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Monte Carlo Method Using Different Types of Quasi- Random Sequences for Estimating Low-dimensional Nonlinear Mixed Effects Model |
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PP: 141-154 |
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doi:10.18576/jsapl/090304
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Author(s) |
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Sukanta Das,
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Abstract |
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| Nonlinear mixed effects models involve both fixed effects and random effects in which some of the fixed and random effects parameters enter nonlinearly to the model function. These models are very popular for analyzing clustered data or unbalanced repeated measures data. There are several methods for estimating the parameters of these models. Most of the available methods are based on the approximation technique. In this study, instead of approximation based methods, quasi-Monte Carlo method is used, which directly solves the intractable multidimensional integrations in the nonlinear mixed effects model. To apply this method, the Michaelis-Menten model with one random effects parameter is used as a nonlinear mixed effects model. For this simulation study, different types of quasi-random sequences (e.g. Halton, Sobol, and Faure) are used with different combination of subjects and intra-subject correlation coefficient. The results of the simulation studies show that the quasi-Monte Carlo method correctly estimates the parameters of the model, and also these estimates are slightly different for using different types of quasi-random sequences. Among the quasi-random sequences, Halton sequences give better estimates than Sobol and Faure sequences for both fixed and random effects parameters of the nonlinear mixed effects models.
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