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help on model selection - step()
2 messages · Rodrigo Gazaffi, Brian Ripley
On Mon, 11 Aug 2008, Rodrigo Gazaffi wrote:
dears R-users, I'm interested in model selection problem, and i have faced some problems that i would like to ask for help. well, this is a very small example with 4 variable (just one var. is the response - z) with 100 individuals i would like to do a stepwise search, for the "best" model, and a use BIC criteria. I know when I have a lot of variables, let's say 120, I know, it's not wise, consider the full model, so starting from "y~1", i can stop the search with the option steps. but when i have the IC with a negative value, is there any way that a can stop the search?
Not in the existing function. The absolute size of AIC (or BIC) has no meaning for a linear model fit (since this is true of the log-likelihood -- it depends on the scale of measurement). But R is Open Source so you can modify step() in any way you like, even to do nonsensical things.
for example: form this data set
the first step gives AIC=3.6, and the 2nd gives -9.03, IS THERE ANY WAY that
a could say, "stop here, the previous one is the best for me"... like here,
my model would be with no variable.
I know that example, looks like silly but a have bigger data, that this
happens in thirtieth iteration, what's why i would like some help
i used the step(), is there other function that could stop this besides
step()?
cheers,
Rodrigo Gazaffi
x1 <- c( 0.3718, 0.3718, 0.3718, 0.3718, 0.3718, 0.3718, 0.3718,
0.3718, -1.0000, 0.3718, 0.3718, 0.3718, 0.3718, 0.3718, 0.3718,
0.3718, 0.3718, 0.3718, 0.3718, 0.3718, 0.3718, 0.3718, 0.0713,
0.1774, 0.3570, 0.3718, 0.3718, 0.3718, -1.0000, 0.3718, -1.0000,
0.1774, 0.3718, 0.3718, 0.0709, 0.1774, -1.0000, -1.0000, 0.3718,
0.3718, 0.0713, 0.0709, 0.3718, 0.3718, 0.3718, 0.3718, 0.2614,
0.2614, -0.9995, -1.0000, 0.1774, 0.3718, -1.0000, -1.0000, 0.1774,
0.3718, 0.1774, 0.3718, 0.3718, -1.0000, 0.3718, 0.3718, 0.3718,
0.3718, 0.3718, -1.0000, 0.3718, 0.3718, 0.3718, 0.3718, 0.0709,
0.0710, 0.3718, 0.3718, 0.3718, 0.3718, 0.3718, 0.0709, 0.3718,
0.0709, 0.0709, 0.3718, 0.0709, 0.3570, 0.3718, 0.3718, 0.3718,
0.0709, 0.3718, 0.3718, 0.3718, -1.0000, 0.3718, 0.3718, 0.3718,
-1.0000, 0.3718, 0.3718, 0.3718, 0.3718)
x2 <- c( 0.3898, -0.9995, 0.3898, 0.3898, 0.3898, 0.1978, 0.3898,
-0.9997, -1.0000, -1.0000, 0.3898, 0.3898, 0.3898, 0.3898, -1.0000,
0.1978, -1.0000, 0.3898, 0.3898, -1.0000, 0.1978, 0.3898, 0.3898,
0.3898, 0.1978, -0.9995, 0.3792, -1.0000, -1.0000, 0.3898, 0.0837,
0.0837, 0.0837, 0.3898, 0.0837, 0.3898, 0.3898, 0.0837, 0.3898,
0.0837, 0.0837, -1.0000, -1.0000, 0.3898, 0.0841, 0.1976, -1.0000,
0.2467, 0.1978, 0.3842, 0.3898, 0.3848, 0.2766, 0.3898, 0.3898,
0.3898, -1.0000, -0.9995, 0.3898, 0.3898, 0.0837, 0.3898, -1.0000,
0.1978, 0.3898, 0.2766, 0.3898, 0.3898, 0.3898, 0.2766, 0.3898,
0.3866, 0.1978, 0.3898, -1.0000, -1.0000, 0.3898, 0.3898, 0.3898,
0.3898, 0.3898, 0.1978, 0.0841, -1.0000, 0.0837, 0.3898, 0.3898,
-1.0000, 0.3898, 0.3898, -1.0000, 0.3898, 0.3898, 0.0837, 0.3898,
0.3898, 0.1976, 0.3898, 0.3898, 0.3898)
x3 <- c( 0.9999, 0.9999, 0.9999, 1.0000, -0.9999, 0.9999, -0.9999,
0.9999, -0.9999, -1.0000, -1.0000, -0.9999, -0.9980, -0.9999, -0.9999,
-1.0000, -0.9999, -0.9999, -0.9999, 1.0000, -1.0000, 1.0000, -1.0000,
-1.0000, -1.0000, -0.9980, 1.0000, -0.9999, -1.0000, -1.0000, -0.9999,
-0.9999, 0.9999, 1.0000, -0.9999, -1.0000, 1.0000, 0.9999, 1.0000,
-0.9999, 0.9999, -1.0000, -1.0000, -0.9999, 0.8356, 0.8356, -0.3241,
0.8356, 0.8353, 0.8356, 1.0000, -1.0000, -1.0000, -1.0000, -1.0000,
-1.0000, -0.9999, 0.9999, 1.0000, -0.9980, 0.9999, 1.0000, -1.0000,
1.0000, -0.9999, 1.0000, 0.9999, -1.0000, 1.0000, -1.0000, 0.9999,
0.9999, -1.0000, -1.0000, 1.0000, -1.0000, -1.0000, 1.0000, 1.0000,
1.0000, -0.9999, 1.0000, -1.0000, 1.0000, -1.0000, 1.0000, -1.0000,
1.0000, 1.0000, 1.0000, -1.0000, -0.9999, -0.8547, -1.0000, -0.7851,
0.8356, -1.0000, -0.9999, -0.9999, 1.0000)
z <- c( -0.006548414, -1.035584950, -0.006548414, 0.180549138,
0.741841793, 1.770878329, -0.848487398, -1.035584950, -2.251719037,
0.461195465, 2.051524656, 1.116036897, -0.193645966, 0.274097913,
0.180549138, 0.274097913, 0.274097913, 0.835390569, 0.928939345,
-1.316231277, 0.087000362, 0.741841793, 1.116036897, 0.180549138,
-0.193645966, 0.274097913, 0.274097913, 1.490232001, -1.222682502,
1.303134449, 0.367646689, -0.100097190, -0.006548414, -1.035584950,
1.490232001, 0.648293017, -2.064621485, -2.625914141, 1.022488121,
-0.006548414, -1.222682502, -0.567841070, -0.942036174, 0.461195465,
1.770878329, 0.461195465, -1.503328829, -1.035584950, -0.848487398,
-0.567841070, 1.396683225, 2.051524656, -0.942036174, -0.754938622,
-1.596877605, 0.648293017, -0.287194742, -0.567841070, 0.461195465,
-0.474292294, -0.100097190, 0.287194742, 0.554744241, -0.006548414,
1.209585673, -1.409780053, 0.928939345, 0.928939345, -0.006548414,
1.396683225, -0.380743518, 0.928939345, 1.490232001, 1.770878329,
-1.129133726, -0.848487398, -0.380743518, 0.274097913, -1.409780053,
-0.100097190, 0.367646689, -0.474292294, 0.554744241, -2.251719037,
0.087000362, -0.848487398, 0.741841793, -2.064621485, -0.006548414,
0.461195465, -0.100097190, -0.006548414, 0.648293017, -0.287194742,
0.928939345, -0.193645966, -0.474292294, -0.006548414, -1.035584950,
0.461195465)
step(lm(z
~1),scope=list(lower=~1,upper=~x1+x2+x3),direction="both",k=log(length(z)))
#########
Start: AIC=3.6
z ~ 1
Df Sum of Sq RSS AIC
+ x1 1 15.671 83.329 -9.028
+ x2 1 12.390 86.610 -5.165
+ x3 1 7.403 91.597 0.433
<none> 99.000 3.600
Step: AIC=-9.03
z ~ x1
Df Sum of Sq RSS AIC
+ x2 1 13.675 69.654 -22.348
+ x3 1 7.078 76.251 -13.299
<none> 83.329 -9.028
- x1 1 15.671 99.000 3.600
Step: AIC=-22.35
z ~ x1 + x2
Df Sum of Sq RSS AIC
+ x3 1 8.930 60.723 -31.463
<none> 69.654 -22.348
- x2 1 13.675 83.329 -9.028
- x1 1 16.956 86.610 -5.165
Step: AIC=-31.46
z ~ x1 + x2 + x3
Df Sum of Sq RSS AIC
<none> 60.723 -31.463
- x3 1 8.930 69.654 -22.348
- x2 1 15.527 76.251 -13.299
- x1 1 16.669 77.392 -11.813
Call:
lm(formula = z ~ x1 + x2 + x3)
Coefficients:
(Intercept) x1 x2 x3
-0.2015 0.9000 0.7269 -0.3083
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Brian D. Ripley, ripley at stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595