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Super low Pvalue for nonlinear coefficients
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3/26/2014 8:23:43 PM Posted: 2 years ago Ok. So I've got a nonlinear model, fitted using MATLAB, with 3 coefficients. The pvalue for the coefficients is extremely low. I'm talking too low to believe for the sample size. Here's one of the pvalues:
pValue b1 6.023e30 Degrees of freedom are 29. My question is, anyone ever seen a pvalue this low before? And does the DurbinWatson statistic apply to nonlinear models? I need to test for Serial Correlation and Multicollinearity. Lastly, if it turns out there isn't any serial correlation or multicollinearity, how reliable would such a low pvalue be? "For I am a sinner in the hands of an angry God. Bloody Mary full of vodka, blessed are you among cocktails. Pray for me now and at the hour of my death, which I hope is soon. Amen."Sterling Archer 
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3/26/2014 11:50:59 PM Posted: 2 years ago I don't know what you're doing, but why do you have so many degrees of freedom? If you have 3 categories of variables (if that's what your 3 coefficients are referring to), then you should have 2 degrees of freedom. If you have 29 degrees of freedom, then this means that there's 30 possible categories, which is larger than what is often considered a small sample size. If, for example, you were counting the number of red cars, blue cars, and other coloured cars, then you have 3 different categories and 2 degrees of freedom (basically, there are 2 variables which you can change which define the third).
With small sample sizes, pvalues (and most other statistics) are less reliable but they can still be useful. I'm not familiar with the DurbinWatson statistic. 
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3/27/2014 9:03:56 AM Posted: 2 years ago At 3/26/2014 11:50:59 PM, Enji wrote: Degrees of freedom are NK1. 2 Variables (x and y), 32 is the sample size, so 3221 = 29. To be honest, it's a really complicated nonlinear model. I'm still trying to diagnose what each coefficient might mean. The model is similar to this: y = ((x^2)/(a+x^3))+((b+x^2)/(c +x^3)). I won't post it here because it's taken me many long hours of crunching numbers and programming to reach this point in my analysis, and I am presenting it next week. The equation was given to me by Matlab itself, I used the raw data and had Matlab use Least Squares to fit a line to the data by writing different types of equations as functions and having Matlab try and fit using the function. DurbinWatson is used to detect Serial Correlation (or Autocorrelation, depending on who you talk to). Since Serial Correlation can cause Tstatistics to be larger than they actually are, and thus Pvalues to be smaller than they actually are, this is a crucial test to see if my equation is reliable. But I've only used it for linear models. If it can't be used for nonlinear models, then I'm sol lol. "For I am a sinner in the hands of an angry God. Bloody Mary full of vodka, blessed are you among cocktails. Pray for me now and at the hour of my death, which I hope is soon. Amen."Sterling Archer 
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3/27/2014 10:03:44 PM Posted: 2 years ago If you use a nonlinear least squares regression with many terms and few data points, you'll end up with a low pvalue because your curve will be fitted to the points. You might want to use simpler models and consider the variance each model explains and select the best model from there; this has the added benefit of being easier to interpret what the different coefficients mean and how the variables relate to each other. But then this is probably a better question for a maths website (like math stack exchange) rather than a ddo.

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3/27/2014 10:10:59 PM Posted: 2 years ago Also, the standard DurbinWatson test does assume a linear distribution, but there are approximations for autocorrelation for nonlinear models. I don't know if you have access to Jstor, but here's a paper on the DurbinWatson test in nonlinear models. [http://www.jstor.org...]
If you don't, hopefully you can find it somewhere free. 