an approach to identifying the dimensions underlying associations among a set of variables by using a covariance matrix of estimated communalites as input. Principal factor analysis assumes that all variables have been measured with some degree of error and requires that dimensions be extracted in a particular way. Specifically, the first dimension extracted must account for the maximum possible variance, having the highest squared correlation with the variables it underlies; the second dimension must account for the next maximal amount of variance and be uncorrelated with the previously extracted dimension; and so forth. The researcher retains a certain number of dimensions based on various criteria, including interpretations of factor loadings.