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Correlated random effects regression analysis for a log-normally distributed variable

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  • Rabindra Nath Das
  • Anis Chandra Mukhopadhyay

Abstract

In regression analysis, it is assumed that the response (or dependent variable) distribution is Normal, and errors are homoscedastic and uncorrelated. However, in practice, these assumptions are rarely satisfied by a real data set. To stabilize the heteroscedastic response variance, generally, log-transformation is suggested. Consequently, the response variable distribution approaches nearer to the Normal distribution. As a result, the model fit of the data is improved. Practically, a proper (seems to be suitable) transformation may not always stabilize the variance, and the response distribution may not reduce to Normal distribution. The present article assumes that the response distribution is log-normal with compound autocorrelated errors. Under these situations, estimation and testing of hypotheses regarding regression parameters have been derived. From a set of reduced data, we have derived the best linear unbiased estimators of all the regression coefficients, except the intercept which is often unimportant in practice. Unknown correlation parameters have been estimated. In this connection, we have derived a test rule for testing any set of linear hypotheses of the unknown regression coefficients. In addition, we have developed the confidence ellipsoids of a set of estimable functions of regression coefficients. For the fitted regression equation, an index of fit has been proposed. A simulated study illustrates the results derived in this report.

Suggested Citation

  • Rabindra Nath Das & Anis Chandra Mukhopadhyay, 2017. "Correlated random effects regression analysis for a log-normally distributed variable," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(5), pages 897-915, April.
    • Handle: RePEc:taf:japsta:v:44:y:2017:i:5:p:897-915
    DOI: 10.1080/02664763.2016.1189518
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    References listed on IDEAS

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    1. Rabindra Nath Das & Jeong-Soo Park, 2012. "Discrepancy in regression estimates between log-normal and gamma: some case studies," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(1), pages 97-111, March.
    2. Youngjo Lee & John A. Nelder, 2006. "Double hierarchical generalized linear models (with discussion)," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(2), pages 139-185, April.
    3. Rabindra Nath Das & Sung H. Park, 2006. "Slope rotatability over all directions with correlated errors," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 22(5‐6), pages 445-457, September.
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