Consider a situation where you have ten observed variables, X1, X2, …, X10. Suppose you want to model these ten variables in terms of two latent factors, F1 and F2. For convenience, it is assumed that the factors are uncorrelated and that each has mean zero and variance one. The model that you want to derive is of the form:

It follows that Var(Xi) = βi12 + βi22 + Var(εi). The portion of the variance of Xi that is attributable to the factors, the common variance or communality, is βi12 + βi22. The remaining variance, Var(εi), is the unique variance, and is considered to be a combination of specific and error variances that are unique to Xi.