T1 function

Function to generate a prediction expression for the two-sided Taguchi (T1) method

T1 generates a prediction expression for the two-sided Taguchi (T1) method. In general_T, the data are normalized by subtracting the mean and without scaling based on unit_space_data. The sample data should be divided into 2 datasets in advance. One is for the unit space and the other is for the signal space.

T1(unit_space_data, signal_space_data, subtracts_V_e = TRUE,
  includes_transformed_data = FALSE)

Arguments

• 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.
• 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.

Returns

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 the 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 from 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_dependent_data: Data transformation function generated from generates_transform_functions

  based on the 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. q equals 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.

Examples

# 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), ]

model_T1 <- T1(unit_space_data = stackloss_center,
               signal_space_data = stackloss_signal,
               subtracts_V_e = TRUE,
               includes_transformed_data = TRUE)

(model_T1$M_hat)

References

Taguchi, G. (2006). Objective Function and Generic Function (12). Journal of Quality Engineering Society, 14(3), 5-9. (In Japanese)

Inou, A., Nagata, Y., Horita, K., & Mori, A. (2012). Prediciton Accuracies of Improved Taguchi's T Methods Compared to those of Multiple Regresssion Analysis. Journal of the Japanese Society for Quality Control, 42(2), 103-115. (In Japanese)

Kawada, H., & Nagata, Y. (2015). An application of a generalized inverse regression estimator to Taguchi's T-Method. Total Quality Science, 1(1), 12-21.

See Also

general_T, generates_transformation_functions_T1, and forecasting.T1