Type Members

1.  class ANCOVA extends Predictor with Error

   The ANCOVA class supports ANalysis of COVAriance (ANCOVA).

   The ANCOVA class supports ANalysis of COVAriance (ANCOVA). It allows the addition of a categorical treatment variable 't' into a multiple linear regression. This is done by introducing dummy variables 'dj' to distinguish the treatment level. The problem is again to fit the parameter vector 'b' in the augmented regression equation

   y = b dot x + e = b0 + b_1 * x_1 + b_2 * x_2 + ... b_k * x_k + b_k+1 * d_1 + b_k+2 * d_2 + ... b_k+l * d_l + e

   where 'e' represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to fit the parameter vector

   b = x_pinv * y

   where 'x_pinv' is the pseudo-inverse.

   See also

   see.stanford.edu/materials/lsoeldsee263/05-ls.pdf

2.  trait GLM extends AnyRef

   A General Linear Model 'GLM' can be developed using the GLM trait and object (see below).

   A General Linear Model 'GLM' can be developed using the GLM trait and object (see below). The implementation currently supports univariate models with multivariate models (where each response is a vector) planned for the future. This version uses parallel processing to speed up execution. It provides factory methods for the following special types of GLMs: Regression - multiple linear regression, RidgeRegression - robust multiple linear regression, TranRegression - transformed (e.g., log) multiple linear regression, PolyRegression - polynomial regression, TrigRegression - trigonometric regression ResponseSurface - response surface regression, ANCOVA - GLM form of ANalysis of COVAriance. The following special types are excluded since they do not utilize large matrices. SimpleRegression - simple linear regression, ANOVA - GLM form of ANalysis Of VAriance,

3.  class PolyRegression extends Predictor with Error

   The PolyRegression class supports polynomial regression.

   The PolyRegression class supports polynomial regression. In this case, 't' is expanded to [1, t, t^{2 ... t}k]. Fit the parameter vector 'b' in the regression equation

   y = b dot x + e = b_0 + b_1 * t + b_2 * t^{2 ... b_k * t}k + e

   where 'e' represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to fit the parameter vector

   b = x_pinv * y

   where 'x_pinv' is the pseudo-inverse.

   See also

   www.ams.sunysb.edu/~zhu/ams57213/Team3.pptx

4.  class Regression extends Predictor with Error

   The Regression class supports multiple linear regression.

   The Regression class supports multiple linear regression. In this case, 'x' is multi-dimensional [1, x_1, ... x_k]. Fit the parameter vector 'b' in the regression equation

   y = b dot x + e = b_0 + b_1 * x_1 + ... b_k * x_k + e

   where 'e' represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to fit the parameter vector

   b = x_pinv * y [ alternative: b = solve (y) ]

   where 'x_pinv' is the pseudo-inverse. Three techniques are provided:

   'Fac_QR' // QR Factorization: slower, more stable (default) 'Fac_Cholesky' // Cholesky Factorization: faster, less stable (reasonable choice) 'Inverse' // Inverse/Gaussian Elimination, classical textbook technique (outdated)

   This version uses parallel processing to speed up execution.

   See also

   see.stanford.edu/materials/lsoeldsee263/05-ls.pdf

5.  class ResponseSurface extends Predictor with Error

   The ResponseSurface class uses multiple regression to fit a quadratic/cubic surface to the data.

   The ResponseSurface class uses multiple regression to fit a quadratic/cubic surface to the data. For example in 2D, the quadratic regression equation is

   y = b dot x + e = [b_0, ... b_k] dot [1, x_0, x_0^{2, x_1, x_0*x_1, x_1}2] + e

   See also

   scalation.metamodel.QuadraticFit

6.  class RidgeRegression extends Predictor with Error

   The RidgeRegression class supports multiple linear regression.

   The RidgeRegression class supports multiple linear regression. In this case, 'x' is multi-dimensional [x_1, ... x_k]. Both the input matrix 'x' and the response vector 'y' are centered (zero mean). Fit the parameter vector 'b' in the regression equation

   y = b dot x + e = b_1 * x_1 + ... b_k * x_k + e

   where 'e' represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to fit the parameter vector

   b = x_pinv * y [ alternative: b = solve (y) ]

   where 'x_pinv' is the pseudo-inverse. Three techniques are provided:

   'Fac_QR' // QR Factorization: slower, more stable (default) 'Fac_Cholesky' // Cholesky Factorization: faster, less stable (reasonable choice) 'Inverse' // Inverse/Gaussian Elimination, classical textbook technique (outdated)

   This version uses parallel processing to speed up execution.

   See also

   statweb.stanford.edu/~tibs/ElemStatLearn/

7.  class TranRegression extends Predictor with Error

   The TranRegression class supports transformed multiple linear regression.

   The TranRegression class supports transformed multiple linear regression. In this case, 'x' is multi-dimensional [1, x_1, ... x_k]. Fit the parameter vector 'b' in the transformed regression equation

   transform (y) = b dot x + e = b_0 + b_1 * x_1 + b_2 * x_2 ... b_k * x_k + e

   where 'e' represents the residuals (the part not explained by the model) and 'transform' is the function (defaults to log) used to transform the response vector 'y'. Use Least-Squares (minimizing the residuals) to fit the parameter vector

   b = x_pinv * y

   where 'x_pinv' is the pseudo-inverse.

   See also

   www.ams.sunysb.edu/~zhu/ams57213/Team3.pptx

8.  class TrigRegression extends Predictor with Error

   The TrigRegression class supports trigonometric regression.

   The TrigRegression class supports trigonometric regression. In this case, 't' is expanded to [1, sin (wt), cos (wt), sin (2wt), cos (2wt), ...]. Fit the parameter vector 'b' in the regression equation

   y = b dot x + e = b_0 + b_1 sin (wt) + b_2 cos (wt) + b_3 sin (2wt) + b_4 cos (2wt) + ... + e

   where 'e' represents the residuals (the part not explained by the model). Use Least-Squares (minimizing the residuals) to fit the parameter vector

   b = x_pinv * y

   where 'x_pinv' is the pseudo-inverse.

   See also

   link.springer.com/article/10.1023%2FA%3A1022436007242#page-1