Modeling Dimensions Converging at the Upper Anchor in Learning Progressions: An Example of Micro-Evolution

Multidimensionality is common in psychological and educational measurements. This study focuses on dimensions that converge at the upper anchor (i.e. the highest acquisition status defined in a learning progression) and compares different ways of dealing with them using the multidimensional random coefficients multinomial logit model and scale alignment methods. Assumptions underlying the four approaches studied are a) ignoring the convergence, b) recognizing the convergence of the dimensions, c) treating convergence as a new dimension, and d) separating the within-category multidimensionality and treating convergence as a new dimension. A learning progression about micro-evolution is used as an example, including model fits, step difficulties, and associations between dimensions, Wright maps are drawn, and inferences are made under the four building blocks of measurement development. Finally, the usefulness and weaknesses of the four approaches are discussed.