Tb: Function to generate a prediction expression for the Tb...
In okayaa/MTSYS: Methods in Mahalanobis-Taguchi (MT) System

Description Usage Arguments Value References See Also Examples

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.

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

`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.

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.

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.

general_T, generates_transformation_functions_Tb, and forecasting.Tb

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

(model_Tb$M_hat)