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- W3149904369 abstract "Arrays of zeros and ones in two or more dimensions may be analysed in terms of scales (Guttman, 1944), the idea being to permute the rows, columns, etc. of the array so that it becomes as monotonic as possible, according to some criterion, in each dimension. Arrays of relative frequencies are also sometimes analysed in this way, especially if most or many of the entries are zero or one. More commonly, however, frequency data are fitted by transformed additive models which decompose the binomial probabilities underlying the data into separate row, column, etc., effects (Cox, 1970; Haberman, 1974). In this paper we Bhow that by suitably formulating the notion of a scale, and by using Haberman's extension of the maximum likelihood criterion to allow singular estimates, the scaling and parametric approaches to the analysis of frequency data are made to coincide. We work in two dimensions, but our definitions, theorem and proofs carry over in obvious ways to higher dimensions. Let P be an m x n array of binomial probabilities where each ptj independently generates rti successes out of N{i > 0 trials. We assume that" @default.
- W3149904369 created "2021-04-13" @default.
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- W3149904369 date "2005-01-01" @default.
- W3149904369 modified "2023-09-27" @default.
- W3149904369 title "Singularities in the analysis of binomial data" @default.
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