Common tools for typological studies

Studies of farming systems, which addressed objectives similar to those of the current study, have used typological analysis to classify prevailing practices among farmers and identified farmer characteristics that determine their tendency to engage in those sets of practices (e.g., Vanclay, Reference Vanclay2005; Chikowo et al., Reference Chikowo, Zingore, Snapp and Johnston2014). Such analyses usually employ multivariate statistical approaches using a variety of techniques (Richarme, Reference Richarme2002). The most commonly applied techniques in this regard include factor analysis (FA), principal component analysis and cluster analysis (McBride and Johnson Reference McBride and Johnson2006; Todde et al., Reference Todde, Murgia, Caria and Pazzona2016; Kamau et al., Reference Kamau, Till, Lisa and Christian2018).

The usefulness of each of these techniques is situation dependent. If the analyst believes that certain underlying constructs influence the covariations among the variables (latent variables), EFA is an appropriate technique to identify the constructs. EFA segregates the variables into parsimonious groups of few inter-correlated ones, influenced by the supposed latent constructs called factors. More specifically, if there is prior evidence of the number and nature (correlated variables) of factors expected to emerge from the analysis, confirmatory factor analysis should be applied (Fabrigar et al., Reference Fabrigar, Wegener, MacCallum and Strahan1999; O'Rourke and Hatcher, Reference O'Rourke and Hatcher2013).

The above classification techniques have generally used a wide range of variables, including farm enterprise structural physical, managerial and financial performance data to identify typologies, which the analysts further characterize using household characteristics, resource endowment, institutional/social capital and farm characteristic variables (see Jha et al., Reference Jha, Gupta and Pandey2000; McBride and Johnson, Reference McBride and Johnson2006; Pandey, Reference Pandey2010).

We defined OFM descriptively as a set of related decisions/actions that a farmer takes at the household level to obtain the input for use (McConnell and Dillon, Reference McConnell and Dillon1997). From the literature and validation by farmers, we identified a universal set of observable organic fertilizer use decisions (see Lagerkvist et al., Reference Lagerkvist, Shikuku, Okello, Karanja and Ackello-Ogutu2015) to support possible sub-sets of decisions by farmers in the study area. Since there is no prior information about how farmers take organic fertilizer decisions, we could not assume any number or nature of expected factors. Hence, we applied EFA on observed decisions/actions of farmers to identify common factors as OFM approaches.

Conceptual framework

Since the 1960s, farms in developing countries are noted to be complex sets of inter-related components, including crop and/or livestock production enterprises as well as farm management. The components function together as a purposeful and open stochastic dynamic system with the various components as subsystems. One cannot deduce the total value of the system function by considering components in isolation (i.e., using the reductionists approach) (McConnell and Dillon, Reference McConnell and Dillon1997). Besides the complexity of the systems, such farms are also managed implicitly: farmers do not formalize what they do by keeping records or institute operational systems. They are, however, able to provide self-reported information on management decisions and practices during formal farm surveys (Norman et al., Reference Norman, Worman, Siebert and Modiakgotla1995). Therefore, farm management studies seeking a full understanding of how farmers manage such systems or any of their components should adopt a systems approach to analyzing farm-level data.

Within a broader context of sustainable soil management, this study examines organic fertilizer use management approaches under conditions where the farm-household cannot buy the input from the market, but must instead generate it through a farm-input generation subsystem. The subsystem becomes a backwardly integrated enterprise that must be managed to produce (McConnell and Dillon, Reference McConnell and Dillon1997) organic fertilizer for use in cereal production enterprise of smallholder farm households.

In order to identify the approaches farmers adopt to manage the subsystem, we assumed they manage the subsystem implicitly according to Mowo et al.'s (Reference Mowo, Bert, Oene, Laura, German, Mrema and Riziki2006) soil fertility decision-framework (see Fig. 1) within which smallholder farmers operate. Under this framework, the farmer plays a triple role: entrepreneurial, managerial and craftsmanship (laborer). As an entrepreneur, he or she defines his/her organic fertilizer use goals and devises strategies to meet the goals. The farmer allocates resources, as a manager, toward implementing the plan to achieve the goals. Systematically, he or she also manages the input generation process following the five-stage soil management decision-cycle shown in Figure 1. A farmer implicitly analyses his/her organic soil fertility needs and thereby decides on specific objectives for using organic fertilizer. He/she then chooses from available alternatives the type of organic fertilizer to use and therefore selects materials needed to process it.

Fig. 1. Smallholder-farmers' decision framework of managing soil nutrients.

Source: Modified after Mowo et al. (Reference Mowo, Bert, Oene, Laura, German, Mrema and Riziki2006).

These decisions feed into plans to source the materials. The farmer executes the plans by procuring the input or its raw materials and processing them. As a craftsperson, the farmer employs skills (own or hired) to carry out and monitor activities required to obtain the input for a given cropping season (Mowo et al., Reference Mowo, Bert, Oene, Laura, German, Mrema and Riziki2006). The process and its performance are, at the end of each season, implicitly evaluated to inform the need for changes in the strategy. Each stage of the operations management-cycle shown in Figure 1 involves several alternative decisions/actions from which a farmer can choose.

Farmers' goals influence their organic fertilizer use strategies (Norman et al., Reference Norman, Worman, Siebert and Modiakgotla1995), which, in turn, influence the decisions/actions taken within the management cycle. A set of decisions/actions taken at the various stages of the cycle forms a trajectory of management, depicting a latent construct underlying farmer's decisions. Different constructs that influence various trajectories of observed organic fertilizer use decisions, in our case, are the equivalence of Mowo et al.'s (Reference Mowo, Bert, Oene, Laura, German, Mrema and Riziki2006) strategies that farmers employ to meet their organic fertilizer use goals. We shall subsequently refer to these strategies as OFM approaches.

The preceding discussion implies that the OFM approach adopted by a farmer is a construct and cannot be observed by the researcher. The analyst, however, does observe a set of decisions/actions that a farmer took. This set of decisions/actions is a manifestation of the underlying approach and therefore identifies a farmers' OFM approach (McBride and Johnson, Reference McBride and Johnson2006). However, it is practically not possible and even needless to identify an individual approach of farmers. Instead, groups of farmers may take the same trajectory of decisions/actions, for that matter, one OFM approach. This implies that observation of a wide range of farmer-decision sets from a population of farmers manifests existing OFM approaches adopted by farmers. One can identify the approaches through a typological analysis of the observed management decisions/actions (see Table 1) (McBride and Johnson, Reference McBride and Johnson2006; Chikowo et al., Reference Chikowo, Zingore, Snapp and Johnston2014; Todde et al., Reference Todde, Murgia, Caria and Pazzona2016).

Table 1. OFM decision/practice variables used in EFA to identify OFM approaches

^a These are variables with almost constant values observed among the surveyed farmers. Thus, they were not included in the analysis.

It is well established in the literature (e.g., Mowo et al., Reference Mowo, Bert, Oene, Laura, German, Mrema and Riziki2006; Kamanga et al., Reference Kamanga, Waddington, Robertson and Giller2009; Shiferaw et al., Reference Shiferaw, Okello and Ratna Reddy2009; Mulwa et al., Reference Mulwa, Paswel, Dil and Menale2017) that farmers' background factors influence their OFM decisions. These factors include inter alia human capital status, physical resource endowment characteristics, farming environment (soil and biodiversity) and the external environment (institutional and social capital, political, technological and economic context). These factors shape their farm objectives, perceptions about cost/benefits associated with various OFM decisions, and set constraints within which the decisions are made.

Assuming, therefore, that a farmer chooses to adopt an OFM approach that maximizes the expected benefit from organic fertilizer use under the constraints set by his/her background factors, a function that characterizes the relationship between the adopted approach and the farmer's background factors can be derived to explain the uptake of the latent approaches (Abdulai and Huffman, Reference Abdulai and Huffman2014; Abdulai, Reference Abdulai2016; Tambo and Wünscher, Reference Tambo and Wünscher2017; Danquah et al., Reference Danquah, Twumasi and Asare2019). Following McBride and Johnson (Reference McBride and Johnson2006), we assumed that the latent OFM approaches are characterized by a set of observed farmer characteristics and farming context variables (see Table 2).

Table 2. Farmer/plot variables used in SUR characterization model

Factor scores of farmers on approaches were obtained by Stata's post-FA command ‘Score.’

^a As in Xiaohao et al. (Reference Xiaohao, Hartog and Sun2010) and Dohmen et al. (Reference Dohmen, Huffman, Schupp, Falk, Sunde and Wagner2011), risk willingness scores were obtained by asking farmers to grade themselves on an eleven-point scale of their readiness to take a risk in general. To validate the scores, farmers were presented with a hypothetical lottery case to make choices, during which they could attempt to play more than once. Options with higher levels of pay-off are associated with fewer numbers of trials possible. Choosing an option with more rounds of trials implies the avoidance of risky situations.

^b We estimated crop diversification as an index by subtracting the Herfindahl index (HI) from one (1 − HI), where HI was calculated as follows: ${\rm HI} = \sum\nolimits_{i = 1}^n {s_i^2 }$, where S _i is the proportion of ith crop, given as $S_i = \lpar A_i/\mathop \sum \nolimits_{i = 1}^n A_i\rpar$ and, A_i = area under ith crop, $\sum\nolimits_{i = 1}^n {A_i = {\rm Total}\,{\rm cropped}\,{\rm area}}$, and i = 1, 2, 3, 4,…, n, the number of crops considered. In this study, we used eight crops common in the study areas to calculate the index. The ranges from 0 (specialization) to 1 (complete diversification). Any value above zero signifies diversification. Precisely, we estimated the index.

Data and description of variables

This study used an observational data set of the 2017/18 crop season, obtained from a multistage random sample of 250 smallholder cereal farmers in northeastern Ghana. The farmers provided the data in response to a set of structured questions during computer-assisted personal interviews (CAPI) with enumerators. The questionnaire solicited two main categories of variables. The first category is the list of organic fertilizer decision variables in Table 1 (referred to as decisions/actions). Many of these decisions have been promoted in the study area by policy agents such as NRGP, AGRA and PAS (Martey, Reference Martey2018). Based on a literature review (e.g., Lagerkvist et al., Reference Lagerkvist, Shikuku, Okello, Karanja and Ackello-Ogutu2015), the questionnaire captured 35 organic fertilizer decisions, but only 25 of these decisions, listed in Table 1, were observed during the face-to-face CAPI with sampled farmers. These are grouped under the five phases (stages) of the decision-cycle in Figure 1.

Variables include organic fertilizer use objectives at phase 1, organic fertilizer types chosen at phase 2 and the main material component used, also at phase 2. Other decision variables indicate the sourcing plan/arrangement(s) a farmer adopts at phase 3 and the alternative model(s) of acquisition used at phase 4. Decisions taken at the monitoring stage (phase 5) have no observable outcomes; hence they are not empirically represented by any observed variable. They, however, directly affect phase 1 decision outcomes.

The second category of variables solicited by the study questionnaire includes farmer background factors, which we shall subsequently refer to as farmer/plot characteristics. These are classified further under four latent background variables. The first is household characteristics, which include gender, age, education of the farmer, household size, family labor force and production purpose. Other household characteristics are participation in organic soil management (training), farmer's risk attitude and diversity of crops on the farm (CDI) (Mulwa et al., Reference Mulwa, Paswel, Dil and Menale2017). We specify these variables to capture the effect of human capital on farmers' tendency to adopt the various OFM approaches (Shiferaw et al., Reference Shiferaw, Okello and Ratna Reddy2009). The second class of background variables comprises the total value of farm assets, non-farm income work, livestock size and plot size measured in hectares. These together represent a farmer's physical resource endowment. The third class of variables captures social capital and information access. These include whether a farmer has benefited from some soil fertility management policy, whether a farmer belongs to a farmer-based organization and whether he/she has contact with extension services. Finally, we also included farm-specific and geographical location variables, which include the cost of mineral fertilizer used per hectare, the distance (walking minutes) to cereal plot from a farmer's home, tenure of farmland, mean score of soil-quality and geographical location (zone) of a farmer/farm. Table 2 provides the list, description and summary statistics of all farmer/plot variables used in this study.

We used the observed OFM decision data for EFA to identify common OFM approaches whereas using the farmer/plot characteristic variables as independent variables in the second-step characterization regressions to identify farmer characteristics that explain the uptake of each of the OFM approaches. We used post-FA factor scores of farmers to represent the OFM approaches as dependent variables in the characterization regressions. In the next section, we present the empirical models and procedure for the two-step multivariate analysis (i.e., EFA and the characterization regressions).

Empirical EFA model and procedure

Assuming that some underlying but unknown number of constructs (latent factors) influence patterns of decisions and actions farmers take to secure organic fertilizer for their plots, EFA can be applied to the data set of observed farmer decisions to identify the latent factors, here referred to as OFM approaches (O'Rourke and Hatcher, Reference O'Rourke and Hatcher2013). The EFA model expresses each OFM decision variable as a linear combination of the underlying OFM approaches to be identified. With J decision variables, J multivariate regressions on an unknown set of management approaches as covariates are specified as (O'Rourke and Hatcher, Reference O'Rourke and Hatcher2013):

(1)$$\left\{{\matrix{ {V_1 = \beta_{11}F_1 + \beta_{21}F_2 + \cdots + \beta_{k1}F_k + \mu_1} \hfill \cr {\quad \,\vdots \quad \quad \quad \vdots \quad \quad \;\;\;\vdots \quad \;\;\vdots \quad \quad \quad \vdots } \hfill \cr {V_j = \beta_{1j}F_1 + \beta_{2j}F_2 + \cdots + \beta_{kj}F_k + \mu_j} \hfill \cr } } \right\}\comma \;$$

where V is an observed OFM decision variable with j = 1, …, J, and F = 1,…, k are the latent factors (underlying OFM approaches) influencing the variables V = 1, …, j, β is a matrix of linear coefficients, known as estimated factor loading of factors 1, …, k on V = 1, …, j, and μ = 1, …, j is a vector of residuals know as unique factors, analogous to regression error terms (Timm, Reference Timm2002; McBride and Johnson, Reference McBride and Johnson2006; O'Rourke and Hatcher, Reference O'Rourke and Hatcher2013).

If the data are normally distributed, the factors are best extracted (i.e., the system of equations is estimated) by maximum likelihood. However, we could not assume a multivariate normal distribution of the data because all variables included in the analysis are binary. We thus applied principal axis factoring (PAF) to extract the factors—a method that does not require normally distributed data. The number of factors obtained from the initial extraction equals the number of OFM approaches. However, only a few of these could be meaningfully interpreted and met other criteria for inclusion in the final extraction (McBride and Johnson, Reference McBride and Johnson2006; O'Rourke and Hatcher, Reference O'Rourke and Hatcher2013; Osborne, Reference Osborne2015). We applied the four criteria in selecting the factors recommended by Beavers et al. (Reference Beavers, Lounsbury, Richards, Huck, Skolits and Esquivel2013) and O'Rourke and Hatcher (Reference O'Rourke and Hatcher2013): (1) Kaiser's (eigenvalue ⩾1) rule, (2) the graphical scree-test, (3) the proportion of total variance explained by a factor and (4) the interpretability (meaningfulness) of factor rules.

The first four of the initial factors met at least three of the criteria and were retained. As recommended for analyses involving human behavior (Osborne, Reference Osborne2015), we expected that some form of correlation exists between potential OFM approaches (the factors). Hence, we rotated the factors by the oblique Promax algorithm, which captures such potential correlation, to arrive at a simple structure. The simple structure, in this case, had each factor loading significantly on only several (3–5) decision/action variables. Following McBride and Johnson (Reference McBride and Johnson2006) and O'Rourke and Hatcher (Reference O'Rourke and Hatcher2013), we considered factor loadings of ⩾0.4 significant for interpreting the results, even though a factor loading of 0.3, under the ideal condition that the factor explains about 50% of the variables' variance, has been suggested (Beavers et al., Reference Beavers, Lounsbury, Richards, Huck, Skolits and Esquivel2013). We labeled each factor (OFM approach) by the description of the OFM decision on which the factor loaded most significantly and described it using all decisions on which the factor loaded.

Characterization using seemingly unrelated regression (SUR) analysis

After EFA identified the OFM approaches, the next objective was to characterize the approaches by farmer/plot characteristics that explain their adoption. Assuming farmers' tendency to adopt a given OFM approach is driven by their background variables (Table 2), we expressed each OFM approach as a function of observed farmer/plot variables to identify characteristics that empirically affect adoption. In this case, the OFM approaches, as dependent variables, are not observed but can be represented by their factor scores. We therefore evaluated each farmer's score on each of the four factors (OFM approaches) following the EFA. These are used as dependent variables, representing the approaches in the characterization regression model.

However, we had to be sure that indeterminacy in the factor-score variables is low enough to allow estimation of empirically reliable characterization equations for the OFM approaches. We thus assessed the degree of factor score determinacy by calculating squared correlation coefficients (ρ ²) of factor score estimates of split samples (Green, Reference Green1976) obtained by regression method and by Barttlet's (Reference Bartlett1937) method. In each case, the ρ ² obtained was higher than 0.75, indicating that factor score indeterminacy is low (<0.25). Since the Barttlet factor score estimates are most likely the true factor scores (DiStefano et al., Reference DiStefano, Min and Diana2009) and produce unbiased regression parameters (Devlieger et al., Reference Devlieger, Mayer and Rosseel2016), we used them as the dependent variables for the characterization analysis. Furthermore, since factor-score estimates are equivalent to z-scores, they should be regressed on z-score standardized values of the independent variables; otherwise, the resultant model estimates cannot be interpreted (Zuccaro, Reference Zuccaro2010). Accordingly, we z-standardized the socio-economic variables in Table 2 before using them as regressors. The characterization model involves K approaches, each to be regressed on (i.e., characterized by) the same set of x = 1, 2, …., m farmer/plot characteristic variables of N = i, …, n observations, forming K = 1, …, k simultaneous equation system:

(2)$$\eqalign{& \left\{{\matrix{ {S_{1i} = \alpha_{11}x_{1i} + \alpha_{21}x_{2i} + \cdots + \alpha_{m1}x_{mi} + \varepsilon_{1i}} \hfill \cr {\quad \,\,\vdots \quad \quad \quad \vdots \quad \quad \quad \vdots \quad \;\;\,\vdots \quad \quad \quad \;\vdots } \hfill \cr {S_{ki} = \alpha_{1k}x_{1k} + \alpha_{2k}x_{2k} + \cdots + \alpha_{mk}x_{mk} + \varepsilon_k} \hfill \cr } } \right\}\comma \;\cr & K = 1\comma \;2\comma \;\ldots \comma \;k\semicolon \;\;x = 1\comma \;2\comma \;\ldots \comma \;m\semicolon \;\;i = 1\comma \;2\comma \;\ldots \comma \;N} $$

where S_ki is the farmer ith score on factor (OFM approach) k, which is to be explained by the kth equation, ɛ_ki is a random error term associated with the ith farmer in the kth equation, whereas α ₁ to α_m are vectors of coefficients (effects) of farm/farmer characteristics on farmers' tendency to adopt the kth OFM approach.

Equation (2) shows that for every ith farmer (observation), there are ɛ _1i to ɛ_ki random errors (i.e., one for each kth equation) to be estimated. Each of these equations can be efficiently and consistently estimated by ordinary least squares (OLS) (e.g., Jha et al., Reference Jha, Gupta and Pandey2000; Pandey, Reference Pandey2010) in a situation where the factor scores (i.e., S_ks) are obtained from orthogonal factors (Osborne, Reference Osborne2015) such that they are uncorrelated, having a mean of E[ɛ_k|x ₁, …, x _m] = 0 and a variance $E [ \varepsilon _k{\varepsilon }^{\prime}_k\vert x_1\comma \;\ldots \comma \;x_m] = \sigma _{kk}I_N$. These conditions imply normal distribution and homoskedasticity of error terms. For oblique factors, as in this case, however, some of the factors (OFM approaches) may not be entirely distinct, i.e., correlated with each other (Gorsuch, Reference Gorsuch1983). Once factor scores are correlated, the error terms associated with farmer i across equations will also correlate with each other. Therefore, the use of oblique factor scores as dependent variables of equation (2) implies correlated cross-equation ɛ_ks of observations. Hence, estimation by OLS will give consistent but not efficient αs (Greene, Reference Greene2018). To obtain consistent and efficient estimates of αs, an econometric setup that captures and isolates the error correlation terms must be employed. We adopted the SUR framework, which, by means of the generalized least squares (GLS) estimation, isolates between-equation error correlation coefficients to obtain efficient parameters. In the SUR setup, we stacked the observations data sets and obtained a compactly specified model as (Rao et al., Reference Rao, Toutenburg and Shalabh2008; Greene, Reference Greene2018):

(3)$$\left[{\matrix{ {S_1} \cr \vdots \cr {S_k} \cr } } \right] = \left[{\matrix{ {{\bi X}_1} & 0 & 0 \cr 0 & \ddots & 0 \cr 0 & 0 & {{\bi X}_{\bi K}} \cr } } \right]\left({\matrix{ {{\bi \alpha }_1} \cr \vdots \cr {{\bi \alpha }_{\bi K}} \cr } } \right) + \left({\matrix{ {{\bi \varepsilon }_1} \cr \vdots \cr {{\bi \varepsilon }_{\bi K}} \cr } } \right) = {\bi X\alpha } + {\bi \varepsilon }\comma \;$$

where X_K is a matrix of observed farmer characteristics, α_K is a vector of coefficients associated with equation k to be estimated, ${\bi \varepsilon } = \left[{\matrix{ {{{\varepsilon }^{\prime}}_1\comma \;} & \ldots & {{{\varepsilon }^{\prime}}_K} \cr } } \right]^{\prime}$ is a KN × 1 vector of measurement errors with conditional expectation, E[ɛ| X₁, …., X_K] = 0. The errors are uncorrelated across observations but are correlated across equations, such that E[ɛ_kiɛ_kn|X₁, …, X _K]) = σ _in, if i = n, and 0 if i ≠ n. The entire model error matrix is given as (Rao et al., Reference Rao, Toutenburg and Shalabh2008; Greene, Reference Greene2018):

(4)$$E[ \varepsilon {\varepsilon }^{\prime}\vert {\bi X}_1\comma \;{\rm \;} \ldots \comma \;{\bi X}_{\bi K}] = \sigma _{in}I_N = \left[{\matrix{ {\sigma_{11}{\bi I}} & \ldots & {\sigma_{1K}{\bi I}} \cr \vdots & \ddots & \vdots \cr {\sigma_{K1}{\bi I}} & \ldots & {\sigma_{KK}{\bi I}} \cr } } \right] = {\rm \;}\sum {\otimes I} \comma \;$$

where $\sum = \left[{\matrix{ {\sigma_{11}} & \ldots & {\sigma_{1K}} \cr \vdots & \ddots & \vdots \cr {\sigma_{K1}} & \ldots & {\sigma_{KK}} \cr } } \right]$ is an M × M error covariance matrix for the ith observation, ⊗ is the Kronecker product operator and I is a K × K identity matrix.

After estimation, if empirical σ _in equals zero for i ≠ n, then the equations are truly unrelated, and there is no efficiency gain in α_k by the use of a GLS estimator over OLS. On the other hand, if for any pair of the equations (i.e., OFM approaches), σ _in is significantly different from zero, the approaches are related through some common OFM decisions/actions. Previous studies (e.g., McBride and Johnson, Reference McBride and Johnson2006) have used the SUR framework in similar circumstances, but only for testing differences in coefficients of paired regressions. Even though we found very weak correlations between the factors, since we assumed correlated factors (OFM approaches) in EFA, we applied the SUR estimator mainly to obtain efficient estimates by correcting any bias arising from such correlations.