2.3.1. Adaptation Model Specification

Considering the multiple adaptation response measures implemented by some of the households, and to facilitate analyses, the higher-level adaptation strategies were categorized as follows: 0 = Off-farm adaptations; 1 = Crop management practices; 2 = Livestock management practices; 3 = Land and soil management practices; and 4 = Water management practices. Given adaptation decisions that involve multiple options, and similar to several related studies such as [23,30,31] the study employed the multinomial logit regression (MNL) techniques to evaluate choice decisions.

The study applied the MNL model as follows.

Let *Ai* be a random variable representing the choice of climate-related adaptation strategy adopted by any household. The assumption is that each household is faced with a set of distinct, mutually exclusive choices of climate change-induced adaptation strategies. The study also assumed that these adaptation strategies are influenced by several socio-economic attributes, household demography, perceptions on climate change, and other factors *X*. The MNL model for adaptation choice illustrated below is specified by the relationship between the probability of choosing adaptation option *Ai*, and a set of explanatory variables *X*, e.g., socio-economic attributes, household demography, perceptions on climate change [32].

$$Prob(A\_i = j) = \frac{e^{\theta\_j^{\prime x\_i}}}{\sum\_{k=0}^j e^{\theta\_k^{\prime} x\_i^{\prime}}}, j = 0, 1, \dots, J \tag{1}$$

where β*<sup>j</sup>* is a vector of coefficients on each of the predictor variables *X*. Equation (1) was normalized to remove indeterminacy in the model and then approximated to produce the j log-odd ratios similar to other studies elsewhere [25,30].

The dependent variable was therefore the log of each adaptation strategy in relation to the reference category (off-farm adaptations). Although the MNL model is relatively easy to compute, the resulting coefficients are difficult to interpret and misleading [32]. Therefore, in order to understand and interpret the influence of explanatory variables on the probability of choosing a particular adaptation strategy, marginal effects (ME) were computed following other studies [30,31]. The ME predict the changes in probability of a particular adaptation strategy being adopted with respect to a unit change in a particular explanatory variable [32]. The signs of the ME may be different from that of their corresponding MNL model coefficients. This is because the sign of the ME depends on both the sign and the magnitude of all the MNL model coefficients.

#### 2.3.2. Model Variables, Variable Description, and Expected Influence

The dependent variable in the empirical model approximation for this analysis was the type of adaptation strategy adopted and implemented by any single household and initially had 6 possible options only, i.e., 0 = No adaptation; 1 = Crop management practices only; 2 = Livestock management practices only; 3 = Land and soil management practices only; 4 = Water management practices only; and 5 = Off-farm adaptations. However, after preliminary analyses of the responses, options 3 and 4

were combined due to fewer responses in the latter. For this model only, the option for "No adaptation" was dropped from the analyses as it had 2 cases only, which did not allow the statistical modelling [32]. Notes that each option of the dependent variable must have at least 12 cases to allow MNL modelling.

The following adaptation options were finally used for the analysis, and these included different combinations of multiple practices: 0 = Off-farm adaptations; 1 = Crop management practices only; 2 = Livestock management practices only; 3 = Land, soil, and water management practices only; 4 = Crop + Livestock management practices combined; 5 = Crop + Land, soil, and water management practices combined; and 6 = Crop + Livestock + Land, soil, and water management practices combined. The off-farm adaptation was used as the reference category. The choice of explanatory variables and the hypothesized direction of influence was guided by empirical literature such as [25,26,31]. Table 1 summarizes the explanatory variables used for empirical estimation together with their expected direction of influence on farm-level adaptations.


**Table 1.** Summary of possible explanatory variables and hypothesized direction of influence.

The expected direction of influence shows the hypothesized influence of each explanatory variable on the uptake of adaptation measures to address the impacts of climate change in Bobirwa sub-district. A positive (+) (negative (−)) sign shows that a particular explanatory variable is expected to enable (hinder) the adoption of specific measures against climate change. Other explanatory variables could either enable or hinder (+/−) the uptake of climate change adaptation measures.
