Choosing a growth model
|Top Previous Next|
This demonstration data set was copied from the paper by Sengul & Kiraz (2005). The data set comprises the age in weeks and body weight in grams of male large white turkeys for the first 18 weeks of their life.
Use File|Open to find and open Male turkey weights.csv (saved by default during installation in the folder C:\Program files\GrowthII\GrowthDemoData)
Once the data set has been opened, Growth II will immediately fit a von Bertalanffy growth curve to the data and plot the result.
A brief glance at this graph and the Regression diagnostics in the grid below shows that the von Bertalanffy is a poor choice (note the size of the Akaike Information Criterion, AIC = 290.165). We will now take you through an investigation of other possible more appropriate models.
Now choose from the Age/Size drop-down menu 3P logistic (logistic growth curve with 3 fitted parameters):
Growth II immediately opens a dialogue box showing the initial guesses for the 3 parameters. The program needs initial guesses as it solves the non-linear regression using the Levenberg-Marquardt method. While the initial guesses can and sometimes have to be changed to get a solution, it is sensible to first try the defaults you are given.
Click OK and the fit is immediately presented:
It is clearly a fair fit, but it seems poor for the youngest age groups. Note the size of the Akaike Information Criterion (AIC = 270.94), this is smaller than that for the von Bertalanffy, suggesting that the logistic is the superior model.
Staying with the logistic we can now fit a 4 parameter logistic by choosing 4P logistic from the drop-down. This fit is clearly a superior fit with with the lowest AIC so far of 248.79:
Trying other models will give the following values for the Akaike Information Criterion:
Exponential - 290.166
3 parameter Gompertz - 281.06
Weibull - 239.748
Morgan-Mercer-Flodin - 239.46
4 parameter Gompertz - 244.668
Janoschek - 239.747
The Richards curves could not be fitted successfully to these data. However, by rescaling the data by dividing by 1000, so that weight is in kilograms and not grams (see file Male turkey weights kg.csv) the 5 parameter Richards was successfully fitted to the data. Comparison with other models using the AIC suggested that this model was inferior to most other models)
The results indicate that the Weibull or closely related Janoschek curve is the best description of the turkey data. However, almost all the models were equally good.
Here is the plot of the Weibull to compare with the logistic above. It is clearly a good fit to the data. The authors of this paper actually used the coefficient of determination, R2, as a measure of fit, and found very high R2 values with all models tested. The coefficient of determination should not be used to measure the goodness of fit of nonlinear regression. Interestingly, they did not fit the Weibull or Janoschek models, but certainly noted that most models gave good fits: