Table 1.

Overview of Different Approaches To Modeling Method Effects in LST Models

	CU	OM	M − 1	IT
Representation of method effects	Correlated error variables for the same indicator over time	Method factors	Method factors	Indicator-specific trait factors and their correlations
Correlated method effects?	No	No	Yes	Yes
Separation of method effects and measurement error?	No	Yes	Yes	Yes
Method effects as separate variance component?	No (confounded with error)	Yes (unique consistency coefficient)	Yes (unique consistency coefficient), except for the reference indicator	No (confounded with trait)
Common consistency	$\mathit{CCO}(Y_{it})=\frac{{\lambda }_{it}^2\mathit{Var}(T)}{\mathit{Var}(Y_{it})}$	$\mathit{CCO}(Y_{it})=\frac{{\lambda }_{it}^2\mathit{Var}(T)}{\mathit{Var}(Y_{it})}$	$\mathit{CCO}(Y_{it})\ast =\frac{{\lambda }_{it}^2\mathit{Var}(T_r)}{\mathit{Var}(Y_{it})}$	--
Unique consistency	--	$\mathit{UCO}(Y_{it})=\frac{{\gamma }_{it}^2\mathit{Var}(M_i)}{\mathit{Var}(Y_{it})}$	$\mathit{UCO}(Y_{it})\ast =I(i\ne r)\frac{{\gamma }_{it}^2\mathit{Var}({TR}_i)}{\mathit{Var}(Y_{it})}$	--
Total consistency	--	$\mathit{TCO}(Y_{it})=\frac{{\lambda }_{it}^2\mathit{Var}(T)+{\gamma }_{it}^2\mathit{Var}(M_i)}{\mathit{Var}(Y_{it})}$	$\mathit{TCO}(Y_{it})\ast =\frac{{\gamma }_{it}^2\mathit{Var}(T_r)+I(i\ne r){\gamma }_{it}^2\mathit{Var}({TR}_i)}{\mathit{Var}(Y_{it})}$	$\mathit{TCO}(Y_{it})=\frac{{\lambda }_{it}^2\mathit{Var}(T_i)}{\mathit{Var}(Y_{it})}$

Note. CU = correlated uniqueness approach; OM = M orthogonal method factor approach; M − 1 = M − 1 correlated method factor approach; IT = indicator specific trait factor approach. The index r denotes the reference indicator. I (i ≠ r) is an indicator variable that has the value 1 if i ≠ r and the value zero if i = r .