A GIC rule for assessing data transformation in regression

The functional form used in regression may be generalized by the Box-Cox transformation. We adopt the generalized information criterion (GIC) approach to determine a need for Box-Cox (J. Roy. Statist. Soc. Ser. B 26 (1964) 211) transformation of the response variable. The utilization of the constructed variable reduces the problem to one of variable selection based on GIC. Our method leads to comparing the partial correlation coefficient between the dependent variable and the constructed variable of an artificial regression, with critical values depending on a penalty parameter. The method is illustrated with simulation examples and several well-known examples from the literature in regression diagnostics.