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 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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Error, Predictor, AnyRef, Any
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Instance Constructors

  1. 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

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  5. def assignDummyVars(): Unit

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

  6. def assignVars(): Unit

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

  7. val b: VectoD
    Attributes
    protected
    Definition Classes
    Predictor
  8. 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.

  9. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  10. def coefficient: VectoD

    Return the vector of coefficients.

    Return the vector of coefficients.

    Definition Classes
    ANCOVA → Predictor
  11. def diagnose(yy: VectoD): Unit

    Compute diagostics for the predictor.

    Compute diagostics for the predictor. Override to add more diagostics. Note, for 'rmse', 'sse' is divided by the number of instances 'm' rather than degrees of freedom.

    yy

    the response vector

    Definition Classes
    Predictor
    See also

    en.wikipedia.org/wiki/Mean_squared_error

  12. val e: VectoD
    Attributes
    protected
    Definition Classes
    Predictor
  13. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  14. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  15. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  16. def fit: VectorD

    Return the quality of fit 'rSquared'.

    Return the quality of fit 'rSquared'.

    Definition Classes
    ANCOVA → Predictor
  17. def fitLabels: Seq[String]

    Return the labels for the fit.

    Return the labels for the fit.

    Definition Classes
    ANCOVA → Predictor
  18. final def flaw(method: String, message: String): Unit
    Definition Classes
    Error
  19. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
  20. def hashCode(): Int
    Definition Classes
    AnyRef → Any
  21. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  22. val mae: Double
    Attributes
    protected
    Definition Classes
    Predictor
  23. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  24. final def notify(): Unit
    Definition Classes
    AnyRef
  25. final def notifyAll(): Unit
    Definition Classes
    AnyRef
  26. 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
  27. 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
  28. val rSq: Double
    Attributes
    protected
    Definition Classes
    Predictor
  29. def residual: VectoD

    Return the vector of residuals/errors.

    Return the vector of residuals/errors.

    Definition Classes
    ANCOVA → Predictor
  30. val rg: Regression[MatrixD, VectorD]
  31. val rmse: Double
    Attributes
    protected
    Definition Classes
    Predictor
  32. val sse: Double
    Attributes
    protected
    Definition Classes
    Predictor
  33. val ssr: Double
    Attributes
    protected
    Definition Classes
    Predictor
  34. val sst: Double
    Attributes
    protected
    Definition Classes
    Predictor
  35. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  36. def toString(): String
    Definition Classes
    AnyRef → Any
  37. def train(): Unit

    Train the predictor by fitting the parameter vector (b-vector) in the regression equation using the least squares method on 'y'.

    Train the predictor by fitting the parameter vector (b-vector) in the regression equation using the least squares method on 'y'.

    Definition Classes
    ANCOVA → Predictor
  38. def train(yy: VectoD): Unit

    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
  39. 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.

  40. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  41. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  42. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  43. val x: MatrixD

Inherited from Error

Inherited from Predictor

Inherited from AnyRef

Inherited from Any

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