C.1 Nonlinear Growth curves in SPSS

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The solutions are provided as an SPSS syntax file file.

Or copy the block below:

GRAPH
  /LINE(SIMPLE)=VALUE(Yt) BY Time.

* NonLinear Regression.
MODEL PROGRAM  Yzero=0.01 r=0.01 K=0.01.
COMPUTE  PRED_=K*Yzero/(Yzero + (K-Yzero) * EXP(-1*(r * K * Time))).
NLR Yt
  /PRED PRED_
  /SAVE PRED
  /CRITERIA SSCONVERGENCE 1E-8 PCON 1E-8.

GRAPH
  /LINE(MULTIPLE)=VALUE(Yt PRED_) BY Time.

COMPUTE T1=Yt * Time.
COMPUTE T2=Yt * (Time ** 2).
COMPUTE T3=Yt * (Time ** 3).
COMPUTE T4=Yt * (Time ** 4).
EXECUTE.

REGRESSION
  /MISSING LISTWISE
  /STATISTICS COEFF OUTS R ANOVA
  /CRITERIA=PIN(.05) POUT(.10)
  /NOORIGIN 
  /DEPENDENT Yt
  /METHOD=ENTER T1 T2 T3 T4
  /SAVE PRED.


GRAPH
  /LINE(MULTIPLE)=VALUE(Yt PRED_ PRE_1) BY Time.
  • The point here is that the polynomial regression appoach is “just” curve fitting … adding components until a nice fit is found … but what does component \(Y_t^4\) represent? A quartic subprocess?
  • Fitting the solution of the the logistic function will give us parameters we can interpret unambiguoulsy: Carrying capacity, growth rate, starting value.