Investigating invariant item ordering in the Mental Health Inventory: An illustration of the use of different methods

• Invariant item ordering is important in scales.
• Invariant item ordering may result from ‘extreme’ items.
• Items expressing suicidal ideation in scales are often extreme.
• Inspecting item pair plots can reveal such extreme items.
• Removing extreme items can reduce or eliminate invariant item ordering.

Invariant item ordering is a property of scales whereby the items are scored in the same order across a wide range of the latent trait and across a wide range of respondents. In the package ‘mokken’ in the statistical software R, the ability to analyse Mokken scales for invariant item ordering has recently been available and techniques for inspecting visually the item response curves of item pairs, have also been included. While methods to assess invariant item ordering are available, there have been indications that items representing extremes of distress in mental well-being scales, such as suicidal ideation, may lead to claiming invariant item ordering where it does not exist. We used the Mental Health Inventory to see if invariant item ordering was indicated in any Mokken scales derived and to see if this was being influenced by extreme items. A Mokken scale was derived indicating invariant item ordering. Visual inspection of the item pairs indicated that the most difficult item (suicidal ideation) was located far from the remaining cluster of items. Removing this item lowered invariant item ordering to an unacceptable level.