WOLFRAM|DEMONSTRATIONS PROJECT

Effect of Outliers on Fit of Growth Models

​
shifted logistic model data generation parameters
y
asym
10.
k
0.2
t
c
30.
pts. to generate
6
data scatter ϵ
0.
seed
0
number of outlier point locators
0
1
2
3
new locator(s)
accept outlier point locator(s)
Gompertz fitting model initial parameter values
y
asym
G
9.
b
16.
c
0.1
Weibull fitting model initial parameter values
y
asym
W
8.
τ
35.
m
2.
fit selected model to data and plot results
before next fit, set initial parameters to
default values
last fitted values
axes maxima
time axis max.
60.
growth axis max.
12.
data generation model:
y
logisticshifted
(t) =
y
asym
S
1
k(
t
c
-t)
e
+1
-
1
k
t
c
e
+1
Gompertz fitting model:
y
Gompertz
(t) =
y
asym
G
-b
-ct
e
e
Weibull fitting model:
y
Weibull
(t) =
y
asym
W
1-
-
m
t
τ
e
Gompertz model fit
Weibull model fit
2
r
= 0.9976
MSE = 0.2051
2
r
= 0.9999
MSE = 0.009045
y
asym
G
= 10.62
y
asym
W
= 9.867
b = 16.06
τ = 32.77
c = 0.1037
m = 4.228
The choice of a population’s growth model is frequently influenced by its fit to experimental growth curves, which in turn can be discernibly affected by the data scatter and presence of outliers. This Demonstration allows visualization and quantification of these effects by generating smooth or randomly scattered growth data with the shifted logistic equation and fitting them with the Gompertz and stretched exponential (Weibullian) models by nonlinear regression. One to three outliers can be added manually at chosen locations and their effect on the fitted growth curve’s shape and fit parameters assessed.