*3.3. Methodology*

The methodology proposed in this research is developed in three phases: Preparation of the constructs of the first order from the application of a factor analysis, analysis of neural networks with the Extreme Learning Machine algorithm, and finally, interpretation of the resulting model using a sensitivity analysis.

A factor analysis was run with a rotation promax on the original data set. Promax rotation allows the factors obtained to be correlated (unlike the varimax rotation or orthogonal rotation). Following the recommendations of Reference [62], items that were not correlated with any specific factor were excluded from the analysis, while the loading used for other factor was 0.40. Variables that are grouped without any logical meaning according to the nature of the problem were also eliminated. The factor analysis revealed the existence of first-order factors for the constructs: Job Demands (JD),

Skill Discretion (SD), Decision Authority (DA) and Supervisor Support (SS). The construct Co-Worker Support (WS) was composed of a single item. Since the input variables were represented in different ranges, it was decided to standardize them to a [0, 1] scale linearly according to the function min (max).

The main analysis was carried out with artificial neural networks. This method has shown satisfactory results in solving complex problems and constitutes a useful tool in data analysis of different areas or disciplines: Medicine, economics, engineering, biology and psychology [63]. Increasingly, more authors appreciate their applicability with regard to models derived from classic statistics [64,65]. From a methodological perspective, the priority themes that apply neural networks deal with the classification of patterns (classification and prediction) and approximation of functions [63]. It is possible that the growing interest in neural networks lies in its capacity for the treatment of nonlinear problems [66], since better yields are achieved because there is independence from the fulfilment of the theoretical assumptions of traditional techniques. Neural networks have proven to be an effective tool for classifying cases under the non-linearity hypothesis. A neural network is a linear model in which the basis functions can be a sigmoid type. In the case that concerns us, the analysis was performed using a neural network in a single layer, which allows for modelling interactions of an order greater than two (and not only multiplicative); interactions will be key to analyzing the moderator effect of job control and social support. The parameters of the model have been estimated using the algorithm Extreme Learning Machine [67]. In this algorithm, the weights of the input layer to the hidden layer (which models the nonlinear part of the system) are initialized randomly. In addition, the parameters that bind the hidden layer with the layer's output are estimated analytically after solving a problem of least squares with regularization.

To finish the investigation, a sensitivity analysis was conducted. The main disadvantage of the models of neural networks is that they are considered a "black box" type, since they are effective at finding hidden relationships between inputs and outputs with a high capacity for approximation, but they do not provide information on how they have managed to do so. This limitation causes many academics to scrap the use of these models in their research. A sensitivity analysis is used to overcome this restriction. The present study uses a global sensitivity analysis inspired by a decomposition functional ANOVA [68]. This method makes it possible to decompose the nonlinear function on a set of elements associated with the parts of the independent variables, the interactions of the variable two by two, to the interactions between variables three to three and so on until all interactions of the input variables are analyzed. This methodology was already proposed for the classification problem and has been adapted ad hoc in this study for the case of regression [69]. To evaluate the stability of the method, an analysis with two subsamples that gave rise to two estimates of parameters of sensitivity (estimate 1 and 2 estimate) was performed.
