Single/multiple and cause/effect indicators

A brief visual note on the possibility of combining cause and effect indicators of latent variables (LV). Ken Bollen noted this possibility of a LV with 1 of each type of indicators in 1984 (evidently this model is not identified as such):

He mentioned such 'mixed' measures several times, see e.g. the depression CES-D one:
"items appear to be a mixture of effect and causal indicators. For instance, "I felt depressed" and "I felt sad" appear to be effect indicators of depressed mood. That is, we expect that a change in the latent depression variable leads to a change in responses to these items. However, "I felt lonely" could be a causal indicator of the same construct in that loneliness may cause depression rather than vice versa. Alternatively, loneliness could be a separate dimension that requires several indicators to measure it. To further complicate things, one could argue that some items are reciprocally related to depression.
For example, individuals may become depressed because they think people dislike them, which makes them appear unattractive, thus other people may avoid them and actually dislike them (i.e., the low affect may be unattractive and offputting)." [1:311]

Note 1:
Les Hayduk explored the 'reciprocally related' ('reactive') indicators in detail in [5]:

Note 2:
Les also advanced the 'finite cycling' feedback/nonrecursive models in [6], which simply says that infinite cycling is not realistic, so one can conceive of: 1. 1 full cycle; 2. 1 & 1/2 cycle; 3. 2 full cycles; etc. (although more than 2 cycles around the effects add up very little). See also in this [6]  great language on why/how one splits an effect η₁ -> η₂ into 2 such effects, see below the quote, referring to his Fig. 1 below:

“To identify the estimates of the effects in a model like Figure 1 (in the absence of additional equality, proportionality, or other constraints on β₂₁ and β₁₂) a variable like ξ₁ is required (Rigdon, 1995). The direct effect of ξ₁ on η₁, and the important absence of a direct effect of ξ₁ on η₂, implies that the covariance between ξ₁ on η₂ arises from the basic indirect effect of ξ₁ on η₂ (namely γ₁₁ β₂₁), which is enhanced by the loop L = β₂₁ β₁₂. The relegation of β₁₂ to a purely enhancing role in accounting for the covariance between ξ₁ and η₂ differentiates or disentangles β₂₁ from β₁₂ and makes it possible to obtain separate estimates of these effects. In the Figure 1 model, ξ₂ similarly contributes to disentangling the reciprocal effects, so as long as the γ₁₁ and γ₂₂ effects are substantial, the β₂₁ and β₁₂ effects in this model should be overidentified (given the independence of the disturbance terms).” [6: 660-661].

1. Bollen, K. A., & Lennox, R. (1991). Conventional wisdom on measurement: A structural equation perspective. Psychological Bulletin, 110(2), 305-314. doi:10.1037/0033-2909.110.2.305
2. Bollen, K. (1984). Multiple indicators: internal consistency or no necessary relationship? Quality and Quantity, 18(4), 377-385.
3. Bollen, K. A., Glanville, J. L., & Stecklov, G. (2001). Socioeconomic status and class in studies of fertility and health in developing countries. Annual Review of Sociology, 153-185.
4. Bollen, K. A., & Bauldry, S. (2011). Three Cs in measurement models: Causal indicators, composite indicators, and covariates. Psychological Methods, 16(3), 265-284. doi:10.1037/a0024448
5. Hayduk, L. A., Robinson, H. P., Cummings, G. G., Boadu, K., Verbeek, E. L., & Perks, T. A. (2007). The weird world, and equally weird measurement models: Reactive indicators and the validity revolution. Structural Equation Modeling: A Multidisciplinary Journal, 14(2), 280-310. 
6. Hayduk, L. A. (2009). Finite Feedback Cycling in Structural Equation Models. Structural Equation Modeling: A Multidisciplinary Journal, 16(4), 658-675.