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A Note on the Use of the Log-Logistic Functional Form for Modelling Saturation Effects

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  • Bacon, Robert W

Abstract

This note suggests that the logistic function is often not suitable for modeling aggregate demand or ownership levels because of the fact that the independent variable is defined to lie between minus and plus infinity (unlike many economic variables which are positive). This imposes strictly positive (possibly large) levels of ownership when the independent variable is zero. The log logistic is proposed as an alternative functional form. This is shown to have logistic function properties as between the dependent variable and the log of the independent variable. The relation between the dependent variable and the independent variable is described, and conditions for this to have a sigmoid shape are given. The use of the two curves is illustrated for the relationship between real income and ownership levels for five consumer durables. Copyright 1993 by Blackwell Publishing Ltd

Suggested Citation

  • Bacon, Robert W, 1993. "A Note on the Use of the Log-Logistic Functional Form for Modelling Saturation Effects," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 55(3), pages 355-361, August.
    • Handle: RePEc:bla:obuest:v:55:y:1993:i:3:p:355-61
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    Cited by:

    1. Gebrenegus Ghilagaber, 2005. "The Extended Generalized Gamma Model and its Special Cases: Applications to Modeling Marriage Durations," Quality & Quantity: International Journal of Methodology, Springer, vol. 39(1), pages 71-85, February.
    2. David D. Hanagal, 2021. "RETRACTED ARTICLE: Positive Stable Shared Frailty Models Based on Additive Hazards," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(3), pages 431-453, December.
    3. Pandey Arvind & Hanagal David D. & Tyagi Shikhar, 2022. "Generalised Lindley shared additive frailty regression model for bivariate survival data," Statistics in Transition New Series, Statistics Poland, vol. 23(4), pages 161-176, December.
    4. Abdisalam Hassan Muse & Samuel M. Mwalili & Oscar Ngesa, 2021. "On the Log-Logistic Distribution and Its Generalizations: A Survey," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(3), pages 1-93, June.

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