## 2 Materials and Methods
### Performance Loss Rate Evaluation Using Mixed-Effects Linear Models  
A random coefficients model (mixed-effects linear model) with random intercept and slope was applied to monthly PR. Three models were defined to evaluate the PR decline rate over time, or \(\Delta\)_PR_%. The first model, denoted as \"null model\", was constructed to evaluate the \(\Delta\)_PR_% when no factors were included. The second model, denoted as \"typology model\", was devised to evaluate the \(\Delta\)_PR_% when factors related to the nature of the modules used in the PV production units were taken into account. To that effect, three covariates were considered: module manufacturer (_Manufacturer_), type of cell used in the modules' lamination (_Technology_), and the nominal power of the modules (_Nominal_P) installed at each PV production unit. The third model, denoted as \"location model\", was conceived to evaluate the \(\Delta\)_PR_% when factors related to the situation of the PV production units, within the facility, were taken into account. Thus, it included two covariates: the edge effect (_Edge_), which takes into account whether or not a PV production unit is located at the facility's eastern border and, therefore, contemplates the impact of being more exposed to local conditions, such as the prevailing winds that this area has (see Figure 5), and the length of the street effect (_LengthSt_), which evaluates the consequences of having a different number of PV production units per street within the installation. Evaluation of the principal effects and interactions of these variables over time allowed to calculate the PR decline rate (\(\Delta\)_PR_%). For this model, the homoscedasticity was assessed by visual inspection of a scatterplot of residuals versus fitted values. The assumption of normality was met, as assessed by the histogram of residuals and by the Kolmogorov test (\(p>0.05\)). Performance Ratio Declination Rate Model  
Let \(y_{ij}\) be the measured performance ratio (_PR_) of plant \(i\) at time \(t_{ij}\) in months, where \(i=1,\ldots,122\) denotes number of PV production units and \(j\) denotes the considered period  
Figure 5: Diagram depicting the SOLTEN facility together with the zone considered as the “edge area” in terms of direct exposure to the prevailing winds. Own elaboration. with \(j=1,\ldots,m_{i}\), where \(m_{i}\leq 96\), that is, from January 2012 until December 2019. The linear degradation model is given by  
\[y_{ij}=b_{0,i}+b_{1,i}\;t_{ij}+\varepsilon_{ij} \tag{2}\]  
where \(b_{0i}\) and \(b_{1i}\) denote the intercept and the gradient of the linear model for plant \(i\), respectively, and \(\varepsilon_{ij}\) denotes a random effect, and moreover,  
\[ \begin{array}{l}b_{0i}=\beta_{0}+b_{0,i}^{*}\\ b_{1i}=\beta_{1}+b_{1,i}^{*}\end{array} \]  
where  
\[ \begin{array}{l}\beta_{0}=\gamma_{00}+\gamma_{01}x_{i1}+\ldots+\gamma_{0k}x_ {ik}\\ \beta_{1}=\gamma_{10}+\gamma_{11}x_{i1}+\ldots+\gamma_{1k}x_{ik}\end{array} \]  
and \(x_{ik}\) are the covariates for the \"typology\" model: \(x_{i1}=``Manufacture\";x_{i2}=``Technology\";x_{i3}=``NominalP\"\) and \"location\" model: \(x_{i1}=``Edge\";x_{i2}=``LengthSt\"\). The \"null\" model only assesses the relation between the PR and time. The intercept and the gradient can be modeled using a bivariate normal distribution, \(\left(b_{0},b_{1}\right)^{t}\sim\text{BVN}(\beta,\mathbf{V})\) with mean vector  
\[\beta=(\beta_{0},\beta_{1})^{t}\]  
and covariance matrix  
\[\mathbf{V}= \begin{pmatrix}\sigma_{b_{0}}^{2}&Cov(b_{0},b_{1})\\ Cov(b_{1},b_{0})&\sigma_{b_{1}}^{2}\end{pmatrix}