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Data mining with Small samples...Regression with Small Samples?

triunk

Community Trekker

Joined:

Nov 20, 2012

Dear all JMP experts, I know that this kind of discussion might be both a silly...very silly and a hot issue simultaneously...but I thought it would be nice to raise it : Which types of linear AND non-linear regression does JMP offer when you have a small sample size (e.g. 50-70 records) and you want to predict a continuous outcome from 5-7 predictors (both categorical and continuous) Can k-fold cross-validated stepwise linear regression OR Partial Least Regression is a remedy to this problem? Are boosted trees OR Neural networks just insane even to think about them? Your responses are GREATLY WELCOMED and VERY MUCH APPRECIATED. Respectfully, Chris

9 REPLIES
paigemiller

Community Trekker

Joined:

Apr 12, 2012

Whether these procedures will work or not at those sample sizes depends on signal-to-noise. If you have lots of signal and low noise, you probably won't even need 50 records. Other way around, low signal and high noise, and you're probably wasting your time.

triunk

Community Trekker

Joined:

Nov 20, 2012

Hi PaigeMiller

Would you please be so kind and elaborate a little bit more about signal and noise? (just one sentence)

Please accept my apologies but for me these two terms are pretty allegorical to my silly mind.

THANK YOU!

Chris

paigemiller

Community Trekker

Joined:

Apr 12, 2012

Would you please be so kind and elaborate a little bit more about signal and noise? (justone sentence)


Please accept my apologies but for me these two terms are pretty allegorical to my silly mind.


Most statistical modeling attempts to determine if there is a signal (a real relationship) that is larger than the variability of the errors (noise). Each modeling technique that I am aware of gives a measure of this signal-to-noise; for example, in standard regression is would be the overall F-test.

There's no reason you can't have a very large signal and very low noise in 50 data points. It depends on the data.

triunk

Community Trekker

Joined:

Nov 20, 2012

That's much clearer. Thank you VERY VERY much

Kind Regards

C

pgstats

Community Trekker

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Aug 30, 2011

The first thing I do with such skimpy datasets is a regression tree analysis. It is a quick and intuitive way to explore the relationship between your dependent and predictor variables. The first three or four nodes are generally meaningful. - PG

triunk

Community Trekker

Joined:

Nov 20, 2012

First of all thank you very much for your prompt reply. I really appreciate it

PGStats do you mean Classification and Regression Tree analysis? CART?

Alternatively do you think that multivariate adaptive regression splines could work also for small sample size?

Many thanks again!

triunk

Community Trekker

Joined:

Nov 20, 2012

P.S. I know that MARS is not offered in JMP but it is offered from SAS...so scipt might help.

pgstats

Community Trekker

Joined:

Aug 30, 2011

Yes I meant CART-type analysis, called Partition in JMP. When dependent variable is continuous, the result is a regression tree, otherwise, it's a classification (or decision) tree. I think regression splines eat up too many degrees of freedom to be applicable to your size of dataset. - PG

triunk

Community Trekker

Joined:

Nov 20, 2012

Thanks PG, this helps. I will check it out.