"Logits"?

"Logit" is a contraction of "Log-Odds Unit" (pronounced "low-jit"). It is no more obscure a measurement unit of an underlying and invisible variable than an "Ampère" is of invisible electric current. The essential ingredient of Amps and logits is that they be additive.

Real apples are not additive. One Apple + One Apple = Two Apples. But Two Apples are twice as much as One Apple only when the Two Apples are perfectly identical. Real apples are not perfectly identical. When we say One Amp + One Amp = Two Amps, we say "all Amps are identical," wherever they appear on the Ammeter. Logits form an equal interval linear scale, just like Amps. When any pair of logit measurements have been made with respect to the same origin on the same scale, the difference between them is obtained merely by subtraction and is also in Logits. This is how Amps work.

Like an Ammeter, the logit scale is unaffected by variations in the distribution of measures that have been previously made, or by which items (resistances) may have been used to construct and calibrate the scale. The logit scale can be made entirely independent of the particular group of items that happen to be included in a test this time, or the particular samplings of persons that happen to have been used to calibrate these items.

We construct a logit scale in the same way that we construct an Amp scale. We deduce a theory that produces equal interval, linear measures and derive a method for applying that theory. In the case of qualitative ordered observations (right/wrong, present/absent, none/some/all), the necessary and sufficient theory is the Rasch model, and the method of application is numerous administrations of similar agents (test items) to relevant objects (persons).

The theory is

This is a "linear" model because all elements can be represented as fixed positions along one straight line. In games of chance, the (Probability of Success)/(Probability of Failure) is called the "odds of success". "Loge[(Probability of Success)/(Probability of Failure)]" is called log-odds. The units of measurement constructed by this theory are called "log-odds units" or "logits".

Not all numbers represent equal interval scales, no matter how equally spaced their values appear. Rank orders are counted with equally spacing, but rank order numbers do not specify whether the distance between 1 and 2 is equal, greater or less than the distance between 2 and 3.

How do we know that logits are equal interval? By observing that when data fit the theory, the specification that a one logit positive difference between any person and any item anywhere on the scale always has the same stochastic consequence.

When data fit, the interval specification of the theory is realized in the data. For these data, the interval scale is established. The implication is that for similar data the scale will continue. This implication, however, is always tested when fit is analyzed for each new application, just as wise use of an Ammeter requires that it too be continually checked. When in the new application, the fit criteria are met, then the linear scale continues - the logit unit is maintained.

Benjamin D. Wright

Logits? Wright BD. … 1993, 7:2 p.288


Logits? Wright BD. … Rasch Measurement Transactions, 1993, 1993, 7:2 p.288

Please help with Standard Dataset 4: Andrich Rating Scale Model



Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez

To be emailed about new material on www.rasch.org
please enter your email address here:

I want to Subscribe: & click below
I want to Unsubscribe: & click below

Please set your SPAM filter to accept emails from Rasch.org

www.rasch.org welcomes your comments:

Your email address (if you want us to reply):

 

ForumRasch Measurement Forum to discuss any Rasch-related topic

Go to Top of Page
Go to index of all Rasch Measurement Transactions
AERA members: Join the Rasch Measurement SIG and receive the printed version of RMT
Some back issues of RMT are available as bound volumes
Subscribe to Journal of Applied Measurement

Go to Institute for Objective Measurement Home Page. The Rasch Measurement SIG (AERA) thanks the Institute for Objective Measurement for inviting the publication of Rasch Measurement Transactions on the Institute's website, www.rasch.org.

Coming Rasch-related Events
Sept. 15-16, 2017, Fri.-Sat. IOMC 2017: International Outcome Measurement Conference, Chicago, jampress.org/iomc2017.htm
Oct. 13 - Nov. 10, 2017, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Oct. 25-27, 2017, Wed.-Fri. In-person workshop: Applying the Rasch Model hands-on introductory workshop, Melbourne, Australia (T. Bond, B&FSteps), Announcement
Jan. 5 - Feb. 2, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Jan. 10-16, 2018, Wed.-Tues. In-person workshop: Advanced Course in Rasch Measurement Theory and the application of RUMM2030, Perth, Australia (D. Andrich), Announcement
Jan. 17-19, 2018, Wed.-Fri. Rasch Conference: Seventh International Conference on Probabilistic Models for Measurement, Matilda Bay Club, Perth, Australia, Website
April 13-17, 2018, Fri.-Tues. AERA, New York, NY, www.aera.net
May 25 - June 22, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 29 - July 27, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
Aug. 10 - Sept. 7, 2018, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Oct. 12 - Nov. 9, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
The HTML to add "Coming Rasch-related Events" to your webpage is:
<script type="text/javascript" src="https://www.rasch.org/events.txt"></script>

 

The URL of this page is www.rasch.org/rmt/rmt72e.htm

Website: www.rasch.org/rmt/contents.htm