Bias Reduction in Estimating Variance Components of Phytoplankton Existence at Na Thap River Based on Logistics Linear Mixed Models

3rd International Seminar On Sciences "Sciences On Precision And Sustainable Agriculture"

Arisanti, R.^1 ; Notodiputro, K.A.^2 ; Sadik, K.^2 ; Lim, A.^3

Department of Statistics, Padjadjaran University, Indonesia^1

Department of Statistics, Bogor Agricultural University, Indonesia^2

Department of Mathematics and Computer Science, Faculty of Science and Technology, Prince of Songkla University, Thailand^3

关键词: Bias-correction methods;    Confidence interval;    Generalized linear mixed models;    Maximum likelihood estimate;    Probability coverage;    Restricted maximum likelihood;    Variance components;    Variance estimation;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/58/1/012014/pdf
DOI  :  10.1088/1755-1315/58/1/012014

来源: IOP

【 摘 要 】

There are two approaches in estimating variance components, i.e. linearity and integral approaches. However the estimates of variance components produced by both methods are known to be biased. Firth (1993) has introduced parameter estimation for correcting the bias of the maximum likelihood estimates. This method is within the class of linear models, especially the Restricted Maximum Likelihood (REML) method, and the resulting estimator is known as the Firth estimator. In this paper we discuss the bias correction method applied to a logistic linear mixed model in analyzing the existence of Synedra phytoplankton along Na Thap river in Thailand. The Firth adjusted Maximum Likelihood Estimation (MLE) is similar to REML but it shows the characteristic of generalized linear mixed model. We evaluated the Firth adjustment method by means of simulations and the result showed that the unadjusted MLE produced 95% confidence intervals which were narrower when compare to the Firth method. However, the probability coverage of the interval for unadjusted MLE was lower than 95%, whereas for the Firth method the probability coverage is approximately 95%. These results were also consistent with the variance estimation of the Synedra phytoplankton existence. It was shown that the variance estimates of Firth adjusted MLE was lower than the unadjusted MLE.