Assessing local influence for specific restricted likelihood: Application to factor analysis

In restricted statistical models, since the first derivatives of the likelihood displacement are often nonzero, the commonly adopted formulation for local influence analysis is not appropriate. However, there are two kinds of model restrictions in which the first derivatives of the likelihood displacement are still zero. General formulas for assessing local influence under these restrictions are derived and applied to factor analysis as the usually used restriction in factor analysis satisfies the conditions. Various influence schemes are introduced and a comparison to the influence function approach is discussed. It is also shown that local influence for factor analysis is invariant to the scale of the data and is independent of the rotation of the factor loadings.