Biology Reference
In-Depth Information
molar alveolus could not be subdivided because it contains too few landmarks, and the
condyloid was divided into three parts, one of which is the condyle). Three of the models
fit equally well based on their nearly equal
Δ
AIC; the only one that we could at least ten-
tatively reject from further consideration is the
Satb2
model (
Table 12.6
). We appear to get
more resolution using the correlation between the observed and expected correlation
matrix; based on this statistic, the Condensation and
Satb2
Gsc models fit best, followed
by the Front/Back and then by the
Satb2
model (
Table 12.7
). But it is not clear if this
greater resolution is an artifact of the test statistic.
Covariance model selection was used to find the model that least deviates from the
data; i.e. the criterion used to select the best model was minimum deviance rather than a
minimum AIC. The search was conducted in a stepwise fashion by adding or deleting an
edge one by one, in random order, until no further changes improved the fit of the model.
This search produced the model shown in
Figure 12.20
, which resembles none of the
a
priori
models. It also does not resemble the best-fitting model produced by mixing the
modules contained in the
a priori
models. What the present result suggests is that parts of
the hypothesized modules are integrated with parts of other modules. For example, the
distal incisor alveolus (but not the proximal incisor alveolus) is integrated with the distal
ramus and the distal coronoid process. The result does not support the hypothesis that
mandibular variation is structurally modular.
1
TABLE 12.6
Results of the Models Fitted to the Observed Correlation Matrix, Obtained by the Matrix
Correlations Between Distance Matrices
2
Model
χ
df
p
Δ
AIC
Front/Back
22.58
32
0.891
41.43
2
Satb2
37.57
37
0.443
2
36.42
Satb2
1
Gsc
62.69
51
0.126
2
39.31
Condensation
82.11
61
0.037
2
39.89
2)
. The relative fit of the
Models are evaluated by the model deviance, which is approximately distributed as a chi-square (
χ
models is assessed by the
Δ
AIC, which is the difference between the AIC of each model and the AIC of the fully saturated
model.
TABLE 12.7
Models Evaluated by the Matrix Correlation, R
M
, Between the Observed and Expected
Correlation Matrices; Statistical Significance of the Matrix Correlation Tested by the Mantel Test
Model
R
M
p
Front/Back
0.291
0.031
Satb2
0.135
0.169
Satb2
/Gsc
0.383
0.001
Condensation
0.392
0.003
