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Super low P-value for nonlinear coefficients

blaze8
Posts: 164
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3/26/2014 8:23:43 PM
Posted: 2 years ago
Ok. So I've got a non-linear model, fitted using MATLAB, with 3 coefficients. The p-value for the coefficients is extremely low. I'm talking too low to believe for the sample size. Here's one of the p-values:

pValue
b1 6.023e-30

Degrees of freedom are 29. My question is, anyone ever seen a p-value this low before? And does the Durbin-Watson statistic apply to non-linear models? I need to test for Serial Correlation and Multi-collinearity. Lastly, if it turns out there isn't any serial correlation or multi-collinearity, how reliable would such a low p-value 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
Enji
Posts: 1,022
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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, p-values (and most other statistics) are less reliable but they can still be useful. I'm not familiar with the Durbin-Watson statistic.
blaze8
Posts: 164
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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:
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, p-values (and most other statistics) are less reliable but they can still be useful. I'm not familiar with the Durbin-Watson statistic.

Degrees of freedom are N-K-1. 2 Variables (x and y), 32 is the sample size, so 32-2-1 = 29. To be honest, it's a really complicated non-linear 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.

Durbin-Watson is used to detect Serial Correlation (or Autocorrelation, depending on who you talk to). Since Serial Correlation can cause T-statistics to be larger than they actually are, and thus P-values 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 non-linear 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
Enji
Posts: 1,022
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3/27/2014 10:03:44 PM
Posted: 2 years ago
If you use a non-linear least squares regression with many terms and few data points, you'll end up with a low p-value 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.
Enji
Posts: 1,022
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3/27/2014 10:10:59 PM
Posted: 2 years ago
Also, the standard Durbin-Watson test does assume a linear distribution, but there are approximations for autocorrelation for non-linear models. I don't know if you have access to Jstor, but here's a paper on the Durbin-Watson test in non-linear models. [http://www.jstor.org...]

If you don't, hopefully you can find it somewhere free.