Using conditional association to identify locally independent item sets

The ordinal, unidimensional monotone latent variable model assumes unidimensionality, local independence, and monotonicity, and implies the observable property of conditional association. We investigated three special cases of conditional association and implemented them in a new procedure that aims at identifying locally dependent items, removing these items from the initial item set, and producing an item subset that is locally independent. A simulation study showed that the new procedure correctly identified 89.5% of the model-consistent items and up to 90% of the model-inconsistent items. We recommend using this procedure for selecting locally independent item sets. The procedure may be used in combination with Mokken scale analysis.