Computing latent variable variance (x... PreviousNext
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Message/Author
 Luke Brooks-Shesler posted on Monday, June 04, 2012 - 12:58 pm
Iím trying to compute the variance of an endogenous latent variable (probid) based on Bengt's (2012) article, which describes a model that contains 2 main effects and 1 interaction.

In the partially latent model below, there are 3 main effects and 1 interaction. The variable expert is a single item observed exogenous variable; all other variables are latent.

ETA_probid = B_reqinno (ETA_reqinno) + B_socexch (ETA_socexch) + B_expert (ETA_expert) + B_expxsoc (ETA_expert◊ETA_socexch) + ZETA_probid

The equation above corresponds to Equation 1 from Muthen, 2012, p. 1.

Question:
Using Equation 5 (Muthen, 2012, p. 3) as a template, would the equation for V(ETA_probid) be as follows?

V(ETA_probid) = B_reqinno(squared) V(ETA_reqinno) + B_socexch(squared) V(ETA_socexch) + B_expert(squared) V(ETA_expert) + 2B_reqinno B_socexch Cov(ETA_reqinno,ETA_socexch) + 2B_reqinno B_expert Cov(ETA_reqinno,ETA_expert) + 2B_expert B_socexch Cov(ETA_expert,ETA_socexch) + Bexpxsoc(squared) V(ETA_expert◊ETA_socexch) + V(ZETA_probid)
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