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.

## See also

- Standard Curves for information on general options and other curves
- Options for choosing which results to display
- Further Output for additional output subsequent to analysis
- Standard Curves with Correlated Errors for fitting curves with correlated errors
- Saving Results for further analysis
- Fitted Model for graphical display of the model
- Model Checking for diagnostic plots for model checking
- Examples of Standard Nonlinear Curves
- Exponential Curves
- Fourier Curves
- Gaussian Curves
- Rational Curves
- Nonlinear Models menu
- Nonlinear Quantile Regression menu
- FITCURVE directive
- FITNONLINEAR directive
- FIT directive
- RQNONLINEAR procedure
- MINIMIZE procedure
- SIMPLEX procedure