[R] Noobie ANOVA intercept question
AllenL
allen.larocque at gmail.com
Wed Apr 1 19:44:33 CEST 2009
Dear R list,
I've been attempting to interpret the results from a three-way ANOVA. I
think I understand contrasts and the R defaults for these (treatment
contrasts). My question is: what is the intercept in this test? As far as I
can tell, its NOT the expected value of a point that belongs to the first
level of all three explanatory factors (because there is only one point that
satisfies these requirements and their values differ). Its not the grand
mean, or any of the treatment means. What is this thing?
(Note: this dataset is from an example I'm working through in Grafen & Hails
2002 text)
Q2: Just noticed that in pasting I lose mono-spaced formatting. Is it
possible to post to the list such that format is maintained?
Thanks in advance!
Relevant output:
> anova(mod1)
Analysis of Variance Table
Response: SQBLOOMS
Df Sum Sq Mean Sq F value Pr(>F)
BED 2 4.1323 2.0661 9.4570 0.0007277 ***
WATER 2 3.7153 1.8577 8.5029 0.0013016 **
SHADE 3 1.6465 0.5488 2.5120 0.0789451 .
Residuals 28 6.1173 0.2185
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> summary(mod1)
Call:
lm(formula = SQBLOOMS ~ BED + WATER + SHADE)
Residuals:
Min 1Q Median 3Q Max
-1.23992 -0.18979 -0.01840 0.17471 0.74686
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.7765 0.2203 17.139 2.23e-16 ***
BED2 0.3185 0.1908 1.669 0.106242
BED3 -0.5044 0.1908 -2.643 0.013293 *
WATER2 0.7842 0.1908 4.109 0.000313 ***
WATER3 0.4489 0.1908 2.353 0.025905 *
SHADE2 0.1969 0.2203 0.894 0.379172
SHADE3 -0.2157 0.2203 -0.979 0.336068
SHADE4 -0.3673 0.2203 -1.667 0.106641
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.4674 on 28 degrees of freedom
(51 observations deleted due to missingness)
Multiple R-squared: 0.6081, Adjusted R-squared: 0.5102
F-statistic: 6.208 on 7 and 28 DF, p-value: 0.0001911
> model.frame(mod1)
SQBLOOMS BED WATER SHADE
1 4.359 1 1 1
2 3.317 1 1 2
3 3.606 1 1 3
4 4.123 1 1 4
5 4.472 1 2 1
6 4.583 1 2 2
7 4.359 1 2 3
8 4.690 1 2 4
9 4.123 1 3 1
10 4.123 1 3 2
11 3.464 1 3 3
12 3.873 1 3 4
13 3.606 2 1 1
14 4.000 2 1 2
15 3.464 2 1 3
16 3.873 2 1 4
17 4.690 2 2 1
18 5.000 2 2 2
19 5.385 2 2 3
20 4.583 2 2 4
21 4.690 2 3 1
22 4.690 2 3 2
23 4.690 2 3 3
24 4.243 2 3 4
25 3.317 3 1 1
26 3.606 3 1 2
27 3.317 3 1 3
28 2.828 3 1 4
29 3.873 3 2 1
30 5.000 3 2 2
31 3.742 3 2 3
32 2.449 3 2 4
33 4.000 3 3 1
34 4.583 3 3 2
35 3.162 3 3 3
36 3.162 3 3 4
> model.tables(mod1,"means",se=TRUE)
Tables of means
Grand mean
4.029028
BED
BED
1 2 3
4.091 4.409 3.587
WATER
WATER
1 2 3
3.618 4.402 4.067
SHADE
SHADE
1 2 3 4
4.126 4.322 3.910 3.758
Standard errors for differences of means
BED WATER SHADE
0.1908 0.1908 0.2203
replic. 12 12 9
Design matrix:
> model.matrix(mod1)
(Intercept) BED2 BED3 WATER2 WATER3 SHADE2 SHADE3 SHADE4
1 1 0 0 0 0 0 0 0
2 1 0 0 0 0 1 0 0
3 1 0 0 0 0 0 1 0
4 1 0 0 0 0 0 0 1
5 1 0 0 1 0 0 0 0
6 1 0 0 1 0 1 0 0
7 1 0 0 1 0 0 1 0
8 1 0 0 1 0 0 0 1
9 1 0 0 0 1 0 0 0
10 1 0 0 0 1 1 0 0
11 1 0 0 0 1 0 1 0
12 1 0 0 0 1 0 0 1
13 1 1 0 0 0 0 0 0
14 1 1 0 0 0 1 0 0
15 1 1 0 0 0 0 1 0
16 1 1 0 0 0 0 0 1
17 1 1 0 1 0 0 0 0
18 1 1 0 1 0 1 0 0
19 1 1 0 1 0 0 1 0
20 1 1 0 1 0 0 0 1
21 1 1 0 0 1 0 0 0
22 1 1 0 0 1 1 0 0
23 1 1 0 0 1 0 1 0
24 1 1 0 0 1 0 0 1
25 1 0 1 0 0 0 0 0
26 1 0 1 0 0 1 0 0
27 1 0 1 0 0 0 1 0
28 1 0 1 0 0 0 0 1
29 1 0 1 1 0 0 0 0
30 1 0 1 1 0 1 0 0
31 1 0 1 1 0 0 1 0
32 1 0 1 1 0 0 0 1
33 1 0 1 0 1 0 0 0
34 1 0 1 0 1 1 0 0
35 1 0 1 0 1 0 1 0
36 1 0 1 0 1 0 0 1
--
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