The methodologies of the studies - Institutional Constraints to Small Farmer Development in Southern Africa - page 303

In line with Hosmer and Lemeshow (2000), Agresti (1990), Gujarati (1992), Liao, (1994),
and Harrell (2001), the right-hand term in Equation A.3 is the natural logarithm of the
modelled variables. A goodness-of-fit test following Hosmer-Lemeshow, can be carried out
by examining the Pearson Chi-square outcomes calculated from the table of observed and
expected frequencies as follows:

X 2 HL = Σ ( Oi - Niπi ) 2

g

(A.12)

Niπi (1 - π )

i =1

where:
N i = the total frequency of the items in the i th group;
O i = the total frequency of obtaining particular event outcomes in the i th group;
π i = the average estimate of the probability that a particular event outcome in the i th group
would be realized.

In addition to the binary and multi-nomial linear models, tests of association and analysis of
variance (ANOVA) were carried out. In the case of market access constraints for small-scale
cattle producers, market off-take rates were calculated using the formula:

Market otake = cattle sold in each municipality in the last 12 months

municipality herd size × 100%

According to Ba et al. (1996), off-take rate is the number of animals sold, donated,
slaughtered, or loaned, as a percentage of the adjusted number of animals. In this project the
prime focus was on market off-take rather than general off-take rate as the one used by Ba et al.
(1996). Market off-take rate is essential in this study, since many development projects try to
encourage small scale farmers to sell more livestock. It is commonly thought that communal
areas are over-stocked and that higher rates of commercial off-take would be good for the
national economy and for the environment (Sieff, 1999; Hendricks et al., 2007).

Farmers in communal areas differ on how they market their cattle. Others sell while others do
not. Therefore, this implies that the problem that needs to be solved needed a method that
was able to explain a binary endogenous variable (yes /no) by a set of covariates that determine
the outcome of the decision. A typical method used to solve such dichotomous variables is
the logistic regression (Hosmer and Lemeshow, 2000). According to Kleinbaum (1994),
there are two main reasons for using logistic regression in economics research. Firstly, the
logistic function is extremely flexible and easily applicable, and secondly the interpretation of
the results is straight forward and meaningful. The logistic model also imposes for threshold
and interaction effects and allows for examination of social interaction.

An important concern when categorical and continuous variables are included together in
the same model is the presence or otherwise of heteroscedasticity or unequal variance of the