class ANCOVA extends Predictor with Error
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
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Instance Constructors
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new
ANCOVA(x_: MatrixD, t: VectorI, y: VectorD, levels: Int, technique: RegTechnique = QR)
- 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)
- technique
the technique used to solve for b in x.t*x*b = x.t*y
Value Members
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final
def
!=(arg0: Any): Boolean
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def
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final
def
asInstanceOf[T0]: T0
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def
assignDummyVars(): Unit
Assign values for the dummy variables based on the treatment vector 't'.
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def
assignVars(): Unit
Assign values for the continuous variables from the 'x' matrix.
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val
b: VectoD
Coefficient/parameter vector [b_0, b_1, ...
Coefficient/parameter vector [b_0, b_1, ... b_k]
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def
backElim(): (Int, VectoD, VectorD)
Perform backward elimination to remove the least predictive variable from the model, returning the variable to eliminate, the new parameter vector, the new R-squared value and the new F statistic.
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def
clone(): AnyRef
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def
coefficient: VectoD
Return the vector of coefficient/parameter values.
Return the vector of coefficient/parameter values.
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val
e: VectoD
Residual/error vector [e_0, e_1, ...
Residual/error vector [e_0, e_1, ... e_m-1]
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eq(arg0: AnyRef): Boolean
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def
finalize(): Unit
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def
fit: VectorD
Return the quality of fit 'rSquared'.
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def
fitLabels: Array[String]
Return the labels for the fit.
Return the labels for the fit. Override when necessary.
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final
def
flaw(method: String, message: String): Unit
Show the flaw by printing the error message.
Show the flaw by printing the error message.
- method
the method where the error occurred
- message
the error message
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def
getClass(): Class[_]
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def
notify(): Unit
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final
def
notifyAll(): Unit
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def
predict(z: VectoD): Double
Predict the value of y = f(z) by evaluating the formula y = b dot z, e.g., (b0, b1, b2) dot (1, z1, z2).
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def
predict(z: VectorI): Double
Given a new discrete data vector z, predict the y-value of f(z).
Given a new discrete data vector z, predict the y-value of f(z).
- z
the vector to use for prediction
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def
residual: VectoD
Return the vector of residuals/errors.
- val rg: Regression[MatrixD, VectorD]
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final
def
synchronized[T0](arg0: ⇒ T0): T0
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def
toString(): String
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def
train(yy: VectorD): Unit
Retrain the predictor by fitting the parameter vector (b-vector) in the multiple regression equation yy = b dot x + e = [b_0, ...
Retrain the predictor by fitting the parameter vector (b-vector) in the multiple regression equation yy = b dot x + e = [b_0, ... b_k+l] dot [1, x_1, ..., d_1, ...] + e using the least squares method.
- yy
the new response vector
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def
train(): Unit
Train the predictor by fitting the parameter vector (b-vector) in the regression equation y = b dot x + e = [b_0, ...
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def
vif: VectorD
Compute the Variance Inflation Factor (VIF) for each variable to test for multi-collinearity by regressing 'xj' against the rest of the variables.
Compute the Variance Inflation Factor (VIF) for each variable to test for multi-collinearity by regressing 'xj' against the rest of the variables. A VIF over 10 indicates that over 90% of the variance of 'xj' can be predicted from the other variables, so 'xj' is a candidate for removal from the model.
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wait(arg0: Long, arg1: Int): Unit
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def
wait(arg0: Long): Unit
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- val x: MatrixD