Tb function

Function to generate a prediction expression for the Tb method

Tb generates a prediction expression for the Tb method. In general_T, the data are normalized by subtracting the center and without scaling based on sample_data. The center is determined by the specific way for the Tb method. For details, please see generates_transformation_functions_Tb. All the sample data are used for both unit space and signal space.

Tb(sample_data, subtracts_V_e = TRUE, includes_transformed_data = FALSE)

Arguments

• sample_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. 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 sample_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 sample_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 sample_data are included.

• M: If includes_transformed_data is TRUE, then the (true) value of the dependent variable after the data transformation for the sample_data are included.

Examples

model_Tb <- Tb(sample_data = stackloss[-c(2, 12, 19), ],
               subtracts_V_e = TRUE,
               includes_transformed_data = TRUE)

(model_Tb$M_hat)

References

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_Tb, and forecasting.Tb