Hello, to use single indicator in SEM , reliability is constrained to cronbach alfa. But when we use continous data we do not calculate cronbach alfa, then can we use single indicator latents for continous data? Thanks in advance
I think that SEM is suitable for any of the estimators used, always recommended WLSMV, and its theoretical model fits the proposed SEM model.
Article Should researchers use single indicators, best indicators, o...
Hi Ceren,
actually I don't think that using Cronbachs alpha is a good basis for constraining single indicators
a) if you have alpha than you have multiple indicators. Hence, better use the indicators or parts of them as indicators of the latent.
b) alpha makes unrealistic assumptions that even in ideal cases are implausibel. In many cases (multidimensional measures or indices) alpha is too low, resulting in nonsensical error variance fixation and an upward bias of structural coefficients
c) The error variance in a CFA or SEM is more than just random error (what the definition of lack of reliability is) but all further random and nonrandom causes of item response. Hence, using alpha or other reliability related meausure don't hit the target.
In the paper, S Kalaiselvan provided, the author Les Hayduk proposes to fix the error variance to a theoretically chosen value that expresses the beliefs of the researcher about the quality of the indicator as well as the conceptual gap between the indicator and the latent variable. This proposal is usually strongly criticized as researcher try to circumvent assumptions as strongly as possible and would like to delegate all theoretical precision to algorithms, statistics, and data (as it is the case, when using alpha). It is so handy :)
Here are a few further sources
Duncan, O. D., Haller, A. O., & Portes, A. P. (1968). Peer influences on aspirations: A reinterpretation. American Journal of Sociology, 74(2), 119-137. doi:10.1086/224615
Hayduk, L. a., Stratkotter, R. F., & Rovers, M. W. (1997). Sexual orientation and the willingness of catholic seminary students to conform to church teachings. Journal for the Scientific Study of Religion, 36(3), 455-467.
Oberski, D. L., & Satorra, A. (2013). Measurement error models with uncertainty about the error variance. Structural Equation Modeling: A Multidisciplinary Journal, 20(3), 409-428.
Onyskiw, J. E., & Hayduk, L. a. (2001). Processes underlying children's adjustment in families characterized by physical aggression. Family Relations, 50(4), 376-385. doi:10.1111/j.1741-3729.2001.00376.x
Best,
Holger
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