why not use vif command (from car library) to caculate the VIF to help you
assess is a collinearity is infulential?
I have never seen any book dealling with this topics by perturbation analysis.
the VIF,tolerance,principal component analysis are the tools dealing with
collinearity.you can get the information from john fox's book.
generally,caculating the correlation directly is not essential.
one more thing,if your purpose of modeling is prediction but not
interpretation,collinearity does not matter much.
On Mon, 11 Apr 2005 12:22:55 +0200 (CEST)
Manuel Gutierrez <[EMAIL PROTECTED]> wrote:
>
> I have a linear model y~x1+x2 of some data where the
> coefficient for
> x1 is higher than I would have expected from theory
> (0.7 vs 0.88)
> I wondered whether this would be an artifact due to x1
> and x2 being correlated despite that the variance
> inflation factor is not too high (1.065):
> I used perturbation analysis to evaluate collinearity
> library(perturb)
> P<-perturb(A,pvars=c("x1","x2"),prange=c(1,1))
> > summary(P)
> Perturb variables:
> x1 normal(0,1)
> x2 normal(0,1)
>
> Impact of perturbations on coefficients:
> mean s.d. min max
> (Intercept) -26.067 0.270 -27.235 -25.481
> x1 0.726 0.025 0.672 0.882
> x2 0.060 0.011 0.037 0.082
>
> I get a mean for x1 of 0.726 which is closer to what
> is expected.
> I am not an statistical expert so I'd like to know if
> my evaluation of the effects of collinearity is
> correct and in that case any solutions to obtain a
> reliable linear model.
> Thanks,
> Manuel
>
> Some more detailed information:
>
> > A<-lm(y~x1+x2)
> > summary(A)
>
> Call:
> lm(formula = y ~ x1 + x2)
>
> Residuals:
> Min 1Q Median 3Q Max
> -4.221946 -0.484055 -0.004762 0.397508 2.542769
>
> Coefficients:
> Estimate Std. Error t value Pr(>|t|)
> (Intercept) -27.23472 0.27996 -97.282 < 2e-16 ***
> x1 0.88202 0.02475 35.639 < 2e-16 ***
> x2 0.08180 0.01239 6.604 2.53e-10 ***
> ---
> Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.'
> 0.1 ` ' 1
>
> Residual standard error: 0.823 on 241 degrees of
> freedom
> Multiple R-Squared: 0.8411, Adjusted R-squared: 0.8398
>
> F-statistic: 637.8 on 2 and 241 DF, p-value: <
> 2.2e-16
>
> > cor.test(x1,x2)
>
> Pearson's product-moment correlation
>
> data: x1 and x2
> t = -3.9924, df = 242, p-value = 8.678e-05
> alternative hypothesis: true correlation is not equal
> to 0
> 95 percent confidence interval:
> -0.3628424 -0.1269618
> sample estimates:
> cor
> -0.248584
>
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