Packages

class ANOVA extends Predictor with Error

The ANOVA class supports one-way ANalysis Of VAriance (ANOVA). It is framed using General Linear Model 'GLM' notation and supports the use of one binary/categorical treatment variable 't'. This is done by introducing dummy variables 'd_j' to distinguish the treatment level. The problem is again to fit the parameter vector 'b' in the following equation

y = b dot x + e = b_0 + b_1 * d_1 + b_1 * d_2 ... b_k * d_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

psych.colorado.edu/~carey/Courses/PSYC5741/handouts/GLM%20Theory.pdf

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Error, Predictor, AnyRef, Any
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Instance Constructors

  1. new ANOVA(t: VectorI, y: VectorD, levels: Int, technique: RegTechnique = QR)

    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. val b: VectoD

    Coefficient/parameter vector [b_0, b_1, ...

    Coefficient/parameter vector [b_0, b_1, ... b_k]

    Attributes
    protected
    Definition Classes
    Predictor
  7. 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.

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

    Return the vector of coefficient/parameter values.

    Return the vector of coefficient/parameter values.

    Definition Classes
    Predictor
  10. val e: VectoD

    Residual/error vector [e_0, e_1, ...

    Residual/error vector [e_0, e_1, ... e_m-1]

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

    Return the quality of fit including 'rSquared'.

    Return the quality of fit including 'rSquared'.

    Definition Classes
    ANOVAPredictor
  15. def fitLabels: Array[String]

    Return the labels for the fit.

    Return the labels for the fit. Override when necessary.

    Definition Classes
    Predictor
  16. 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

    Definition Classes
    Error
  17. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
  18. def hashCode(): Int
    Definition Classes
    AnyRef → Any
  19. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  20. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  21. final def notify(): Unit
    Definition Classes
    AnyRef
  22. final def notifyAll(): Unit
    Definition Classes
    AnyRef
  23. def predict(z: VectoD): Double

    Predict the value of y = f(z) by evaluating the formula y = b dot z, e.g., (b_0, b_1, b_2) dot (1, z_1, z_2).

    Predict the value of y = f(z) by evaluating the formula y = b dot z, e.g., (b_0, b_1, b_2) dot (1, z_1, z_2).

    z

    the new vector to predict

    Definition Classes
    ANOVAPredictor
  24. 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

    Definition Classes
    Predictor
  25. def residual: VectoD

    Return the vector of residuals/errors.

    Return the vector of residuals/errors.

    Definition Classes
    ANOVAPredictor
  26. val rg: Regression[MatrixD, VectorD]
  27. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  28. def toString(): String
    Definition Classes
    AnyRef → Any
  29. 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] dot [1, d_1, ... d_k] + e using the least squares method.

    yy

    the new response vector

  30. def train(): Unit

    Train the predictor by fitting the parameter vector (b-vector) in the regression equation y = b dot x + e = [b_0, ...

    Train the predictor by fitting the parameter vector (b-vector) in the regression equation y = b dot x + e = [b_0, ... b_k] dot [1, d_1, ... d_k] + e using the least squares method.

    Definition Classes
    ANOVAPredictor
  31. 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.

  32. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  33. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  34. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  35. val x: MatrixD

Inherited from Error

Inherited from Predictor

Inherited from AnyRef

Inherited from Any

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