Table 3.

Model parameter counts (K >1). The 1st row counts all parameters. The 2nd through 4th rows list three parameterizations of a baseline model. The remaining rows list models whose invariant parameters are noted in Column 1. For all rows, $\frac{1}{2}m(m-1)G$ factor covariances are not listed but counted. Negative numbers are the number of constraints on diag(Σ). The entry with *** is pKG − (G − 1)(p + m).

	T	Λ	ν	diag(Θ)	κ	diag(Φ)	diag(Σ)	Total
Total	pKG	pG	pG	pG	mG	mG	0	G(p(K + 3) + m(m + 3)/2)
Condition 7	pKG	pG	0	pG	0	0	−pG
Condition 8	pKG	pG	0	0	0	0	0	G(p(K + 1) + m(m − 1)/2)
MYT	***	(p − m)G	0	pG	m(G − 1)	mG	−p
T	pK	pG	p(G − 1)	pG	0	0	−p	p(K − 2) + G(3p + m(m − 1)/2)
Λ	pKG	0	0	pG	0	0	0	same as baseline
ν or Θ	same as Condition 8							same as baseline
T & Λ	pK	p	p(G − 1)	pG	0	m(G − 1)	−p	G(2p + m(m + 1)/2) + p(K − 1) − m
T & ν	pK	pG	0	pG	mG	0	−p	G(2p + m(m + 1)/2) + p(K − 1)
T & Θ	pK	pG	p(G − 1)	p	0	0	−p	G(2p + m(m − 1)/2) + p(K − 1)
Λ & ν	same as loading invariance							same as baseline
Λ & Θ	pKG	p	0	p	0	m(G − 1)	−p	G(pK + m(m + 1)/2) + p − m
ν & Θ	same as Condition 8							same as baseline
T, Λ & ν	pK	p	0	pG	m(G − 1)	m(G − 1)	−p	G(p + m(m + 3)/2) + pK − 2m
T, Λ & Θ	pK	p	p(G − 1)	p	0	m(G − 1)	−p	G(p + m(m + 1)/2) + pK − m
T, ν & Θ	pK	pG	0	p	mG	0	−p	G(p + m(m + 1)/2) + pK
Λ, ν & Θ	same as loading and unique variance invariance
all four	pK	p	0	p	m(G − 1)	m(G − 1)	−p	Gm(m + 3)/2 + p(K + 1) − 2m