Longitudinal analysis of early semantic networks: preferential attachment or preferential acquisition?

Abstract

Analyses of adult semantic networks suggest a learning mechanism involving preferential attachment: A word is more likely to enter the lexicon the more connected the known words to which it is related. We introduce and test two alternative growth principles: preferential acquisition-words enter the lexicon not because they are related to well-connected words, but because they connect well to other words in the learning environment-and the lure of the associates-new words are favored in proportion to their connections with known words. We tested these alternative principles using longitudinal analyses of developing networks of 130 nouns children learn prior to the age of 30 months. We tested both networks with links between words represented by features and networks with links represented by associations. The feature networks did not predict age of acquisition using any growth model. The associative networks grew by preferential acquisition, with the best model incorporating word frequency, number of phonological neighbors, and connectedness of the new word to words in the learning environment, as operationalized by connectedness to words typically acquired by the age of 30 months.

Fig. 1

Networks of the nouns used in this study: (a) feature-based network and (b) associations-based network for nouns normatively acquired by 30 months of age. For visual clarity, only links representing two or more shared features are shown in (a). The arrows indicating links in (b) point from the stimulus (cue) to the response (target). See the text for details on network construction.

Fig. 1

Networks of the nouns used in this study: (a) feature-based network and (b) associations-based network for nouns normatively acquired by 30 months of age. For visual clarity, only links representing two or more shared features are shown in (a). The arrows indicating links in (b) point from the stimulus (cue) to the response (target). See the text for details on network construction.

Fig. 2

Networks of the nouns used in this study: (a) feature-based network and (b) associations-based network for nouns normatively acquired by 20 months of age. For visual clarity, only links representing two or more shared features are shown in (a). The arrows indicating links in (b) point from the stimulus (cue) to the response (target). See the text for details on network construction.

Fig. 3

Log-log plot of the cumulative degree distribution for the 30-month feature network (left) and associative network (right). The graphs show the probability that a randomly chosen node is of degree equal to or higher than k.

Fig. 4

Degree for each word in the 30-month network as a function of the age of acquisition. Results are shown separately for the feature network (top panel) and associative network (bottom panel). Best-fitting regression lines are shown.

Fig. 5

The three growth models depicted in a simplified network. The network is the same in all three models, but the models assign different values to the unknown words. Gray shading and solid lines indicate nodes and links in the existing network (known words: A–D); no shading and dotted lines indicate nodes and links not yet incorporated into the known network (possible new nodes: N1, N2, and N3). Black lines indicate links relevant to the growth models, and gray lines indicate unimportant links. The “Add” column in each illustration indicates which node is favored for learning by the growth model in question; this is determined by the relative growth values of the possible new nodes. The growth values computed in this example are based on indegree for a directed network; arrow direction is important. For undirected networks, such as a feature network, arrow direction is not relevant. In the preferential-attachment model, the value of a new node is the average degree of the known nodes it would attach to (e.g., N1 is attached to A, which has an indegree of 3). In the preferential-acquisition model, the value of a new node is its degree in the learning environment—that is, the full network (e.g., N3 has an indegree of 3, which includes one link from a known node and two links from unknown nodes). In the lure-of-the-associates model, the value of a node is its degree with respect to known words (e.g., N3 has a value of 1, based on its one connection from a known node).

Fig. 6

Negative log likelihoods of the lure-of-the-associates (LOA) and preferential-acquisition (PA) models and their combinations. Two preferential-acquisition models were tested: One in which the learning environment was represented by the child's network at 30 months ("30 mts") and one in which the learning environment was represented by the adult network ("Adult"). Brackets and asterisks indicate nested models that were significantly different from each other in a likelihood-ratio test, p < .05.