Hockey stick function

When high-school cross-country runners were exposed for 1 h to photochemical oxidants at 0.03-0.3 ppm, their performance decreased with increasing concentration. A statistical test for threshold values (regression using/ hockey stick functions) applied to these data gives a threshold estimate of 0.12 ppm, with a 95% confidence interval of 0.067-0.163 ppm. ... 

Hasselblad, V., G. Lowrimore, W. C. Nelson, J. Creason, and C. J. Nelson. Regression Using Hockey Stick Functions. Durham. N.C. U.S. Department of Health. Education, and Welfare. Public Health Service. Environmental Health Service, National Air Pollution Control Administration (in-house report, 1970). 5 pp. 

The relationship between a covariate and individual model parameters should be exploratively investigated by a graphical presentation which often suggests a mathematical function that might best describe the relationship. The most commonly used functions are linear functions, so called hockey stick functions as well as exponential functions. The linear relationship can be implemented according the following equation ... 

The hockey stick function assumes a linear relationship until a node point is reached afterwards another relationship can be used. In the above equation, the median was chosen as the node point and for all individuals having a larger covariate value than the median value no influence of the covariate was assumed. 

V. Hasselblad, J.P. Creason, and W.P.Nelson (1976), Regression using Hockey stick functions, EPA report 600/1-76-024, Research Triangle Park, NjC. 

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