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**CHAPTER THREE RESEARCH METHODOLOGY**

**Introduction**

This chapter presents the methodological approaches followed in this study. The chapter describes the study area, size, and location on the map, the population and the agro-ecological zones with regard to maize production in the study area. It also elucidates the sampling techniques, data collection, data analysis and the econometric modeling to address the objectives of the study. Summary of the chapter is also included.

**Study area**

The study was carried out in Ngaka Modiri Molema District Municipality of the North West Province. The province is located in the north of South Africa sharing a border with the republic of Botswana and the Kalahari Desert to the west, where Gauteng province is found on the east and the Free State to the south. North West province is the fourth smallest province in the country. It was established in 1994, acquiring 8.7 percent of land area (106 512 km²) in South Africa. Its landscape is demarcated by Magaliesberg Mountain in the northeast, which covers about 130 kilometers from Pretoria to Rustenburg, while the Vaal River is located on the South border of the Province. Mahikeng (previously Mafeking) is the capital and most economic activities in the province (over 80 percent) take place around Potchefstroom, Klerksdorp and Rustenburg. Mining is the major contributor to the economy of the Province followed by farming activities in which maize is predominantly planted.

North West Province consists of four district municipalities. They are Ngaka Modiri Molema District Municipality, Bojanala Platinum District Municipality, Dr. Ruth Segomotsi Mompati District Municipality and Dr. Kenneth Kaunda District Municipality. The districts are divided into 18 local municipalities. However, the study was carried out in Ngaka Modiri Molema District Municipality. The district is the capital of the Province which is situated at the centre of the province and shares a border with Botswana. The district consists of Mahikeng, Ditsobotla, Ramotshere Moiloa, Tswaing, and Ratlou. The area of the district is 28,206 km2 with a population of 842,699 (Stats SA, 2017). The main economy is agriculture.

**Population, sampling procedure and sample size**

Data were collected from Ngaka Modiri Molema district municipality in North West Province, which consists of 5 local municipalities as shown in Figure 3.3. The list of small and emerging maize farmers in the district comprising about 575 farmers was obtained from Department of Agriculture, Forestry and Fisheries (DAFF) and also from Grain SA. Raosoft sample size calculator was used to determine the sample size from the population of the small and emerging maize farmers in the study area. The sample size calculator took into account the confidence level, the response distribution and the margin of error as indicated below:

x = Z (c/100)2 r (100-r)

n = N x/(N-1)E2 + x)

E = Sqrt [(N – n)x/n(N-1)]

A total number of 346 questionnaires were administered to the farmers in the district using stratified random sampling technique. This technique was employed to group the population of the farmers from the 5 local municipalities in the district into strata. Thereafter, random sampling was used to select from each stratum. A specific number of the sample size was selected from each stratum as shown in Table 3.1.

**Method of data collection**

This research used a quantitative design method. Approval to collect data was conceded by each local municipality’s office in the district. The data used in the research were primary and secondary data. Primary data were used to collect opinions from the farmers through the use of questionnaires, while the secondary data supplied additional information and other existing literature and evidence to equipoise the primary data collected, through use of published books and journals. The questionnaires were explained to the local extension officers before the survey because they understood the farmers better and could translate the questions into the local language. Face to face interviews and focus group discussions were conducted in each local municipality where each session lasted for about 45 minutes.

**Research instrument**

An appropriately-designed questionnaire written in English was used as a research instrument to collect data. The questionnaires were filled in anonymously as no personal questions regarding names, addresses and identity numbers were asked. Section A comprised of rational questions which accommodated and focused on issues involving: (a) demographic and household characteristics, (b) land characteristics, (c) climate change related issues, (d) climate change awareness, (e) climate change and livelihood, (f) adaptation measures options were asked from respondents.

**Validity and reliability**

In the study, prior to empirical research data collection, the questionnaires were tested and validated to the respondents. During the pre-testing period, a sample of 20 households was randomly selected and interviewed in the two district municipalities. Questions that were found to overlap during the questionnaire’s pre-testing were deleted and others that were ambiguous were modified to ensure clarity. The questionnaire’s pre-testing also helped to improve the translation of the questionnaire into Setswana, the local language for the respondent to understand better.

A half technique was used to determine the reliability of the instrument. A reliability coefficient of r = 0.80 was obtained which was considered to be good for the instrument used. The questionnaires were reliable, consistent and accurate in response to the objectives of the study to minimize error. It measured the attributes it was designed to measure. The questionnaires showed the likelihood of obtaining the same results when the researcher measures the same variable more than once, or when more than one person measures the same variable.

**Analytical techniques and methods**

The data collected were captured and analyzed using the Statistical Package for Social Sciences (SPSS, version 23, 2015) software. SPSS software can be used to assist in calculating a variety of statistical analysis which has dynamic data processing ability. This was used in this study to achieve descriptive statistics, binary logistic regression model, and other data analytical interpretations (See Table 4.1, 4.2, 4.3, 4.4, 4.5 and 5.2). STATA software was used to achieve the test of multicollinearity of variables (See Table 5.1, 6.2 and 7.1). EVIEWS software was employed to analyse Tobit regression model and Two-stage least square regression model (See Table 6.3 and 7.2) while the XLSTAT software was used to bring clarity at some point during the study to perform Principal Component Analysis (PCA) and determine the Eigen values (See Table 6.1). XLSTAT is a suite of statistical add-ins for Microsoft Excel which can be used for statistical analysis. Also, it enhances the analytical capabilities of Microsoft Excel. There are different analytical tools used according to the objectives of the study. These consist of descriptive and inferential statistics.

**Descriptive statistics**

Descriptive analysis was used to analyse the socio-economic characteristics of the respondents and to identify the adaptation options and mitigation strategies used in the study area which are objectives 1 and 2 of the study respectively. Graphical representations, percentages, frequency distributions, and statistical calculations such as standard deviations, mean, variance and standard error were used.

**Binary logistic regression (BLR).**

In order to determine the awareness of climate change among the respondents, BLR was employed. This approach takes into account only two values or variables. Logistic regression is a multivariate technique analysis which can be used to study the relationship between a dichotomous dependent variable and one or more independent variables (Molla-Bauza et al., 2005). The model is appropriate when attempting to model a dichotomous dependent variable.

Let Y be a binary response variable

Yi = 1, Respondent is aware of climate change i

Yi = 0, Respondent is not aware of climate change i

X = (X1, X2……Xk) be a set of explanatory variables which can be discrete, continuous, or a combination. Xi is the observed value of the explanatory variables for observation i.

Assuming that climate change awareness is a function of household gender (X 1), household age (X2)………………. X n. The initial model will be given as:

Ƴ= α + β1 + β2 2 + β3 3 + β4 4 + β5 5 +……+ β +Ɛ

Where:

The variable Ɛ is called the error term or disturbance. It is termed “noise” reflecting other factors that influence climate change awareness. It captures the factors other than X affecting Y.

Ƴ = dependent variable

X = independent variables

βi = regression coefficients

α = is the constant term

The model for logistic regression analysis assumes that the outcome variable, Ƴ, is categorical (e.g., dichotomous). Hypothetically, population proportion of cases for which Ƴ = 1 is defined as p = P (Ƴ =1). Then, the proportion of cases for which Ƴ = 0 is 1 – p = P (Ƴ = 0). In the absence of other information, we can estimate p by the sample proportion of cases for which Ƴ = 1. However, in the regression context, it is assumed that there is a set of predictor variables, X1…….Xk, that are

related to Ƴ and, therefore, provide additional information for predicting Ƴ.

Logit (Pi) = ln (Pi / 1-Pi) = α + β1 X 1 + …+βn X n + Ut

Where:

ln (Pi / 1-Pi) = logit for farmers awareness (Yes or No)

Pi = Farmers who are aware;

1 – Pi = Farmers who are not aware;

46

β = coefficient

X 1 = covariates

Ut = error term

Then, the logistic regression model can be expressed as:

Logit (πi) = log = β0+β1Xi

πi = ()

()

When the variables are fitted into the model, the model is presented as:

ln (Pi / 1-Pi) = α + β1 X 1 + β2 X 2 + β3 X 3 + β4 X 4…..+ Ut

**Principal component analysis and Tobit regression.**

Principal Component Analysis (PCA) and Tobit regression analysis were used to identify factors that influenced climate change among the respondents in the study area.

(a) Principal component analysis

PCA is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. It defines a new orthogonal coordinate system that optimally describes variance in a single dataset, and it is sensitive to the relative scaling of the original variables. With a large number of variables, the dispersion matrix may be too large to study and interpret properly. There would be too many pairwise correlations between the variables to consider. To interpret the data in a more meaningful form, it is, therefore, necessary to reduce the number of variables to a few interpretable linear combinations of the data. Each linear combination will correspond to a principal component. This transformation is expressed in such a way that the first principal component has the largest possible variance and each succeeding component, in turn, has the highest variance possible under the constraint that it is orthogonal to the preceding components. The number of principal components is less than or equal to the smaller of the number of original variables or the number of observations.

The results of a PCA are usually discussed in terms of component scores, sometimes called factor scores or factor loadings. Data set can be deconstructed into eigenvectors and eigenvalues. Eigenvectors and eigenvalues exist in pairs and every eigenvector has a corresponding eigenvalue. An eigenvector is a direction while an eigenvalue is a number that shows how much variance there is in the data in that direction. The eigenvector with the highest eigenvalue is, therefore, the principal component, where the eigenvector with the lowest eigenvalue contains less information which cannot be retained.

Mathematically, PCA is defined as an orthogonal linear transformation that transforms the data to a new coordinate system such that the greatest variance by some projection of the data comes to lie on the first coordinate (called the first principal component), the second greatest variance on the second coordinate, and so on. Mathematically, the transformation is defined by a set of p-

dimensional vectors of weights or loadings: () = ( ,…………., )() that map each row vector

() of X to a new vector of principal component scores () = ( ,,,…………., , )() ,

Given by

()

= ().

()

for i= 1, ………, n

k = 1, …….., m

Assuming we are converting a set of original data set or variables into Xj (j=1, 2, k) into a new set of uncorrelated variables called principal components, PCI (I=1,2…, k), which were linear combinations of original variables (Koutsoyiannis, 1972).

Consider the linear combinations

Where = the ith principal component,

aij = component loadings (coefficients)

And Xj = original variables.

Thus, the linear combinations give rise to: first principal component ( ) accounts for the

maximum possible proportion of the total variation in the Xj’s, the second principal component ( ) accounts for the maximum of the remaining variation (variance) in the Xj’s and so on. In

this manner we have: var ( ) ≥ var ( ) ≥ var ( ) ≥… ≥ var ( ), where var ( ) expresses the variance of in the data set being measured.

(b) Tobit regression

The Tobit model, also called a censored regression model, was employed to estimate linear relationships among variables when there is either left or right-censoring in the dependent variable. In other words, the factors influencing climate change adaptation in the study area were estimated using Tobit regression analysis. The model was developed by Tobin (1958). The adaptation to climate change is the dependent variable. It was targeted at evaluating the effect of numerous endogenous variables on the extent of adaptation strategies adopted by each respondent. Following Schwarze (2004), since the dependent variable is bounded between 0 and 1 (i.e, the variables are censored at 0.0 and 1.0), conventional regression methods fail to take into account the qualitative difference between zero and continuous observations. Furthermore, Rhaji (2000), opined that Tobit model combines the properties of multiple regression and Probit/Logit model. Therefore, Tobit model which was initially established for censored data was applied for the analysis. The model is specified as:

Yi = βXiifi* = βXi + ui> Ti

Yi = β0 + βiXi + ui

Where:

uί = normally distributed with zero mean and constant variance Xi = vector of explanatory variables

βi = vector of the parameter estimate

The model is fully estimated as follows:

yi* = β0+ β1xi + εi = xi’β + εi, εi ~ N(0,σ2)…………………………….…………(3.15)

If yi* > 0 => yi = climate change = yi* = xi’β + εi. ………………………….………..….. (3.16)

If yi* ≤ 0 => yi = 0(y* can be negative, but if it is, y=0)…………………….….….….…. (3.17)

Probability Model –εi ~ N(0, σ2)…………………………………………..…..…….….…..(3.18)

Prob(y=0|x) = Prob(y* ≤ 0|x) = Prob [(y*- Xβ)/σ ≤ (0- Xβ)/σ|x]…………….……..……… (3.19)

Prob[z ≤ – Xβ/σ|x] = Φ(-Xβ/σ) = 1- Φ(Xβ/σ)……………………..………….….….….……(3.20)

Prob(y>0|x) = Prob(y* > 0|x) = 1- Φ(-Xβ/σ) = Φ(Xβ/σ)…………………………………….(3.21)

Yi = Climate change adaptation strategies index determined by dividing the number of climate change adaptation strategies used by the individual farmers by all the climate change adaptation strategies available in the study area. Thus, the value of the climate change adaptation strategies index ranges between zero (0) and one (1). Thus, the explanatory variables used in the analysis include the socioeconomic variable of the household head and information pertaining to climate change and its adaptation, which are:

X1 = Number of years of farming (years)

X2 = Farm size (hectares)

X3 = Household size (number of persons in the household)

X4 = Gender of household head (Male = 1; Female = 0)

X5 = Age of household head (years)

X6 = Marital status

X7 = Household head educational level

X8 = Household head source of income (R)

X9 = Type of farm

X10 = Who manage the farm

X11 = Who owns the farm

X12 = Land acquisition

X13 = Climate change awareness

X14 = Information receive on climate change

X15 = Source of climate change information

X16 = Climate change information through extension services

X17 = Channel of information on climate change

X18 = Support received on climate change

X19 = Climate change adaptation

X20 = Adaptation barrier

3.7.4 Two stage least square regression

Lastly, a two stage least square regression was used to analyse the effect of climate change on respondents’ livelihood in the study area. Two stage least square is a method of estimating a causal effect in the instrumental variables settings. It involves running Ordinary Least Square (OLS)

twice. In the first stage, two stage least square (TSLS) finds the portions of the endogenous and

exogenous variables that can be attributed to the instruments. This stage involves estimating an

OLS regression of each variable in the model on the set of instruments. The second stage is a

regression of the original equation, with all of the variables replaced by the fitted values from the

first-stage regressions. The coefficients of this regression are the TSLS estimates. The predicted

values from these regressions replace the original values of the endogenous variables in the second

stage regression model.

Mathematically written:

Assume we want to estimate the coefficients of the linear model

Ƴ1=˳ + 1X11 + ………… + kXk+ i…….………………………………………..…..…. (3.22)

But some of the variables Xji are correlated with the error term. OLS estimation of this equation will be biased and inconsistent. Suppose that we have a collection of q > p instruments, Z1i. . . Zqi. The two-stage least squares estimator of β will be as follows:

Regress each Xj on Z and save the predicted values, Xj. If Xj is included in Z, we will have j =Xj. Estimate β via the OLS estimate of the regression model

Ƴ1=˳ + 1 11 + ………… + k k1 + i …………………………………………..………… (3.23)

3.8 Ethical consideration and respondents’ consent to collect data

Ethical clearance was obtained from the College’s Ethics committee. Permission from local authorities and consent from respondents to collect data were obtained before the start of the interviews. The respondents’ information was kept private and confidential. Mutual respect was accorded to all the respondents.

**Limitations of the study**

One of the limitations of the study is that the outcome of the research may not reflect the entire situation in the Province, as data were collected in one district municipality of the Province. The study was limited to one district municipality with 5 local municipalities and data samples were collected and conducted between the months of October and December 2016. Lack of information was a challenge during the course of collecting data in this research as some of the respondents did not have a proper record. They only relied on memory which could be prone to error.

**Summary**

In this chapter, research design, sample size and selection procedure were explained. Sampling, data collection and tools of collecting data, data capturing and data analysis were equally elucidated. The different models used and motivation for their usage in the study were extensively discussed. The next chapter presents research results, findings, and the discussions.

**TABLE OF CONTENTS**

**DEDICATION **

**DECLARATION **

**ACKNOWLEDGEMENTS **

**ABSTRACT **

**LIST OF TABLES **

**LIST OF FIGURES **

**LIST OF ACRONYMS **

**CHAPTER ONE INTRODUCTION**

1.1 Background to the study

1.2 Problem statement

1.3. Research questions

1.4 Research objectives

1.5 Research hypotheses

1.6 Motivation for the study

1.7 Summary

**CHAPTER TWO LITERATURE REVIEW**

2.1 Introduction

2.2 Concept of livelihood

2.3 Rural livelihood

2.4 Rural livelihood and agriculture

2.5 Sustainable livelihood framework

2.6 Sustainable livelihood framework analysis

2.7 Maize farming and sustainable livelihood

2.8 Understanding of climate change

2.9 Impacts of climate change on livelihood

2.10 Impact of climate change on agricultural production

2.11 Climate change adaptation

2.12 Summary

**CHAPTER THREE RESEARCH METHODOLOGY**

3.1 Introduction

3.2 Study area

3.3 Population, sampling procedure and sample size

3.4 Method of data collection

3.5 Research instrument

3.6 Validity and reliability

3.7 Analytical techniques and methods

3.8 Ethical consideration and respondents’ consent to collect data

3.9 Limitations of the study

3.10 Summary

**CHAPTER FOUR SOCIO-ECONOMIC CHARACTERISTICS OF FARMING HOUSEHOLDS AND ADAPTATION MEASURES**

4.1 Empirical results and discussion

4.2 Socio-economic characteristics of respondents in the study area

4.3 Climate change related information in the study area

4.4 Adaptation strategies among the respondents in the study area

4.5 Impact of climate change on livelihoods of respondents in the study area

4.6 Summary

**CHAPTER FIVE CLIMATE CHANGE AWARENESS IN THE STUDY AREA**

5.1 Introduction

5.2 Awareness of climate change among the respondents

5.3 Summary

**CHAPTER SIX CLIMATE CHANGE ADAPTATION AND THE INFLEUNCING FACTORS AMONG THE FARMERS IN THE STUDY AREA**

6.1 Introduction

6.2 Factors that influenced climate change adaptation in the study area

6.3 Summary

**CHAPTER SEVEN THE EFFECT OF CLIMATE CHANGE ON FARMERS’ LIVELIHOOD CAPITALS**

7.1 Introduction

7.2 Estimates of Two-stage least-squares regression model

7.3 Summary

**CHAPTER EIGHT SUMMARY, CONCLUSION AND RECOMMENDATIONS**

8.1 Introduction

8.2 Research findings and summary

8.3 Conclusion

8.4 Recommendations

REFERENCES

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