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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Instance Constructors
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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
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final
def
!=(arg0: Any): Boolean
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final
def
##(): Int
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def
==(arg0: Any): Boolean
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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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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.
- Definition Classes
- Predictor
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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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final
def
eq(arg0: AnyRef): Boolean
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def
equals(arg0: Any): Boolean
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def
finalize(): Unit
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def
fit: VectorD
Return the quality of fit including 'rSquared'.
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def
fitLabels: Array[String]
Return the labels for the fit.
Return the labels for the fit. Override when necessary.
- Definition Classes
- Predictor
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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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final
def
getClass(): Class[_]
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def
hashCode(): Int
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final
def
isInstanceOf[T0]: Boolean
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def
ne(arg0: AnyRef): Boolean
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final
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., (b_0, b_1, b_2) dot (1, z_1, z_2).
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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
- Definition Classes
- Predictor
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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] dot [1, d_1, ... d_k] + 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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final
def
wait(): Unit
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def
wait(arg0: Long, arg1: Int): Unit
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final
def
wait(arg0: Long): Unit
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- val x: MatrixD