General function to generate a prediction expression for a family of Taguchi (T) methods
general_T is a (higher-order) general function that generates a prediction expression for a family of Taguchi (T) methods. Each T method can be implemented by setting the parameters of this function appropriately.
general_T(unit_space_data, signal_space_data, generates_transform_functions, subtracts_V_e = TRUE, includes_transformed_data = FALSE)
unit_space_data: Matrix with n rows (samples) and (p + 1) columns (variables). The 1 ~ p th columns are independent variables and the (p + 1) th column is a dependent variable. Underlying data to obtain a representative point for the normalization of the signal_space_data. All data should be continuous values and should not have missing values.signal_space_data: Matrix with m rows (samples) and (p + 1) columns (variables). The 1 ~ p th columns are independent variables and the (p + 1) th column is a dependent variable. Underlying data to generate a prediction expression. All data should be continuous values and should not have missing values.generates_transform_functions: A function that takes the unit_space_data as an (only) argument and returns a list containing three functions. A data transformation function for independent variables is the first component, a data transformation function for a dependent variable is the second component, and an inverse function of the data transformation function for a dependent variable is the third component. The data transformation function for independent variables takes independent variable data (a matrix of p columns) as an (only) argument and returns the transformed independent variable data. The data transformation function for a dependent variable takes dependent variable data (a vector) as an (only) argument and returns the transformed dependent variable data. The inverse function of the data transformation for a dependent variable takes the transformed dependent variable data (a vector) as an (only) argument and returns the untransformed dependent variable data.subtracts_V_e: If TRUE, then the error variance is subtracted in the numerator when calculating eta_hat.includes_transformed_data: If TRUE, then the transformed data are included in a return object.A list containing the following components is returned.
beta_hat: Vector with length q. Estimated proportionality constants between each independent variable and the dependent variable.
subtracts_V_e: Logical. If TRUE, then eta_hat was calculated without subtracting the error variance in the numerator.
eta_hat: Vector with length q. Estimated squared signal-to-noise ratios (S/N) coresponding to beta_hat.
M_hat: Vector with length n. The estimated values of the dependent variable after the data transformation for signal_space_data.
overall_prediction_eta: Numeric. The overall squared signal-to-noise ratio (S/N).
transforms_independent_data: Data transformation function generated from generates_transform_functions
based on unit_space_data. The function for independent variables takes independent variable data (a matrix of p columns) as an (only) argument and returns the transformed independent variable data.
transforms_dependent_data: Data transformation function generated in generates_transform_functions based on the unit_space_data. The function for a dependent variable takes dependent variable data (a vector) as an (only) argument and returns the transformed dependent variable data.
inverses_transformed_dependent_data: Inverse function generated in the generates_transform_functions
based on unit_space_data. The function of the takes the transformed dependent variable data (a vector) as an (only) argument and returns the dependent variable data inversed from the transformed dependent variable data.
m: The number of samples for signal_space_data.
q: The number of independent variables after the data transformation. According to the data transoformation function, q may be equal to p.
X: If includes_transformed_data is TRUE, then the independent variable data after the data transformation for the signal_space_data are included.
M: If includes_transformed_data is TRUE, then the (true) value of the dependent variable after the data transformation for the signal_space_data are included.
# The value of the dependent variable of the following samples mediates # in the stackloss dataset. stackloss_center <- stackloss[c(9, 10, 11, 20, 21), ] # The following samples are data other than the unit space data and the test # data. stackloss_signal <- stackloss[-c(2, 9, 10, 11, 12, 19, 20, 21), ] # The following settings are same as the T1 method. model <- general_T(unit_space_data = stackloss_center, signal_space_data = stackloss_signal, generates_transform_functions = generates_transformation_functions_T1, subtracts_V_e = TRUE, includes_transformed_data = TRUE) (model$M_hat)
T1, Ta, and Tb