beekeepers with higher output levels are more likely to be able to supply honey in bulk quantities. The finding corroborates Borena et al. (2023), who found that the amount of honey produced affected the market outlet choice.

This study had a number of limitations, which were taken into account when interpreting the results. First, the cross-sectional observations used to conduct the analysis mean that the analysis cannot be used to make causal inferences. The estimated relationships represent statistical correlations of explanatory variables and participation in market outlets as opposed to causal influences.

Second, the empirical model has numerous equations and explanatory variables that are approximated at a comparably small scale of 197 observations. Although the Multivariate Probit model is highly appropriate in dealing with interdependent decisions, model complexity and sample size can restrict the statistical power and accuracy of specific coefficient estimates.

Third, the Multivariate Probit model is based on excellent distributional assumptions that involve joint normality of error terms across equations. Although this framework is widely used in studies of multiple discrete choices, violations of these assumptions may affect the robustness of the estimates.

Lastly, the analysis fails to consider data on output prices, transaction costs and contractual issues related to various market outlets. These factors are expected to have a significant role in influencing the decisions of market participation, however this information could not be reliably collected because most honey transactions in the study area are informal, with prices negotiated individually and contracts rarely standardized.

Future studies can overcome these shortcomings by using panel data or experimental designs with greater causal identification. The gathering of detailed price, contract and transaction cost data would also provide a more comprehensive analysis of the honey market outlet selection. Also, future research may investigate the dynamic nature of outlet participation and investigate how market decisions change over time with the adaptation to changes in production conditions, institutions and policy environments.