Using the Box-Cox Power Transformation to Predict Temporally Correlated Longitudinal Data

R. C. Hwang

《Journal of Data Science》 2卷3期 (2004/07) Pp. 259-272

https://doi.org/10.6339/JDS.2004.02(3).141

並列摘要

In this paper, the repeated measurement linear model proposed by Diggle (1988) is applied to two real data examples to predict future values for temporally correlated longitudinal data. This model incorporates the population mean, variability among individuals, serial correlation within an individual, and measurement error. In practice, however, the original data may not fit well with the linearity assumption imposed on the mean function by Diggle's model, thereby deteriorating the overall prediction ability of the model. To overcome this potential drawback, the Box-Cox power transformation (Box and Cox 1964) is considered, and two different ways of conducting power transformations are suggested. One of these two approaches performs transformation inside of Diggle's model, and the other performs transformation outside of Diggle's model. Given Diggle's model using the power transformed data, two prediction methods (the maximum likelihood method and the approximate Bayesian approach) are used to predict future values. Using our real data examples, it is shown that both values of mean absolute difference and mean absolute relative difference for each of these two prediction methods without power transformation can be reduced by more than 10% by simply performing power transformation. Results indicate that the prediction ability of Diggle's model can be significantly improved by employing power transformation, because lower levels of both mean absolute difference and mean absolute relative difference can be obtained.

並列關鍵字

Approximate Bayesian approach ； Box-Cox power transformation ； inverse gamma distribution ； maximum likelihood method ； noninformative prior ； repeated measurement linear model