Oxford English Dictionary: Logit (pronounced "low-jit")
"The natural logarithm [ log or ln or loge ] of the quotient of a probability and its complement."
Lod "The logarithm to the base 10 [ log or log10 ] of the quotient of a probability and its complement."
1944. J. Berkson in Jrnl. Amer. Statistical Assoc. 39. 361. "Instead of the observations [1-pi =] qi we deal with their logits li = ln(pi/qi). [Note] I use this term for ln(p/q) following Bliss, who called the analogous function which is linear on x for the normal curve `probit'."
Oxford English Dictionary: Lod
"The logarithm of the odds in favor of or against a given event; also, the logarithm of the ratio of two odds."
1949. G. A. Barnard in Jrnl. R. Statistical Soc. B. XI. 116: "There are great advantages in working in terms of odds rather than in terms of probabilities and greater advantages still in working in terms of logarithms of odds... This suggested the adoption of log odds (or, as they are called below, lods) as the fundamental idea in the theory [of sequential tests], in place of probabilities."
1955. N. E. Morton in Amer. Jrnl. Human Genetics VII. 292: "The scores in a sequential test are lods, or logarithms of the probability ratio... Tables 4-8 give the possible certain matings and the lod scores appropriate to them."
From this it would appear that "lod" and "logit", "lod score" and "logit measure" are synonymous. And they can be, but Barnard's "calculus of lods" is idiosyncratic. He writes "We can look forward to an experiment, or we can look back on it. ... To distinguish between the two senses of likelihood involved here, we shall refer to the first as forward likelihood, or f-likelihood, and to the second as backward likelihood of b-likelihood." This leads to f-lods and b-lods.
As A. W. F. Edwards notes (Nature, 333/26, 308, 1988):
"Lod, log-odds, was first defined by Barnard ... Indeed, the word odds itself is nowhere else used in this backward sense introduced by Barnard. The common name being the likelihood ratio."
"Their [linkage workers'] Lod score is simply the log-likelihood to the base 10, standardized as is customary by the addition of a constant, in this case such as to make the log-likelihood zero at a recombination fraction of one-half."
Barnard G.A. (2001) "Logit", "Lod" and Log-Odds. Rasch Measurement Transactions 14:4 p.785
"Logit", "Lod" and Log-Odds. Barnard G.A. Rasch Measurement Transactions, 2001, 14:4 p.785
|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|
|Forum||Rasch 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|
|Oct. 11 - Nov. 8, 2019, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|Nov. 3 - Nov. 4, 2019, Sun.-Mon.||International Outcome Measurement Conference, Chicago, IL, http://jampress.org/iomc2019.htm|
|Nov. 15, 2019, Fri.||XIII International Workshop "Rasch Models in Business Administration", IUDE of Universidad de La Laguna. Tenerife. Canary Islands. Spain, https://www.ull.es/institutos/instituto-universitario-empresa/|
|Jan. 30-31, 2020, Thu.-Fri.||A Course on Rasch Measurement Theory - Part 1, Sydney, Australia, course flyer|
|Feb. 3-7, 2020, Mon.-Fri.||A Course on Rasch Measurement Theory - Part 2, Sydney, Australia, course flyer|
|Jan. 24 - Feb. 21, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|Apr. 14-17, 2020, Tue.-Fri.||International Objective Measurement Workshop (IOMW), University of California, Berkeley, https://www.iomw.org/|
|May 22 - June 19, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 26 - July 24, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
|June 29 - July 1, 2020, Mon.-Wed.||Measurement at the Crossroads 2020, Milan, Italy , https://convegni.unicatt.it/mac-home|
|July 1 - July 3, 2020, Wed.-Fri.||International Measurement Confederation (IMEKO) Joint Symposium, Warsaw, Poland, http://www.imeko-warsaw-2020.org/|
|Aug. 7 - Sept. 4, 2020, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com|
|Oct. 9 - Nov. 6, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 25 - July 23, 2021, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
The URL of this page is www.rasch.org/rmt/rmt144h.htm