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Research articles

ScienceAsia 39 (2013): 561-565 |doi: 10.2306/scienceasia1513-1874.2013.39.561

Maximum likelihood estimation of linear structural relationship model parameters assuming the slope is known

Abu S.M.A. Mamuna,*, Ghapor A. Hussinb, Yong Z. Zubairia, Rahmatullah A.H.M. Imonc

ABSTRACT:     A number of statistical techniques have been proposed by many authors to estimate the parameters in a linear structural relationship model, but only few papers discuss the precision of these estimators. In this study, we derive the maximum likelihood estimate (MLE) of the parameters by assuming the slope parameter β is known. β is estimated separately by a nonparametric method and is assumed to be known when other parameters are estimated by an MLE. We obtain closed-form estimates of parameters as well as the variance-covariance matrix. Using a simulation study and a real-world example we show that the estimated values of the parameters are unbiased and consistent.

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a Mathematics Division, Centre for Foundation Studies in Science, University of Malaya, 50603 Kuala Lumpur, Malaysia
b Faculty of Science and Defence Technology, National Defence University of Malaysia, Kuala Lumpur, Malaysia
c Department of Mathematical Sciences, Ball State University, Muncie, IN 47306, USA

* Corresponding author, E-mail: mithun_stat@yahoo.com

Received 7 Oct 2012, Accepted 16 Aug 2013