DTMV attributes selection

Attributes selection process involved various consultations and collaborations with stakeholders such as the International Institute of Tropical Agriculture (IITA) responsible for the deployment of DTMA intervention specifically in Kano State, Nigeria where the study took place. Within the team, we consulted with the plant breeders in the IITA under the DTMA Nigeria team to understand existing varieties and attributes in the study location. The collaborative effort also includes discussing with team leads at the forefront of DTMV interventions, this includes extension workers, key farmers working with a network of farmers, and seed dealers in the regions under study. An additional effort was exploring a database of existing maize varieties that are drought tolerant and have been deployed for farmers on the Nigeria seed portal database. The attributes (yield, maturity/duration, resistance to Striga, nitrogen use efficiency, cob size, grain size, price, and tolerance to drought) and their levels are illustrated in Table 1.

Table 1. DCE attributes and corresponding levels

Yield, from as early as the green revolution era is important for food availability and overall farm households' welfare (Evenson and Gollin, Reference Evenson and Gollin2003; Golin et al., Reference Golin, Morris and Byerlee2005). To design yield attributes and levels, we considered potential yield attainable under favorable conditions as designed by plant breeders for varieties of drought-tolerant maize, ranging from a lower to a higher rank—3.0, 6.0, 8.5, and 9.0 t ha⁻¹. Studies have shown potential yield as high as 10 t ha⁻¹ in drought-prone zones, provided conditions are favorable (African Centre for Biodiversity (ACB), Reference Africa Centre fro Biodiversity2017).

Duration or maturity periods are also significant attributes of improved maize seeds. For example, late maize varieties when sown earlier can utilize the longer period of grain filling which helps to gain more yield than early maturing varieties (O. B. et al., Reference Omolaran, Abdulmaliq, Ige, Mahamood, Oluleye, Azeez and Afolabi2012). At the same time, late maize varieties tend to have high plant height which makes them susceptible to lodging, in contrast, early varieties are shorter, high yielding, have better nitrogen use efficiency, and agronomic performance (Liu and Wiatrak, Reference Liu and Wiatrak2011). In our experimental choice survey, we designed three levels for duration/maturity attributes: this includes early for varieties that mature within 90 days; medium for varieties that mature between 90 and 120 days; and late for varieties that mature after 120 days.

Nitrogen is one of the yield-limiting nutrients in maize production in Nigeria (Kamara, Ewansiha and Menkir, Reference Kamara, Ewansiha and Menkir2014). It is highly mobile and subject to excessive loss in the soil (Pasley et al., Reference Pasley, Camberato, Cairns, Zaman-Allah, Das and Vyn2020). Among the existing varieties deployed are maize cultivars that perform well under low nitrogen conditions (Bänziger and Lafitte, Reference Bänziger and Lafitte1997; Kamara et al., Reference Kamara, Menkir, Ajala and Kureh2005; Badu-Apraku et al., Reference Badu-Apraku, Talabi, Fakorede, Fasanmade, Gedil, Magorokosho and Asiedu2019). Also, cultivars that are tolerant to drought are efficient in the uptake of nitrogen suggesting that such cultivars require less investment in nitrogen fertilizer application (Kamara, Ewansiha and Tofa, Reference Kamara, Ewansiha and Tofa2019). Based on this, in our experimental study, we incorporated three levels of nitrogen use efficiency: low, medium, and high.

Cob size and grain size are common attributes in maize cultivars (Abate et al., Reference Abate, Menkir, MacRobert, Tesfahun, Abdoulaye, Setimela, Badu-Apraku, Makumbi and Magorokosho2013; Buah et al., Reference Buah, Kombiok, Kanton, Denwar, Haruna, Wiredu and Abdulai2013; Tadesse, Medhin and Ayalew, Reference Tadesse, Medhin and Ayalew2014) and their sizes have a lot to do with the potential yield and marketability of outputs (Kassie et al., Reference Kassie, Abdulai, Greene, Shiferaw, Abate, Tarekegne and Sutcliffe2017). In our experimental design, cob-size levels include small, medium, and large, while grain size levels are small and large. We varied drought-tolerant levels into low, medium, and high to assess households' perception of their degree of preference for drought-tolerance attributes in maize. The price attribute represents the common cost of a kg of DTMVs seed farm households ever purchased.

D-optimal choice set design

In designing choice sets, it is important to control for the non-dominance of one attribute over the other. The D-optimal design approach takes this into account by explicitly considering the importance of attribute levels and at the same time ensuring that the alternatives in the choice set provide more information about the trade-off between the different attributes (Carlsson and Martinsson, Reference Carlsson and Martinsson2003). We specified the D-optimality criterion using a modified Federov search algorithm based on calculating the determinants of the variance–covariance matrix of the parameters from a non-linear logit model as applied in similar contexts (Shee, Turvey and Marr, Reference Shee, Turvey and Marr2020). From the eight attributes, we generated varying choices using JMP software. In the design process, we considered varying four key attributes while four remain fixed. This is to give the respondents a clearer view of choices and to understand the changes appropriately. The fixed attribute in the sample choice card includes yield, maturity/duration, price of maize grain per kg, and tolerant to drought, while others vary. The result generated a set of 50 unique choice sets which were assigned to five different blocks, such that each respondent was required to respond to 10 choice sets. The choice set was constructed with three alternatives including an opt-out option (see Fig. 1). In the case of this study, the opt-out option is necessary as it represents real-life situation and reflects existing preferences for non-drought tolerant or traditional varieties. Overlooking the effect of opt-out effect in DCE simply infer that participants' preferences are not adequately considered and could lead to inaccurate measurement of attribute preferences and error in policy recommendation (Boxall, Adamowicz and Moon, Reference Boxall, Adamowicz and Moon2009; Campbell and Erdem, Reference Campbell and Erdem2019). Also, the DCE is highly susceptible to hypothetical bias (Usk and Chroeder, Reference Usk and Chroeder2009; Moser, Raffaelli and Notaro, Reference Moser, Raffaelli and Notaro2014). However, an unforced situation such as the use of the opt-out option does not completely exclude errors in estimation, the common bias in the experimental process is the omission and avoiding choice which may include opting for the opt-out option which is simpler to understand (Boxall, Adamowicz and Moon, Reference Boxall, Adamowicz and Moon2009). To control for this, participants are repeatedly reminded of the free will to choose between the designed drought-tolerant varieties. Such an approach culminates into a repeated reminder of the opt-out approach which has been found to reduce or mitigate hypothetical bias (Ladenburg and Olsen, Reference Ladenburg and Olsen2014; Alemu and Olsen, Reference Alemu and Olsen2018). In our experimental approach, the opt-out option is repeated in each choice card and participants are made to understand that opt-out options represent their non-interest in any of the drought-tolerant choices and indicate their preferences for the lowest levels in each attribute which are relatively close to attributes of traditional varieties and serves as the status quo for this study.

Figure 1. Sample choice card.

In the data collection stage, aside presentation of choice cards, a short survey was presented to households covering their respective socioeconomic characteristics.

Mixed logit and hierarchical Bayesian estimation model

To derive the marginal values for DTMV attributes (yield, maturity, resistance to Striga, nitrogen use efficiency, cob size, grain size, and price), we model farm household choices based on the behavioral framework of random utility theory (McFadden, Reference McFadden1974). For the choice scenarios presented to farmers (Maize seed A, Maize seed B, Maize Seed C, and Opt-Out—see Fig. 1), we assume that the indirect utility associated with maize farmer n choosing alternatives j in a choice set t is defined as follows:

(1)$$u_{njt} = {x}^{\prime}_{njt}\;\beta _n + \varepsilon _{njt}\;$$

where ${x}^{\prime}_{njt}$ represents the vector of choice attributes of alternatives j, β represents the preference parameters for each DTMV attributes, and $\varepsilon _{njt}$ is the error components of utility independently and identically distributed across maize farmers and alternatives. The opt-out option takes similar modeling approach and, in this context, is represented by maize farmer non-interest in any of the DTMV options and it is indicative of the lowest level of attributes which are related to current traditional management practices. In a conditional or multinomial logit model, the random parameters $\varepsilon _{njt}$ are Gumbel-distributed errors, and are specified to be the same for all choices made by individual maize farmers, and are illustrated as follows for a maize farmer n chooses alternatives i from among J alternatives:

(2)$$P_{nit} = \displaystyle{{\exp \;( {{{x}^{\prime}}_{nit}\beta } ) } \over {\mathop \sum \nolimits_{J = 1}^J {\rm exp}( x^{\prime}_{njt} \beta ) }}$$

There is however a shortcoming in the assumption of the independence of irrelevant alternatives property and inability to conduct random test variation. The mixed logit model also known as the random parameter logit overcomes this limitation by allowing random test variation and observing substitution patterns (McFadden and Train, Reference McFadden and Train2000).

To account for preference heterogeneity, we interact farmers socioeconomic characteristics with attributes of DTMVs, and the researcher specified distribution for β _n, $f( \beta \vert \vartheta )$ where $\vartheta$ are the parameters of the distribution which has a mean vector b and covariance matrix S, β _n ~ N(b, S). The unconditional probability of sequences of choices is defined as follows:

(3)$$P_n( \vartheta ) = \coprod_t\displaystyle{{\exp ( {x_{nit}^{\rm^{\prime}} \beta_n} ) } \over {\mathop \sum \nolimits_{\,j = 1}^J \exp ( {x_{njt}^{\rm^{\prime}} \beta_n} ) }}f( \beta \vert \vartheta ) d\beta$$

The mixed logit model presented can be estimated using the maximum simulated likelihood approach.

For robustness analysis, this study also employs the hierarchical Bayesian estimation procedure. The advantage of the hierarchical Bayesian procedures over the classical mixed logit method is that the common approach of using maximization of the likelihood function in classical methods is not required in the Bayesian procedure; this help to overcome the problems of convergence which can be due to poor starting values in the model or the inclusion of bounded distributions (Train, Reference Train2012). Also, the Bayesian procedure under more relaxed conditions attains desirable estimation properties such as consistency and efficiency (Train, Reference Train2012).

Following the standard procedure, we specified the prior beliefs about b and S are specified as b ~ N(0, v), v is large, and S ~ IG(v, 1) for v → 1, where IG stands for inverted Gamma distribution. The parameters b and S are called population level parameters. We use Gibbs sampling to estimate three sets of parameters $b, \;\;S, \;\;and\;\;\beta _i\forall i.$ The posterior for $b, \;\;S\;and\;\beta _i\forall i$ is

(4)$$K( b, \;\;S, \;\beta _i\vert Y) \propto \;\mathop \coprod \limits_i \displaystyle{{\exp ( {x_{tin}^{\rm^{\prime}} \beta_i} ) } \over {\mathop \sum \nolimits_{\,j = 1}^j \exp ( {x_{tin}^{\rm^{\prime}} \beta_i} ) }}\;\emptyset ( {\beta_i{\rm \vert }b, \;\;S} ) k( {b, \;S} ) $$

The Gibbs sampling involves taking a sequence of draws in which each draw for a parameter is estimated conditional on the parameters in the model in a hierarchical procedure. During estimation, the algorithm starts with initial values of b ⁰, S ⁰, and $\beta _i^0$. The nth iteration of the Gibbs sampling can be estimated using the following steps (1) take a draw of b ⁿ, from f(β, S) where β is the mean conditional on S ⁰ and $\beta _n^0$; (2) take a draw of S ⁿ conditional on b ⁿ and $\beta _i^0$, and (3) take a draw of $\beta _i^n$ conditional on b ⁿ and S ⁿ. These steps are repeated sequentially over many iterations until the values have converged to draws in the posterior. Several draws from the posterior are then used to calculate the required statistics.

Using Stata 16, we fit the Bayesian mixed logit model using ‘bayesmixedlogit’ which uses the adaptive Markov chain Monte Carlo sampling from the posterior distribution of individual level coefficients and fixed coefficients (Baker, Reference Baker2023).