Impact Assessment of the Logarithm Transformation on the Error Component of the Multiplicative Error Model (Published)
In this study we examine the implication of logarithm transformation on the two most popular distributions (Gamma and Weibull) of the error component of the multiplicative error model. The kth moment ( k =1, 2, 3, …) of the logarithm transformed Gamma distribution was established while that of the log-transformed Weibull distribution was found not to be solvable in its closed form hence further investigations were limited to the Gamma distributed error component. The mean of the log-transformed Gamma distribution as required in statistical modeling was found to exist for while its variance exits for . However using simulations the region for successful application of log-transformed distribution was found to be . Furthermore, it was discovered that the log-transform led to a significant reduction of the variance of the distribution, however the expected zero-mean assumption after linearing a multiplicative model with a logarithm transformation is not met even though there were decreases in the mean values after the transformation.
Finally as a result of the findings of this study, we recommend in statistical modeling, that logarithm transformation is not appropriate in a multiplicative error model (with a unit mean error component) for either linearizing or stabilizing the variance of the model or both since it leads to a distribution whose kth moment ( k = 1, 2, 3, . .) is not solvable in a closed form (for the Weibull distrib
Keywords: Gamma Distribution, Logarithm Transformation, Moments, Multiplicative Error Model, Weibull Distribution