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