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IS THE ASSUMPTION OF UNIFORM INTRA‐CLASS CORRELATION EVER NEEDED?
Author(s) -
Brewer K.R.W.,
Tam S.M.
Publication year - 1990
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1990.tb01035.x
Subject(s) - mathematics , correlation , zero (linguistics) , constant (computer programming) , sign (mathematics) , class (philosophy) , population , matrix (chemical analysis) , statistics , covariance matrix , regression analysis , regression , mathematical analysis , computer science , geometry , artificial intelligence , composite material , programming language , philosophy , linguistics , materials science , demography , sociology
Summary When modelling a finite population it is sometimes assumed that the residuals from the regression model expectations are distributed with a uniform non‐zero intra‐class correlation. It is shown that if a certain vector is spanned by the columns of the design matrix (in the homoskedastic case this vector corresponds to the inclusion of a constant term) then such a model is underidentified and the assumption of a known non‐zero correlation has almost no impact on the results of the regression analysis. When this vector is not spanned by the columns of the design matrix, a simpler alternative model can usually be fitted equally well to observations from any single population. The only exception occurs when the the intra‐class correlation required is negative in sign.