Function to generate data transformation functions for the Tb methods
generates_transformation_functions_Tb is the argument for the parameter generates_transform_functions in genera_T, which is used in the Tb method.
generates_transformation_functions_Tb(sample_data)
sample_data: Matrix with n rows (samples) and (p + 1) columns (variables). The Tb method uses all data to generate the unit space. All data should be continuous values and should not have missing values.generates_transformation_functions_Tb returns a list containing three functions. For the first component, the data transformation function for independent variables is a function that subtracts the center of each independent variable. The center is determined in a specific manner for the Tb method. The center consists of each sample value which maximizes the signal-to-noise ratio (S/N) per independent variable. The values are determined independently so that different samples may be selected for different variables. For the second component, the data transformation function for a dependent variable is a function that subtracts the dependent variable of the sample which maximizes the S/N per independent variable. For the third component, the inverse function of the data transformation function for a dependent variable is a function that adds the weighted mean of a dependent variable. The weighted mean is calculated based on the S/N and the frequency of being selected in independent variables.
# The value of the dependent variable of the following samples mediates # in the stackloss dataset. stackloss_center <- stackloss[c(9, 10, 11, 20, 21), ] tmp <- generates_transformation_functions_Tb(stackloss_center) center_subtraction_function <- tmp[[1]] subtracts_ys <- tmp[[2]] adds_M_0 <- tmp[[3]] is.function(center_subtraction_function) # TRUE is.function(subtracts_ys) # TRUE is.function(adds_M_0) # TRUE
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.
Tb