One Degree of Freedom for Nonadditivity: Applications with Generalized Linear Models and Link Functions

SUMMARY The unreplicated two-way table of observations is considered with generalized linear models being fitted. The predictor, which is linear in row and column effects, is extended to include an interaction term that is multiplicative in the row and column effects and equivalent to the one-degree-of-freedomfor-nonadditivity term of Tukey (1949, Biometrics 5, 232-242). Various interpretations of the model are given, including the suggestion of a new link function. An example involving a 3 x 5 table of insect catch data is analyzed. Extensions are considered.

[1]  J. Tukey.  One Degree of Freedom for Non-Additivity , 1949 .

[2]  John W. Tukey,et al.  Exploratory Data Analysis. , 1979 .

[3]  John Mandel,et al.  Non-Additivity in Two-Way Analysis of Variance , 1961 .

[4]  D. Pregibon.  Goodness of Link Tests for Generalized Linear Models , 1980 .

[5]  E. J. Williams.  THE INTERPRETATION OF INTERACTIONS IN FACTORIAL EXPERIMENTS , 1952 .

[6]  P. McCullagh,et al.  Generalized Linear Models , 1984 .

[7]  H. F. Gollob,et al.  A statistical model which combines features of factor analytic and analysis of variance techniques , 1968, Psychometrika.

[8]  R. Fisher,et al.  STUDIES IN CROP VARIATION , 2009 .

[9]  Frederick Mosteller,et al.  Data Analysis and Regression , 1978 .

[10]  A. J. Wright.  The analysis and prediction of some two factor interactions in grass breeding , 1971, The Journal of Agricultural Science.

[11]  F. Yates.  A Monte-Carlo trial on the behaviour of the non-additivity test with nonnormal data , 1972 .

[12]  D. Pregibon.  Score Tests in GLIM with Applications , 1982 .

[13]  R. W. Wedderburn.  Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method , 1974 .

[14]  K. W. Finlay,et al.  The analysis of adaptation in a plant-breeding programme , 1963 .

[15]  G. H. Freeman.  The analysis and interpretation of interactions , 1985 .

[16]  Ronald D. Snee,et al.  Nonadditivity in a Two-Way Classification: Is it Interaction or Nonhomogeneous Variance? , 1982 .

[17]  David V. Hinkley,et al.  Transformation diagnostics for linear models , 1985 .

[18]  J. Nelder,et al.  An extended quasi-likelihood function , 1987 .