[R] polymars

From: <tastard_at_cict.fr>
Date: Mon 14 Mar 2005 - 18:29:28 EST


Can you help me interpret the output I get with “polymars”? I'd like to find a regression model to predict 2 dependent variables (then called Y1 and Y2) with 2 independent variables (then called X1 and X2).

Here is the output:
polymars(responses = data[, 13:14], predictors = data[, 2:3])

Model fitting

   0/1 		size     	RSS 1     	RSS 2       	 GCV
1    1    	1	0.2486744 	0.6520499 	0.01756785
2    1    	2 	0.2316042 	0.3820036 	0.01391882
3    1    	3 	0.2312835 	0.3819480 	0.01637875
4    1    	4 	0.2299605 	0.3766946 	0.01935784
5    1   		5 	0.2243804 	0.3766148 	0.02331277
6    1    	6	0.2243499 	0.3764709 	0.02893749
7    0    	5	0.2243804 	0.3766148 	0.02331277
8    0    	4 	0.2299605 	0.3766946 	0.01935784
9    0    	3	0.2312835 	0.3819480 	0.01637875
10   0    	2 	0.2316042 	0.3820036 	0.01391882
11   0   	1	0.2486744 	0.6520499 	0.01756785


Model produced

  pred1 knot1 pred2 knot2     Coefs 1     Coefs 2       SE 1       SE 2
1     0    NA     0    NA  0.40139070  0.14049628 0.02195431 0.02819553
2     2    NA     0    NA -0.02146696 -0.08538267 0.01047337 0.01345076

RESPONSES : 2 Rsquared : 0.069 0.414

If I have well understood, polymars tries to build several models for each dependent variable (with one function if it is homogeneous or more ones if it is not homogeneous) and selects the best one. I suppose the model is the best one when the GCV is smallest. So here I thought I should have had a model with 2 functions for each dependent variable (size 2).

Why do I get only one result (1 function for each dependent variable)? How can I get a model with different functions over different ranges of the independent variables? Do you think it would be a better model?

Are these the good equations?
Y1 = 0,40139 – 0,02147 X2
Y2 = 0,1405 – 0,08538 X2

Does polymars take the interaction between Y1 and Y2 into account ?

Thanks



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