Estimating a boundary line model for a biological response by maximum likelihood
Article first published online: 22 SEP 2006
2006 Association of Applied Biologists
Annals of Applied Biology
Volume 149, Issue 2, pages 223–234, October 2006
How to Cite
Milne, A.E., Ferguson, R.B. and Lark, R.M. (2006), Estimating a boundary line model for a biological response by maximum likelihood. Annals of Applied Biology, 149: 223–234. doi: 10.1111/j.1744-7348.2006.00086.x
- Issue published online: 22 SEP 2006
- Article first published online: 22 SEP 2006
- Received: 20 April 2006; revised versionaccepted: 31 July 2006.
- Boundary line;
- censored probability distribution;
- maximum likelihood
The boundary line model was proposed to interpret biological data sets, where one variable is a biological response (e.g. crop yield) to an independent variable (e.g. available water content of the soil). The upper (or lower) boundary on a plot of the dependent variable (ordinate) against the independent variable (abscissa) represents the limiting response of the dependent variable to the independent variable value. Although the concept has been widely used, the methods proposed to define the boundary line have been subject to criticism. This is because of their ad hoc nature and lack of theoretical basis. In this article, we present a novel method for fitting the boundary line to a set of data. The method uses a censored probability distribution to interpret the data structure. The parameters of the distribution (and hence the boundary line parameters) are fitted using maximum likelihood and related confidence intervals deduced. The method is demonstrated using both simulated and real data sets.