[Rasch] Odds ratio as a scale
Luis Carlos Orozco
lcorovar at gmail.com
Wed Mar 9 02:56:38 EST 2011
These are a couple of references that may give some light
Book: Rasch models: foundations, recent developments, and applications.
chapter 2 * *by Fischer Derivation of the Rasch Model
web paper: Rasch Measurement Transactions 9:4 p. 457. 1996 available at
Luis C. Orozco
2011/3/8 Svend Kreiner <S.Kreiner at biostat.ku.dk>
> Dear A & T.
> A ratio scale is a scale where the unit of measurement is arbitrary.
> Comparisons of measurements by *ratios* are therefore invariant in the
> sense that they do not depend on the unit of measurement.
> Rasch (1960) himself asserted this. You can find discussions of this in
> Chapter II, Section 3 and in Chapter V he talks about the meaning of
> statements like "one person has *twice* the ability of another" and he
> says that the probability of the RM is a function of the *ratio* (not the
> difference) between the degree of ability of the person and the difficulty
> of the problem. And in Chapter VII (pages 109-110) where he says that he
> "undertook, along general lines, a discussion of what may "reasonably" be
> read into such concepts as measuring on a ratio scale "the ability of a
> person" and the "difficulty of a problem"." And later, page 115) "*Where
> this law can be applied it provides a principle of measurement on a ratio
> scale of both stimulus and object parameters*" (Rasch's italics).
> He never talked about interval scales, and you could argue that the logit
> scale is not a proper interval scales but just a logarithmic ratio scale
> because a true interval scale has both an arbitrary origin and an arbitrary
> unit. On the logit scale as such, there is no unit. Or there was no unit
> before Steven Humphrey defined his Rasch models for multiple frameworks.
> Den 08-03-2011 12:27, Bond, Trevor skrev:
> Dear Anthony
> May I possibly have some explanations on why odds ratio is a ratio scale
> I think you misconstrue...a ratio measurement scale and the mathematical
> ratio between the probabilities you mention are two entirely different
> I doubt that anyone could seriously assert that RM produces ratio scale
> measurement – some claim it produces interval level measurement scales.
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> Svend Kreiner
> Department of Biostatistics
> University of Copenhagen
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> Email: S.Kreiner at biostat.ku.dk
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