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# Growth Curves

A class of sigmoid and monotonic curves, often used to model the growth of biological subjects. Five types of growth curve are provided in Genstat, all types of logistic.

## Logistic

Y = a + c/(1 + e-b(X-m)) ( Y = a + c / (1 + EXP(-b * (X-m))) )

## Generalized logistic

Y = a + c/(1 + te-b(X-m))-1/t ( Y = a + c / (1 + t * EXP(-b*(X-m)))**1/t )

## Gompertz

Y = a + ce-e-b(X-m) ( Y = a + c * EXP(-EXP(-b * (X-m))) )

## Emax

Y = a + c/(1 + e-b(log(X)-m)) ( Y = a + c / (1 + EXP(-b * (log(X)-m))) )

## Generalized Emax

Y = a + c/(1 + te-b(log(X)-m))-1/t ( Y = a + c / (1 + t * EXP(-b*(log(X)-m)))**1/t )

## Direction of response

For the Gompertz curve, the direction of response can be selected. The effect of direction on the parameters of the curves is as follows: when b > 0, direction right gives c > 0 and direction left gives c < 0. However, when b < 0 this is reversed: see Examples of Standard Nonlinear Curves for a graphical illustration.