Keywords
enumeration, numeracy, number, vision, cumulative link model
Abstract
Based on three core assumptions about mental representations of number, this model of visual enumeration specifies analysis methods that can identify when observers rely on different processes to estimate the numerosity of a visual display. Specifically, the model provides a clear criterion for identifying domains of numerosity that correspond to different perceptual or cognitive processes that have been described in numeracy literature, e.g. subitizing. The model predicts how the requirement to give integer responses in enumeration tasks can produce spurious discontinuities in accuracy measures that can be misidentified as evidence for a subitizing process. It is proposed that cumulative link models (CLMs, a kind of ordinal regression) are a correct method for quantifying mental representations of number. Work based on this model gives procedures for constructing CLMs of enumeration responses, normalizing CLM parameters, and testing the significance of discontinuities in the latent representation of number revealed by CLMs. We present data from an experiment where these procedures show evidence that observers relied on different processes to enumerate quantities less than or greater than 7.
Start Date
15-5-2019 2:00 PM
End Date
15-5-2019 2:30 PM
Location
Blacksburg, VA
Included in
Modeling Visual Enumeration Using Cumulative Link Regression.
Blacksburg, VA
Based on three core assumptions about mental representations of number, this model of visual enumeration specifies analysis methods that can identify when observers rely on different processes to estimate the numerosity of a visual display. Specifically, the model provides a clear criterion for identifying domains of numerosity that correspond to different perceptual or cognitive processes that have been described in numeracy literature, e.g. subitizing. The model predicts how the requirement to give integer responses in enumeration tasks can produce spurious discontinuities in accuracy measures that can be misidentified as evidence for a subitizing process. It is proposed that cumulative link models (CLMs, a kind of ordinal regression) are a correct method for quantifying mental representations of number. Work based on this model gives procedures for constructing CLMs of enumeration responses, normalizing CLM parameters, and testing the significance of discontinuities in the latent representation of number revealed by CLMs. We present data from an experiment where these procedures show evidence that observers relied on different processes to enumerate quantities less than or greater than 7.