Concurso de acreedores en Cuba La quiebra

Although an ordered probit model was used to identify the relationship between different incentives and the corresponding level of participation of user group members in the governance of common property resources, it was unable to deal with the multicollinearity that existed, in particular, in the incentive variables. Moreover, the

Output Ordered Probit Model Factor Analysis Participation Indicators Participation Index (Dependent Variable) Incentive Variables (Explanatory variables) Parameter estimates Relationship between incentive and level of

participation

Marginal effects of explanatory variables on probability of different levels of participation

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participation index is a subjective decision ranking. The participation index was constructed and 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. The 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.

The use of possible alternative models, such as multiple regression analysis, canonical

correlation analysis, discriminant function analysis and partial least squares (PLS)

regression, were also explored for data analysis, depending upon the suitability of the

model for the data collected from the field. However, the PLS regression was found to be the most suitable, amongst these possible alternative models, to estimate the influence of individual incentives on each of the participation indicators. The PLS regression is also probably the least restrictive regression model compared to the alternatives, since these other multivariate methods do not extract the factors underlying the Y and X variables from cross-product matrices involving both the Y and X variables, but the PLS regression does extract these factors (StatSoft, 2010). In other words, the PLS method can deal with multiple Y’s and multiple X’s simultaneously: and hence, this method was used to further analyse the data.

The PLS regression, which is a multivariate data analysis method, is a statistical tool designed to deal with multiple regression problems, where the number of observations is limited and correlations between variables are high (Yang et al., 2007). PLS

regression is suitable to predict a set of dependent variables from a large set of explanatory variables (Abdi, 2010). It aims to transform a set of correlated explanatory variables into a new set of uncorrelated variables, called PLS factors. The PLS factors capture most of the information for the explanatory variables that is useful for explaining and predicting the dependent variables: and it reduces the dimensionality of the regression by using fewer PLS factors than the number of explanatory variables (Yang et al., 2007). Unlike the usual factor analysis, where factors are formed and

based on the X-variables only, the PLS method forms factors by using the covariance between the X-variables and Y-variables.

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Model Description

The PLS regression produces factor scores as linear combinations of the original predictor variables (Abdi, 2010; Yang et al., 2007). Let Y be the matrix of response

variables and X be the matrix of predictors35_{. The PLS method starts with a linear}

combination T = XW of the predictors, where T is called the factor score matrix or score

vector of predictors and W is its associated weight vector, and a linear combination U = YQof the responses, where U is the score vector of responses and Q is its associated

weight vector (Malinowski, 2002; Yang et al., 2007). The PLS method predicts both X

and Y by regression on T:

X = TP + E Y = TC + F

where, P and C are called the X- and Y-loadings, and E and F are the matrices of

residuals of X and Y, respectively. The PLS algorithms choose successive PLS factors that maximise the covariance between each T (factor score matrix of predictors) and the corresponding U (factor score matrix of responses): and these factors stand for variance information of X and Y as much as possible (Yang et al., 2007). The first few

factors, for an efficient PLS model, show a high correlation between T and U. In order to obtain the best predictive performance, a cross-validation method is used which determines the number of PLS factors that optimise the predictive ability of the model (Yang et al., 2007). The standard algorithm for computing PLS regression components

or factors is nonlinear iterative partial least squares (NIPALS) (Malinowski, 2002).

Frames of Analysis

The PLS procedure in SAS software has been used in this study. The participation indicators are used as the dependent variables and the incentives variables are used as the explanatory variables in this analysis. The output datasets include percent variation accounted for by PLS factors; dependent variable weights; model effect loadings; cross-validation for the number of extracted factors; and parameter estimation for centred and scaled data. The frames of analysis are shown in Figure 4.4.

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Figure 4.4: Partial lease-squares regression approach to study relationship between participation and incentives