Modeling Infant Free Play Using Hidden Markov Models

Abstract

Infants' free-play behavior is highly variable. However, in developmental science, traditional analysis tools for modeling and understanding variable behavior are limited. Here, we used Hidden Markov Models (HMMs) to capture behavioral states that govern infants' toy selection during 20 minutes of free play in a new environment. We demonstrate that applying HMMs to infant data can identify hidden behavioral states and thereby reveal the underlying structure of infant toy selection and how toy selection changes in real time during spontaneous free play. More broadly, we propose that hidden-state models provide a fruitful avenue for understanding individual differences in spontaneous infant behavior.

Keywords: Behavior Modeling; Developmental Science.

Figure 1.

Example of annotated play session for one infant. Each row corresponds to a different toy and the x-axis denotes the 20-minute timeline of the session. Solid lines indicate interaction intervals for each toy. Time segment 1 shows an interval where the infant switched among a variety of toys; time segment 2 shows nearly complete focus on one toy.

Figure 2.

Result of Leave-One-Out Cross-Validation for different time discretizations (1.5-, 2-, 2.5-minutes). Note that log-likelihoods are not directly comparable for the three time discretizations. We see that for the 2-minute discretization, 5-states is the best value. See text for discussion of the other curves.

Figure 3.

Estimated 5-state HMM for 2-minute windows. (A) Transition diagram: Each state is a circle with arrows pointing to successor states labeled by the transition probability. Only transitions with significant probabilities are shown. (B) Full state transition matrix with the initial state distribution in bottom row. (C) Observation distributions. Each row corresponds to a state and each column a feature. Each histogram shows the value distribution of the feature for the corresponding state. Features: Number of toy switches: number of times the toy set changes during the interval, number of toys interacted with in the interval, number of new toys (toys not played for the last 2 minutes) played during this interval, favorite toy ratio: duration of time that the infant plays with the favorite toy divided by the window size, toy intersection over union (IOU): intersection over union of two consecutive toy sets.

Figure 4.

Left panel: Number of infants in focus vs explore states over the play session. Right panel: Number of infants in F1 and F2 vs Fset vs explore states over the play session.

Figure 5.

(a) Scatterplot of Δ_bm vs. Δ_me for each infant, where Δ_bm and Δ_me are the change in percent of focus states from beginning (b) to middle (m) and from middle (m) to end (e), respectively. (b) Exemplar infants from the group with decreasing then increasing focus. For each infant, the three bars correspond to the beginning, middle, and end intervals of the play session. (c) Exemplar infants from the group with increasing then decreasing focus.

Figure 6.

Average distance (cm) traveled per second over the 20 infants for each of the behavioral states.