[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
www.rasch.org

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.
>
> Best
>
> Svend
>
>
> 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
> measure?
>
> I think you misconstrue...a ratio measurement scale and the mathematical
> ratio between the probabilities you mention are two entirely different
> concepts.
> I doubt that anyone could seriously assert that RM produces ratio scale
> measurement – some claim it produces interval level measurement scales.
> best
> T
>
>
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>
> --
> Svend Kreiner
> Professor
> Department of Biostatistics
> University of Copenhagen
>
> Øster farimagsgade 5, entr. B
> P.O. Box 2099
> DK-1014 Copenhagen K, Denmark
>
> Email: S.Kreiner at biostat.ku.dk
> Phone: (+45) 35 32 75 97
>
> Fax: (+45) 35 32 79 07
>
>
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