trait GLM extends AnyRef
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.
It provides factory methods for the following special types of GLMs:
SimpleRegression - simple linear regression,
Regression - multiple linear regression using Ordinary Least Squares 'OLS'
Regression_WLS - multiple linear regression using Weighted Least Squares 'WLS'
RidgeRegression - robust multiple linear regression,
TranRegression - transformed (e.g., log) multiple linear regression,
PolyRegression - polynomial regression,
TrigRegression - trigonometric regression
ResponseSurface - response surface regression,
ANOVA - GLM form of ANalysis Of VAriance,
ANCOVA - GLM form of ANalysis of COVAriance.
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def
apply(x_: MatrixD, t: VectorI, y: VectorD, levels: Int): ANCOVA
Build an ANalysis of COVAriance (ANCOVA) model.
Build an ANalysis of COVAriance (ANCOVA) model.
- x_
the data/design matrix of continuous variables
- t
the treatment/categorical variable vector
- y
the response vector
- levels
the number of treatment levels (1, ... levels)
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def
apply(t: VectorI, y: VectorD, levels: Int): ANOVA
Build an ANalysis Of VAriance (ANOVA) model.
Build an ANalysis Of VAriance (ANOVA) model.
- t
the treatment/categorical variable vector
- y
the response vector
- levels
the number of treatment levels (1, ... levels)
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def
apply(x_: MatrixD, y: VectorD, cubic: Boolean): ResponseSurface
Build a Response Surface model.
Build a Response Surface model.
- x_
the input vectors/points
- y
the response vector
- cubic
the order of the surface (false for quadratic, true for cubic)
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def
apply(ty: MatrixD, k: Int, p: Int): TrigRegression
Build a Trigonometric Regression model.
Build a Trigonometric Regression model.
- ty
the combined input vector and response vector
- k
the maximum multiplier in the trig function 'kwt'
- p
extra parameter to make apply methods unique (pass in 0)
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def
apply(t: VectorD, y: VectorD, k: Int, p: Int): TrigRegression
Build a Trigonometric Regression model.
Build a Trigonometric Regression model.
- t
the input vector: 't_i' expands to 'x_i'
- y
the response vector
- k
the maximum multiplier in the trig function 'kwt'
- p
extra parameter to make apply methods unique (pass in 0)
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def
apply(ty: MatrixD, k: Int): PolyRegression
Build a Polynomial Regression model.
Build a Polynomial Regression model.
- ty
the combined input vector and response vector
- k
the order of the polynomial
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def
apply(t: VectorD, y: VectorD, k: Int): PolyRegression
Build a Polynomial Regression model.
Build a Polynomial Regression model.
- t
the input vector: t_i expands to x_i = [1, t_i, t_i2, ... t_ik]
- y
the response vector
- k
the order of the polynomial
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def
apply(xy: MatrixD, transform: FunctionS2S): TranRegression
Build a Transformed Multiple Linear Regression model.
Build a Transformed Multiple Linear Regression model.
- xy
the combined input/design m-by-n matrix and response m-vector
- transform
the transformation function
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def
apply(x: MatrixD, y: VectorD, transform: FunctionS2S): TranRegression
Build a Transformed Multiple Linear Regression model.
Build a Transformed Multiple Linear Regression model.
- x
the input/design m-by-n matrix
- y
the response m-vector
- transform
the transformation function (e.g., log)
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def
apply(xy: MatrixD, lambda: Double): RidgeRegression[MatrixD, VectorD]
Build a Multiple Linear Robust Regression model.
Build a Multiple Linear Robust Regression model.
- lambda
the shrinkage parameter (0 => OLS) in the penalty term 'lambda * b dot b'
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def
apply(x: MatrixD, y: VectorD, lambda: Double): RidgeRegression[MatrixD, VectorD]
Build a Multiple Linear Robust Regression model.
Build a Multiple Linear Robust Regression model.
- x
the centered input/design m-by-n matrix NOT augmented with a first column of ones
- y
the centered response vector
- lambda
the shrinkage parameter (0 => OLS) in the penalty term 'lambda * b dot b'
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def
apply(x: MatrixD, y: VectorD, w: VectorD): Regression_WLS[MatrixD, VectorD]
Build a Multiple Linear Regression model using Weighted Least Squares 'WLS'.
Build a Multiple Linear Regression model using Weighted Least Squares 'WLS'.
- x
the input/design m-by-n matrix
- y
the response m-vector
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def
apply(xy: MatrixD): Regression[MatrixD, VectorD]
Build a Multiple Linear Regression model using Ordinary Least Squares 'OLS'.
Build a Multiple Linear Regression model using Ordinary Least Squares 'OLS'.
- xy
the combined input/design m-by-n matrix and response m-vector
-
def
apply(x: MatrixD, y: VectorD): Regression[MatrixD, VectorD]
Build a Multiple Linear Regression model using Ordinary Least Squares 'OLS'.
Build a Multiple Linear Regression model using Ordinary Least Squares 'OLS'.
- x
the input/design m-by-n matrix
- y
the response m-vector
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def
apply(x: VectorD, y: VectorD): SimpleRegression
Build a Simple Linear Regression model, automatically prepending the column of ones (form matrix from two column vectors [ 1 x ]).
Build a Simple Linear Regression model, automatically prepending the column of ones (form matrix from two column vectors [ 1 x ]).
- x
the input/design m-by-1 vector
- y
the response m-vector
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