Modeling growth and individual differences in spatial tasks.

The goal of the present research is to understand individual differences and growth of children's and adolescents' performance on two spatial tasks through a formal model framework. In Study 1, 579 subjects aged 7-16 years old drew lines to represent their water-level task predictions for eight tilted rectangular vessels. In the verticality task, called the "van task," subjects drew lines representing their predictions concerning the orientation of a plumb line suspended from the ceiling of a van parked on eight different inclines. In Study 2, 185 subjects aged 9-16 years were presented with video displays on a computer monitor and were instructed to adjust lines on the screen to indicate their predictions for the same stimuli used in Study 1. Later, they responded to a multiple-choice verbal analogies test and answered interview questions concerning their task performance strategies for the van and water-level tasks. In both studies, responses on the van and water-level tasks were scored as correct or incorrect on the basis of empirically derived scoring criteria that varied with age. The number of correct responses for each subject on the van and water-level tasks was modeled as a binomial random variable. Individual differences, growth differences, and sex differences in task performance were modeled as mixtures of binomial distributions, a model that may be viewed as a latent class model. Data for Study 1 subjects 11 years and older were combined so that the joint structure of the water-level and van tasks could be studied. This structure was modeled as a mixture of bivariate binomial distributions. On the basis of their task performance, subjects in Study 1 were assigned to their corresponding latent classes. Once classified, the original response distributions of subjects within each latent class were explored in an effort to understand their various response strategies. Additionally, the correspondence between verbal explanations and van and water-level task performance was investigated in Study 2. Results include the following: 1. A two-component binomial mixture distribution fit well the van and water-level task data for each age and sex group; each binomial component may be viewed as a different latent class. Variance accounted for under the model often exceeded 90%. One binomial component (latent class) modeled the poor performers with poor task success rates, and the second component modeled the remaining good performers who consistently performed well.(ABSTRACT TRUNCATED AT 400 WORDS)