A New Item Response Theory Modeling Approach with Applications to Unidimensionality Assessment and Ability Estimation
ILLINOIS UNIV AT URBANA PSYCHOMETRIC GROUP
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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 unidimensionality. Essential unidimensionality implies the existence of a unique unidimensional latent ability. Essential unidimensionality is equivalent to the consistent estimation of this latent ability in an ordinal scaling sense using any balanced linear formula scoring scheme. A variation of this estimation approach allows consistent estimation of ability on the given latent ability scale.
- Statistics and Probability