A correlation matrix of predictors discovered no significant bivariate correlations greater than r = 0.25.
To ensure that no single predictor swamps the effects of others, the matrix of predictors (X) is centered and scaled, and then λ is chosen by cross-validation.
PLS regression is particularly suited to cases in which the matrix of predictors has more variables than observations, or when there is multi-collinearity among variables [76].
In the model, Y = X * B where Y represents the d' data across all participants in our study, X represents the matrix of predictors corresponding to the variables found to be significant from our analysis, and B the vector of regression coefficients that provides the optimal least squares fit.
Here X i is the matrix of predictors of dataset i and cor ^ denotes Pearson's correlation.
The matrix of predictors X, in equation (9), was generated mimicking the covariance structure of datasets from Table 2.
X = x ij (i = 1,..., n; j = 1,..., p) is the matrix of predictors (p is the total size of predictors).
In technical terms, in PCA, the coefficient vectors of the extracted linear function are eigenvectors of the covariance matrix of predictors.
In eq 10, W is the matrix of predictor variables used to develop the regression (corresponding to the observed conditions), W̃ is a matrix of predictors with reduced nutrient levels, σ r is the variance of the model residuals, and I is the identity matrix.
In short, the SAR models are a particular case of GLM: Y = Xβ + e; where Y is the dependent variable, β are the coefficients, X is the matrix of predictors, and e is the error term.
