El Registro de mediadores Mediador Concursal

In the context of common property resource governance, a member has various choices situations where s/he can decide whether to participate or not (Lise, 2007). Knowledge of whether a person is a member of a user group (or not a member) is not sufficient for measuring the extent of users’ participation, because it does not account for changes in perception during the participation process. Some members may be involved very actively but still acquire less benefits, whilst others only reap the benefits without any active participation (Lise, 2007). To separate these different groups of people, in terms of their extent of participation, it is necessary to quantify participation, and this can be done by constructing an index of participation. The index of participation, which is used as the dependent variable for investigating the relationship between the incentives and participation, was constructed by employing a factor analysis out of a set of indicators of participation that measure users’ participation (e.g., Atmiú et al., 2007; Dolisca et al., 2006; Kerapeletswe & Lovett, 2002; Lise, 2000, 2007).

Indicators of Participation

The index of participation is constructed and based upon six indicators of participation that are all highly correlated with one another. This study adopts the dimensions of participation proposed by Cohen & Uphoff (1980, p. 219), in order to define a number

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of choice situations, which are interpreted as the indicators of participation. These indicators of participation comprise the key factors for strengthening resource governance and improving the livelihoods of the user group (see, e.g., Agarwal, 2001;

Dev et al., 2003; Dolisca et al., 2006; Kanel, 2004; Lise, 2000, 2007; MFSC, 1989, 1995;

Ostrom, 1990; Springate-Baginski et al., 2003; The World Bank, 2001). In consideration

of the equal importance of each individual indicator of participation, they were all given an equal weight in the construction of the participation index (see e.g., Atmiú et al.,

2007; Dolisca et al., 2006; Kerapeletswe & Lovett, 2002).

The list of indicators of participation, prepared and based upon the literature review on participation in the governance and management of common property resources, was used to build a set of questions to be asked of the respondents, in order to collect answers relating to their participatory attitudes, which stipulate their actual level of participation. The list of indicators, however, was finalised after incorporating the responses from the key informants’ interviews and the focus group discussions, during the pre-testing of the questionnaire. The six indicators of participation in the governance and management of common property resources are shown in Table 4.1 below.

Table 4.1: Indicators of Participation

Name of Indicator Definition

Membership length Number of years that a household has been member of the CFUG

Representation on the executive committee Whether at least one member of the household is represented on the executive committee of the group

Level of participation at the meeting Users’ rating on their level of participation at meetings, in terms of contributing to the meeting

Level of participation in decision making Users’ rating on their level of participation in decision-making

Level of participation in implementation Users’ rating on their level of participation in implementation

Level of participation in overall benefits Users’ rating on the major benefits they derive from being a member of the group

The membership length was recorded as the actual number of years that a household has been a member of the CFUG, whilst representation on the executive committee was recorded as Yes or No, depending on whether at least one member of the

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the users’ rating on their level of participation in different group activities was framed in such a way that a higher number stands for a higher level of participation. The respondents were asked to rate their responses on a five-point Likert scale from 1 to 5, with 1 representing No (or very low level of participation) and 5 indicating a very high

level of participation.

Factor Analysis

A factor analysis is a statistical approach used to analyse interrelations or correlations amongst a large number of variables and to explain these variables, in terms of their common underlying dimensions: that is, factors (Hair et al., 2005; Kerapeletswe &

Lovett, 2002). It is a statistical method with a basic concept of dimensionality reduction and it is used to describe variability amongst observed variables, in terms of fewer unobserved variables called factors, which will offer a better understanding of the data structure. This method is used for translating a large set of variables into a few orthogonal variables (with minimum loss of information) and it determines the number of underlying dimensions to be used in subsequent analyses, where each factor will represent an independent choice (Hair et al., 2005; Kerapeletswe & Lovett, 2002). The

basic principle that underlies factor analysis is that it reduces the data to more manageable proportions, by computing factor scores to represent the multiple indicators that are correlated with one another (Dolisca et al., 2006; Kerapeletswe &

Lovett, 2002). Once the factor scores are extracted, the subsequent analyses become much more manageable, with the use of one or a few factor scores, depending upon the choice of the user, instead of using several component items (Kerapeletswe & Lovett, 2002; Knoke, 1988).

Choice of Factor Analysis Implementation

There are many methods for performing a factor analysis, which usually differ in determining the number of common factors required and estimating factor loadings and specific variances. The Descriptive Factor Analysis is the simpler and more commonly used approach to finding factors and it uses the properties of principal component analysis (PCA). Although factor analysis has similar aims to PCA, there are basic differences between them (Figure 4.1). PCA is a mathematical procedure which transforms the correlated variables into a smaller number of uncorrelated variables called principal components. PCA summarises the total variation of the original

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variables, whereas FA attempts to identify any underlying latent factors and it describes the behaviour of each original variable, in terms of latent variables or factors.

Figure 4.1: Differences between factor analysis and PCA

In PCA, new uncorrelated variables are obtained as linear combinations of the original variables, whilst in factor analysis the original variables are expressed as linear combinations of uncorrelated latent factors. For principal component model specifications, if X1, X2, ... Xp are the p correlated variables, the principal component

analysis model can be presented as the linear combinations of X1, X2, ... Xp to produce

new variables Y1, Y2, ... Yp that are uncorrelated, that is,

Yi = ai1X1 + ai2X2 + ... + aipXp, i = 1, 2, ... p.

PCA takes into account all variability within the variables, so that the results will include as many principal components as there are variables, but factor analysis estimates how much of the variability is due to common factors (Hair et al., 2005; Kerapeletswe &

Lovett, 2002). Therefore, this study did not use descriptive factor analysis to construct the index of participation, but instead it was used as the initial or trial step towards the iterative factor analysis.

The maximum likelihood factor analysis (MLFA) and the iterated principal factor analysis (PCFA) are the other two commonly used factor analysis methods. The MLFA is the most commonly used and statistically superior procedure, which assumes normality on the given data and on the common factors and specific variates (Manly, 2005). One useful advantage of this method is that it does not have scaling problems: that is, it provides the same results, whether the raw data (covariance matrix) or the standardised data (correlation matrix) are used. The PCFA, on the other hand, is another popular but heuristic method, which is based on performing principal component analysis on covariance (or correlation) matrix, adjusted for the specific variances called reduced covariance matrix or reduced correlation matrix. However, this method does not assume normality on the data (Manly, 2005) and hence, it becomes preferable to MLFA, when the assumption of normality on the data is

Summary of what happened PCA Why the data happened

Factor Analysis

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questionable. However, this method is not scale-invariant, i.e., it does matter whether the data is standardised or not. Therefore, the multivariate normality of the data will be tested before determining which method is to be used for the data analysis. If the participation indicator variables data follow the multivariate normal distribution, the MLFA will be used: otherwise, the PCFA will be adopted.

Factor Analysis Model Specification

For factor analysis model specifications, it can be supposed that X1, ..., Xp are

observed p variables on n individuals. Theoretically, there are m underlying factors

with m<½(p-1) (Chatfield & Collins, 1980), which are usually denoted by F1, ... ,Fm.

The observed variables are modelled as linear combinations of the factors, plus error

terms (Manly, 2005) such that:

X1 = a11 F1 + a12 F2 + … + a1m Fm + İ1

X2 = a21 F1 + a22 F2 + … + a2m Fm + İ2

.

Xp = ap1 F1 + ap2 F2 + … + apm Fm + İp

Generalising the above equations:

Xi = ai1 F1 + ai2 F2 + … + aim Fm + İi, i = 1, 2, ... ,p (1)

Since the latent variables (or the factors) are common to all original variables, they are often called common factors. The common factors are independent of one another and

they are standardised variables with zero mean and unit variance (Manly, 2005). The error terms İi are called specific variates associated individually with each of the original

variables and these variates measure the residual information unexplained by the latent factor. The constants aik are called factor loadings, loading of the ith variable on the kth

factor, which measures the correlation between the original variables and the factors.

From equation (1), for each i = 1, 2, ... , p,

var (Xi) = ai12 var(F1)+ ai22 var(F2)+ … + aim2 var(Fm)+ var(İi),

= ai12 + ai22 + … + aim2 + var(İi), (since Fk are standardised with unit variance)

m

=

™

m

Here, ™ aik2 is called the communality of Xi, which is the variance of Xi explained by the

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common factors. Communality is the total amount of variance an original variable shares with all other variables included in the analysis. The var(İi) is called the specific

variance of Xi, which is the variance of Xi that is not explained by the common factors.

In the case of standardised data, communality cannot exceed 1, since -1 ” aik” 1.

Once the factor scores were computed, these were used to construct the participation index as a proxy for the users’ participation in the governance of common property resources. The participation index was constructed based on the normalised weighted sum of the factor scores of each respondent household and computed directly by the factor analysis. The weights used were the proportion of variation accounted for by each of the factors. Natural cut-off points of the normalised factor scores were used to define the participation index. The respondent households were then grouped by the participation index, in such a way that the higher the normalised factor score, the higher is the household participation index.

4.2.2 Estimating Relationship between Participation and Incentives: The