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prj
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 Posted - 11/29/2004 : 12:45:54 PM
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Origin Version: 5.0
Operating System: XP
Can someone help me with a simple chi-square question; I appear unable to figure it out on my own! I have fitted a sigmoidal curve (Boltzman) to some growth data, and amongst the parameter estimates it provides a chi-square value. What does this mean, and how does this relate a probability or goodness of fit of the model? I am confused because the iterative process minimizes the value (so presumably a lower value is good), while it appears that the 'typical' chi-square table in books wants increasing values for higher significance? Help! Thanks, PJ |
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ML
USA
63 Posts |
Posted - 11/30/2004 : 1:13:57 PM
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Generally, the smaller chi-sq, the better.
Under the following circumstances:
1. The measurement errors are used during the fit;
2. They are normally distributed;
one can use the value of chisq to compute the goodness-of-fit after the fitting has been completed. The relevant statistics is:
Q = 1. - INCGAMMA(0.5 * nonreducedchisq, 0.5 * dof)
Here nonreducedchisq = nlsf.ssr is the sum of squares of deviations of the fitted curve from the data, and dof = nlsf.dof is the number of degrees of freedom. Both nlsf.ssr and nlsf.dof are accessible from LabTalk at the end of the fit. INCGAMMA is incomplete gamma function, which is accessible from LabTalk as well.
Generally, the values of Q >~ 0.001 or so are considered to present a good fit. But even for the smaller values the fit could still be good, in which case the above assumptions might not be satisfied.
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chi-square values