Formal models in animal-metacognition research: the problem of interpreting animals' behavior

Abstract

Ongoing research explores whether animals have precursors to metacognition-that is, the capacity to monitor mental states or cognitive processes. Comparative psychologists have tested apes, monkeys, rats, pigeons, and a dolphin using perceptual, memory, foraging, and information-seeking paradigms. The consensus is that some species have a functional analog to human metacognition. Recently, though, associative modelers have used formal-mathematical models hoping to describe animals' "metacognitive" performances in associative-behaviorist ways. We evaluate these attempts to reify formal models as proof of particular explanations of animal cognition. These attempts misunderstand the content and proper application of models. They embody mistakes of scientific reasoning. They blur fundamental distinctions in understanding animal cognition. They impede theoretical development. In contrast, an energetic empirical enterprise is achieving strong success in describing the psychology underlying animals' metacognitive performances. We argue that this careful empirical work is the clear path to useful theoretical development. The issues raised here about formal modeling-in the domain of animal metacognition-potentially extend to biobehavioral research more broadly.

Keywords: Associative learning; Comparative psychology; Metacognition; Metamemory; Modeling; Primate cognition.

Fig. 1

Proportion of uncertainty responses (solid circles), sparse responses (open squares), and dense responses (open triangles) made by the macaque Murph in the sparse-uncertain-dense task of Smith et al. (2013). The horizontal axis indicates the objective density of the trial (Levels 1–30: Sparse; Levels 31–60: Dense)

Fig. 2

A reinforcement-history portrayal of performance in a sparse-dense discrimination with a third response assumed to manage stimulus aversion and response avoidance. The horizontal axis indicates the subjective impression created by the objective stimulus on the trial. The solid line instantiates the idea that the third response could be the default option with a constant response strength that is selected when aversion or avoidance weakens the tendency to respond sparse or dense. The dotted line instantiates the idea that response strength for the sparse and dense responses would wane exponentially going inward as the frequency of errors increased

Fig. 3

Murph’s performance in the sparse-uncertain-dense task of Smith et al. (2013), depicted with symbols as described in the legend to Fig. 1. Also shown are the best-fitting predictions produced by an “associative” model as it fit those observed data using a third response to manage stimulus aversion and response avoidance (solid line aversion-avoidance response; dashed line sparse responses; dotted line dense responses). Details of the model and model fitting are described in the text

Fig. 4

Murph’s performance in the sparse-uncertain-dense task of Smith et al. (2013), depicted with symbols as described in the legend to Fig. 1 caption. Also shown are the best-fitting predictions produced by a “metacognitive” model as it fit those observed data assuming that the macaque monitored psychological signals of uncertainty and was able to place two confidence criteria along the Sparse-Dense continuum (solid line uncertainty responses; dashed line sparse responses; dotted line dense responses). Details of the model and model fitting are described in the text

Fig. 5

The convergence between the associative and metacognitive formal model. To make this graph, the best-fitting prediction of the associative model—as it fit the macaque’s observed discrimination data (Fig. 1)—was used as the data-fitting target, and that target was then fit by the metacognitive model. The horizontal axis indicates the objective density of the trial (Levels 1–30, sparse; Levels 31–60, dense). Shown are the proportions of aversion-avoidance responses (open circles), sparse responses (open squares), and dense responses (open triangles) originally produced by the associative model, and the best-fitting proportions of uncertainty responses (black circles), sparse responses (black squares), and dense responses (black triangles) produced by the metacognitive model fitting the prediction of the associative model

Fig. 6

The convergence between the associative and metacognitive formal models. To make this graph, we produced 17 simulated performers who performed according to the predictions of the metacognitive model. They had Sparse-Uncertainty and Uncertainty-Dense confidence criteria, respectively, placed at Levels 30–30, Levels 29–31, Levels 28–32, and so forth out to Levels 14–46. As the width of the uncertainty region increased (e.g., 46–14 = width 32), the uncertainty response was used more generously. Each of 17 performance profiles was then fit by the associative model, so that we could assess the relationship between the width of the metacognitive uncertainty region in the metacognitive model (x-axis) and the height of the aversion-avoidance threshold in the associative model (y-axis). The two parameters—uncertainty-region width and aversion-avoidance threshold height—have a perfect mathematical correspondence (solid symbols). A simple logistic function recovered this relationship perfectly (open symbols)

Fig. 7

The proportion of times a macaque endorsed into a learned category to-be-categorized test items that were outside the category (rand.), non-typical category members (high-level distortions), typical members (low-level distortions), highly typical members (v. low-level distortions), or prototypical members (prot.). Also shown is the best-fitting predicted profile (E) when a standard exemplar-based categorization model fit the macaque’s performance as well as it could. From “Prototype abstraction by monkeys (Macaca mulatta),” by J. D. Smith, J. S. Redford, and S. M Haas, Journal of Experimental Psychology: General, 137, 390–401. Copyright 2008 by the American Psychological Association. Reprinted with permission