Abstract
Publisher: School of Statistics, Renmin University of China, Journal: Journal of Data Science, Title: Using the Box-Cox Power Transformation to Predict Temporally Correlated Longitudinal Data, Authors: R. C. Hwang
Highlights
The repeated measurement linear model proposed by Diggle (1988) is an extremely popular method of predicting future values for temporally correlated longitudinal data
According to the results obtained by applying the maximum likelihood method (MLM) to both (1.2) and (1.3), the likelihood function of β, σV2, φ1, φ2, φ3 and λ, given Y, can be expressed by
In order to employ the prior distribution specified in (2.5), Rissanen (1986) and Lee and Tsao (1993) suggest using the minimum accumulated prediction error (MAPE) criterion to choose the values of the hyperparameters ζ and θ of the inverse gamma distributions
Summary
The repeated measurement linear model proposed by Diggle (1988) is an extremely popular method of predicting future values for temporally correlated longitudinal data. Using the model specified by (1.1) and (1.2), the purpose of this paper is to predict the future value yj at the design point x = (1, p + 1), given the total observed data Y = (Y1T , · · ·, YnT )T. The original data may not fit well with such linearity assumptions In such a case, the prediction ability of the associated model may deteriorate. The second approach does not treat λ as a parameter of Diggle’s model It and directly transforms the original data such that the power transformed data set have the best linear fit. It takes the minimizer λ∗ of the function TSSE(λ) defined below as the selected value of λ.
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