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Conventional analyses, with a general linear model (GLM), partition the variance in the measured response variable into partitions described by a design matrix of explanatory variables.

Let y= y1,…,y n )′ be the vector of observations and x= x1,…,x n )′ be the n×k design matrix of explanatory variables.

We note well, after this correlation matrix of explanatory variables, that there is no problem of multicollinearity between the variables studied.

The hat matrix, H, maps the vector of fitted values to the vector of observed values, and describes the influence each observed value has on each fitted value [3], where H = X X T X − 1 X T. It is the orthogonal projection onto the column space of the matrix of explanatory factors, X.

Where Y i is the dependent variable that takes a value of 1 for the i-th household who collect NTFP from FGR and 0 if otherwise, X i is a matrix of explanatory variables related to collection and utilization of NTFPs βik are the vector of parameters to be estimated and ε i is the error term with a logistic distribution.

First, a principal component analysis is performed on the data matrix of explanatory variables.

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where y is the response vector, X and Z are matrices of explanatory variables corresponding to fixed and random effects, respectively, β and u are the corresponding vectors of parameters for the respective fixed and random effects, and ε is a vector of random errors.

where y is the response vector, X and Z are matrices of explanatory variables corresponding to fixed and random effects respectively, β and u are the corresponding vectors of parameters for the respective fixed and random effects, ε is a vector of random errors and f is a nonlinear function.

Table 5 reports the correlation matrix of the explanatory variables.

For this, audits are required to be ranging from the simple correlation matrix of the explanatory variables to other statistics such as the inflation factor of the variance (VIF), the most used indicator by software (Joeveer 2013; Kötter et al. 2009).

(tilde {boldsymbol {X}}=left (tilde {boldsymbol {X}}_{1}^{prime },tilde {boldsymbol {X}}_{2}^{prime },ldots,tilde {boldsymbol {X}}_{M}^{prime }right)^{prime }), where (tilde {boldsymbol {X}}_{g}=(boldsymbol {X}_{g},boldsymbol {omega }_{g})) is a matrix stacking together the network-level matrices of exogenous explanatory variables and (own) network statistics of interest.

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