A New Item Response Theory Modeling Approach with Applications to Unidimensionality Assessment and Ability Estimation

Abstract

Using an infinite item test framework, it is argued that the usual assumption of local independence be replaced by a weaker assumption, essential independence. A fortiori, the usual assumption of unidimensionality is replaced by a weaker and arguably more appropriate statistically testable assumption of essential unidimennsionality. Essential unidimennsionnality implies the existence of a “unique” unidimensional latent ability. Essential unidimensionality is equivalent to the “consistent” estimation of this latnet ability in an ordinal scaling sense using any Balanced empirical scaling. A variation of this estimation approach allows consistent estimation of ability on the given latent ability scale.

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