Experimenting The Box-Cox Family Transformation on Likert Scale Data for Non-Normal Residuals in Linear Regression

Abstract

Neglecting the necessity for normality of residuals leads to failing in meeting the assumptions of error term in linear regression. Addressing a violation of this assumption requires an appropriate data transformation. The first objective of this study is to identify a suitable Box-Cox transformation (BCT) family for Likert scale data to handle non-normal residuals in multiple linear regression (MLR). When confronting with non-normally distributed MLR residuals, some scholars argue that the ordinary least squares estimation approach, commonly used in linear regression, consistently produces a reliable estimated value even when the error term deviates from a normal distribution. Given these conflicting opinions, one asserting that non-normally distributed error terms result in inaccurate estimates and the other maintains that such deviations do not compromise the consistency of estimates; thus, the second objective of this experiment is to reaffirm the differences in viewpoint by comparing the consistency of estimation values in MLR between cases of normal (transformed) and non-normal (non-transformed) residuals. The study suggested that the optimal BCT occurred at a lambda value 0.5. This specific lambda value corresponds to a logarithmic transformation, signifying a fundamental shift in Likert scale data toward a more normalized distribution or residuals. In the context of conflicting opinions regarding the impact of non-normally distributed error terms on estimates in MLR, this study revealed a significant difference in the mean of estimated values between the transformed and non-transformed models. The empirical evidence suggests that non-normally distributed error terms do lead to inconsistency in estimation values in MLR. Appropriate transformation does contribute to more reliable and interpretable results in MLR.