class ANOVA1 extends Predictor with Error
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
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Instance Constructors
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new
ANOVA1(t: VectoI, y: VectoD, levels: Int, technique: RegTechnique = QR)
- t
the binary/categorical treatment 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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final
def
==(arg0: Any): Boolean
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final
def
asInstanceOf[T0]: T0
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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
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def
assignDummyVars(tt: VectoI = t): Unit
Assign values for the dummy variables based on the treatment vector 't'.
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val
b: VectoD
- Attributes
- protected
- Definition Classes
- Predictor
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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
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def
build(x: MatriD, y: VectoD): Predictor
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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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def
diagnose(yy: VectoD): Unit
Compute diagostics for the predictor.
Compute diagostics for the predictor. Override to add more diagostics. Note, for 'mse' and 'rmse', 'sse' is divided by the number of instances 'm' rather than the degrees of freedom.
- yy
the response vector
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- See also
en.wikipedia.org/wiki/Mean_squared_error
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val
e: VectoD
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final
def
eq(arg0: AnyRef): Boolean
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def
equals(arg0: Any): Boolean
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def
eval(yy: VectoD = y): Unit
Compute the error and useful diagnostics.
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def
finalize(): Unit
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def
fit: VectoD
Return the quality of fit.
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def
fitLabels: Seq[String]
Return the labels for the fit.
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final
def
flaw(method: String, message: String): Unit
- Definition Classes
- Error
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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
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final
def
getClass(): Class[_]
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def
hashCode(): Int
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val
index_rSq: Int
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final
def
isInstanceOf[T0]: Boolean
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val
mae: Double
- Attributes
- protected
- Definition Classes
- Predictor
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def
metrics: Map[String, Any]
Build a map of selected quality of fit measures/metrics.
Build a map of selected quality of fit measures/metrics.
- Definition Classes
- Predictor
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val
mse: Double
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final
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: Int): 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
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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
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val
rSq: Double
- Attributes
- protected
- Definition Classes
- Predictor
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def
residual: VectoD
Return the vector of residuals/errors.
- val rg: Regression[MatrixD, VectoD]
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val
rmse: Double
- Attributes
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val
sse: Double
- Attributes
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val
ssr: Double
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val
sst: Double
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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: VectoD = y): Regression[MatrixD, VectoD]
Train the predictor by fitting the parameter vector (b-vector) in the multiple regression equation
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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.
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final
def
wait(): Unit
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final
def
wait(arg0: Long, arg1: Int): Unit
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final
def
wait(arg0: Long): Unit
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- val x: MatrixD