Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Type II analysis by projections

사영을 이용한 제2종 분석

  • Received : 2012.10.17
  • Accepted : 2012.11.17
  • Published : 2012.11.30
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Abstract

This paper suggests a method for getting sums of squares due to sources of variation under the assumption of two-way fixed effects model. The method used for calculating the quantities due to fixed-effects is based on the projections of an observation vector y on the column space generated by the model matrix X under the assumed model. The suggested method shows that the calculation of Type II sums of squares by projections is much easier than the classical Type II analysis.

본 논문은 이원 고정효과모형의 가정하에 실험자료를 분석할 때 고정효과와 관련된 변동량을 구하는 문제를 다루고 있다. 고정효과에 따른 변동량의 계산을 위한 방법으로 제2종 분석을 이용하고 있다. 모형비교의 방식을 이용하여 고정효과에 따른 변동량을 계산하는 제2종 제곱합은 비교하는 모형의 적합에서 주어지는 잔차제곱합의 차에 근거를 두고 있다. 이와는 달리, 본 논문에서는 고정효과와 관련된 모형행렬로의 사영에 의한 변동량의 계산방법을 다루고 있다. 사영에 의한 제2종 제곱합의 계산은 기존의 방법보다 간편하고 효율적임을 보여준다.또한 사영에 의한 제2종 분석으로 변동량의 계산에 있어 균형자료와 달리 불균형자료에 있어서 어떤 점에서 차이가 있는가를 구체적으로 논의하고 있다.

Keywords

References

  1. Choi, J. S. (2010). A mixed model for repeated split-plot data. Journal of the Korean Data & Information Science Society, 21, 1-9.
  2. Choi, J. S. (2011). Type I analysis by projections, The Korean Journal of Applied Statistics, 24, 373-381. https://doi.org/10.5351/KJAS.2011.24.2.373
  3. Galecki, A. T. (1994). General class of covariance structures for two or more repeated factors in longitudinal data analysis. Communications in Statistics-Theory and Methods, 23, 3105-3119. https://doi.org/10.1080/03610929408831436
  4. Graybill, F. A. (1976). Theory and application of the linear model, Wadsworth Publishing Company, Inc., Belmont.
  5. Graybill, F. A. (1983). Matrices with applications in statistics, Wadsworth Publishing Company, Inc., Belmont.
  6. Johnson, R. A. and Wichern, D. W. (1988). Applied multivariate statistical analysis, 2nd edition, Prentice Hall, Inc., Englewood Cliffs.
  7. Milliken, G. A. and Johnson, D. E. (1984). Analysis of messy data, Van Nostrand Reinhold, New York.
  8. Searle, S. R. (1971). Linear models, John Wiley and Sons, Inc., New York.

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