Statistical Glossary
Local Independence:
The local independence postulate plays a central role in latent variable models . Local independence means that all the manifest variable s are independent random variables if the latent variable s are controlled (fixed).
Technically, the local independence may be described by formula
|
where (y1, ... ,yL) is the vector of all the manifest variables, x is the latent variable , P(·|x) is the conditional probability for y=(y1,...,yL) given x ; Pl(·|x) are conditional probabilities for each manifest variable yl separately. If the manifest variables {yl} are continuous, then P(·|x) and Pl( ·| X ) are probability densities, not probabilities.