[R] genralized linear regression - function glm - number of
David Winsemius
dwinsemius at comcast.net
Thu Nov 18 17:37:10 CET 2010
On Nov 18, 2010, at 11:00 AM, Christine SINOQUET wrote:
> Hello,
>
> Performing a linear regression through the function glm ("yi ~ X$V1
> + X$V2 + X$V3 + X$V4 + X$V5 + X$V6 + X$V7 + X$V8 + X$V9 + X$V10"), I
> then edit the information about the coefficients:
>
> print(coefficients(summary(fit)))
>
> I note that the number of coefficients (7) is lower than the number
> of predictors (10).
> In this case, I work on simulated data for which I forced yi to be a
> linear function of the 10 predictors.
>
What code was used to make the simulation?
> intercept: 0.0180752965003802
> predictor 1: -0.0111046268531608
> predictor 2: -0.0185366138753851
> predictor 3: 0.107341157096227
> predictor 4: 0.00162924662836275
> predictor 5: 0.00162924629403743
> predictor 6: -0.0171999854554059
> predictor 7: -0.0171999856835917
> predictor 8: -0.057207682945982
> predictor 9: -0.0171999856239631
> predictor 10: 0.134643228957395
>
>
> "yi ~ X$V1 + X$V2 + X$V3 + X$V4 + X$V5 + X$V6 + X$V7 + X$V8 + X$V9 +
> X$V10"
> Estimate Std. Error t value Pr(>|t|)
> (Intercept) 0.018062134 5.624517e-17 3.211322e+14 0
> X$V1 -0.011104627 3.084989e-17 -3.599567e+14 0
> X$V2 -0.018536614 3.241635e-17 -5.718291e+14 0
> X$V3 0.107341157 4.884358e-17 2.197651e+15 0
> X$V4 0.003258493 3.286878e-17 9.913643e+13 0
> X$V6 -0.051599957 4.203840e-17 -1.227448e+15 0
> X$V8 -0.057207683 3.049835e-17 -1.875763e+15 0
> X$V10 0.134643229 3.849911e-17 3.497308e+15 0
>
>
> I am sure to have regressed the right number of variables, since I
> check that the formula is correct:
> "yi ~ X$V1 + X$V2 + X$V3 + X$V4 + X$V5 + X$V6 + X$V7 + X$V8 + X$V9 +
> X$V10"
>
> Could somebody explain to me
> 1) why there are mismatches between the "true" coefficients for
> predictors 4 and 6
> and
Your std errors are incredibly small (effectively zero from a
numerical perspective) suggesting you have created a dataset with
extremely small amounts of noise. The coefficients are different (than
expected) because of the answer to the next question.
> 2) why there is no information edited for predictors 5, 7 and 9 ?
You most likely had each of those set up as a linear combination of
the retained predictors. Collinear variables are dropped and usually
there is a warning, bust since you have not given a console session I
cannot be sure.
--
David Winsemius, MD
West Hartford, CT
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