class TranRegression[MatT <: MatriD, VecT <: VectoD] extends Regression[MatT, VectoD]
The TranRegression
class supports transformed multiple linear regression.
In this case, 'x' is multi-dimensional [1, x_1, ... x_k]. Fit the parameter
vector 'b' in the transformed regression equation
transform (y) = b dot x + e = b_0 + b_1 * x_1 + b_2 * x_2 ... b_k * x_k + e
where 'e' represents the residuals (the part not explained by the model) and 'transform' is the function (defaults to log) used to transform the response vector 'y'. Common transforms include 'log (y)', 'sqrt (y)' when 'y > 0', or even 'sq (y)', 'exp (y)'. More generally, a Box-Cox Transformation may be applied.
- See also
www.ams.sunysb.edu/~zhu/ams57213/Team3.pptx
citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.469.7176&rep=rep1&type=pdf Use Least-Squares (minimizing the residuals) to fit the parameter vector 'b' Note: this class does not provide transformations on columns of matrix 'x'.
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Instance Constructors
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new
TranRegression(x: MatT, y: VecT, transform: FunctionS2S = log, transInv: FunctionS2S = exp, technique: RegTechnique = QR)
- x
the design/data matrix
- y
the response vector
- transform
the transformation function (defaults to log)
- transInv
the inverse transformation function to rescale predictions to original y scale (defaults to exp)
- technique
the technique used to solve for b in x.t*x*b = x.t*y
Type Members
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type
Fac_QR = Fac_QR_H[MatT]
- Definition Classes
- Regression
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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var
aic: Double
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final
def
asInstanceOf[T0]: T0
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val
b: VectoD
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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
- Definition Classes
- Regression
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var
bic: Double
- Attributes
- protected
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- Regression
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def
build(x: MatriD, y: VectoD): Predictor
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def
clone(): AnyRef
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- protected[java.lang]
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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
df: Int
- Attributes
- protected
- Definition Classes
- Regression
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def
diagnose(yy: VectoD): Unit
Compute diagostics for the regression model.
Compute diagostics for the regression model.
- yy
the response vector
- Attributes
- protected
- Definition Classes
- Regression → Predictor
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val
e: VectoD
- Attributes
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final
def
eq(arg0: AnyRef): Boolean
- Definition Classes
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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
Compute the error and useful diagnostics
- yy
the response vector
- Definition Classes
- TranRegression → Regression → Predictor
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var
fStat: Double
- Attributes
- protected
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val
fac: Factorization
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def
finalize(): Unit
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def
fit: VectoD
Return the quality of fit.
Return the quality of fit.
- Definition Classes
- Regression → Predictor
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def
fitLabels: Seq[String]
Return the labels for the fit.
Return the labels for the fit.
- Definition Classes
- Regression → Predictor
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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
- Definition Classes
- Regression
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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
k: Int
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val
m: Double
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val
mae: Double
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- protected
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- Predictor
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def
metrics: Map[String, Any]
Build a map of diagnostics metrics for the overall quality of fit.
Build a map of diagnostics metrics for the overall quality of fit.
- Definition Classes
- Regression → Predictor
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val
mse: Double
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- protected
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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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var
p: VectoD
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- Definition Classes
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def
predict(z: MatT): VectoD
Predict the value of y = f(z) by evaluating the formula y = b dot z for each row of matrix z.
Predict the value of y = f(z) by evaluating the formula y = b dot z for each row of matrix z.
- z
the new matrix to predict
- Definition Classes
- TranRegression → Regression
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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).
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
- TranRegression → Regression → Predictor
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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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var
rBarSq: Double
- Attributes
- protected
- Definition Classes
- Regression
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val
rSq: Double
- Attributes
- protected
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- Predictor
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val
r_df: Double
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- protected
- Definition Classes
- Regression
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def
report(): Unit
Print results and diagnostics for each predictor 'x_j' and the overall quality of fit.
Print results and diagnostics for each predictor 'x_j' and the overall quality of fit.
- Definition Classes
- Regression
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def
residual: VectoD
Return the vector of residuals/errors.
Return the vector of residuals/errors.
- Definition Classes
- Predictor
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val
rmse: Double
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- protected
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val
sse: Double
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val
ssr: Double
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val
sst: Double
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var
stdErr: VectoD
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- protected
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final
def
synchronized[T0](arg0: ⇒ T0): T0
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var
t: VectoD
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def
toString(): String
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def
train(yy: VectoD = y): Regression[MatT, VectoD]
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, x_1 , ... x_k] + e
using the ordinary least squares 'OLS' method.
- yy
the response vector to work with (defaults to y)
- Definition Classes
- Regression → Predictor
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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.
- Definition Classes
- Regression
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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: MatT
- Attributes
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val
y: VectoD
- Attributes
- protected
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- Regression