Dear List Members,

I have encountered two problems when using the step function to
select models. To better illustrate the problems, an R image
(step.add1.test.RData)
which includes the objects needed to run the code (step.add1.test.R) can be
found at
www.biostat.wisc.edu/~pwang/r-help/<http://www.biostat.wisc.edu/%7Epwang/r-help/>

lm.data.frame have factor variables with 3 levels.

The following run shows the first problem. AICs (* and **) are different.
I noticed that the Df for rs13482096:rs13483699 is 4, while I think
Df should be 6, 2 from rs13483699 and 4 from interactions. When I ran
add1 directly, I got Df=6 and AIC 848.75.

> step2.bic.out <- step(step.bic.out, scope=list(lower=scope.lower2,
upper=scope.upper2),
+                       direction="both", k=log(length(step.bic.out$y)),
trace=1)
Start:  AIC=841.18
pheno.dat ~ rs13479085 + rs13480057 + rs13482096 + rs8254221

                       Df Deviance    AIC
+ rs13482096:rs13483699  4   216.63 840.63 (*)
<none>                       233.82 841.18
- rs8254221              2   244.08 842.90
- rs13482096             2   245.20 844.31
......

Step:  AIC=848.75 (**)
pheno.dat ~ rs13479085 + rs13480057 + rs13482096 + rs8254221 +
   rs13482096:rs13483699

> add1(step.bic.out, scope="rs13482096:rs13483699",
k=log(length(step.bic.out$y)))
Single term additions

Model:
pheno.dat ~ rs13479085 + rs13480057 + rs13482096 + rs8254221
                     Df Deviance    AIC
<none>                     233.82 841.18
rs13482096:rs13483699  6   214.28 848.75 (**)

When I used add1 to handle terms to be added together and separately,
I got different results. The example is shown below. This might explain
the discrepancy shown above.
> add1(step.bic.out, scope=int.terms[11:12], k=log(length(step.bic.out$y)))
Single term additions

Model:
pheno.dat ~ rs13479085 + rs13480057 + rs13482096 + rs8254221
                     Df Deviance    AIC
<none>                     233.82 841.18
rs13479085:rs13475933  6   224.95 863.66
rs13480057:rs13475933  4   226.72 854.62 (***)
> add1(step.bic.out, scope=int.terms[11], k=log(length(step.bic.out$y)))
Single term additions

Model:
pheno.dat ~ rs13479085 + rs13480057 + rs13482096 + rs8254221
                     Df Deviance    AIC
<none>                     233.82 841.18
rs13479085:rs13475933  6   224.95 863.66
> add1(step.bic.out, scope=int.terms[12], k=log(length(step.bic.out$y)))
Single term additions

Model:
pheno.dat ~ rs13479085 + rs13480057 + rs13482096 + rs8254221
                     Df Deviance    AIC
<none>                     233.82 841.18
rs13480057:rs13475933  6   215.95 851.12 (***)

Another problem is that the final model seems to be the first
model that satisfies (bAIC >= AIC + 1e-07) if steps haven't used up,
rather than the one before that. Please see below.

> formula(step2.bic.out)
pheno.dat ~ rs13479085 + rs13480057 + rs13482096 + rs8254221 +
   rs13482096:rs13483699

> step2.bic.out$anova
 Step Df Deviance Resid. Df Resid. Dev      AIC
1      NA       NA       298   233.8226 841.1784

Any insights would be greatly appreciated. Thanks much !

Ping Wang

-- 
Ping Wang
Graduate Student
Department of Statistics
University of Wisconsin-Madison
Medical Sciences Center (1245)
1300 University Avenue
Madison, Wisconsin 53706

http://www.biostat.wisc.edu/~pwang/

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