Looking represents choosing in toddlers: Exploring the equivalence between multimodal measures in forced-choice tasks

In the two-alternative forced-choice (2AFC) paradigm, manual responses such as pointing have been widely used as measures to estimate cognitive abilities. While pointing measurements can be easily collected, coded, analyzed, and interpreted, absent responses are often observed particularly when adopting these measures for toddler studies, which leads to an increase of missing data. Although looking responses such as preferential looking can be available as alternative measures in such cases, it is unknown how well looking measurements can be interpreted as equivalent to manual ones. This study aimed to answer this question by investigating how accurately pointing responses (i.e., left or right) could be predicted from concurrent preferential looking. Using pre-existing videos of toddlers aged 18–23 months engaged in an intermodal word comprehension task, we developed models predicting manual from looking responses. Results showed substantial prediction accuracy for both the Simple Majority Vote and Machine Learning-Based classifiers, which indicates that looking responses would be reasonable alternative measures of manual ones. However, the further exploratory analysis revealed that when applying the created models for data of toddlers who did not produce clear pointing responses, the estimation agreement of missing pointing between the models and the human coders slightly dropped. This indicates that looking responses without pointing were qualitatively different from those with pointing. Bridging two measurements in forced-choice tasks would help researchers avoid wasting collected data due to the absence of manual responses and interpret results from different modalities comprehensively.     

Theoretical considerations on the C-D effect in self-thinning plant populations

A model for describing the competition–density (C-D) effect in self-thinning populations was developed on the basis of the following three basic assumptions: (1) the growth of mean phytomass follows a general logistic equation; (2) final yield is independent of initial population density; and (3) there exists a functional relationship between actual and initial population densities at any given time. The resultant equation takes the same reciprocal form as the reciprocal equation of the C-D effect derived from Shinozaki–Kira's theory (i.e., the logistic theory of the C-D effect), which deals with the density effect in nonself-thinning populations. However, one of the two time-dependent coefficients is quite different in mathematical interpretation between the two reciprocal equations. The reciprocal equation for self-thinning populations is essentially the same as the reciprocal equation assumed in the derivation of the functional relationship between actual and initial population densities. The establishment of the reciprocal equation is supported by the empirical facts that the reciprocal relationship between mean phytomass and population density is discernible in not only nonself-thinning populations but also in self-thinning populations. The present model is expected to systematically interpret underlying mechanisms between the C-D effect, which is observed at a time constant among populations with various initial densities, and self-thinning, which is observed along a time continuum in a given population. Received: August 5, 1998 / Accepted: January 7, 1999