The early origins of the logit model

Abstract This paper describes the origins of the logistic function and its history up to its adoption in bio-assay and the beginning of its wider acceptance in statistics, ca. 1950. The function was probably first invented in 1838 to describe population growth by the Belgian mathematician Verhulst, who gave it its name in 1845; but it was rediscovered independently several times over in the next eighty years, both for this purpose and for the description of autocatalytic chemical reactions. Its adoption in an altogether different role in bio-assay has been determined decisively by the individual actions and personal histories of a few scholars: the widespread acceptance of the growth function is due to Pearl and Reed, the general recognition of Verhulst’s primacy to Yule, and the introduction of the function in bio-assay to Berkson.

[1]  P. Verhulst.  Recherches mathématiques sur la loi d’accroissement de la population , 2022, Nouveaux mémoires de l'Académie royale des sciences et belles-lettres de Bruxelles.

[2]  A. Quételet,et al.  Du système social et des lois qui le régissent , 1848 .

[3]  C. I. Bliss,et al.  THE METHOD OF PROBITS--A CORRECTION. , 1934, Science.

[4]  K. Pearson,et al.  Tables for statisticians and biometricians , 1914 .

[5]  C. I. Bliss.  THE CALCULATION OF THE DOSAGE-MORTALITY CURVE , 1935 .

[6]  T. Brailsford Robertson,et al.  The chemical basis of growth and senscence , 1923 .

[7]  E B Wilson,et al.  The Determination of L.D.50 and Its Sampling Error in Bio-Assay. , 1943, Proceedings of the National Academy of Sciences of the United States of America.

[8]  C. I. Bliss,et al.  THE METHOD OF PROBITS. , 1934, Science.

[9]  R. Pearl,et al.  The Biology of Death , 1923 .

[10]  H. A. David,et al.  Annotated Readings in the History of Statistics , 2001 .

[11]  R. A. Fisher,et al.  Statistical Tables for Biological, Agricultural and Medical Research , 1956 .

[12]  D. Meadows,et al.  The limits to growth. A report for the Club of Rome's project on the predicament of mankind. , 1972 .

[13]  J. Berkson.  Application of the Logistic Function to Bio-Assay , 1944 .

[14]  Lloyd Pj,et al.  American German and British antecedents to Pearl and Reed's logistic curve. , 1967 .

[15]  G. Fechner.  Elemente der Psychophysik , 1998 .

[16]  R. Pearl,et al.  The biology of population growth , 2005, Zeitschrift für Induktive Abstammungs- und Vererbungslehre.

[17]  Calcul des probabilités et théorie des erreurs , 1930 .

[18]  Rory A. Fisher,et al.  256: The Analysis of Variance with Various Binomial Transformations. , 1954 .

[19]  W. Ostwald.  Studien zur chemischen Dynamik; Erste Abhandlung: Die Einwirkung der Säuren auf Acetamid , 1883 .

[20]  R Pearl,et al.  A Further Note on the Mathematical Theory of Population Growth. , 1922, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Raymond Pearl.  Studies in human biology , 1925 .

[22]  Raymond Pearl,et al.  On the Rate of Growth of the Population of the United States since 1790 and Its Mathematical Representation. , 1920, Proceedings of the National Academy of Sciences of the United States of America.

[23]  W. Ostwald.  Studien zur chemischen Dynamik , 1884 .

[24]  P. Verhulst,et al.  Deuxième Mémoire sur la Loi d'Accroissement de la Population. , 2022 .

[25]  Joseph Berkson,et al.  The Application of the Logistic Function to Experimental Data. , 1928 .

[26]  M. J. Farrell.  The Demand for motor-cars in the United States , 1954 .

[27]  C. W. Emmens,et al.  THE DOSE/RESPONSE RELATION FOR CERTAIN PRINCIPLES OF THE PITUITARY GLAND, AND OF THE SERUM AND URINE OF PREGNANCY , 1940 .

[28]  J. Berkson.  Why I Prefer Logits to Probits , 1951 .

[29]  E B Wilson.  The Logistic or Autocatalytic Grid. , 1925, Proceedings of the National Academy of Sciences of the United States of America.

[30]  J. Berkson.  MINIMUM CHI-SQUARE, NOT MAXIMUM LIKELIHOOD! , 1980 .

[31]  R. Pearl,et al.  THE LOGISTIC CURVE AND THE CENSUS COUNT OF I930. , 1930, Science.

[32]  J. Aitchison,et al.  The Lognormal Distribution. , 1958 .

[33]  M. W. Green,et al.  2. Handbook of the Logistic Distribution , 1991 .