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Four parameters logistic regression - There and back again

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Four parameters logistic regression - There and back again


Giuseppe Cardillo


11 Sep 2012 (Updated )

Fit data points with a four points logistic regression or interpolate data.

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One big holes into MatLab cftool function is the absence of Logistic Functions. In particular, The Four Parameters Logistic Regression or 4PL nonlinear regression model is commonly used for curve-fitting analysis in bioassays or immunoassays such as ELISA, RIA, IRMA or dose-response curves. It is characterized by it’s classic “S” or sigmoidal shape that fits the bottom and top plateaus of the curve, the EC50, and the slope factor (Hill's slope). This curve is symmetrical around its inflection point.
The 4PL equation is:
F(x) = D+(A-D)/(1+(x/C)^B)
A = Minimum asymptote. In a bioassay where you have a standard curve, this can be thought of as the response value at 0 standard concentration.
B = Hill's slope. The Hill's slope refers to the steepness of the curve. It could either be positive or negative.
C = Inflection point. The inflection point is defined as the point on the
curve where the curvature changes direction or signs. C is the concentration of analyte where y=(D-A)/2.
D = Maximum asymptote. In an bioassay where you have a standard curve, this can be thought of as the response value for infinite standard concentration.
In this submission there are 2 functions:
L4P - to find the 4 parameters and to fit your data (as calibrators...);
L4Pinv - to interpolate data of unknown samples onto calibrators curve.


Required Products Curve Fitting Toolbox
MATLAB release MATLAB 7.11 (R2010b)
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Comments and Ratings (8)
30 Sep 2014 Giuseppe Cardillo

Giuseppe Cardillo

I don't know. I should see your data points

Comment only
29 Sep 2014 Ufop


why i get this error? I have two data measured, X and Y. I just put:

load x.txt
load y.txt

[cf G]=L4P(x,y) , and appears this error:

Error using fit>iFit (line 415)
NaN computed by model function, fitting cannot continue.
Try using or tightening upper and lower bounds on coefficients.

Error in fit (line 109)
[fitobj, goodness, output, convmsg] = iFit( xdatain, ydatain, fittypeobj, ...

Error in L4P (line 194)
[cf G] = fit(x(ok_),y(ok_),ft_,fo_);


Comment only
05 Mar 2014 Andrew


23 Apr 2013 Hugo Gasca-Aragon

Hugo Gasca-Aragon

C is the mean response point where y=(D+A)/2. The inflection point is where F''(x)=0, this is C*((B-1)/(B+1))^(1/B).

02 Apr 2013 Giuseppe Cardillo

Giuseppe Cardillo

sorry, I did an error when I created the zip file. I'm uploading the correct version

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02 Apr 2013 Daniel


Dear Giuseppe,
I cannot find your m file L4Pinv, is it uploaded somewhere else?
Thank you!

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02 Apr 2013 Daniel


29 Jan 2013 Jessica Inskip

Jessica Inskip

My apologies. I had not read through the notes thoroughly; I have found the fitted curve plot.

Comment only
03 Apr 2013

I uploaded L5Pinv instead of L4Pinv

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