Study Design and Sampling procedures
Case study research could be utilized in both quantitative and mixed method research designs(Mills, Durepos, & Wiebe, 2009). The study employed cross-sectional research design with both quantitative and qualitative approach. This study employed purposive and simple random sampling to select countries with respective catchments and households respectively. Three catchments in the three study countries were selected based on the presence of agroforestry practice, availability of species diversity, contribution to food security, climate change adaptation activities, and women's participation in agroforestry practice. Households were selected using simple random sampling from the lists in the sampling frame of male and female headed households across study catchments. Based on Yin (2018), if the same number of interviewees happened to suit a multiple-case study replication design, interviews of 20 to 30 people would be more than adequate using multiple sources of evidence. Therefore, a total of 180 households (60 per country); 33 (KII) (11 per country), and 6 (FGD) (2 per country; 1 male and one female group of smallholder farmers) were included to gather relevant data. Among 180 households, 90 households (30 per country) were female-headed households. Moreover, model farmers, village chief, developmental agents from three departments (such as from natural resource management, plant protection, and animal production), woman, and youth representative, religious’ leader, elder, from regionally available environment and forest-related departments per country has participated as a key informant’s participant for sharing their experience and knowledge related to the context of the study areas.
The study used primary and secondary data sources. In the case study, multiple sources of data are required to employ (Yin, 2009, 2018) which includes; desktop research, households survey, Key Informants Interview (KII), and Focus Group Discussion (FGD). Originally the survey questions were prepared in English and it was translated into the local language of each case study area. There were pilot visits to check the validity and reliability of the survey in the three cases studies. Based on this visit result, the ambiguous terms, phrases, and questions were modified. The data collection was conducted 29 July-16 August 2022.
The sources of Desktop research comprise each country’s target catchment agroforestry management policy, practices, vulnerability indicators such as sensitivity, exposure and adaptive capacity; and the contribution of agroforestry for climate change adaptation, mitigation strategies, food security, and gender participation. Published and unpublished documents produced by academic and research institutions and other organizations were used to describe the state of the art. A series of well-structured questions such as scheduled interviews was designed to collect quantitative data on households’ characteristics, farming activities, income sources, food availability and gaps, gender role in agroforestry practices, management practices, market access, and other vulnerability indicators were captured.
Data gained from focus group discussions and key informants interviews include agroforestry practice, gender specific challenges during agroforestry practices such as flood, drought, pests, market fluctuation, and land degradation; seasonal calendar of rainfall, laboure, food and water availability; technology adoption, agroforestry information, and other gender participations in agroforestry practices.
Data Analysis
The study employed SPSS-version 23 to encode the data and STATA version 14.1 for analysis purpose of the quantitative data. The vulnerability indices were constructed using a weighted average approach to measure households’ access to a set of values. The sub-components or indicators were changed into a standardized index based on UNDP (2010) and Sietz, Boschütz, and Klein (2011).
\(Standardizedindexvalue = \frac{Observed\left(averagevalue\right)-Minimumvalues}{Maximum-Minimumvalues}\) Equation [1]
The identification of the appropriate indicators is a basic prerequisite for designing operative future policy and intervention (Atara et al., 2020; Field, 2009). The normalized sub-component value is ranged from 0 to 1; with 0 denoting least vulnerable and 1 denoting most vulnerable (Nguyen et al., 2013). Based on Hahn, Riederer, and Foster (2009 ), after normalizing the sub-component values, the value of each major component was calculated. The principal component analysis(PCA) and facto analysis(FA) was employed based on (Noy & Yonson, 2018) to --- ascertaining appropriate variables and giving weights. A positive factor scores in a factor related to the sensitivity dimension indicates more vulnerability than the mean, while a negative factor scores in a factor related to the sensitivity dimension indicates less vulnerability than the mean. While the opposite is true in adaptive capacity (Aroca-Jiménez et al., 2020). This indicates variables with greater factor scores have a higher influence on vulnerability (Olufemi et al., 2018).
The factor analysis prerequisite was checked ;(1) Kaiser Meyer-Olkin (KMO) helps to test whether the surveyed sample is adequate to run factor analysis or not. Based on Kaiser 1958 cited in Gambo Boukary et al. (2016), if the KMO value is greater than 0.5, it is acceptable to run factor analysis; (2) Bartlett Test of Sphericity, and the existence of multicollinearity. For a good model, the determinant of the R-matrix is expected to be more than 0.00001, which helps to test the correlation coefficients matrix of the variables in the model (Field, 2009). Moreover, factor analysis is valued less in the identity matrix (Balasundaram, 2009). According to Kaiser (1960) cited in Kebede et al. (2016), for extractions of factor, the Eigen value should have to be greater than or equal to one.
The first step of vulnerability level analyses was estimating the proxy variables separately. The proxy indicators have been standardized and agglomerated to obtain the respective major components. These components, thereafter, have been combined to obtain the overall vulnerability index. This can be implemented by performing first-stage factor analysis. Therefore, variables that will help to estimate the vulnerability of households are exposure, adaptive capacity, and sensitivity (Aroca-Jiménez et al., 2020).
Moreover, factor analysis can give appropriate weight to each indicator (Demeke and Tefera, 2013) and used to estimate latent variables like vulnerability indices (Bollen, 2002). The basic idea of a latent variable approach for vulnerability measurement is that “there are one or more latent variables that create the association between unobserved variables” (Bollen, 2002). The mathematical relationship is written as follows.
Whereas:
\({\gamma }_{i}=\) Observed indicator for the \({i}^{th}\) case
\({\lambda }_{0}=\) Intercept term
\({\epsilon }_{i1}\dots {\epsilon }_{ik}=\) Factor loading for the \({1}^{st}\) through \(k\) case
\({u}_{i}\)= unique variable or error term
If the variable has a factor loading of 0.72 and above for a sample size greater than 50, is considered significant (Field, 2009). The higher the load is the most important it is and greater attention should be paid to it (Atara et al., 2020; Field, 2009). The result of vulnerability indices can be between 0 and 1. When the index is close to one it means vulnerability is high and vice versa (Ahsan and Warner, 2014). T-test is applied to investigate whether there is a mean difference between the vulnerability index between male and female-headed households or not. Furthermore, quantitative categorical type of data was analyzed using percentage, frequency tables, cross tabulation, and chi square tests. Qualitative information collected through focus group discussions, and key informant interviews was processed manually and used in the analysis to complement the quantitative information.