Expansion of verb-argument construction repertoires in L2 English writing

: This paper investigates the use of English verb-argument constructions (VACs) in second language writing in light of usage-based constructionist approaches to language development. It employs a comprehensive list of VACs to analyze every sentence in 390 essays written by L2 learners of three levels, i.e., Low, Mid, and High, and examines the theoretical hypotheses that the repertoires of VACs expand along with L2 pro ﬁ cient pro ﬁ le and that individual VACs, albeit varying in their expansion patterns, compose a structured inventory based on constructional information. Re-sults indicate that L2 learners of higher pro ﬁ ciency used signi ﬁ cantly more types of VACs than those of lower pro ﬁ ciency. It is also found that signi ﬁ cant expansions of individual VACs appeared at di ﬀ erent L2 pro ﬁ ciency levels. For example, the use of [Verb + NP complement] construction signi ﬁ cantly increased between Low and Mid, not between Mid and High, whereas the [Verb + Prepositional object] construction signi ﬁ cantly expanded throughout the three pro ﬁ ciency levels. Finally, there were strong cluster e ﬀ ects in the expansion of VACs as small sets of VACs showed similar by-text co-occurrence patterns.


Introduction
Verb-argument constructions (VACs, also referred to as argument structure constructions) have been a major research topic in the field of second language (L2) acquisition, especially in L2 English research (Ellis 2008;Gries and Wulff 2005;Herbst 2016). VACs serve as the framing templates for the overall forms and meanings of English sentences (Goldberg 1995(Goldberg , 2006. For example, the ditransitive construction consistently forms the structure of SVO 1 O 2 and expresses the transfer of the theme (O 2 ) from the agent (S) to the recipient (O 1 ), regardless of the verb, as in she gave/got/ sent/threw/kicked me a ball. VACs pertain to a variety of important linguistic phenomena such as syntactico-semantic projection of lexical verbs (Levin 1993), event construal via linguistic encoding (Wittenberg and Levy 2017), and cognitive entrenchment and abstraction (Tomasello 2006).
It has been observed that there are significant developmental patterns of VACs in L2 English acquisition. From the early stages of L2 English acquisition, a variety of VACs are provided with different sets of lexical verbs in language input, but only a small number of frequent VACs are used with prototypical verbs (e.g., give O 1 O 2 ) in novice L2 English learners' language output (Choi and Sung 2020;Ellis and Ferreira-Junior 2009;Kim et al. 2020). When the L2 learners become more proficient in English, their repertoires of VACs expand to be associated with multiple sets of linguistically relevant verbs (Ellis and Ferreira-Junior 2009;Valenzuela and Rojo 2008).
However, the research on L2 English VACs has been limited, albeit conducted with a wide range of L1 backgrounds (De Knop and Gilquin 2016;Kim and Rah 2016;Li et al. 2014;Liang 2002), because most of the studies have focused on a handful of VACs such as the locative, ditransitive and resultative constructions (e.g., Ellis and Ferreira-Junior 2009;Ellis et al. 2016;Römer and Berger 2019;Song and Sung 2017). For example, Ellis et al.'s (2016) monograph focused on analyzing three VACs (i.e., verb locative, verb object locative, and ditransitive) and provided empirical evidence that strongly supports usage-based approaches to language acquisition and processing. More recently, Römer and Berger (2019) investigated the 19 types of the 'V preposition n' VAC (e.g., V about n, V with n) in L2 writings and found that the emergence of L2 constructions is characterized by "an expansion of the learners' VAC repertoire in terms of VAC types" (p. 19); for the analysis of the 'V preposition n' VAC in L2 speaking, see Römer and Garner (2019).
In other words, L2 acquisition trajectories of major VACs have been extensively investigated, but less effort has been devoted to investigating how an entire repertoire of VACs gradually expands as "a structured inventory" in L2 English (Ellis and Ferreira-Junior 2009: 370). To our knowledge, there have been a handful of studies that provided a comprehensive account of all the VACs used by L2 learners (Kyle and Crossley 2017;Kyle et al. 2021;Römer 2019).
Although these studies have proved that a full consideration of VACs in the English language contributes to our better understanding of L2 English development, not much has been answered to the question 'what are the cardinal variations in the VAC repertoire among different levels of L2 learners?' For example, it would be of great interest to identify a cluster of VACs that emerge as a major part of the VAC repertoire between novice and intermediate levels. Therefore, the present study analyzes every sentence in L2 English writings produced by three proficiency groups based on a comprehensive list of VACs and investigates how the L2 repertoire of VACs expands across proficiency. More specifically, we identify VACs that account for the crucial differences in the expanding VAC repertoires across the proficiency. We also examine if any clusters of VACs show similar patterns when emerging to be a major part of L2 VAC repertoire in the course of L2 development.
2 Literature review 2.1 Verb-argument constructions Verb-argument structures and their contributions to sentence form and meaning have been at the center of theoretical linguistics and psycholinguistic models of sentence processing for years (Bencini and Goldberg 2000). Linguists with constructional approaches (Fillmore et al. 1999;Goldberg 1995;Jackendoff 1997;Michaelis and Lambrecht 1996) claim that knowledge of language consists of constructions, i.e., learned pairings of form and meaning at different levels. Goldberg (2006) defined constructions as follows: Any linguistic pattern is recognized as a construction as long as some aspect of its form or function is not strictly predictable from its component parts or from other constructions recognized to exist. In addition, patterns are stored as constructions even if they are fully predictable as long as they occur with sufficient frequency. (p. 6) Constructions encompass not only lexical units such as words and idioms (Hilpert 2009) but also phrasal or clausal ones such as verb-argument structures (Goldberg and Suttle 2010). The structural configurations of a verb and arguments carry constructional meaning that is not predictable from the components, which in turn contributes to the sentence meaning. For example, the ditransitive form 'SVO 1 O 2 ' is paired with the meaning of transfer, i.e., 'X causes Y to receive Z' (Bencini and Goldberg 2000), so the ditransitive sentence expresses the meaning of transfer even when the verb lacks such meaning, e.g., he sliced me a tomato. These sentence-or clause-level parings between form and meaning are called verb-argument constructions (VACs) and analyzed as independent constructions in English (Ellis and Ferreira-Junior 2009;Goldberg 1995Goldberg , 2006 as well as other languages (De Knop and Gilquin 2016;Hilpert 2009). In her seminal book, Goldberg (1995) studied VACs for basic sentence types, which were thought to reflect basic event types that humans experience. Some of the VACs studied by Goldberg (1995) and Bencini and Goldberg (2000) are provided in Table 1.

Expansion of L2 VAC repertoires
As shown in Table 1, constructional approaches to VACs highlight surface-level observations and generalizations and thus do not impose abstract derivations of verbargument structures (Goldberg 2002). The importance of surface-level patterns and generalizations has been also acknowledged by some corpus-informed grammarians. They studied the verb-argument structures with an interest in the patterned nature of language and described English grammar for learners in a comprehensive and systematic manner. For example, Francis et al. (1996) listed all the verb patterns in the Collins COBUILD English Dictionary, and their work was published as COBUILD Grammar Patterns 1: Verbs. Biber et al. (1999), in Longman Grammar of Spoken and Written English, identified major clause patterns that are comparable to VAC types identified by constructionists. Some of these major patterns can be further divided in terms of complementation types, as described by Quirk et al. (1985). For example, variants of the monotransitive construction SVO can be identified by the grammatical category of the object argument, e.g., NP, that-clause, to-infinitive, etc.
In the present study, we analyzed the VACs in L2 learner essays, grounded on the works by the above-mentioned constructionists and usage-based grammarians. Constructionists noted that VACs are independent linguistic units that deserve linguistic analyses, and usage-based grammarians provided detailed lists of VACs in English. The present study attempted to examine every sentence in learner output, using a comprehensive list of VACs based on Quirk et al. (1985), Francis et al. (1996), andBiber et al. (1999). The list is presented in Table 2, and the coding procedure will be described in Section 3.2.

Verb-argument constructions in L2 English
The ontological status of VACs in L2 English has been attested with a variety of experimental designs. Gries and Wulff (2005) provided evidence from three different methods-namely, priming, sorting, and corpora-to suggest the psychological validity of VACs in L2 English. For example, when German learners of L2 English were asked to sort 16 sentences generated by four verbs and four constructions, they showed a marked tendency toward a construction-based sorting, not a verb-based sorting. Similar observations of the construction-based sorting were reported for L2 English learners with various mother tongues such as Italian, Korean, Chinese, and Spanish (Baicchi and Della Putta 2019; Kim and Rah 2016;Liang 2002;Valenzuela and Rojo 2008). Then, how do L2 English learners come to know and use VACs? This question has been extensively addressed with usage-based models of construction grammar (Ellis and Ferreira-Junior 2009;Gries and Wulff 2005;Kim et al. 2020;Li et al. 2014;Römer and Berger 2019;Tyler and Ortega 2018). Usage-based approaches to L2 acquisition hold that language learning is primarily driven by "learners' exposure to L2 input in use" and that learners employ domain-general cognitive mechanisms in language learning (Ellis and Wulff 2020: 63). These principles have been addressed in Table : Verb-argument structures.

Major & sub-types
Expansion of L2 VAC repertoires complementary areas such as cognitive linguistics (construction grammar), corpus linguistics, and psycholinguistics. Cognitive linguists explain that accumulated exposure to English input facilitates acquisitional mechanisms such as entrenchment, prototype-based generalization, and abstraction (Barlow and Kemmer 2000;Bybee 2008;Eskildsen 2009Eskildsen , 2017Ellis 2008). Psycholinguistic and corpus linguistic research have provided empirical evidence for the roles of input frequency and saliency in language acquisition (e.g., Crossley et al. 2016;Godfroid 2016). With regard to the acquisition of VACs, it is assumed that L2 learners gradually expand their repertoires of VACs in the function of multiple factors such as L2 input variables (Ellis and Ferreira-Junior 2009), acquisitional mechanisms (Tomasello 2006), and constructional complexity (Sung and Kim 2022).
In the early stages of L2 acquisition, learners heavily rely on a few basic VACs such as the NP-V or NP-V-NP constructions (Ellis 2006(Ellis , 2013. These constructions express intransitive and transitive events, which correspond to basic human experience (Goldberg 1995), using simple structural configurations. More complex VACs such as the NP-V-NP-NP and NP-V-NP-AP constructions tend to emerge at the later stages of L2 acquisition (Kim and Sung 2019;Song and Sung 2017). These VACs have complex syntactic and semantic structures and require L2 learners to integrate a variety of linguistic information (Goldberg 1995;Jackendoff 1997).
The knowledge of simple and complex VACs is known to have formal and functional structures based on constructional information (Ellis and Ferreira-Junior 2009;Goldberg 1995Goldberg , 2006. This idea is best captured in the concept of hierarchical inheritance network, which explains that VACs are interconnected to one another by linguistically motivated inheritance links such that the learning of a VAC may influence the learning of other related VACs (Goldberg 1995(Goldberg , 2006. For example, the caused-motion construction (e.g., she rolled the ball down) is linked to the intransitive motion construction (e.g., the ball rolled down) via a subpart link because every constructional role of the intransitive motion construction (i.e., THEME and PATH) is included in the semantic frame of the caused-motion construction (i.e., AGENT, THEME, and PATH). This idea leads to the hypothesis that the learning of one motion construction may facilitate the learning of the other motion construction, and the hypothesis has been supported by empirical evidence from L2 research (Kim and Rah 2021;Sung 2018;Sung and Yang 2016). Therefore, an L2 learner's knowledge of VACs forms a structured inventory, and the expansion of L2 VAC repertoires should always involve structural reconfigurations of the inventory.
To sum up, L2 learners of English acquire VACs based on usage-based mechanisms such as entrenchment and abstraction and expand their repertoires of VACs as conventionalized form-meaning pairings as in the case of L1 acquisition (Sethuraman et al. 1997;Snyder 2001). Different VACs appear to emerge at different stages of L2 learning. For instance, simple VACs such as intransitives and monotransitives are among the earliest VACs in L2 development (e.g., Lee and Kim 2011), whereas complex VACs such as resultatives and causatives develop in later stages of L2 acquisition (Sung 2018;Sung and Kim 2022). The expanding repertoire of L2 VACs forms a structured inventory in which VACs are linked to one another based on constructional information.
However, L2 research of English VACs has a limited capacity for providing an entire course of acquisitional progress because previous studies have focused on a handful of VACs such as the passive construction (Jarvis et al. 2003), the transitive constructions (Choi and Sung 2020), V + that clause (Crossley and McNamara 2014), the locative constructions (Ellis and Ferreira-Junior 2009) and the resultative constructions (Kim and Sung 2019).
In that sense, recent studies (e.g., Kyle and Crossley 2017;Kyle et al. 2021;Römer 2019), which investigated how the VAC repertoires of L2 English learners change over time or across different levels of proficiency, appear to present new opportunities for future research of L2 VAC development. Using Kyle's (2016) NLP model for retrieving VACs from learner corpora, Römer (2019) identified the 10 most frequent VACs among L1 German learners of English at CEFR level A1, three of which (i.e., rank 1, 2, and 6) had the copula be as the main verb. Römer also highlighted major differences in frequent VACs between A1-and B2-level learners, such as B2-level learners' frequent use of modal verbs, and showed the expansion of L2 VAC repertoire by means of the increasing normalized VAC type frequencies from A1 through C1 levels. Similarly, Kyle and Crossley (2017) found that writers of higher-quality TOEFL essays tend to have larger VAC repertoires. On the other hand, Kyle et al. (2021) introduced a novel way of quantifying the VAC usage in L2 writing. They assigned each VAC with a frequency value based on the VAC's token frequency in the reference native corpus (i.e., written sections of COCA) and used the mean frequency value of all the VAC types in an L2 essay as the VAC frequency index of the essay. The VAC frequency index was used to examine if L2 learners first use higher-frequency VACs (e.g., verb + direct object) and gradually expand their VAC repertoires to include lowerfrequency VACs.
In line with these recent studies, the present study investigates how L2 learners expand their repertoires of VACs and how VACs emerge in the early or later stages of L2 acquisition to form a structured inventory. More specifically, it examines the use of 40 VAC types in L2 English writings produced by three proficiency groups (N = 390). The novelty of the present study lies in its focus on individual learners and individual VACs, which enables us to address the following research questions. RQ 1. Do Korean learners of higher English proficiency have larger VAC repertoires than those of lower proficiency? RQ 2. How do individual VACs expand among Korean learners of English at different proficiency levels? RQ 3. Does the expansion of L2 VACs show cluster effects?
The first research question asks if the recent findings of Römer (2019) and Kyle and Crossley (2017) are applicable to another L2 population, i.e., L1 Korean learners of L2 English. The other questions examine how individual VACs expand and cluster in the spectrum of L2 development.

Corpus
The data for the present study came from a corpus, and its proficiency was compiled for an independent study (Park 2017). The corpus consists of essays written by 390 learners of English whose L1 is Korean (203 college students and 187 high school students). About half of the college students were seniors, and the other half were sophomores and freshmen. The college students were pursuing various majors. Most of the high school students were in their second year (age 16). The average number of years studying English was 12.6 years (SD = 3.72).
The students wrote an essay for 30 min. Half of the students were asked to write an argumentative essay, and the other half a narrative essay. The topic of the argumentative essay was group-based assessments such as team projects and group presentations, whereas the topic of the narrative essay was a particularly good or bad teacher/professor one had.
After the writing task, the students took an English proficiency test. The test was in the form of a C-test with a maximum possible score of 42. The reliability of the test was estimated using Cronbach's alpha, which was 0.94. The students read three texts and filled in the words beginning with the given letters. The average score was 16.25 (range: 0-40). Based on the writers' proficiency test scores, the essays were divided into three groups. Those written by the participants who scored over 60% and below 30% were placed into the High (n = 94, M = 29.70, SD = 3.56) and the Low group (n = 153, M = 5.88, SD = 3.51), respectively. The rest were placed into the Mid group (n = 143, M = 18.51, SD = 3.61). Table 3 shows the distribution of essays and the mean C-test scores according to the writers' proficiency group and genre. The mean C-test scores increased across groups regardless of the genre. A factorial ANOVA confirmed a statistical main effect of Proficiency (F(2, 384) = 1,341.84, p < 0.001, η p 2 = 0.88). A post hoc Tukey HSD showed statistical differences between all three proficiency groups. However, neither a main effect of Genre (F(1, 384) = 0.51, p = 0.48, η p 2 = 0.00) nor the interaction effect between Proficiency and Genre (F(2, 384) = 0.02, p = 0.98, η p 2 = 0.00) was identified. The results show that the distribution of essays across proficiency groups was balanced for each genre.

VAC analysis
All instances of VACs in the corpus were identified and hand-coded. First, the essays were part-of-speech (POS) tagged by TagAnt (Anthony 2014a). Then the instances of finite verbs and the following arguments were retrieved by a concordance software, AntConc (Anthony 2014b). The list of concordance lines was pasted onto a Microsoft Excel worksheet for coding.
The coding procedures were as follows. First, the linear structure of each line was identified using the POS tags. Second, phrase structures were identified by grouping constituents together. Then, VAC codes were assigned. Based on the summaries of English sentence structures in corpus linguistics and construction grammar, the coding began with the list of 11 VAC types: (1) V, (2) V + obligatory adverbial, (3) V + subjective predicative, (4) V + direct object, (5) V + prepositional object, (6) V + indirect object + direct object, (7) V + direct object + prepositional object, (8) V + direct object + object predicative, (9) V + direct object + obligatory adverbial, (10) there construction, and (11) passive construction.
The coding process was iterative, as the set of verb-argument structures identified evolved through repeated coding and grouping. Cleft, extraposition, and ellipsis constructions as well as sub-types of several sentence structures emerged during this procedure. In the end, a total of 40 VAC types were identified (see Table 2 in Section 2.1). The coding was performed by the first author, and the corresponding author analyzed 10% of the data independently. The level of inter-coder reliability was found to be sufficient, as measured by agreement rate (0.90)

Research questions revisited and statistical analyses
The present study analyzed the VAC of every finite clause in L2 English writings across the three proficiency groups to investigate how L2 learners expand their repertoires of VACs. The research questions are revisited, as follows: RQ 1. Do Korean learners of higher English proficiency have larger VAC repertoires than those of lower proficiency? RQ 2. How do individual VACs expand among Korean learners of English at different proficiency levels?
RQ 3. Does the expansion of L2 VACs show cluster effects? Each research question was addressed by a set of statistical methods in the jamovi version 1.6 based on R packages (R Core Team 2020; The jamovi Project 2021). For the first question, we counted how many types of VACs were used by each learner (i.e., the type frequency of VACs) and conducted a one-way ANOVA to examine whether the mean type frequencies were significantly different among the three proficiency groups.
For the second research question, we analyzed how many learners used each VAC and conducted a series of Fisher exact tests (cf. Gries and Stefanowitsch 2004) to see whether the proportional distributions of the learners using each VAC were significantly different among the proficiency groups. For this, we inputted a 3-by-2 contingency table containing the numbers of (non-)users for a target VAC across the three groups (see Table 4).
For every significant distributional variance, a post hoc analysis was performed for two pairs of adjacent proficient groups (Low-Mid and Mid-High) using 2-by-2 contingency tables, at the adjusted α value of 0.025 by Bonferroni correction. Based on the outcomes, the VACs were categorized into five expansion patterns: (a) not significant, (b) significant only between Low and Mid, (c) significant only between Mid and High, (d) significant in both pairs (i.e., Low-Mid and Mid-High), and (e) generally significant but no significant pairs. Finally, we performed a hierarchical cluster analysis, which is increasingly employed in L2 acquisition research (Crowther et al. 2021), to examine cluster effects based on the assumption that the co-occurring VACs are the constituents of L2 knowledge at a certain stage (Laakso and Smith 2007). For example, low-level learners who used three types of VACs can be evaluated as having the three VACs in their L2 knowledge, whereas high-level learners who used the same three types as well as five other types of VACs can be evaluated as having the eight VACs in their L2 knowledge. Therefore, the co-occurrence information of VACs in L2 writings was compiled by calculating the number of writings that every possible pair of VACs cooccurred. We included the co-occurrence with oneself as the cluster analysis requires a complete data set, so the total of 1,444 pairs (the square of 38 VACs: cf. two of 40 VACs, Type 4.8 and 12, did not occur in the corpus and thus were excluded from the cluster analysis) were examined. Table 5 shows a small portion of the data (81 out of 1,444 pairs: 5.61%) for the hierarchical cluster analysis. It unveils several interesting patterns. For example, Type 3.7 (VC V-ing ) was used by 11 participants, and all of them used Type 3.1 (VC AdjP ).
The Ward2 method using the euclidean distance measure (Murtagh and Legendre 2014) was employed to create a dendrogram of hierarchical clusters where VACs with similar co-occurrence distributions were placed closer to one another. The identification of major clusters could be decided by either a threshold of the summarized distance or the number of clusters. We chose the latter and grouped three major clusters considering our data set consisted of the three proficiency groups. For each major cluster, the distance in the dendrogram was analyzed to discuss the similarities and clustering sequences of VACs. The alphabets (a∼f) are the numbers of learners for the combinatorial conditions. For example, (a) is the number of the learners in the Low group who used the target VAC (type ), whereas (d) is the number of the learners in the Low group who did not use the VAC. The sum of (a) and (d) is always the total number of learners in the Low group (=).
Expansion of L2 VAC repertoires 4 Results and discussion

VAC type frequencies across L2 proficiency groups
We analyzed how many types of VACs were used by the writers in the three proficiency groups. Notable differences were found between the L2 groups (see Table 6). The mode and mean type frequencies of VACs were higher in the more proficient groups, and the between-group differences were greater between the Low and Mid groups than between the Mid and High groups. Between the Low and Mid groups and between the Mid and High groups, the mode type frequencies increased by 4 and 1, and the mean type frequencies increased by 3.22 and 1.88, respectively. In every group, the mode and mean type frequencies were adjacent (e.g., 6 and 6.54 in the Low group), with no integer intervening between the two. Thus, as seen in Figure 1, the proportions of the participants by type frequency peaked around the vertical lines of the mean value in all groups. The mode is the VAC type frequency information that appears most often in each group. The ANOVA test found that the mean type frequencies of VACs in the three groups were significantly different, F(2, 387) = 117.92, p < 0.001, η 2 = 0.379. Post hoc analyses using the Tukey HSD test indicated that the mean type frequency of VACs in the Low group was significantly lower than any of the other groups and that the mean frequency of VACs in the High group was significantly higher than any of the other groups (all ps < 0.001). Regarding the first research question of the present study, these results indicate that L2 English learners expand their repertoire of VACs as they become more proficient.
This finding is in line with previous studies which reported the relationship between L2 proficiency and constructional knowledge (Kim and Rah 2016;Kyle and Crossley 2017;Kyle et al. 2021;Römer 2019). For example, Kyle and Crossley (2017) showed that higher-quality essays written by L2 English learners with various L1 backgrounds had a larger VAC repertoire, and Römer (2019) found that German learners of English expand their VAC repertoire as they become more proficient. The present study expands the ongoing discussion about the expansion of L2 VAC repertoire to a new L2 population. More notably, it includes a theory-based list of VACs and reveals the significant increase in constructional diversity along with L2 proficiency. In the next section, we investigate the development of individual VACs based on the varying proportions of the participants using the VACs across the three proficiency groups.

Use of individual VACs across L2 groups
In order to examine the use of individual VACs by proficiency group, we examined how many participants used each VAC. Table 7 presents the proportions of user-participants for 10 VACs that were used by more than 30% of the total participants (N = 390).

Expansion of L2 VAC repertoires
Among these, eight VACs were used by more than a half of the total participants: 4.1 VO NP (e.g., I get a high score), 3.1 VC AdjP (e.g., he was humorous), 3.2 VC NP (e.g., She is a science teacher), 4.2 VO that-clause (e.g., I heard my teacher will leave our school), 1 V (e.g., Nobody would laugh), 11 passive (e.g., My group project was done by two people), 5 VO PP (e.g., they can contribute to the group differently), and 4.5 VO to V (e.g., I want to be a teacher) (listed in the order of proportion). These VACs were used by a majority of the Mid and the High groups, with two additional VACs-namely, therestructure and VL-being used by a majority of the High group. However, three of the above-mentioned eight popular VACs (i.e., passive, VO PP , VO to V ) were not used by a majority of the Low group, which may imply these three VACs develop at later stages of L2 development.
A closer look at the results for all 40 individual VACs revealed that the proportions of participants generally increased along with the three proficiency levels.
To assess the increase of the user-participant proportions statistically, we conducted a series of Fisher exact tests for every VAC using 3 × 2 contingency tables based on three proficiency levels and two usage patterns (i.e., use versus non-use) of the target VAC (cf. Table 3, Section 3.3). We found that the increases in the proportion of the user-participants were statistically significant for 25 VACs, and these VACs were further examined by post hoc pairwise analyses between the adjacent levels (i.e., Low-Mid; Mid-High) at the adjusted a level of 0.025. The results are summarized in Table 8 (for the exact by-group proportions of the participants using each VAC, see the Appendix). We found four distinctive patterns for the 25 VACs with statistical significance. First, 14 VACs had significant increases only between Low and Mid, such as Type 4.1 VO NP (p < 0.001) and Type 3.1 VC AdjP (p < 0.001). Second, three VACs, i.e., Type 3.3 VC CP , 4.6 VO V-ing , and 8.7 VO NP C V-ing , had significant increases only between Mid and High (all ps < 0.025). Third, four VACs, i.e., Type 3.5 VC to V , Type 5 VO PP , Type 4.5 VO to V , and Type 13 extraposition, were found to have significant increases both between Low and Mid and between Mid and High (all ps < 0.025). Finally, the rest four VACs were found to have no significant increases between any pair of adjacent proficiency groups (all ps > 0.05).
These four distributional patterns of participants across the proficiency levels imply that the major expansion of individual VACs may occur at different stages of L2 learning. The first pattern was that the proportion of participants using 14 VACs significantly increased only between the Low and Mid groups, and this may indicate that the major development of these VACs occurs at the early stages of L2 learning. Interestingly, these VACs may not show a meaningful increase in the later stages of L2 learning, regardless of the popularity of individual VACs. For example, Type 3.2, 4.1, and 4.2, all of which were used by over 80% of the participants in the Mid group, may be understood to have achieved a certain level of usage and thus have little room for further expansion at the later stages of L2 learning (i.e., ceiling effect). In contrast, Type 4.4, 6.5, 8.2, and 14 were used by less than 10% of the participants in the Mid group; however, these VACs did not show a significant increase for the High group despite the plenty room for expansion.
The second pattern regarding Type 3.3, 4.6, and 8.7 may claim that the expansion of certain VACs is delayed until the later stages of L2 learning. This claim is also supported by the observation that these three VACs were used by small portions of the Low group (9.8%, 3.3%, and 0%, respectively) and the Mid group (14.7%, 4.9%, and 0.7%).
The third pattern was that four VACs were used by the significantly increasing numbers of participants at both phases (i.e., Low-Mid and Mid-High). This may imply that these four VACs show notable development at multiple stages of L2 acquisition. Meanwhile, it should be noted that two of the three VACs (i.e., Type 5 and 4.5) were used by the majority in the High group (both 76.6%), whereas the other two VACs (i.e., Type 13 and 3.5) were used by smaller portions of the High group (35.1% and 25.5%). Thus, the notable increase of a VAC throughout L2 proficiency profile may not guarantee its full expansion, as in the case of Type 13 and 3.5. It is also likely that the use of the two VACs might expand among the learners who are more proficient than the High-group learners in the present study.
Lastly, we found that four VACs (Type 6.1, 6.3, 8.3, and 9) showed significant changes among the three groups, but not for the pairs of adjacent proficiency levels. In other words, these four VACs should be understood to gradually develop along with general L2 development.
It may be noteworthy that one of the 13 VACs that showed no significant difference among the L2 groups was Type 3.1 VC AdjP (e.g. he is happy), which was the second most popular VAC among the participants. This VAC was used by over 90% of the participants in every group. Therefore, it can be argued that the VAC was successfully acquired and productively used at the initial stages of L2 acquisition.

Cluster effects in VAC expansion
The co-occurrence information of VACs in all the texts of the L2 corpus was summarized into a dendrogram output of the hierarchical cluster analysis (see Figure 2). Considering the number of the proficiency groups, three clusters-labeled A, B, and C -were distinguished by the Ward2 criterion value. The most significant correlation was found at a sub-cluster in Cluster A between Type 3.1 (VC AdjP ) and 4.1 (VO NP ), as indicated by their distance value being the closest to zero in Figure 2. The two VACs were very similar in their usage. Both VACs were the most popular ones as over 90% of the participants in every proficiency group used the VACs: Type 3.1 was used by 366 participants and Type 4.1 by 379 participants (see Table 5 above). In addition, 356 participants (91.3%) used both of the VACs in their essays. Based on this usage information, the likelihood that a Korean learner of English who uses VO NP will use VC AdjP is 97.26%, and the likelihood of the inverse case is 93.93%.
The other sub-cluster in Cluster A (i.e., among Type 1, Type 3.2, and Type 4.2) also showed highly frequent co-occurrence in L2 essays. For instance, Type 1 (V) was used by 285 participants, and 276 (96.84%) of them used either Type 3.2 (VC AdjP ) or Type 4.2 (VO that-clause ), and 186 participants (47.69% of the total participants) used all the three constructions in their writings.
Most of the other popular VACs were observed in Cluster B, which appears to have two sub-clusters (see Figure 2). The first sub-cluster consisted of Type 4.5 (VO toV ), 5 (VO PP ), and 11 (passive). These VACs showed notable similarities. First, they are all related to the semantic concept of transitivity. Second, they have a nonnominal element in the postverbal region such as phases beginning with to (e.g., … want to … )., at (e.g., … looked at … ), and by (e.g., … was done by … ). Finally, they were used by fifty-some percent of the learners: 55.38% (Type 11), 54.87% (Type 5), and 52.82% (Type 4.5). On the other hand, the second sub-cluster in Cluster B had Type 2 (VL) and 6.1 (VO NP O NP ). The two VACs showed significant increases of userparticipants between the Low and Mid groups, reaching over 30% of the learners in the Mid group, but no significant differences between the Mid and High groups.
It seems that VACs popular among the learners belonged to Cluster A or B, except Type 10 (there-structure), which was used by 144 learners (36.9%: 9th rank in popularity). Type 10 was plotted at the leftmost corner of Cluster C in Figure 2, which indicates that its usage pattern is dissimilar to other popular VACs in Cluster A and B.
In Cluster C, the greatest similarity, based on the distance, was found between Type 6.4 (VO NP O wh-to V ) and 8.7 (8.7 VO NP C V-ing ), which were the two least popular VACs among the learners: each was used by only 6 and 3 learners, respectively. Likewise, most of the sub-clusters in Cluster C were composed of similarly less popular VACs, except the leftmost sub-cluster of six VACs (Type 10, 13, 3.3, 4.3, 7, and 8.5). The mean number of user-participants for these VACs was 86.8 (22.26% of the total participants: Min = 70; Max = 144). Except for these six VACs, all the VACs in Cluster C were used by less than 15% of the learners, with the mean proportion of user-participants being 5.8%.
The results of the hierarchical cluster analysis allowed us to identify three meaningful cluster effects among the 11 most popular VACs, each of which was used by over a quarter of the participants. First, the five VACs in Cluster A were distinguished from the other VACs in their popularity among the Low group. Each of the five VACs was used by a majority of the Low group with the mean proportion being 75.8% (Min = 62.7%; Max = 93.5%). Considering that any other VAC was used by less than 40% of the Low group, the five VACs in Cluster A appear to be a major linguistic resource from the early stage of L2 learning. Second, we found notable similarities among the five VACs in Cluster B. These VACs shared syntactico-semantic features such as transitivity and prepositional elements and marked the significant increases of userparticipants between the Low and Mid groups. Thus, the cluster effect may indicate that the intermediate-level learners acquired the syntactico-semantic features and productively used these VACs in writing. Finally, we found that Type 10 (there-structure) was not clustered with other popular VACs but located at the leftmost corner of Cluster C. The dissimilarity between Type 10 and other popular VACs may be attributed to its unique characteristics: Type 10 has a non-nominal expression (i.e., there) in the canonical slot for the subject and deliver the sense of existence (Biber et al. 1999).

Conclusions
We have found that L2 learners do expand their repertoires of VACs in writing as they become more proficient. In other words, higher-level learners use a greater variety of VACs than lower-level learners. This finding, as well as similar observations in Kyle and Crossley (2017) and Römer (2019), may suggest that L2 VAC repertoire should be considered an important indicator of L2 writing proficiency in terms of grammar range (Park 2017). One may want to test whether the repertoire or range of VACs predicts L2 proficiency better than other types of grammar range such as tense systems and subordination patterns.
We have also found that the general expansion of VACs appears to be comprised of distinctive patterns of individual VACs expanding at different stages of L2 acquisition. Some VACs such as VO NP and VC AdjP may expand at earlier stages whereas other VACs such as VO V-ing and VO NP C V-ing may expand at later stages. Given that L2 acquisition is primarily driven by input (Crossley et al. 2016;Godfroid 2016), the input frequencies of VACs may have affected the timings of acquisition: frequent VACs are likely to be acquired early. In addition, the input at early stages of L2 acquisition may be qualitatively and quantitatively different from that at late stages of L2 acquisition. For example, a certain VAC is particularly frequent in early input from textbooks while another VAC appears only in late input. Such variations in the use of VACs between early and late input may explain why different VACs expand at different stages of L2 acquisition.
These varying expansion patterns have been found to show cluster effects related to usage information and syntactico-semantic features. There were clusters of two, three, or five VACs, and these clusters hold popular VACs in L2 writing. This seems to indicate that the expansion of L2 VAC repertoire occurs by a set of related VACs, not by an isolated single VAC. In fact, this idea concurs with Goldberg's (1995Goldberg's ( , 2006 discussion of hierarchical inheritance networks in that VACs are interconnected to form a structured inventory of linguistic knowledge. On the other hand, some VACs appear to be seldom used by advanced learners, let alone lower-level learners. This may indicate that input alone is not sufficient for the learning of these VACs. Therefore, instructional treatments such as input enhancement or explicit instruction should be administered to facilitate L2 acquisition of these VACs.
Finally, this paper has several limitations that should be addressed in future research. First, it investigated L2 learners' use of VACs in narrative and argumentative writing, so the findings of this paper need to be examined in comparison with L1 speakers' use of VACS in the same genres of writing. Second, this paper developed the model of 40 VAC types based on linguistic theories such as constructional approaches and descriptive grammar, but this model has not been proven better than other models with varying level specifications. Future studies should develop multiple models of VACs based on different theoretical frameworks and compare the relative reliabilities of the models for the task of analyzing L2 VACs.
Appendix: Proportions of user-participants for 38 VACs and Fisher exact test (a part of this information is provided in Park (2022)