Fitting logistic curve to growth data

[DP_Sydney]

Hi all,

 I need to fit a curve to data on mass gain, which follows a sigmoidal pattern and is best described using a logistic equation (based on similar published data, with which I wish to compare my data) of the form:
 
Y = A/(1 + e^-K(d-i))
where Y = mass
         A = asymptotic mass
         K = growth rate
         d = age (time)
         i = inflection point
        (note ^ indicates to the power)

The data I have are body mass recorded daily for several individuals (nestling birds), which will be analysed separately.

I need to output the parameters (A, K, i) rather than just produce a curve. I've searched the archives and Google but haven't found instructions for how to do this (I have instructions for running this in GENSTAT but of course do not have GENSTAT).

Any help would be great...but beware I am a drop-down menus and buttons person when it comes to software :-)

Regards,
Dean

[Maguin, Eugene]

Dean,

Have you looked at the curvefit procedure? It has a logistic function and,
although I haven't used it for quite a while, I recall that it yields
coefficient values.

Gene Maguin

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
DP_Sydney
Sent: Wednesday, December 28, 2011 6:07 AM
To: [hidden email]
Subject: Fitting logistic curve to growth data

Hi all,

 I need to fit a curve to data on mass gain, which follows a sigmoidal
pattern and is best described using a logistic equation (based on similar
published data, with which I wish to compare my data) of the form:

Y = A/(1 + e^-K(d-i))
where Y = mass
         A = asymptotic mass
         K = growth rate
         d = age (time)
         i = inflection point
        (note ^ indicates to the power)

The data I have are body mass recorded daily for several individuals
(nestling birds), which will be analysed separately.

I need to output the parameters (A, K, i) rather than just produce a curve.
I've searched the archives and Google but haven't found instructions for how
to do this (I have instructions for running this in GENSTAT but of course do
not have GENSTAT).

Any help would be great...but beware I am a drop-down menus and buttons
person when it comes to software :-)

Regards,
Dean



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[David Marso]

See the NLR (Non Linear Regression) Procedure.
Following is an example of simulated data and the set up and results of NLR.
Note that the parameter estimates used to generate the data are recovered quite nicely!
You will wish to consult the docs on how to set up and run NLR from the dialog boxes.
HTH, David
---
INPUT PROGRAM.
COMPUTE #K=1.5 .
COMPUTE #A=4.0.
COMPUTE #i= 1.7 .
LOOP ID=1 TO 1000.
COMPUTE d= Uniform(1)+4.
COMPUTE Y=#A/(1+EXP(-#K * (d-#i)))+ UNIFORM(.01).
END CASE.
END LOOP.
END FILE.
END INPUT PROGRAM.
EXE.

GRAPH
  /SCATTERPLOT(BIVAR)=d WITH y
  /MISSING=LISTWISE .

* NonLinear Regression.
MODEL PROGRAM A=3 K=1 I=1 .
COMPUTE PRED_ = A/(1+EXP(-K * (d-I))).
NLR y
  /PRED PRED_
  /CRITERIA SSCONVERGENCE 1E-8 PCON 1E-8 .

All the derivatives will be calculated numerically.




 Iteration  Residual SS           A           K           I

     1      1064.692791  3.00000000  1.00000000  1.00000000
     1.1    1.348304567  3.99063649  1.49442721  1.88384875
     2      1.348304567  3.99063649  1.49442721  1.88384875
     2.1    .0146986193  4.00583423  1.47908955  1.69332655
     3      .0146986193  4.00583423  1.47908955  1.69332655
     3.1    .0080481338  4.00572338  1.47960600  1.66912002
     4      .0080481338  4.00572338  1.47960600  1.66912002
     4.1    .0080459976  4.00572123  1.47971278  1.66884117
     5      .0080459976  4.00572123  1.47971278  1.66884117
     5.1    .0080459976  4.00572119  1.47971372  1.66884238

Run stopped after 10 model evaluations and 5 derivative evaluations.
Iterations have been stopped because the relative reduction between successive
residual sums of squares is at most SSCON = 1.000E-08


Nonlinear Regression Summary Statistics     Dependent Variable Y

  Source                 DF  Sum of Squares  Mean Square

  Regression              3    15524.41480     5174.80493
  Residual              997   8.045998E-03   8.070208E-06
  Uncorrected Total    1000    15524.42285

  (Corrected Total)     999         .74860

  R squared = 1 - Residual SS / Corrected SS =     .98925

                                           Asymptotic 95 %
                          Asymptotic     Confidence Interval
  Parameter   Estimate    Std. Error     Lower         Upper

  A          4.005721193   .001171063  4.003423162  4.008019224
  K          1.479713721   .026491205  1.427728805  1.531698638
  I          1.668842378   .036748380  1.596729333  1.740955424

  Asymptotic Correlation Matrix of the Parameter Estimates

                   A         K         I

  A           1.0000    -.9791    -.9656
  K           -.9791    1.0000     .9981
  I           -.9656     .9981    1.0000

DP_Sydney wrote

Hi all,

 I need to fit a curve to data on mass gain, which follows a sigmoidal pattern and is best described using a logistic equation (based on similar published data, with which I wish to compare my data) of the form:
 
Y = A/(1 + e^-K(d-i))
where Y = mass
         A = asymptotic mass
         K = growth rate
         d = age (time)
         i = inflection point
        (note ^ indicates to the power)

The data I have are body mass recorded daily for several individuals (nestling birds), which will be analysed separately.

I need to output the parameters (A, K, i) rather than just produce a curve. I've searched the archives and Google but haven't found instructions for how to do this (I have instructions for running this in GENSTAT but of course do not have GENSTAT).

Any help would be great...but beware I am a drop-down menus and buttons person when it comes to software :-)

Regards,
Dean