Bayesian change-point analysis reveals developmental change in a classic theory of mind task

Abstract

Although learning and development reflect changes situated in an individual brain, most discussions of behavioral change are based on the evidence of group averages. Our reliance on group-averaged data creates a dilemma. On the one hand, we need to use traditional inferential statistics. On the other hand, group averages are highly ambiguous when we need to understand change in the individual; the average pattern of change may characterize all, some, or none of the individuals in the group. Here we present a new method for statistically characterizing developmental change in each individual child we study. Using false-belief tasks, fifty-two children in two cohorts were repeatedly tested for varying lengths of time between 3 and 5 years of age. Using a novel Bayesian change point analysis, we determined both the presence and-just as importantly-the absence of change in individual longitudinal cumulative records. Whenever the analysis supports a change conclusion, it identifies in that child's record the most likely point at which change occurred. Results show striking variability in patterns of change and stability across individual children. We then group the individuals by their various patterns of change or no change. The resulting patterns provide scarce support for sudden changes in competence and shed new light on the concepts of "passing" and "failing" in developmental studies.

A Bayesian framework for the development of belief-desire reasoning: Estimating inhibitory power

“…What is the nature, rate, and types of ToM learning trials Bin the wild^? What does developmental change look like within the individual child who, unlike the averaged group, is the actual site of the computational mechanisms of learning (S. Baker, Leslie, Gallistel, & Hood 2016)? Assumed to play a central role, yet almost completely unstudied, the nature of experience in change is mostly a matter of speculation.…”

“…Indeed, group-averaged data is enshrined in the very notion that younger preschoolers Bfail^while older preschoolers Bpass.^However, such findings are irretrievably ambiguous. As Baker et al (2016) point out, 70% failure could be mean 70% of three's fail 100% of the time, or 100% pass 70% of the time, or any combination of probabilities as long as they average at or around 70% failure; likewise, with 70% passing for four's. Moreover, given that there is no such thing as a Bgroup brain^wherein learning and development take place, the site of the shift must be the individual brain in the individual child.…”

“…This in turn requires novel statistical methods. Baker et al (2016) developed such a method, called Bayesian change-point analysis. The authors gathered longitudinal data in the form of multiple single-case studies yielding individual cumulative records for 52 children followed for a year or more between three and five years old.…”

“…For example, theory-theory posits that the rational (adult) model for belief-desire reasoning is not present until the age four shift and must be absent earlier and certainly absent in infancy. Although theory-theory makes similar predictions to ToMM for the developmental trajectory from three to four years (but see S. Baker et al, 2016), it does not make specific predictions about the facilitatory effect of LD tasks in younger children. By contrast, because ToMM assumes that younger children possess the same rational model as adults in theory-of-mind reasoning, it also predicts that changes in task demand can improve performance, even for children with lower inhibitory power.…”

“…To succeed in predicting Sally's behavior, children have to inhibit their own true belief about the object's location. The inhibitory power to overcome one's own perspective develops slowly from three to four years of age (Beck, Schaefer, Pang & Carlson, 2011;Carlson, 2005;Diamond, Carlson & Beck, 2005); individual false-belief performance typically remains unstable for long periods (S. Baker, Leslie, Gallistel, & Hood, 2016), giving rise to the familiar developmental pattern only through group averaging.…”