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Appendix
A
Notation
q = the number of parameters
= the vector of parameters (of order q)
G = the number of groups
= the number of observations in group g
= the total number of observations in all groups combined
= the number of observed variables in group g
= the number of sample moments in group g. When means and intercepts are
explicit model parameters, the relevant sample moments are means,
variances, and covariances, so that . Otherwise,
only sample variances and covariances are counted so that
.
= the number of sample moments in all groups combined
= the number of degrees of freedom for testing the model
= the r-th observation on the i-th variable in group g
= the r-th observation in group g
= the sample covariance matrix for group g
γ
N
g()
NN
g()
g 1=
G
∑
=
p
g()
p
*
g
()
p
*
g
()
p
g()
p
g()
3+()2⁄=
p
*
g
()
p
g()
p
g()
1+()2⁄=
pp
*
g
()
g 1=
G
∑
=
dpq–=
x
ir
g
()
x
r
g
()
S
g()