*3.4. Empirical Strategy*

In assessing the relationship between farm production diversity and household food consumption diversity, we first examine determinants of farm production diversity and then analyze how this diversity is associated with household food consumption diversity outcomes.

#### 3.4.1. Analyzing the Determinants of Farm Production Diversity

Observed farm production diversity may be influenced by different household, farm, institutional and locational characteristics. Farm production diversity is represented as a score for both diversity indicators i.e., crop-livestock count, and the number of food groups produced. We therefore use a Poisson regression model which is suitable for analyzing count variables. Following Green [41], the model is specified as:

$$E(y\_i|x\_i) = \exp(\boldsymbol{\alpha} + \boldsymbol{X}^\prime \boldsymbol{\beta}) y\_i = 0, 1, \dots, i \tag{1}$$

where *yi* represents the level of farm production diversity by household *i*, *Xi* represents a vector of explanatory variables and *β* is a vector of parameters to be estimated.

Drawing from literature on farm production diversity, the predicting variables include household, farm and locational characteristics. Household socio-demographic characteristics such as age and gender are important in influencing the skills, experiences, risk attitude, willingness and ability to maintain different levels of diversity in their production [22]. These may influence farm production diversity either positively or negatively. For example, while older household heads may be less able and eager to maintain higher diversity especially for new crop or livestock varieties as compared to younger ones, the accumulated skills and experience in farm production may influence farm production positively. Also, depending on the level of control of household productive assets such as land, labor and equipment, female headed households may maintain more or less diversity at the farm. Education, on the other hand, is expected to influence farm production diversity positively as it enhances skills and use of information for maintaining different varieties of crops and livestock [22]. Household productive assets such as land and labor are expected to have a positive influence on farm production diversity [22]. Locational factors are equally important. As distances to key services and markets increase, transaction costs increase thus compelling households to allocate land to more diverse production to cater for expected consumption [8,22].

## 3.4.2. Analyzing the Influence of Farm Production Diversity on Consumption Diversity

Food consumption diversity may be influenced by farm production diversity as well as a set of other factors. Specifically, household socio-economic characteristics (such as age, gender and education) and market related factors are important when analyzing diversity of food consumption at the household beyond farm production diversity. For example, gender of the household may determine the control of household resources and how they are allocated [3]. Household income in female-headed household may be spent more on quality diets than that of male-headed households. Household productive assets such as land, labor and livestock may also enhance household's production capacity and thus influencing food consumption diversity positively. Household wealth is expected to play a strong positive role in enhancing food consumption diversity because it increases the ability of households to afford diverse diets [3]. Households with higher consumption expenditure are therefore expected to have higher food consumption diversity. Equally important is the fact that food consumption diversity may also be influenced by market access [9]. Proximity to markets and purchasing power to access different food items are expected to raise household food consumption diversity. Proximity to markets enables market-oriented smallholders to take advantage of lucrative product markets thereby enhancing incomes which may be spent on accessing diverse diets [3]. In addition, income from non-farm self-employment and other sources is essential in raising household's purchasing power, thus expected to enhance food consumption diversity.

In assessing the link between food consumption diversity and farm production diversity, we also use a Poisson regression model following the basic specification in Equation (1). In this, food consumption diversity is measured as a score based on HDDS and FVS. However, Poisson regressions assume equi-dispersion (that is, the conditional mean of the dependent variable is equal to its variance). In absence of equi-dispersion, the estimates from Poisson regression may be inefficient and biased [41]. A negative binomial regression model is appropriate in this case as it can be used in case of violation of the equi-dispersion assumption. This model is given by:

$$E(y\_i|\mathbf{x}\_{i\prime}\varepsilon) = \exp(\mathbf{a} + X^{\prime}\boldsymbol{\beta} + \varepsilon) \text{ With variance } Var(y\_i|\mathbf{x}\_{i\prime}\varepsilon) = \boldsymbol{\hat{\lambda}}\_i - \mathbf{a}\boldsymbol{\lambda}\_i^2 \tag{2}$$

From its functional form, a negative binomial regression model relaxes the assumption of equi-dispersion and thus suitable in cases of over-dispersion. We therefore employ this regression model, when tests suggest that a Poisson regression model is inappropriate.

Furthermore, we test for potential collinearity among independent variables and also use robust standard errors to address problems of heteroscedasticity in the estimates. Given the cross-sectional nature of the data, our analysis is restricted to potential relationships between key explanatory factors and food consumption diversity. Thus, results should not be interpreted as causal but rather correlational.
