Packages

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 solve for the parameter vector 'b' using the Normal Equations:

x.t * x * b = x.t * y b = fac.solve (.)

See also

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

Linear Supertypes
Error, Predictor, AnyRef, Any
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Instance Constructors

  1. new ANCOVA(x_: MatriD, t: VectoI, y: VectoD, 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

  1. def assignDummyVars(): Unit

    Assign values for the dummy variables based on the treatment vector 't'.

  2. def assignVars(): Unit

    Assign values for the continuous variables from the 'x' matrix.

  3. def backwardElim(cols: Set[Int]): (Int, VectoD, VectoD)

    Perform backward elimination to remove the least predictive variable from the existing model, returning the variable to eliminate, the new parameter vector and the new quality of fit.

    Perform backward elimination to remove the least predictive variable from the existing model, returning the variable to eliminate, the new parameter vector and the new quality of fit. May be called repeatedly.

    cols

    the columns of matrix x included in the existing model

  4. def coefficient: VectoD

    Return the vector of coefficients.

    Return the vector of coefficients.

    Definition Classes
    ANCOVA → Predictor
  5. def crossVal(k: Int = 10): Unit

    Perform 'k'-fold cross-validation.

    Perform 'k'-fold cross-validation.

    k

    the number of folds

  6. def eval(): Unit

    Compute the error and useful diagnostics.

    Compute the error and useful diagnostics.

    Definition Classes
    ANCOVA → Predictor
  7. def eval(xx: MatriD, yy: VectoD): Unit

    Compute the error and useful diagnostics for the test dataset.

    Compute the error and useful diagnostics for the test dataset.

    xx

    the test data matrix

    yy

    the test response vector FIX - implement in classes

    Definition Classes
    Predictor
  8. def fit: VectoD

    Return the quality of fit 'rSquared'.

  9. def fitLabel: Seq[String]

    Return the labels for the fit.

  10. def fitMap: Map[String, String]

    Build a map of quality of fit measures.

  11. final def flaw(method: String, message: String): Unit
    Definition Classes
    Error
  12. def forwardSel(cols: Set[Int]): (Int, VectoD, VectoD)

    Perform forward selection to add the most predictive variable to the existing model, returning the variable to add, the new parameter vector and the new quality of fit.

    Perform forward selection to add the most predictive variable to the existing model, returning the variable to add, the new parameter vector and the new quality of fit. May be called repeatedly.

    cols

    the columns of matrix x included in the existing model

  13. 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).

    Predict the value of y = f(z) by evaluating the formula y = b dot z, e.g., (b0, b1, b2) dot (1, z1, z2).

    z

    the new vector to predict

    Definition Classes
    ANCOVA → Predictor
  14. def predict(z: VectoI): 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

    Definition Classes
    Predictor
  15. def residual: VectoD

    Return the vector of residuals/errors.

    Return the vector of residuals/errors.

    Definition Classes
    ANCOVA → Predictor
  16. val rg: Regression
  17. def train(yy: VectoD = y): Regression

    Retrain the predictor by fitting the parameter vector (b-vector) in the multiple regression equation

    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 response vector

    Definition Classes
    ANCOVA → Predictor
  18. def vif: VectoD

    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.

  19. val x: MatrixD