3. RESEARCH METHODOLOGY
3.8. Data analysis
The tools for data analysis were descriptive statistics such as percentages, frequencies, mean and standard deviations; t-test and χ2 were also employed to test the continuous and discrete variables, respectively. SPSS version 12 was used to analyze quantitative data. Any item that cannot be captured through quantitative analysis was analyzed qualitatively based upon interview and group discussion with extension workers and beekeepers. For identifying financial benefit of adopting improved box hive partial budgeting was employed. A partial budget is a technique for assessing the benefits and costs of a practice relative to not using the practices. It takes into account only those changes in costs and returns that result directly from using a new practice. As noted by Upton (1987), Partial budgets are useful to evaluate changes such as:
• Adopting a new technology
• Expanding an enterprise
• Alternative enterprises
• Different production practices
• Hiring a custom operation rather than purchasing equipment
• Making a capital improvement
Partial budgeting is based on the principle that a change in the organization of a farm or ranch business will have one or more of the following effects:
Eliminate or reduce some costs.
Eliminate or reduce some returns.
Cause additional costs to be incurred.
Cause additional returns to be received.
Analytical model selected for this study is binary logit model, which significantly identifies the influences of determinants of improved box hive adoption. It is also possible to analysis adoption behavior of farmers using simple correlation, linear probability functions etc.
However, these models have their own limitations such as t- ratios are incorrect, exhibit hetroscedasticity, non normality; their estimated probabilities (Pi) may be greater than one or below zero and assume pi increases linearity with X (Maddala, 1983, Gujarati, 1995). The Logit and Probit models overcome such drawbacks as both are based on a commutative distribution function. It is also true that various adoption studies so far done on crop, livestock, soil conservation etc. have used Probit and Logit models for identifying the impact of independent variables on dependent variables. However, as of Aldrich and Nelson, (1984), the outputs of Probit and logit models are usually similar. Even though their outputs are similar the logit model is easier in estimation. It is also appropriate to express the probability of adoption and the intensity of use after technology adoption. Due to this fact, selecting binary logit model is thought to be appropriate for this study.
Model specification
Following Maddala (1983), Aldrich and Nelson (1984), Green (1991) and Gujarati (1995) the logistic distribution for the adoption decision of improved box hives can be specified as:
Pi = 1 Equation --- 1 (1+e-zi)
Where, Pi is a probability of adoption of improved box hive for the ith farmer e- represents the base of natural logarithms
Zi - is the function of a vector of n explanatory variables which is expressed as
m
Zi = Po +
∑
Pixi +ui I=1Z - is an underlying and unobserved stimulus index for the ith farmer i- are observation on variables for the adoption model
Po- is the constant term
Pi - are the unknown parameters to be estimated Ui- the disturbance term
m- the number of explanatory variables identified for the study
If pi is the probability of adopting improved box hive their 1-Pi represents the probability of not adopting the technology and expressed as
1-Pi = 1 - 1 = e-zi = 1 Equation --- 2 (1+e-zi) (1+e-zi) (1+ezi)
Then, the odd ratio of the equation 1 and 2 is expressed as
Pi = 1+e zi = e zi Equation --- 3 1-pi (1+e-zi )
Equation 3, Pi defines the probability of adoption of improved box hive to non 1-Pi
adoption of the technology. Finally, the logit model is expressed as follows by taking the natural logarism of odd ratio
Li =ln Pi = ln e Po+
∑
Pixi = zi = Po +∑
Pixi Equation--- 4 1-Pi i=1Where li= log of the odds ratio in favor of improved box hive adoption, which is not only linear in xi but also linear in the parameters.
Thus, if the stochastic disturbance term (ui) is introduced the logit model becomes
Zi =Po + P1xu +B2x2 +---+Bnxi +ui Equation--- 5
Estimation procedure
Before using the model, multicollinearity was checked to exclude one of the highly correlated explanatory variables. With this particular study, there is no serious multicollinearity problem (Appendix 3 and 4). As to Gujarati (1995) there are various indicators of multicollinearity and no single diagnostic will give us a complete handle over the collinearity problem. Accordingly, Variance Inflation Factor (VIF) and condition index (CI) were used for continues variables.
If there is larger value of VIFi, there is more troublesome. As a rule of thumb, if the VIF of a variable exceeds 10 (this will happen if Ri2 exceeds 0.95), that variable is said to be highly collinear (Gujarati, 1995). Following Gujarati (1995), the VIFj is given as:
VIF (Xj) = 2 1
1 Rj
−
Where, Rj2 is the coefficient of determination when the variable Xj is regressed on the other explanatory variables.
There may also be interaction between qualitative variables, which can lead to the problem of multicollinearity. To detect this problem, coefficients of contingency were compounded.
The contingency coefficient was compounded as follows:
2 2
χ n C χ
= +
Where, C is coefficient of contingency χ2 is chi-square test and
n = total sample size.
The iterative maximum likelihood (ML) estimation procedure was used to estimate the parameters of the models. Maximum likelihood is the most efficient (and sometimes the only) way to estimate the parameters of specifications that involve limited dependent variables. In very general sense, the method of ML yields values for the unknown parameters, which maximize the probability of obtaining the observed set of data (Liao, 1994).
3.9. Hypotheses and definition of variables
Hypothesis
Adoption of improved box hive technology is significantly influenced by personal, environmental, and socio-economic factors.
The variables of the study
Adoption of improved box hive technology is the dependent variable of the study. It is represented by 1 if the beekeepers adopt the box hive and 0, other wise.