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 (y_{1}, ... ,y_{L}) is the vector of all the manifest variables, x is the latent variable , P(·x) is the conditional probability for y=(y_{1},...,y_{L}) given x ; P_{l}(·x) are conditional probabilities for each manifest variable y_{l} separately. If the manifest variables {y_{l}} are continuous, then P(·x) and P_{l}( · X ) are probability densities, not probabilities.