[R] [FORGED] standard error for regression coefficients corresponding to factor levels
Rolf Turner
r.turner at auckland.ac.nz
Fri Mar 17 00:41:31 CET 2017
You have been posting to the R-help list long enough so that you should
have learned by now *not* to post in html. Your code is mangled so as
to be unreadable.
A few comments:
(1) Your data frame "data1" seems to have a mysterious (and irrelevant?)
column named "data1" as well.
(2) The covariance matrix of your coefficient estimates is indeed (as
you hint) a constant multiple of (X^T X)^{-1}. So do:
X <- model.matrix(~response*week,data=data1)
S <- solve(t(X)%*%X)
print(S)
and you will see the same pattern of constancy that your results exhibit.
(3) You could get the results you want much more easily, without all the
fooling around buried in your (illegible) code, by doing:
mod <- lm(response ~ (region - 1)/week,data=data1)
summary(mod)
cheers,
Rolf Turner
--
Technical Editor ANZJS
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276
On 17/03/17 07:26, li li wrote:
> Hi all,
> I have the following data called "data1". After fitting the ancova model
> with different slopes and intercepts for each region, I calculated the
> regression coefficients and the corresponding standard error. The standard
> error (for intercept or for slope) are all the same for different regions.
> Is there something wrong?
> I know the SE is related to (X^T X)^-1, where X is design matrix. So does
> this happen whenever each factor level has the same set of values for
> "week"?
> Thanks.
> Hanna
>
>
>
>> mod <- lm(response ~ region*week, data1)> tmp <- coef(summary(mod))> res <- matrix(NA, 5,4)> res[1,1:2] <- tmp[1,1:2]> res[2:5,1] <- tmp[1,1]+tmp[2:5,1]> res[2:5,2] <- sqrt(tmp[2:5,2]^2-tmp[1,2]^2)> res[1,3:4] <- tmp[6,1:2]> res[2:5,3] <- tmp[6,1]+tmp[7:10,1]> res[2:5,4] <- sqrt(tmp[7:10,2]^2-tmp[6,2]^2)
>
>> colnames(res) <- c("intercept", "intercept SE", "slope", "slope SE")> rownames(res) <- letters[1:5]> res intercept intercept SE slope slope SE
> a 0.18404464 0.08976301 -0.018629310 0.01385073
> b 0.17605666 0.08976301 -0.022393789 0.01385073
> c 0.16754130 0.08976301 -0.022367770 0.01385073
> d 0.12554452 0.08976301 -0.017464385 0.01385073
> e 0.06153256 0.08976301 0.007714685 0.01385073
>
>
>
>
>
>
>
>> data1 week region response
> 5 3 c 0.057325067
> 6 6 c 0.066723632
> 7 9 c -0.025317808
> 12 3 d 0.024692613
> 13 6 d 0.021761492
> 14 9 d -0.099820335
> 19 3 c 0.119559235
> 20 6 c -0.054456186
> 21 9 c 0.078811180
> 26 3 d 0.091667189
> 27 6 d -0.053400777
> 28 9 d 0.090754363
> 33 3 c 0.163818085
> 34 6 c 0.008959741
> 35 9 c -0.115410852
> 40 3 d 0.193920693
> 41 6 d -0.087738914
> 42 9 d 0.004987542
> 47 3 a 0.121332285
> 48 6 a -0.020202707
> 49 9 a 0.037295785
> 54 3 b 0.214304603
> 55 6 b -0.052346480
> 56 9 b 0.082501222
> 61 3 a 0.053540767
> 62 6 a -0.019182819
> 63 9 a -0.057629113
> 68 3 b 0.068592791
> 69 6 b -0.123298216
> 70 9 b -0.230671818
> 75 3 a 0.330741562
> 76 6 a 0.013902905
> 77 9 a 0.190620360
> 82 3 b 0.151002874
> 83 6 b 0.086177696
> 84 9 b 0.178982656
> 89 3 e 0.062974799
> 90 6 e 0.062035391
> 91 9 e 0.206200831
> 96 3 e 0.123102197
> 97 6 e 0.040181790
> 98 9 e 0.121332285
> 103 3 e 0.147557564
> 104 6 e 0.062035391
> 105 9 e 0.144965770
>
> [[alternative HTML version deleted]]
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