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
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