Sorghum *(Sorghum Bicolor L. Moench)* is one of the main staple crops for the world’s poorest and food-insecure people. It is the second major crop (after maize) across all ecologies in Africa and is one of the main staples for people in Eastern and Southern Africa (ESA). Sorghum is a dual-purpose crop where both grain and stover are highly valued outputs. Globally, sorghum is grown in 46 million hectares accounting for an annual production of 60 million tones [1]. Developing countries account for 90% of total area and 70% of total output, with Africa and Asia each accounting for 20% to 30% of the global production. In Africa sorghum is mainly cultivated by small-scale resource poor farmers and production is characterized by limited use of fertilizer and improved seeds [2]. In Kenya, sorghum is an important traditional food crop in the dry land areas of Nyanza, Eastern, and Coast provinces. On average, the crop occupies an area of 139,000 hectares with an annual production of 110,000 tons [3]. The country’s per-capita sorghum consumption is approximately 3.0 kg per year.

Despite the numerous benefits of sorghum, its production in Kenya has remained heavily constrained by diseases, insect pest damages, and rainfall variability. In response to these constraints, national and international research organizations have developed and released several high-yielding and stress tolerant varieties of sorghum with desirable agronomic and market traits. The development of improved sorghum varieties in Kenya started in the early 1970s and by the year 2005, at least seven varieties had been released in the country [4]. They include; Gadam, Serena, Seredo, KARI Mtama 1, KARI Mtama 3, IS76#23, and KAK 7780. The release of the varieties was followed by an intensive promotion programme by the Ministry of Agriculture under the orphan crop multiplication programme and the Eastern province horticulture and traditional food crops project. Reports indicate that the adoption of the sorghum varieties has been good both in the medium and marginal low potential areas of the province [5].

Although technology adoption remains one of the most researched areas in agricultural economics, very few studies [6–9] have looked at the adoption of improved sorghum varieties. Further, the existing studies have focused on the role of socioeconomic, institutional, and policy factors in explaining the adoption of improved sorghum varieties. This paper distinguishes itself by providing a greater insight into sorghum studies by focusing on the effect of variety attributes on adoption.

Another motivation for this study is that, many previous adoption studies have only focused on one improved variety (for example, [10–12] by using the conventional logit or probit approach. However, in the present study, more than one improved varieties exist each with varying production, consumption, and marketing traits and farmers are more likely to simultaneously adopt more than one variety in order to address their multiple needs. We use a multivariate probit regression which allows estimation of several correlation binary choices jointly [13]. The multi variateprobit model takes into account the potential interdependence in technology choice and the possible correlation in the adoption of alternative improved varieties. The probability of adoption of any particular sorghum variety is estimated conditional on the choice of any other related variety.

This paper is based on data collected from a stratified random sample of 140 sorghum farmers in Mbeere South County of Kenya. Mbeere South County is in an ASAL area of Kenya and sorghum is mainly grown as a food crop to edge farmers against the risk of crop failure. The rest of the paper is organized as follows:section two presents the methods and the variables used in the empirical analysis while section three reports and discusses the results; section four concludes.

### Empirical model

A multivariate probit was used to analyze the effect of varietal characteristics on adoption of improved sorghum varieties. A multivariate probit has been used previously in a number of adoption studies [14–16], the model accounts for simultaneous adoption of multiple varieties and the potential correlations among the adoption decisions. The multivariate probit is an extension of the probit model [13] and is used to estimate several correlated binary outcomes jointly.

The model is specified as follows:

${{\mathit{Y}}_{\mathit{im}}}^{*}={\mathit{\beta}}_{\mathit{m}}{\mathit{X}}_{\mathit{im}}+{\mathit{\u03f5}}_{\mathit{im}}$

(1)

Where ${\mathit{Y}}_{\mathit{im}}^{*}\left(\mathit{m}=1,\dots ,\mathit{k}\right)$ represent the unobserved latent variable of improved sorghum varieties adopted by the *i*^{
th
} farmer. (*i* = 1, …,*n*). Out of the seven improved varieties released to farmers in the study area, only two varieties were widely adopted (Gadam and Serena), very few farmers had adopted Seredo and KARI Mtama 1 while no farmer had adopted KARI Mtama3, IS76#23, and KAK 7780. Therefore, the analysis was limited to only two improved varieties; Kimbeere variety (the most common local variety) was also included in the analysis for comparison purposes. Therefore, in this case k = *Serena*,*Gadam*, *and Kimbeere. X*_{
im
} is a 1 × *k* vector of observed variables that affect the variety adoption decision, the variables include household socioeconomic, institutional factors, and variety attributes. *β*_{
m
} is a *k* × 1 vector of unknown parameters to be estimated *ϵ*_{
im
}, *m* = 1, …, *M* are the error terms distributed as multivariate normal, each with a mean of zero, and variance-covariance matrix V , where V has values of 1 on the leading diagonal and correlations [17].

Equation (

1) is a system of

*m* equations that as shown in Equation

2 below;

$\left\{\begin{array}{l}{\displaystyle {\mathit{Y}}_{1}^{*}}={\displaystyle {\mathit{X}}_{1}}{\displaystyle {\mathit{\beta}}_{1}}+{\displaystyle {\mathit{\u03f5}}_{1}}{\displaystyle {\mathit{Y}}_{1}}=1\phantom{\rule{0.3em}{0ex}}\mathit{if}\phantom{\rule{0.3em}{0ex}}{\displaystyle {\mathit{Y}}_{1}^{*}}\succ 0,{\displaystyle {\mathit{Y}}_{1}}=0\phantom{\rule{0.5em}{0ex}}\mathit{otherwise}\\ {\displaystyle {\mathit{Y}}_{2}^{*}}={\displaystyle {\mathit{X}}_{2}}{\displaystyle {\mathit{\beta}}_{2}}+{\displaystyle {\mathit{\u03f5}}_{2}}{\displaystyle {\mathit{Y}}_{2}}=1\phantom{\rule{0.3em}{0ex}}\mathit{if}\phantom{\rule{0.3em}{0ex}}{\displaystyle {\mathit{Y}}_{2}^{*}}\succ 0,{\displaystyle {\mathit{Y}}_{2}}=0\phantom{\rule{0.5em}{0ex}}\mathit{otherwise}\\ {\displaystyle {\mathit{Y}}_{3}^{*}}={\displaystyle {\mathit{X}}_{3}}{\displaystyle {\mathit{\beta}}_{3}}+{\displaystyle {\mathit{\u03f5}}_{3}}{\displaystyle {\mathit{Y}}_{3}}=1\phantom{\rule{0.3em}{0ex}}\mathit{if}\phantom{\rule{0.3em}{0ex}}{\displaystyle {\mathit{Y}}_{3}^{*}}\succ 0,{\displaystyle {\mathit{Y}}_{3}}=0\phantom{\rule{0.5em}{0ex}}\mathit{otherwise}\end{array},\phantom{\rule{1.1em}{0ex}}\right\}$

(2)

This system of equations is jointly estimated using maximum likelihood method.

The implicit functional form of the empirical model is specified as follows: decision to adopt = *f* (age, gender, education, farming experience, household size, farm size, off-farm income, distance to the market, extension visits, non-livestock asset value, group membership, yield, drought tolerance, pest resistance, maturity, farm gate price, cooking qualities, striga resistance, brewing qualities, and taste) + ϵ.