Principal component analysis reveals multiple consistent responses to naturalistic stimuli in children and adults

Abstract

Functional MRI (fMRI) study of naturalistic conditions, for example, movie watching, usually focuses on shared responses across subjects. However, individual differences have been attracting increasing attention in search of group differences or associations with behavioral outcomes. Individual differences are typically studied by directly modeling the pair-wise intersubject correlation matrix or projecting the relations onto a single dimension. We contend that it is critical to examine whether there are one or more consistent responses underlying the whole sample, because multiple components, if exist, may undermine the intersubject relations using the previous methods. We propose to use principal component analysis (PCA) to examine the heterogeneity of brain responses across subjects and project the individual variability into higher dimensions. By analyzing an fMRI dataset of children and adults watching a cartoon movie, we showed evidence of two consistent responses in the supramarginal gyrus and other regions. While the first components in many regions represented a response pattern mostly in older children and adults, the second components mainly represented the younger children. The second components in the supramarginal network resembled a delayed version of the first PCs for 4 s (2 TR), indicating slower responses in the younger children than the older children and adults. The analyses highlight the importance of identifying multiple consistent responses in responses to naturalistic stimuli. This PCA-based approach could be complementary to the commonly used intersubject correlation to analyze movie-watching data.

Keywords: development; individual difference; movie watching; naturalistic condition; principal component analysis; supramarginal gyrus; theory of mind.

FIGURE 1

Illustrations of developmental effects of shared responses in a brain region. (a) and (b) illustrate two hypothetical developmental functions of consistent responses. The age range was set between 0 and 30 years, which overlaps with the empirical data. Note that the consistent responses in (a) and (b) may be independent. (c) shows the scenario where the two separate consistent components are present. (d–f) show the pair‐wise correlation matrices across subjects. (g–i) show the intersubject correlations calculated using the leave‐one‐out (LOO) method against the subjects' age. (j–l) show the percentage of variances explained by the first 10 principal components (PCs) from principal component analysis (PCA). (m–o) show the PC loadings of the first one or two PCs against age

FIGURE 2

(a) Maps of 15 independent components (ICs) that are included in the current analysis. The group averaged maps were thresholded at z > 2.3. (b) Percentage of variance explained by the first three principal components for the 15 networks (ICs). The bar colors correspond to the network colors in panel (a). The asterisk represents p < .001 by using a circular time‐shift randomization method. The brain networks were visualized with BrainNet Viewer (RRID: SCR_009446) (Xia, Wang, & He, 2013)

FIGURE 3

(a) Correlation matrix of the supramarginal gyrus network (independent component 17) across the 82 subjects. The subjects were sorted by age in an ascending order. (b and c) Principal component (PC) loadings for the first and second PCs as functions of age. (d) Leave‐one‐out (LOO) intersubject correlations as a function of age. The brain slice illustrates the location of the network

FIGURE 4

(a) Principal component (PC) scores of the first two PCs in the supramarginal network (independent component 17). The brain slice illustrates the location of the network. (b) Cross‐correlations between the first two PCs. The red lines indicate p < .05 of absolute peak cross‐correlations. (c) Time shifts of individual's time series with reference to the first PC score as a function of the PC2 loading

FIGURE 5

Correlations between theory of mind (ToM) performance (proportion of correct) and principal component (PC) loadings for the first two PCs of the supramarginal gyrus network (independent component 17). The brain slice illustrates the location of the network

FIGURE 6

Percentage of variance explained by the second (a) and first (b) principal components (PCs) from the voxel‐wise analysis (c). The voxels in (a) were thresholded at p < .001. The voxels in B were thresholded at 9%. The brain networks were visualized with BrainNet Viewer (RRID: SCR_009446) (Xia et al., 2013)

FIGURE 7

(a) The time series of the first two principal components (PC scores) for the precuneus region (depicted in the brain slice). (b and c) The first and second principal component (PC) loadings as functions of age. (d) The cross‐correlations between the two PCs. The red lines indicate p < .05 of absolute peak cross‐correlations

FIGURE 8

(a) The time series of the first two principal components (PC scores) for the left sensorimotor region (depicted in the brain slice). (b and c) The first and second principal component (PC) loadings as functions of age. (d) The cross‐correlations between the two PCs. The red lines indicate p < .05 of absolute peak cross‐correlations

FIGURE 9

Upper row, correlations between the squared mean intersubject correlations using leave‐one‐out (LOO) method and the variance explained by the first principal component (PC). Lower row, the correlations between the first PC loadings and individual LOO correlations as functions of the variance explained by the first PC