• Journal of the Korean Data and Information Science Society
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• v.23 no.3
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• pp.487-494
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• 2012

This paper discusses a method for getting a basis set of estimable functions of model parameters in a two-way fixed effects model. Since the fixed effects model has more parameters than those that can be estimated, model parameters are not estimable. So it is not possible to make inferences for nonestimable functions of parameters. When the assumed model of matrix notation is reparameterized by the estimable functions in a basis set, it also discusses how to use projections for the estimation of estimable functions.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.366-375
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• 1995

A method is presented for finding estimable functions in a row-column design. It can easily be applied because the method consists of solving equations derived from the design eithout using the design matrix. It determines not only the estimability of treatment effects but also between row(or column)and treatment effects.

• The Korean Journal of Applied Statistics
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• v.29 no.2
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• pp.291-299
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• 2016

This paper discusses how to establish estimable functions when there are fixed and random effects in design models. It proves that estimable functions of mixed models are not related to random effects. A fitting constants method is used to obtain sums of squares due to random effects and Hartley's synthesis is used to calculate coefficients of variance components. To test about the fixed effects the degrees of freedom associated with divisor are determined by means of the Satterthwaite approximation.

• The Korean Journal of Applied Statistics
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• v.27 no.4
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• pp.553-560
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• 2014

This paper deals with estimable functions of parameters of less than full rank linear model. In general, the parameters of an overspecified model are not uniquely determined by least squares solutions. It discusses how to formulate linear estimable functions as functions of parameters in the model and shows how to use projection matrices to check out whether a parameter or function of the pamameters is estimable. It also presents a method to form a basis set of estimable functions using linearly independent characteristic vectors generating the row space of the model matrix.

• The Korean Journal of Applied Statistics
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• v.30 no.3
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• pp.335-344
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• 2017

This paper discusses a method of analyzing data from split-plot experiments by projections. The assumed model for data has two experimental errors due to two different experimental sizes and some random components in treatment effects. Residual random models are constructed to obtain sums of squares due to random effects. Expectations of sums of squares are obtained by Hartley's synthesis. Estimable functions of fixed effects are discussed.

• Communications for Statistical Applications and Methods
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• v.6 no.3
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• pp.707-718
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• 1999

Non-regular designs such as the Plackett-Burman(PB) design have traditionally been used for screening only main effects because of complex aliasing. But it was found that these designs could be used to estimate the 2-factor interactions as well as main effects through the hidden projection property. The goal of this paper is to propose the estimable model when projecting the 12-run PB design using the algebraic geometric method. The core of this method considers the design as a affine variety and the Grbner basis of the design ideal for this affine variety gives the estimable polynomial models. As the results of applying the 12-run PB design it is actually found that this design has the models not only with 2-factor interactions but with 3-factor. This design is the maximal fan in 4-factor projection.

• 한국데이터정보과학회:학술대회논문집
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• 2005.04a
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• pp.69-82
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• 2005

Factorial experiments are studied in this paper. The Designs, thus, have factorial balance with respect to estimable main effects and interactions. John and Lewis (1983) considered generalized cyclic row-column designs for factorial experiments. A simple method of constructing confounded designs using the classical method of confounding for block designs is described in this paper.

• Proceedings of the Korean Statistical Society Conference
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• 2004.11a
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• pp.313-317
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• 2004

Confounded row-column designs for factorial experiments are studied in this paper. The Designs, thus, have factorial balance with respect to estimable main effects and interactions. John and Lewis (1983) considered generalized cycle row=column designs for factorial experiments. A simple method of constructing confounded designs using the classical method of confounding for block designs is described in this paper

• Communications for Statistical Applications and Methods
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• v.23 no.2
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• pp.179-187
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• 2016

The fixed effects panel probit model faces "incidental parameters problem" because it has a property that the number of parameters to be estimated will increase with sample size. The maximum likelihood estimation fails to give a consistent estimator of slope parameter. Unlike the panel regression model, it is not feasible to find an orthogonal reparameterization of fixed effects to get a consistent estimator. In this note, a hierarchical Bayesian model is proposed. The model is essentially equivalent to the frequentist's random effects model, but the individual specific effects are estimable with the help of Gibbs sampling. The Bayesian estimator is shown to reduce reduced the small sample bias. The maximum likelihood estimator in the random effects model is also efficient, which contradicts Green (2004)'s conclusion.

• Journal of Korean Society for Quality Management
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• v.38 no.1
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• pp.42-51
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• 2010

For the fractional factorial designs, the resolution-IV designs can be used when we want to estimate the main effects and to investigate the structure of the non-negligible two-factor interaction effects, when the three-factor and higher order interaction effects are all negligible. However we need to add the additional treatment combinations in order to identify the influential interactions for the resolution-IV fractional factorial designs. In this paper we investigate the statistical structure for 3-level resolution-IV designs constructed by fold-over scheme and introduce a method for analyzing the influential two-factor interactions.