Hi All,
I am trying to perform a nested ANOVA in R to test for repeatability and
subjectivity of landmark placements on three randomly chosen images. I have
landmarked each image 10 times, in 2 separate bouts (a few months apart).
This is my result from incorporating the entire data set into a nested
ANOVA:
#nested ANOVA
error <- procD.lm(f1=ALLlp.shape~ind/bout/rep, iter=999, RRPP=TRUE,
data=NULL)
error <- nested.update(error, ~ind/bout/rep)
summary(error)
Call:
procD.lm(f1 = ALLlp.shape ~ ind/bout/rep, iter = 999, RRPP = TRUE,
data = NULL)
Type I (Sequential) Sums of Squares and Cross-products
Randomized Residual Permutation Procedure Used
1000 Permutations
Df SS MS Rsq F
Z Pr(>F)
ind 2 0.71265 0.35632 0.98767 1410.6169 19.2446
0.001 **
ind:bout 1 0.00276 0.00276 0.00383 10.9405 13.4952
0.001 **
ind:bout:rep 36 0.00108 0.00003 0.00150 0.1191 0.2891 1.000
Residuals 20 0.00505 0.00025
Total 59 0.72155
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
I was concerned, however, that these results are comparing between
individuals (images) which I do not want, since all three images are of
different individuals. Really, I just want to test variance between bouts
and reps, so I performed separate nested ANOVAs for each individual. Here
is the result for one of the individuals (note: it will not let me put the *ind
*factor in since for each separate test there is only one category (1 image)
):
> error = procD.lm(f1=CochaClp.shape~bout/rep, iter=999, RRPP=TRUE,
data=NULL)
> error <- nested.update(error, ~bout/rep)
> summary(error)
Call:
procD.lm(f1 = CochaClp.shape ~ bout/rep, iter = 999, RRPP = TRUE, data
= NULL)
Type I (Sequential) Sums of Squares and Cross-products
Randomized Residual Permutation Procedure Used
1000 Permutations
*** F values, Z scores, and P values updated for nested effects
Df SS MS Rsq F
Z Pr(>F)
bout 1 0.00238108 0.00238108 0.75651 55.925 9.0398 0.001
**
bout:rep 18 0.00076637 0.00004258 0.24349 1.0534
0.001 **
Residuals 0 0.00000000
Total 19 0.00314745
I also performed an ANOVA on just the bout factor to see. I don't know if
the residual sum of squares and mean squares should match the bout:rep
numbers above, but it doesn't seem right to me.
> errorb = procD.lm(CochaClp.shape~bout, iter=999, RRPP=TRUE)
> summary(errorb)
Call:
procD.lm(f1 = CochaClp.shape ~ bout, iter = 999, RRPP = TRUE)
Type I (Sequential) Sums of Squares and Cross-products
Randomized Residual Permutation Procedure Used
1000 Permutations
Df SS MS Rsq F
Z Pr(>F)
bout 1 0.00238108 0.00238108 0.75651 55.925 9.5151 0.001 **
Residuals 18 0.00076637 0.00004258
Total 19 0.00314745
Additionally, on a simpler note, I performed an ANOVA testing the
significance of centroid size on shape. The results here do not make sense
to me either - it states a significant variance but the variance of the
centroid sizes is so small.
> csize <- centroid.size(CochaClp.shape)
> csize
[1] 1.000062 1.000067 1.000064 1.000068 1.000059 1.000075 1.000071
1.000074 1.000079 1.000066
[11] 1.000070 1.000122 1.000065 1.000093 1.000071 1.000098 1.000117
1.000097 1.000072 1.000083
> var(csize)
[1] 3.170611e-10
Call:
procD.lm(f1 = CochaClp.shape ~ log(csize), iter = 999, seed = NULL,
RRPP = TRUE, int.first = FALSE, data = NULL)
Type I (Sequential) Sums of Squares and Cross-products
Randomized Residual Permutation Procedure Used
1000 Permutations
Df SS MS Rsq F Z Pr(>F)
log(csize) 1 0.00098216 0.00098216 0.31205 8.1646 4.1957 0.002 **
Residuals 18 0.00216529 0.00012029
Total 19 0.00314745
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
I believe, as a whole, I am either doing something wrong in my coding with
procD.lm, or interpreting it incorrectly. Any input or suggestions would be
extremely helpful. Thank you!
Brenna
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