The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지

The Marginal Model for Categorical Data Analysis of $3\times3$ Cross-Trials

$3\times3$ 교차실험을 범주형 자료 분석을 위한 주변확률모형

  • Published : 2001.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

The marginal model is proposed for the analysis of data which have c(2: 3) categories in the 3 x 3 cross-over trials with three periods and three treatments. This model could be used for the counterpart of the Kenward-Jones' joint probability one and should be the generalization of Balagtas et ai's univariate marginal logits one, which analyze the treatment effects in the 3 x 3 cross-over trials with binary response variables[Kenward and Jones(1991), Balagtas et al(1995)]. The model equations for the marginal probability are constructed by the three types of link functions. The methods would be given for making of the link function matrices and model ones, and the estimation of parameters shall be discussed. The proposed model is applied to the analysis of Kenward and Jones' data.

세 처리, 세 기간을 갖는 3$\times$3 교차실험에서 c($\geq$3)개의 범주를 가진 자료의 분석에 사용될 수 있는 주변확률모형을 제안한다. 이 모형은 Kenward and Jones(1991)의 결합확률 모형의 대조물 (counterpart)로 사용될 수 있고 2항 변수를 갖는 3$\times$3 교차실험에서 처리 효과를 분석하기 위한 Balagtas et al(1995)의 일변량주변로지트모형의 일반화이다. 세 종류의 링크변화를 사용하여 주변확률모형방정식의 구성된다. 링크변환행렬과 모형행렬을 구성하는 방법이 주어지고, 모수의 추정이 논의된다. 제안된 모형을 Kenward and Jones 자료의 분석에 응용한다.

Keywords

References

  1. Introduction to the Statistical Analysis of Categorical Data Anderson, E. B.
  2. The Statistician v.3 The Two-Period Crossover Trial Armitage, P.;Hills, M. P.
  3. Appl. Statist. v.44 Marginal Modeling of Categorical Data from Crossover Experiments Balagtas, C. C.;Becker, M. P.;Lang, J. B.
  4. JASA v.84 Analysis of repeated categorical measurements with conditional likelihood methods Conaway, M. R.
  5. Computational Statistics & Data Analysis v.3 Maximum likelihood methods for linear and log-linear models in categorical data Harber, H.
  6. The Design and Analysis of Cross-over Trials Jones, B.;Kenward, M. G.
  7. Statistics in Medicine v.10 The Analysis of Categorical Data from Cross-over Trials using a Latent Variable Model Kenward, M. G.;Jones, B.
  8. Cross-over Experiments Ratkowsky, D. A.;Evans, M. A.;Alldredge, J. R.