Packages

class ANOVA1 extends PredictorVec

The ANOVA1 class supports one-way ANalysis Of VAriance (ANOVA), i.e, it allows only one binary/categorial treatment variable. 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 solve for the parameter vector 'b' using the Normal Equations:

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

See also

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

ANCOVA for models with multiple variables

Linear Supertypes
PredictorVec, Error, Predictor, AnyRef, Any
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  1. ANOVA1
  2. PredictorVec
  3. Error
  4. Predictor
  5. AnyRef
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Instance Constructors

  1. new ANOVA1(t: VectoD, levels: Int, y: VectoD, technique: RegTechnique = QR)

    t

    the binary/categorical treatment variable vector double with integer values

    levels

    the number of treatment levels (1, ... levels)

    y

    the response vector

    technique

    the technique used to solve for b in x.t*x*b = x.t*y

Value Members

  1. def assignDummyVar(lev: Int): VectorD

    Assign values for the dummy variables based on a treatment variable's level 'lev'.

    Assign values for the dummy variables based on a treatment variable's level 'lev'.

    lev

    treatment level of the variable

  2. def assignDummyVars(tt: VectoD = t): Unit

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

  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

    Definition Classes
    PredictorVec
  4. def coefficient: VectoD

    Return the vector of coefficients.

    Return the vector of coefficients.

    Definition Classes
    PredictorVec → Predictor
  5. def crossVal(k: Int, ord: Int): Unit

    The 'crossVal' abstract method must be coded in implementing classes to call the above 'crossValidate' method.

    The 'crossVal' abstract method must be coded in implementing classes to call the above 'crossValidate' method. The 'algor' parameter may be specified as a lambda function to create the prediction algorithm.

    k

    the number of crosses and cross-validations (defaults to 10x).

    ord

    the given order

    Definition Classes
    ANOVA1 → PredictorVec
  6. def crossValidate(algor: (VectoD, VectoD, Int) ⇒ PredictorVec, ord: Int, k: Int = 10): Array[Statistic]
    Definition Classes
    PredictorVec
  7. def eval(tt: VectoD, yy: VectoD): Unit

    Compute the error and useful diagnostics for the test dataset.

    Compute the error and useful diagnostics for the test dataset.

    yy

    the test response vector

    Definition Classes
    PredictorVec
  8. def eval(): Unit

    Compute the error and useful diagnostics for the entire dataset.

    Compute the error and useful diagnostics for the entire dataset.

    Definition Classes
    PredictorVec → Predictor
  9. 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
  10. def expand(t: Double): VectoD

    Expand the scalar 't' into a vector of terms/columns.

    Expand the scalar 't' into a vector of terms/columns.

    t

    the scalar to expand into the vector

    Definition Classes
    ANOVA1 → PredictorVec
  11. def expand(t: VectoD): MatriD

    Expand the vector 't' into a matrix.

    Expand the vector 't' into a matrix.

    t

    the vector to expand into the matrix

    Definition Classes
    PredictorVec
  12. def fit: VectoD

    Return the quality of fit measures including 'rSq'.

    Return the quality of fit measures including 'rSq'.

    Definition Classes
    PredictorVec
  13. def fitLabel: Seq[String]

    Return the labels for the fit.

    Return the labels for the fit.

    Definition Classes
    PredictorVec
  14. def fitMap: Map[String, String]

    Build a map of quality of fit measures.

    Build a map of quality of fit measures.

    Definition Classes
    PredictorVec
  15. final def flaw(method: String, message: String): Unit
    Definition Classes
    Error
  16. 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

    Definition Classes
    PredictorVec
  17. def predict(z: Double): 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
    ANOVA1 → PredictorVec
  18. 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 expanded/orhogonalized vector to predict

    Definition Classes
    PredictorVec → Predictor
  19. 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
  20. def residual: VectoD

    Return the vector of residuals/errors.

    Return the vector of residuals/errors.

    Definition Classes
    PredictorVec → Predictor
  21. def train(yy: VectoD = y): Regression

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

    Train 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 response vector

    Definition Classes
    ANOVA1 → PredictorVec → Predictor
  22. 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.

    Definition Classes
    PredictorVec
  23. val x: MatrixD