class TranRegression extends Predictor with Error
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: log (y), sqrt (y) when y > 0 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 = x_pinv * y where 'x_pinv' is the pseudo-inverse. Caveat: this class does not provide transformations on columns of matrix 'x'.
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Instance Constructors
-
new
TranRegression(x: MatrixD, y: VectorD, transform: FunctionS2S = log, technique: RegTechnique = QR)
- x
the design/data matrix
- y
the response vector
- transform
the transformation function (defaults to log)
- technique
the technique used to solve for b in x.t*x*b = x.t*y
Value Members
-
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.
-
def
coefficient: VectoD
Return the vector of coefficient/parameter values.
Return the vector of coefficient/parameter values.
- Definition Classes
- Predictor
-
def
diagnose(yy: VectoD): Unit
Compute diagostics for the predictor.
Compute diagostics for the predictor. Override to add more diagostics. Note, for 'rmse', 'sse' is divided by the number of instances 'm' rather than degrees of freedom.
- yy
the response vector
- Definition Classes
- Predictor
- See also
en.wikipedia.org/wiki/Mean_squared_error
-
def
fit: VectorD
Return the quality of fit.
Return the quality of fit.
- Definition Classes
- TranRegression → Predictor
-
def
fitLabels: Seq[String]
Return the labels for the fit.
Return the labels for the fit.
- Definition Classes
- TranRegression → Predictor
-
final
def
flaw(method: String, message: String): Unit
- Definition Classes
- Error
-
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 → Predictor
-
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
-
def
residual: VectoD
Return the vector of residuals/errors.
Return the vector of residuals/errors.
- Definition Classes
- TranRegression → Predictor
- val rg: Regression[MatrixD, VectorD]
-
def
train(): Unit
Train the predictor by fitting the parameter vector (b-vector) in the regression equation on 'yt'.
Train the predictor by fitting the parameter vector (b-vector) in the regression equation on 'yt'.
- Definition Classes
- TranRegression → Predictor
-
def
train(yy: VectoD): Unit
Retrain the predictor by fitting the parameter vector (b-vector) in the multiple regression equation
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, x_1, x_2 ... x_k] + e
using the least squares method.
- yy
the response vector
- Definition Classes
- TranRegression → Predictor
-
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.
- val yt: VectorD