Identifying determinants of adoption

Often system technologies are adopted partially, that is, only some of the components are applied by the farmer. Adoption of such technologies has been estimated previously using different models such as multivariate Bayesian (Aldana et al., Reference Aldana, Foltz, Barham and Useche2011) or ordered probit models (Wollni et al., Reference Wollni, Lee and Thies2010). ISFM adoption, in particular, has previously been estimated as a binomial process whereby it is either adopted or not adopted (Mugwe et al., Reference Mugwe, Mugendi, Mucheru-Muna, Merckx, Chianu and Vanlauwe2009; Odendo et al., Reference Odendo, Obare and Salasya2009; Adolwa et al., Reference Adolwa, Okoth, Mulwa, Esilaba, Mairura and Nambiro2012) or as a correlated binomial process of discrete choices (Marenya and Barrett, Reference Marenya and Barrett2007). However, the adoption of additional components of ISFM leads to an increase in AE justifying the use of an ordered regression model (ORM).

According to Long and Freese (Reference Long and Freese2001) the ORM is given as:

(1)$$y_i^{\ast} = X_i {\rm \beta} + {\rm \varepsilon} _i, $$

where y* is the latent variable for farmer i, ε_i is the random error, X _i is a vector of independent variables, and β represents the parameters to be estimated. The measurement model divides y* into J ordinal categories:

(2)$$y_{i\;} = m{\rm \;} \;{\rm if}\;T_m - 1\; \le \; y_i^{\ast} \lt T_{m}, \;{\rm for}\;\; m\; = 1\; \;{\rm to}\;\; J,$$

where the cut-points T ₁ through T _J−1 are estimated with the assumption that T ₀ = −∞ and T _J = ∞.

In our case, the observed independent categories are tied to the latent variable by the measurement model:

(3)$$y_{i\;} = \left\{ {\matrix{ {1 \to {\rm no}\,{\rm adoption}} & {{\rm if}\;T_0 = - \infty \le y_i^{\ast} \lt T_{1\;} \;} \cr {2 \to {\rm partial}\,{\rm adoption}\;{\rm 1}} & {{\rm if}\;T_1 \le y_i^{\ast} \lt T_2} \cr {3 \to {\rm partial}\,{\rm adoption}\;{\rm 2}} & {{\rm if}\;T_2 \le y_i^{\ast} \lt T_3} \cr {4 \to {\rm complete}\,{\rm adoption}} & {{\rm if}\;T_3 \le y_i^{\ast} \lt T_4 = \infty.} \cr}} \right.$$

For a given value of x the probability of an observed outcome is given as:

(4)$${\rm Pr(}y = m\left \vert {{\rm \;} x} \right.{\rm )} = {\rm Pr(}T_{m - 1} \le y^{\ast} \lt T_m \left \vert x \right..$$

As shown in equation (4), the probability of observing y = m for a given value of x relates to the region of the distribution where y* falls between the cut-points T_m−1 and T_m. If y* is substituted with Xβ + ε then the predicted probability in the ORM becomes:

(5)$${\rm Pr(}y = m\left \vert {x} \right.{\rm )} = F(T_m - X{\rm \beta} ) - F(T_{m - 1} - X{\rm \beta} ),$$

where F is the cumulative distribution function (cdf) for ε. Since we estimate an ordinal logit model, F is logistic with Var (ε) = π²/3. Equation (5) can thus be simplified to:

(6)$${\rm Pr} \le = F(T_m - X{\rm \beta} )\;\; {\rm for} \; {\rm m} = 1\;{\rm to}\;J_1. $$

Equation (6) can be used to compute cumulative probabilities for the ORM, which is equivalent to J−1 binary regressions assuming that the slope coefficients (β) are identical across each regression. This important assumption for the ORM is known as the parallel regression or proportional odds assumption (Long and Freese, Reference Long and Freese2001). The Stata command ‘omodel’ developed by Wolfe and Gould (Reference Wolfe and Gould1998) was used to test this assumption by an approximate likelihood-ratio (LR) test.

It is common in empirical work that some β’s differ across values of J resulting in the violation of the parallel regression assumption. The partial proportional odds model overcomes these restrictions by allowing some β coefficients to be the same for all values of J, whereas others can differ (Williams, Reference Williams2006). The model is given as:

(7)$$\eqalign{P\left( {Y_i \gt J} \right) & = \displaystyle{{{\rm exp(\alpha} _j X1_i {\rm \beta} 1 + X2_i {\rm \beta} 2 + X3_i {\rm \beta} 3_j {\rm )}} \over {1 + \left\{ {{\rm exp(\alpha} _j + X1_i {\rm \beta} 1 + X2_i {\rm \beta} 2 + X3_i {\rm \beta} 3_j {\rm )}} \right\}}}, \cr & \qquad J = 1,2, \ldots, \; m - 1.}$$

In the equation above the β’s for X1 and X2 are the same for all categories J, while those of X3 are allowed to differ.

Description and specification of the models

An approximate LR test of proportionality of odds across categories was carried out on the ordinal logistic regression models for Tamale and Kakamega. The parallel lines assumption was rejected at the 5% level in both cases; Tamale (χ² (23) = 44.39; Prob > χ² = 0.0047) and Kakamega (χ² (26) = 45.75; Prob > χ² = 0.0097). The violation of this assumption requires the use of the partial proportional odds model. In the case of Tamale, constraints for parallel lines were removed for slope and plot size (P < 0.05). For Kakamega, the parallel lines assumptions was violated for plot area (P = 0.015), % sand (P = 0.006), total carbon (P = 0.034), and number of adult members in the household (P = 0.015). The final models for both cases do not violate the parallel lines assumption as their test statistics were insignificant (Tamale-χ² (20) = 27.73; Prob > χ² = 0.116 and Kakamega-χ² (18) = 15.21; Prob > χ² = 0.647). Given that there were four adoption categories, a series of logistic regression models were estimated in case of violation of the assumption:

• • Model 1 – NA versus PA1 (combination of 2 components) and PA2 (combination of 3 components) and CA (combination of all 4 components);

• • Model 2 – NA and PA1 versus PA2 and CA;

• • Model 3 – NA and PA1 and PA2 versus CA.

If the variables met the proportional odds assumption their parameter estimates would be identical in the three models and could be combined into a single model. If this was not the case different estimates are shown for the unique models. The models were estimated in Stata 12 using the gologit2 (Williams, Reference Williams2006) program.

The study sites

The study was conducted in Tamale, Ghana and Kakamega, Kenya (Fig. 1). Both sites are located in the moist savanna and woodland zone that includes the Guinea Savanna of West Africa and East Africa's Highland Mosaic (Sanginga and Woomer, Reference Sanginga and Woomer2009).

Fig. 1. Map of the two study sites in Ghana and Kenya.

Tamale is a rapidly growing agglomeration and is considered the fastest growing city in West Africa (Gyasi et al., Reference Gyasi, Fosu, Kranjac-Berisavljevic, Mensah, Obeng, Yiran and Fuseini2014). It is Ghana's third largest city and the capital of its northern region. Agricultural production is dominated by vegetable production in backyards and open spaces within city confines. However, cereal cultivation, particularly of maize (Zea mays L.) is still common even within the urban areas. Maize is a major staple crop in Tamale and Kakamega and constitutes a large share of the dietary intake of the local communities (Odendo et al., Reference Odendo, Ojiem, Bationo and Mudeheri2007; Chagomoka et al., Reference Chagomoka, Unger, Drescher, Glaser, Marschner and Schlesinger2016). At the fringes of the city, beyond a 3 km radius from the center, peri-urban agriculture is dominated by cultivation of cereals such as maize and rice (Oryza sativa and Oryza glaberrima), tuber crops and vegetables. The rural areas surrounding the city have predominantly cereal-based cropping systems with maize as the dominant crop. Groundnut (Arachis hypogaea) is the most common legume. Other crops grown include yams (Dioscorea spp.), cowpea (Vigna unguiculata) and vegetables that are mostly grown along field edges. Tamale receives an annual rainfall of about 1100 mm, which is uni-modally distributed. Although the landscape is flat, sheet erosion is common due to limited tree cover. The average altitude is 183 m above sea level (asl). ISFM activities in the study area have been carried out by organizations such as the Savanna Agricultural Research Institute (SARI) for the past four years but mainly concentrated on rural areas.

Kakamega County is one of the administrative units of Kenya and consists of several urban centers including Kakamega (the headquarters of the county). The rest of the county is pre-dominantly rural. In the towns, mainly vegetables such as cabbage (Brasssica oleracea), cowpea and kale (Brassica oleracea) are grown. Other crops common in urban and peri-urban areas include banana, bean (Phaseolus vulgaris) and maize. In the rural areas, maize is the dominant staple grown mainly for subsistence. Cash crops are also grown alongside maize; in the wetter zone tea (Camellia sinensis) is cultivated, whereas in the less humid zone sugarcane (Saccharum officinarum) is the main cash crop. Cereal-legume intercropping systems dominate the area with maize–bean systems being the most common. Due to extensive ISFM activities over the last ten years soybean (Glycine max), which has a high potential for value addition, has gradually been incorporated in the cropping systems. Kakamega receives as much as 2000 mm of rainfall per annum in a bi-modal pattern. Therefore, most farmers take advantage of this to crop twice per year. The landscape is steep in some areas and average altitude is 1535 m asl.

Data collection: survey and laboratory analysis

Data were collected in a household survey between July 2014 and February 2015. To select respondents, a stratified random sampling approach was utilized at both sites. Farming households were stratified into participants in ISFM activities and non-participants. Participant farmers were randomly selected from lists of participating farmers, which were compiled with the assistance of extension officers, local research institutions, village elders and lead farmers who had been involved in disseminating ISFM activities. Non-participants were randomly selected from a list of farmers, which was obtained from the Urban Food^plus project in Tamale (Bellwood-Howard et al., Reference Bellwood-Howard, Häring, Karg, Roessler, Schlesinger and Shakya2015) and from the Agricultural Sector Development Support Programme of Kenya in Kakamega (Agricultural Sector Development Support Programme, 2014). In this way, a total of 285 farmers were selected in Tamale but information from three farmers was not utilized for analysis due to missing data. In Kakamega, a total of 300 farmers were selected, but one farmer had to be dropped because his soil samples got lost. Face-to-face interviews using a structured questionnaire were conducted. The questionnaire contained sections on socio-demographic characteristics of household members, farm characteristics, crop production and management, as well as off-farm activities. The reference period for all economic activities comprised the last 12 months prior to the interview.

In addition, soil samples (0–20 cm depth) were drawn from 322 and 459 maize plots belonging to farmers interviewed in Tamale and Kakamega, respectively. Some of these maize plots were closer to their homesteads (in-fields) whereas others were further away (out-fields). These samples were taken to capture information on soil fertility indicators influencing ISFM uptake at the plot level. Farmers often use local soil quality indicators such as tilth (or the ‘feel’ of the soil), soil color, workability of the soil, productivity in terms of crop yield, vigor of growth or intensity of leaf color and the presence of soil fauna (Barrios et al., Reference Barrios, Delve, Bekunda, Mowo, Agunda, Ramisch, Trejo and Thomas2006; Mairura et al., Reference Mairura, Mugendi, Mwanje, Ramisch, Mbugua and Chianu2007). Therefore, we deemed it appropriate to collect data on key chemical and physical indicators such as soil organic carbon (SOC), total C, total nitrogen (N), available phosphorus (P), pH and soil texture (% clay, % sand, % silt) that may mirror these indigenous criteria. To this end three to five sub-samples were collected from each maize field cultivated (as long as it was accessible) in the previous season. These sub-samples, mixed to form a composite sample, were immediately air-dried and sieved to 2-mm. Subsequently, a subsample of the soil (about 10%) was subjected to laboratory analysis: SOC (Walkley–Black method), available P as Bray-P, pH water (2.5 : 1 water) and soil texture were determined according to Okalebo et al. (Reference Okalebo, Gathua and Woomer1993). Elemental analysis (combustion method) was used to determine total N and C after grinding samples to 0.5 mm. The FLASH 2000 Organic Elemental Analyzer Thermo Scientific (Thermo Fisher Scientific Inc. Waltham, MA, USA) was used for this purpose. This instrument allows rapid, precise and environmental-friendly determinations of C, N and sulfur in soils and other materials (Jimenez and Ladha, Reference Jimenez and Ladha1993). The dry combustion used by this instrument provides more reliable data of SOC than the Walkley–Black method (Terhoeven-Urselmans et al., Reference Terhoeven-Urselmans, Vagen, Spaargaren and Shepherd2010). Unused portions of the samples were subjected to mid-infra-red (MIR) analysis. Non-destructive infra-red spectroscopy (NIRS) methods offer a quick, efficient, accurate and cost-efficient means of analyzing large numbers of soil samples (Viscarra Rossel et al., Reference Viscarra Rossel, Walvoort, McBratney, Janik and Skjemstad2006). The instrument used for analysis was a TENSOR 27 HTS-XT (Bruker Co., Billerica, MA, USA) MIR spectrometer. This instrument captures MIR spectral data using the HTS-XT diffuse reflectance method with spectral measurement ranging between 4000 and 400 cm⁻¹ with 4 cm⁻¹ resolution (3578 data points). Each sample was loaded onto an aluminum microtiter plate, which has 96 wells or shallow holes, in two replicates. Two spectra from each sample were averaged before calibration and analysis. For principal components analysis (PCA) and partial least-squares regression, about 90% of the MIR spectra were chosen for calibration and the remaining 10% were used for validation. Partial least-squares regression was carried out on the calibration set with reference values obtained from the conventional soil analysis. Following Terhoeven-Urselmans et al. (Reference Terhoeven-Urselmans, Vagen, Spaargaren and Shepherd2010), prediction performance was determined using the coefficient of determination (r ²) of the linear regression of predicted against measured values, the root-mean-square errors of calibration (RMSEC), and the root-mean-square errors of prediction (RMSEP).

Hereby RMSEC is computed as

(8)$${\rm RMSEC} = \sqrt {\displaystyle{{\mathop \sum \nolimits_{i = 1}^N (y_i - x_i )^2} \over {N - A - 1}}}, $$

where A is the number of principal components used in the model.

In general, good predictions have an r ² ⩾ 0.75, whereas satisfactory predictions have an r ² of 0.65–0.74 (Shepherd and Walsh, Reference Shepherd and Walsh2002; Terhoeven-Urselmans et al., Reference Terhoeven-Urselmans, Vagen, Spaargaren and Shepherd2010). R software was used to conduct PCA and partial least-squares regression, which were in turn utilized to generate predicted values for the soil variables.