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The Efficiency of Split Panel Designs in an Analysis of Variance Model.

Liu X, Wang WG, Liu HJ - PLoS ONE (2016)

Bottom Line: We further consider the efficiency of split panel design, given a budget, and transform it to a constrained nonlinear integer programming.Specifically, an efficient algorithm is designed to solve the constrained nonlinear integer programming.Moreover, we combine one at time designs and factorial designs to illustrate the algorithm's efficiency with an empirical example concerning monthly consumer expenditure on food in 1985, in the Netherlands, and the efficient ranges of the algorithm parameters are given to ensure a good solution.

View Article: PubMed Central - PubMed

Affiliation: School of Economics and Management, Liaoning Shihua University, Fushun, China.

ABSTRACT
We consider split panel design efficiency in analysis of variance models, that is, the determination of the cross-sections series optimal proportion in all samples, to minimize parametric best linear unbiased estimators of linear combination variances. An orthogonal matrix is constructed to obtain manageable expression of variances. On this basis, we derive a theorem for analyzing split panel design efficiency irrespective of interest and budget parameters. Additionally, relative estimator efficiency based on the split panel to an estimator based on a pure panel or a pure cross-section is present. The analysis shows that the gains from split panel can be quite substantial. We further consider the efficiency of split panel design, given a budget, and transform it to a constrained nonlinear integer programming. Specifically, an efficient algorithm is designed to solve the constrained nonlinear integer programming. Moreover, we combine one at time designs and factorial designs to illustrate the algorithm's efficiency with an empirical example concerning monthly consumer expenditure on food in 1985, in the Netherlands, and the efficient ranges of the algorithm parameters are given to ensure a good solution.

No MeSH data available.


The effect of inner iteration number on the objective function value.
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pone.0154913.g004: The effect of inner iteration number on the objective function value.

Mentions: Second, we set the initial temperature E0, the temperature decrease rate m, the termination temperature ε, and the inner iteration number are changed from 500 to 3,000 to ensure that the algorithm reaches the balanced state. The optimal proportion values and the corresponding objective values are shown in Fig 3. From Fig 3, the higher the inner iteration number is, the more easily the algorithm moves from the local optimal value and converges to the global optimal value. Conversely, the higher the inner iteration number is, the longer the implementation time. In this study, the implementation time based on the set of parameters is in 10 minutes. As such, we do not consider that the inner iteration numbers increases implementation time. From Fig 4, when the inner iteration number is more than 2,000, the objective values and the optimal proportion values converge to 0.007 and 0.2, respectively. Therefore, the inner iteration number can be chosen between 2,000 and 2,500.


The Efficiency of Split Panel Designs in an Analysis of Variance Model.

Liu X, Wang WG, Liu HJ - PLoS ONE (2016)

The effect of inner iteration number on the objective function value.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4862657&req=5

pone.0154913.g004: The effect of inner iteration number on the objective function value.
Mentions: Second, we set the initial temperature E0, the temperature decrease rate m, the termination temperature ε, and the inner iteration number are changed from 500 to 3,000 to ensure that the algorithm reaches the balanced state. The optimal proportion values and the corresponding objective values are shown in Fig 3. From Fig 3, the higher the inner iteration number is, the more easily the algorithm moves from the local optimal value and converges to the global optimal value. Conversely, the higher the inner iteration number is, the longer the implementation time. In this study, the implementation time based on the set of parameters is in 10 minutes. As such, we do not consider that the inner iteration numbers increases implementation time. From Fig 4, when the inner iteration number is more than 2,000, the objective values and the optimal proportion values converge to 0.007 and 0.2, respectively. Therefore, the inner iteration number can be chosen between 2,000 and 2,500.

Bottom Line: We further consider the efficiency of split panel design, given a budget, and transform it to a constrained nonlinear integer programming.Specifically, an efficient algorithm is designed to solve the constrained nonlinear integer programming.Moreover, we combine one at time designs and factorial designs to illustrate the algorithm's efficiency with an empirical example concerning monthly consumer expenditure on food in 1985, in the Netherlands, and the efficient ranges of the algorithm parameters are given to ensure a good solution.

View Article: PubMed Central - PubMed

Affiliation: School of Economics and Management, Liaoning Shihua University, Fushun, China.

ABSTRACT
We consider split panel design efficiency in analysis of variance models, that is, the determination of the cross-sections series optimal proportion in all samples, to minimize parametric best linear unbiased estimators of linear combination variances. An orthogonal matrix is constructed to obtain manageable expression of variances. On this basis, we derive a theorem for analyzing split panel design efficiency irrespective of interest and budget parameters. Additionally, relative estimator efficiency based on the split panel to an estimator based on a pure panel or a pure cross-section is present. The analysis shows that the gains from split panel can be quite substantial. We further consider the efficiency of split panel design, given a budget, and transform it to a constrained nonlinear integer programming. Specifically, an efficient algorithm is designed to solve the constrained nonlinear integer programming. Moreover, we combine one at time designs and factorial designs to illustrate the algorithm's efficiency with an empirical example concerning monthly consumer expenditure on food in 1985, in the Netherlands, and the efficient ranges of the algorithm parameters are given to ensure a good solution.

No MeSH data available.