KEY ASPECTS OF BILINGUAL LANGUAGE EXPERIENCE

Language development requires language input, that is, direct evidence relevant to the acquisition of particular aspects of language. Language acquisition theories differ in what constitutes necessary input, and modeling the availability of usable input in the language environment is not straightforward (see Carroll, Reference Carroll2017 for discussion). It is, however, reasonable to assume that language exposure is a reliable proxy for language input. Indeed, variation in language exposure has been shown to affect many aspects of language development in bilingual children (see e.g., Grüter & Paradis, Reference Grüter and Paradis2014; Hoff et al., Reference Hoff, Core, Place, Rumiche, Señor and Parra2012; Paradis, Reference Paradis2011; Paradis et al., Reference Paradis, Rusk, Duncan and Govindarajan2017; Place & Hoff, Reference Place and Hoff2011; Thordardottir, Reference Thordardottir2011; Thordardottir, Rothenberg, Rivard, & Naves, Reference Thordardottir, Rothenberg, Rivard and Naves2006; Unsworth, Reference Unsworth2013b, Reference Unsworth, Nicoladis and Montanari2017; Unsworth, Persson, Prins, & De Bot, Reference Unsworth, Persson, Prins and De Bot2014).

Bilingual children’s language exposure is by its very nature extremely varied in terms of relative quantity and context (De Houwer, Reference De Houwer2007). Some children are exposed to both languages at birth or thereafter, others are exposed to a second language later in childhood (De Houwer, Reference De Houwer2011; Meisel, Reference Meisel2009). Relative exposure to the two languages may also vary over time, leading to different amounts of cumulative exposure to each over the course of their lives (Gutiérrez-Clellen & Kreiter, Reference Gutiérrez-Clellen and Kreiter2003; Thordardottir, Reference Thordardottir2011; Unsworth, Reference Unsworth2013b). Given the heterogeneity of the bilingual language experience, it is now recognized that bilingualism should be conceptualized as a continuous variable rather than a categorical one (Kaushanskaya & Prior, Reference Kaushanskaya and Prior2015; Luk, Reference Luk2015).

Studies that have investigated the relationship between language exposure and language proficiency in bilingual children have typically focused on a snapshot of the child’s language experience at the time of assessment (De Houwer, Reference De Houwer2009; Jia & Aaronson, Reference Jia and Aaronson2003; Paradis, Reference Paradis2011). Recently, the notion of cumulative exposure has gained traction in the context of a more holistic approach to the child’s language history (Gutiérrez-Clellen & Kreiter, Reference Gutiérrez-Clellen and Kreiter2003; Unsworth, Reference Unsworth2013b). Indeed, proficiency at time x, however it is measured, is the result of the child’s language experience over time and not just at time x. This is particularly relevant in the case of sequential bilingual children who may experience rather abrupt changes in the relative exposure to their two languages when they start formal childcare placements or school.

The impact of bilingual children’s language use on proficiency has hitherto received comparatively less attention (but see Bohman, Bedore, Peña, Mendez-Perez, & Gillam, Reference Bohman, Bedore, Peña, Mendez-Perez and Gillam2010; Ribot, Hoff, & Burridge, Reference Ribot, Hoff and Burridge2017; Unsworth, Reference Unsworth, Silva-Corvalán and Treffers-Daller2015). Research with adult bilinguals has shown that the opportunity to use the language is an important factor in determining the degree of bilingualism (Jia, Aaronson, & Wu, Reference Jia, Aaronson and Wu2002). There is reason to believe that, for children too, the extent to which they use a language will be a determinant of the proficiency attained in that language. Some studies with child bilinguals explicitly include a measure of language use, based on children’s experience at the time of testing (Bedore et al., Reference Bedore, Peña, Summers, Boerger, Resendiz, Greene, Bohman and Gillam2012; Bohman et al., Reference Bohman, Bedore, Peña, Mendez-Perez and Gillam2010; Goldstein, Bunta, Lange, Rodriguez, & Burrows, Reference Goldstein, Bunta, Lange, Rodriguez and Burrows2010; Gutiérrez-Clellen & Kreiter, Reference Gutiérrez-Clellen and Kreiter2003). Similarly to language exposure, language use is likely to change over time as children’s circumstances and their opportunities to use their two languages vary.

This study investigates how to best predict language proficiency based on language experience, by comparing different ways of operationalizing language experience as a continuous measure. First, we ask if a combined measure of cumulative language exposure and use predicts (various aspects of) proficiency in the school/societal language. Then we compare that measure to alternative measures (cumulative exposure only, and current measures of exposure and use) to ascertain which is the most informative predictor in the population of interest.

COGNITIVE AND SOCIAL DETERMINANTS OF LANGUAGE PROFICIENCY

Memory skills, both short-term memory (STM) and working memory (WM) have been shown to be positively associated with language skills in monolingual children (Baddeley, Gathercole, & Papagno, Reference Baddeley, Gathercole and Papagno1998). STM is strongly associated with word learning skills (Avons, Wragg, Cupples Wragg, & Lovegrove, Reference Avons, Wragg, Cupples Wragg and Lovegrove1998; Majerus, Poncelet, Greffe, & Van der Linden, Reference Majerus, Poncelet, Greffe and Van der Linden2006), but the extent to which it is predictive of other language skills is less clear. Some studies have found a positive relationship between STM and the comprehension of syntactically complex sentences in adults (Lauro, Reis, Cohen, Cecchetto, & Papagno, Reference Lauro, Reis, Cohen, Cecchetto and Papagno2010; Papagno, Cecchetto, Reati, & Bello, Reference Papagno, Cecchetto, Reati and Bello2007), others have failed to find such a direct link in children, in spite of a strong effect of STM on sentence repetition (SRep) abilities (Willis & Gathercole, Reference Willis and Gathercole2001). WM, however, is more clearly associated with metalinguistic abilities (McDonald, Reference McDonald2008) and sentence comprehension (Montgomery, Reference Montgomery1995; Montgomery, Magimairaj, & O’Malley, Reference Montgomery, Magimairaj and O’Malley2008), particularly the comprehension of structurally complex sentences (see Kidd, Reference Kidd2013) for a recent review of the role of WM in children’s sentence comprehension.

As for children who are exposed to more than one language, Thorn and Gathercole (Reference Thorn and Gathercole1999) have shown a positive relationship between the ability to recall digits and nonwords in two STM tasks and the receptive and expressive vocabulary skills of English-French bilingual between the ages of 4 and 8 in their two languages. STM as measured by nonword repetition has been shown to be more weakly associated with amount of exposure than vocabulary skills are (Thordardottir & Brandeker, Reference Thordardottir and Brandeker2013). To date very few studies have simultaneously investigated STM and WM in bilingual school-age children, and their relationship with lexical and grammatical skills. Engel de Abreu, Gathercole, and Martin (Reference Engel de Abreu, Gathercole and Martin2011) explored this relationship in a group of Luxembourgish-German bilinguals between 5 and 6 years of age. STM was found to be predictive of vocabulary knowledge independently of WM, suggesting a highly specific association. WM and fluid intelligence (jointly interpreted as the capacity for controlled processing) were found to predict higher-order language processing (e.g., the understanding of syntactic contrasts). Compatible results were obtained by Verhagen and Leseman (Reference Verhagen and Leseman2016), based on the comparison between a group of monolingual Dutch 5 year olds and an age-matched group of Turkish-Dutch bilingual children exposed to both languages naturalistically. The results of a confirmatory factor analysis showed that verbal STM predicted receptive vocabulary skills in Dutch, and that both verbal STM and verbal WM were predictive of grammar skills after controlling for vocabulary and SES.

While STM and WM can be considered child-internal determinants of language acquisition, a child-external factor that has been shown to be of great significance is the SES of the child, indirectly measured using parental information. SES has been variously conceptualized in the literature in terms of household income, parental occupation, or parental (often maternal) education. Given the typically high correlation between these variables, studies have often used them interchangeably.

The relative contribution of SES to bilingual children’s language skills is not easy to identify. As highlighted by Hoff (Reference Hoff2013), both bilingualism and SES have an impact on language development, and not enough research has yet considered the relative contribution of amount of language exposure and SES to disentangle these two factors. However, those studies that have included bilingual children from different SES backgrounds (see the following text) have typically found that SES can be an independent predictor of language proficiency.

To date, four studies have simultaneously evaluated the effect of SES and bilingualism on children’s different linguistic and cognitive domains. Calvo and Bialystok (Reference Calvo and Bialystok2014) focused on receptive vocabulary, nonverbal intelligence, and executive function tasks in a linguistically heterogeneous group of 6 to 7 year olds in Canada with 26 different home languages (HLs). Gathercole, Kennedy, and Môn Thomas (Reference Gathercole, Kennedy and Môn Thomas2016) assessed vocabulary, grammar, and cognitive skills in Welsh-English bilinguals in Wales. Chiat and Polišenská (Reference Chiat and Polišenská2016) included Turkish-English and Spanish-English bilinguals in England and included measures of nonword repetition and vocabulary. Most recently Meir and Armon-Lotem (Reference Meir and Armon-Lotem2017) addressed the independent and combined effect of SES and bilingualism in Russian-Hebrew bilinguals in Israel on expressive vocabulary and verbal STM.

The results for vocabulary measures are consistent across the four studies showing significant effects of SES and bilingualism, with bilingual children and children from lower SES performing more poorly. A lack of interaction between the two factors indicates that SES affects monolingual and bilingual children similarly.

Performance on a test of nonverbal intelligence in the Calvo and Bialystok (Reference Calvo and Bialystok2014) study was not affected by either SES or bilingualism, while executive functioning was adversely affected by low SES, but positively affected by bilingualism. In the study by Gathercole et al. (Reference Gathercole, Kennedy and Môn Thomas2016), SES, but not bilingualism, was a significant predictor of performance on cognitive measures.

As for memory, Chiat and Polišenská (Reference Chiat and Polišenská2016) report that neither SES nor bilingualism affected children’s performance on their nonword repetition tasks. By contrast, Meir and Armon-Lotem (Reference Meir and Armon-Lotem2017) found that performance on a forward digit task was only affected by SES but not by bilingualism, even after controlling for vocabulary. For a nonword repetition task neither SES nor bilingualism had an effect, with the exception of a negative effect of bilingualism on a subset of nonwordlike stimuli that disappeared after controlling for vocabulary. In a SRep task, there was a significant effect both of SES and bilingualism, but the latter was nonsignificant after controlling for vocabulary.

The risk conferred by low SES is not induced by poverty, but by poverty of the child’s environment, which translates into lower quantity and quality of the language addressed to the child. Factors such as high lexical diversity, syntactic complexity, and the frequency of decontextualized language use are all features of good quality input that facilitate the acquisition process, and they tend to be less well represented in parents from lower SES backgrounds (Hoff, Reference Hoff2006; Huttenlocher, Waterfall, Vasilyeva, & Vevea, Reference Huttenlocher, Waterfall, Vasilyeva and Vevea2010; Rowe, Reference Rowe2012).

This study will probe the impact of SES on language proficiency in two ways. Assuming SES is a proxy for the richness of the language environment, we will investigate how it interacts with the amount of language exposure experienced by the child. Also, given that both SES and cognitive abilities are predictive of performance in language proficiency tasks, and that SES predicts many aspects of cognitive development, we will investigate the extent to which SES predicts language proficiency over and above the effect of cognitive predictors.

BILINGUALISM PROFILES

It is not uncommon to be faced with the question of “how bilingual” a child is. Parents of bilingual children who understand the home language but answer back in the societal language ask themselves if their child is “truly bilingual.” Teachers wonder which of the bilingual children in their care may need additional support with the school language. Researchers seeking to assess the impact of bilingualism on other aspects of a child’s development need to consider whether the children in their study are “bilingual enough” for an effect to be detectable—or may have as a primary question what the relevant threshold is.

Two questions are of particular interest. The first one relates to functional thresholds within the bilingualism continuum. The second one relates to language dominance more generally.

SENTENCE REPETITION

The SRep test can be analyzed in different ways, depending on the criterion against which the children’s utterances are evaluated (Marinis & Armon-Lotem, Reference Marinis, Armon-Lotem, Armon-Lotem, de Jong and Meir2015):

1. (7) a. Exact repetition of the target sentence (Full Accuracy)

2. b. Grammatical production of the targeted structure (Target Accuracy)

3. c. Grammaticality of the sentence produced (whether or not it fully matches the target) (Grammaticality)

4. d. Types of mismatches (i.e., omissions, substitutions or additions) compared with the target sentence) in the following categories:

   1. (i) Lexical

   2. (ii) Inflectional

   3. (iii) Functional

The distribution of raw scores according to the first three types of analysis is plotted in Figure 4. Utterances containing unintelligible material were excluded (total: 208, i.e., 4% of the data).

FIGURE 4.

Pirate plots showing the distribution of the raw SRep test scores (according to three different scoring methods). Each plot shows group mean (thick line), confidence intervals (lighter area around the mean), 10% and 90% quantiles (whiskers), and individual scores.

SENTENCE COMPREHENSION

Although not designed for bilingual populations, the CELF is frequently used to evaluate the proficiency of bilingual children (e.g., Barac & Bialystok, Reference Barac and Bialystok2012; Paradis, Crago, Genesee, & Rice, Reference Paradis, Crago, Genesee and Rice2003).

The distribution of mean scores in the CELF Sentence Structure task is shown in Figure 5.

FIGURE 5.

Pirate plot showing individual mean CELF scores, showing group mean (thick line), confidence intervals (lighter area around the mean), and 10% and 90% quantiles (whiskers).

LEXICAL-SEMANTICS

We analyze the lexical-semantic tests of the DELV separately from the discourse-semantic test, as they tap into different domains of language competence: the lexical-semantic tests tap into the organization of the lexicon, and the discourse-semantic tests taps into the child’s ability to express contrasts in information status through the appropriate use of determiners.

The distribution of raw scores on the lexical-semantic tests is plotted in Figure 6.

FIGURE 6.

Distribution of the scores on the DELV subtests, in bilingual and monolingual children (showing mean, 95% CI, and full range).

DISCOURSE-SEMANTICS

The distribution of the mean scores for the articles test of the DELV are plotted in Figure 7.

FIGURE 7.

Pirate plots for individual mean scores in the articles test, showing mean (thick line), confidence intervals (lighter area around the mean), and 10% and 90% quantiles (whiskers).

SENTENCE REPETITION

Using the methodology described in the preceding text, we fitted a mixed-effect model to bilingual children’s accuracy data. The response variable was the correct repetition of the target structure on each it the SRep test items (see [7-b]). It indexes children’s ability to produce structures of increasing grammatical complexity (listed in Table 3) independently of their ability to remember exactly all the words in the sentence.^{Footnote 16}

Table 7 summarizes the effect of the significant predictors of accuracy of the production of the target structure by the bilingual children (expressed in our model as the probability of reproducing that structure correctly), as per the optimal model. The estimates in the model summary report the likelihood of a correct response^{Footnote 17} for each predictor, compared with the likelihood observed at the intercept. As all the continuous predictors were transformed into z-scores, the intercept is based on the combination of the mean values: the average score for SES, memory, age, and BPI characterizing the bilingual group. In terms of categorical variables, the intercept is calibrated for SRep Level 1 and Gender: Female.

TABLE 7.

Fixed effects of the optimal Generalized Linear Mixed Model of accurate repetition of target structures in the SRep test by bilingual children. Random effects: participant, item

As seen in the model summary, the BPI is the strongest child-related predictor (β = ‒.7026, p = .0008). Children’s ability to reproduce the target structure is negatively correlated with the amount of experience in their HL: a higher BPI score decreases the probability of a correct response significantly. Children’s performance was also predicted by their SES (β = .5842, p = .002) and their STM (β = .5556, p = .006). The effect of age (over and above that of STM) also approached significance (β = .4082, p = .069). Structural complexity (SRep Level) had a significant impact on performance. The more complex the targeted structure, the poorer the performance: even Level 2 yielded significantly poorer results than Level 1 (β = ‒.9938, p = .041).

There was no interaction between structural complexity level and children’s amount of bilingual experience (β = .13, p = .45). WM had no significant effect β = ‒.05, p = .77). The random effects for participant and item had a variance of 2.55 and 1.12, respectively.

The same predictors were found to be significant in the other overall accuracy analyses of the bilingual children’s performance in the SRep test (not reported here). The proportion of variance captured by STM compared with the other predictors is greater in the Full Accuracy analysis. In the Grammaticality analysis, the level of difficulty (SRep Level) is a lower-ranking predictor (which is to be expected as this analysis does not penalize avoidance strategies), with no significant difference between complexity levels 1 and 2. The relative ranking of predictors by decreasing order of importance in each model are listed in (9) (where SRep Level stands for the items’ level of difficulty):

1. (9) a. Full Accuracy (7-a):

   • STM > SRep Level > SES > BPI

2. b. Grammaticality (7-c):

   • STM > SES > BPI > SRep Level

Error analysis was performed according to the domain affected (functional, inflectional, lexical). Errors are illustrated in the following text for the functional domain (10), the inflectional domain (11), and the lexical domain (12), respectively.

1. (10) Target: He will feed the cow before he waters the plants.

He will feed the cow when he waters the plants. (Functional error)

1. (11) Target: The children were taken to the office.

The children taked to the office. (Inflectional error)

1. (12) Target: The mum bakes the meal that the children are eating.

The mum makes food for the children. (Lexical errors)

Three accuracy scores were obtained for each sentence by dividing the number of errors of each type from the total number of relevant words (Marinis et al., Reference Marinis, Chiat, Armon-Lotem, Gibbons and Gipps2010).

We tested the significance of the same predictors as in the preceding analyses. The full models are reported in the Online Supplement. The relative importance of predictors (and their statistical significance) differs across error types, as shown in (13) (nonsignificant predictors are omitted).

1. (13) Functional: SRep Level > BPI > STM > SES

Inflectional: SRep Level > STM

Lexical: SRep Level = STM > SES > BPI

Neither the BPI nor SES turn out to be significant predictors of inflectional errors. The relative importance of the BPI is highest in the model predicting functional errors. The relative importance of STM is highest in the model predicting lexical errors.

SENTENCE COMPREHENSION

A linear regression analysis of the CELF Sentence Structure data reveals that bilingual children’s scaled scores were not predicted by children’s BPI (β = ‒.18, p = .58), nor their SES (β = .51, p = .09), or their STM (β = .14, p = .67). Instead, the strongest predictors were WM (β = .58, p = .03) and cognitive flexibility, (β = 1.36, p = .00001).

In De Cat (2019), I argue that the CELF Sentence Structure test does not probe children’s ability to deal with linguistic aspects of structural complexity, as these are confounded with cognitive complexity in the task. The lack of significance of English exposure (as the counterpart of HL exposure) as a predictor is most likely due to that confound. It is unclear whether the CELF Sentence Structure scores can be interpreted as a reliable index of language proficiency. We will therefore not consider them any further in this article.

LEXICAL-SEMANTICS

Given the different distribution of scores across tests in the bilingual group (Welch’s F (3, 190.795) = 31.0695, p < .0001), we did not use a composite score in the first instance. We carried out a MANOVA to identify the significant predictors of performance in the four DELV subtests (in one go) without inflating the Type 1 error rate.

Using Pillai’s trace, a statistically significant MANOVA effect on the performance of bilingual children was observed for the BPI (V = .2, F(4, 77) = 4.7, p = .002), SES (V = .18, F(4, 77) = 4.23, p = .004), STM (V = .18, F(4, 77) = 4.36, p = .003), and cognitive flexibility (V = .23, F(4, 77) = 5.77, p = .0004). Age approached significance (V = .11, F(4, 77) = 2.38, p = .0586), and WM was not significant (V = .063, F(4, 76) = 1.28, p = .28).

After the MANOVA had identified the significant predictors, linear regression models were fitted to predict the accuracy score on each of the DELV subtests. The BPI was a significant predictor of poorer performance in the Preposition Contrast task (t (82) = -2.63, p = .01) and the Real Verb Mapping task (t (82) = -2.39, p = .02), and approached significance in the Verb Contrast task (t (82) = -1.80, p = .07). It was not significant in the Novel Verb Mapping task (t (82) = -0.81, p = .42). SES significantly predicted performance in the Verb Contrast task (t (82) = 2.57, p = .01), and approached significance in the Real Verb Mapping task (t (82) = 1.96, p = .05). It was not significant in the Preposition Contrast task (t (82) = 1.47, p = .14) nor in the Novel Verb Mapping task (t (82) = 1.37, p = .17). STM significantly predicted performance in the Real Verb Mapping task (t (82) = 4.26, p < 0.0001) and the Novel Verb Mapping task (t (82) = 3.32, p = .001). It approached significance in the Verb Contrast task (t (82) = 2.56, p = .1), and was not a significant predictor in the Preposition Contrast task (t (82) = 1.47, p = .14). This is summarized in Table 8.

TABLE 8.

Predictor significance in the DELV lexical-semantic tests (* indicates significance; . indicates a trend)

If the four scores are combined into a composite score, the following factors are found to predict bilingual children’s performance (in order of importance), as summarized in Table 9: STM, BPI, and WM. SES and Age are not significant.

TABLE 9.

Coefficients of the optimal linear regression model fitted to bilingual children composite score in the DELV lexical-semantic tests

DISCOURSE-SEMANTICS

Analysis was performed by fitting a linear regression model to the children’s overall score. Performance was negatively correlated with the BPI (β = ‒.0485, p = .012). This was more than compensated by SES, which was a stronger predictor of performance in the bilingual children (β = .0549, p = .0074). The following factors proved nonsignificant predictors of the bilingual children’s performance: age (β = .0306, p = .12), STM (β = .0125, p = .53), and WM (β = .029, p = .14). Table 10 reports the summary of the optimal model.

TABLE 10.

Coefficients of the optimal Linear Regression Model predicting bilingual children’s accuracy score in the discourse semantics task

QUESTION 2.1: COST-BENEFIT ANALYSIS: WHICH LANGUAGE EXPERIENCE MEASURE TO USE AS A PREDICTOR?

The BPI indexes the cumulative amount of exposure and use of the HL, and it is strongly correlated with alternative measures of language exposure (see Figure 8). Our rationale in choosing the BPI as predictor over these alternative measures was based on a number of considerations: (a) calibrating language experience on the HL makes it possible to include monolinguals in the continuum “naturally” (as they have had zero experience of a HL different to English); (b) encompassing language use (as well as exposure) yields a more precise measure, which in turn should increase the power of our analyses; and (c) focusing on cumulative experience further increases the accuracy of the measure, as it reflects the quantitative effect of sequential bilingualism.^{Footnote 18} It is, however, possible that the higher level of precision of the BPI does not afford a substantial benefit over a simpler measure. In this section, we compare the BPI with simpler, alternative measures of language experience: cumulative exposure, cumulative use, current exposure, and current use.

To determine the optimal language experience measure predicting SL proficiency, we exploited the method described in Burnham and Anderson (Reference Burnham and Anderson2003): an information-theoretic approach to inform model selection and multimodel inference. Choosing between alternative statistical models requires estimating which of them best approximates the “true” process underlying the phenomenon under study. If several models compete closely, the “true” process should be inferred by combining the information from these models. In this approach, both processes are informed by the Akaike weight associated with statistical models.

The Akaike weight of a model is based on the AIC, which was defined previously as an indicator of the trade-off between the accuracy and the complexity of a given model (i.e., a measure of the relative goodness of fit of the model to reality). When considering two nested alternative models (i.e., models that differ only in the presence or absence of one or more variables), the model with the lowest AIC should be chosen as the best model.

By contrast, when several models need to be compared, AIC weights are used—under the assumption that one of the models in the set is the optimal model. These models can be nested or nonnested (i.e., including alternative predictors). AIC weights, therefore, indicate the strength of the evidence in favor of a model in a particular set of competing models (Burnham and Anderson, Reference Burnham and Anderson2003). The model with the highest AIC weight is taken as the one that best approximates the “true” process underlying the phenomenon under study, and the other models are evaluated in relation to that optimal model. This evaluation is based on Delta values, which correspond to the difference in AIC between the best model in the set and a particular competitor model. The following rules of thumb are usually applied to decide which models need to be considered along with the best model:

1. (14) AIC weights interpretation Burnham and Anderson (Reference Burnham and Anderson2003)

2. a. A model with a Delta value within 1‒2 of the best model has substantial support in the data, and should be considered along with the best model.

3. b. A Delta value within only 4‒7 units of the best model has considerably less support.

4. c. A Delta value > 10 indicates that the worse model has virtually no support and can be omitted from further consideration.

This method can be used for variable selection, that is, to determine which predictor variable has the greatest influence, among a set of competitors (Burnham and Anderson, Reference Burnham and Anderson2003). In our case, it can be used to compare the BPI with alternative language experience predictors. This is done by summing the Akaike weights of variables across all the models where the variables occur. The competing variables are then ranked using these sums. The larger this sum of weights, the more important the variable.

Following the method explained in the preceding text, we created a set of alternative models with the following alternative measures of language experience:

1. (15) a. The BPI

2. b. Cumulative exposure the school language (English)

3. c. Current exposure to the school language (English)

4. d. Cumulative use the school language (English)

5. e. Current use of the school language (English)

As all the children in this sample were exposed to two languages only, SL measures and HL measures are equivalent from a statistical modeling perspective (albeit yielding opposite coefficients). Here we report on the measures calibrated on the SL (English).

Using the optimal model for the bilingual children’s SRep data (reported in Table 7), we replaced the BPI with each of the preceding predictors in turn (i.e., refitting the model four times, once per predictor other than the BPI). As the models differed only with respect to the language experience measure, the one with the best fit can be considered the one with the most reliable predictor of language proficiency. The results of the comparison are summarized in Table 11, ordered by model weight.

TABLE 11.

Model selection for the effect of alternative measures of language experience (listed in column 1) on bilingual children’s language proficiency (indexed by the SRep score) fit to 2,477 observations (i.e., total 2,468 degrees of freedom) with 3,105 null deviance. The weight indicates the probability that the model is the best one in the set. Delta is the AIC difference of a model compared with the best one.

There is a 37% probability that the model using Cumulative English Exposure as a predictor is the best in the set. When the difference in AIC between two models (dAIC or Delta) is < 2, it is reasonably safe to consider that both models have approximately equal weight in the data (Burnham and Anderson, Reference Burnham and Anderson2003). There is strong evidence (Delta = 1.30) for the need to take Cumulative English Use into account alongside Cumulative English Exposure—which is in effect what the BPI does. With a Delta value of .30, the BPI can be considered to be roughly as good a predictor of English-language proficiency as Cumulative Exposure.^{Footnote 19} It has a 32% likelihood of being the best model in the set—which is not far off the 37% likelihood of the model based on Cumulative English Exposure.

The answer to first part of Research Question 2 (as to whether a simpler measure of language experience might fare better than a complex measure) is that the BPI, as a combined measure of cumulative language exposure and use, is not more informative as a predictor of SL proficiency, compared with a simple measure of cumulative language exposure. As explained in the preceding text, the BPI can be interpreted as a measure of cumulative exposure to the HL, adjusted for HL use: two children with the same amount of Cumulative HL Exposure will have a different BPI if one of them is relatively passive in the HL (i.e., if s/he tends to answer back in English when addressed in the HL). However, the additional information encapsulated in the BPI (compared with a simple measure of cumulative language exposure) does not improve its predictive potential. This could be because language use does not have much of an effect over and above that of language exposure.

With respect to the cumulative-current comparison, cumulative measures are indeed more informative than current measures, as predictors of SL proficiency.

We now turn to the second part of Research Question 2, regarding the specific impact of language use as predictor of SL proficiency.

QUESTION 2.2: TEASING APART THE EFFECT OF EXPOSURE AND USE

If the amount of language use (estimated from the parental questionnaires) was perfectly correlated to the amount of language exposure, it would not be possible to disentangle their effect statistically as predictors of language proficiency. In the group under study, however, an imbalance between language use and exposure is observed: many children tended to be relatively “passive” in their HL, as shown in Figure 10. Passivity reflects the extent to which the child used their HL in relation to the extent they were exposed to it, and it can be calculated by dividing Cumulative HL Use by Cumulative HL Exposure. Children with the highest score (100%) are as active in their HL as they are exposed to it. Lower scores indicate relative passivity in the HL: the child uses that language less than they are exposed to it (0% indicating no output in the HL at all, which was the case for nine children). Importantly, a high score does not necessarily correlate with a high amount of HL exposure in our population sample: high usage is observed across the whole range of HL exposure.

FIGURE 10.

(Im)balance between cumulative use and cumulative exposure of the HL, ranging from an equal amount of both (100% active usage) to no use (total “passivity”).

Children who are relatively passive in their HL are (by implication) more active in their SL, as they answer back in English in some or all the contexts in which they are addressed in the HL. It is possible that this “extra” amount of English use confers a proficiency advantage in that language. This is what we investigate in the text that follows.

As explained in the “Methods of Analysis” section, it is not possible to include strongly correlated predictors in the same regression model, as is the case for our exposure and use measures. To remedy this problem, we derived a measure of the difference between Cumulative SL Exposure versus use (by subtracting Cumulative SL Exposure from Cumulative SL Use). This new measure, which we will call SL Difference, is significantly but only marginally correlated with Cumulative SL Exposure (r = ‒.19, p < .0001), which makes it possible to consider the two together in the same regression model.

We refitted the optimal model of the SRep accuracy data (by item), with Cumulative SL Exposure and SL Difference as language experience predictors. The effect of SL Difference was not significant (β = ‒.005, p = .84), and allowing for an interaction between Cumulative SL Exposure and SL Difference led to nonconvergence.

Given the lack of convergence with linear regression, we turned to a more powerful algorithm to investigate the relationship between SL exposure and use as predictors of SL proficiency.

The data was reanalyzed with a generalized additive mixed model (GAMM— Baayen, Vasishth, Kliegl, & Bates, Reference Baayen, Vasishth, Kliegl and Bates2017; Wood, Reference Wood2006) using the R-package “mgcv” (version 1.8-28). GAMMs are a variant of the linear models introduced in the preceding text. Nonlinear regression models operate according to the same broad principles as their linear variants, except that the regression line fitted through the scatterplot of observations can feature a certain amount of “wiggliness” instead of a straight line. The linear effects are included as parametric terms in the model (as previously mentioned), and the nonlinear effects are included as smooths.^{Footnote 20} The model has an in-built optimizer to avoid overfitting by allowing too much “wiggliness” in the smooths. In the model reported in the following text, the random effects were modeled as smooths. To probe the relationship (or lack thereof) between SL cumulative exposure and SL Difference, we allowed a nonlinear interaction of the two HL measures (Cumulative Exposure and HL Difference).

Allowing the nonlinear interaction of Cumulative SL Exposure and SL Difference did yield a significant improvement in model fit, compared with a nonlinear model without that interaction. The interaction between Cumulative SL Exposure and SL Difference reached a statistical significance (χ ^{Footnote 2} = 10.45, edf = 3, p = .015), suggesting a crossover effect of exposure and use affecting mainly children with a high amount of cumulative exposure to the SL.

To test the robustness of the modest significance level of the interaction between language exposure and use, we fitted an alternative model allowing our other main environmental predictor of interest (i.e., SES) to interact nonlinearly with language exposure.

This alternative model revealed a much more important nonlinear interaction at play in the SRep data, which renders the impact of SL passivity nonsignificant (even in interaction with cumulative SL exposure): the nonlinear interaction between SES and cumulative SL exposure turns out to be the strongest predictor of accuracy in the SRep test (χ ^{Footnote 2} = 30.69, edf = 3, p = .000001). Figure 11 shows that, at relatively low levels of cumulative exposure to the SL, SES does not confer an advantage in the SRep test; but at medium-to-high levels of cumulative SL exposure, accuracy in the SRep test is strongly correlated with SES.

FIGURE 11.

Nonlinear interaction between Cumulative SL Exposure and SES as predictors of bilingual children’s accuracy in the SRep task estimated through a GAMM. Average SRep performance corresponds to 0 on the color gradient.

SUMMARY

In answer to Research Question 2, we have demonstrated that cumulative exposure to the SL is the best predictor of proficiency in that language, both compared with current measures and compared with a combined measure of cumulative exposure and use. In attempting to tease apart the impact of language exposure and language use, we discovered that language use was not a robust predictor of SL proficiency. The marginally significant nonlinear interaction between language exposure and use was trumped by a very strong nonlinear interaction between language exposure and SES. Children with below-average exposure to the SL did not benefit from an SES advantage (in terms of proficiency score). But in children with above-average exposure to the SL, performance improved exponentially as the levels of language exposure and SES increased.

We now turn to the “catch up” question (Research Question 3): From what amount of cumulative exposure to the SL do bilingual children perform within the monolingual range?

CUMULATIVE EXPOSURE THRESHOLDS

Our starting point is the optimal (nonlinear, mixed-effect) model for the SRep data, which had been fitted to the target accuracy data for the bilingual children only. We rely on cumulative exposure as our reference measure for bilingual language experience, as this proved the best predictor in the population under study. We first refit this model to the entire cohort of children (including monolinguals)—using exposure to English as a predictor. When the model is fitted to the entire cohort using that predictor, age no longer accounts for any unique variance. We therefore exclude it from the model. After confirming the significance of the nonlinear interaction between SES and Cumulative SL exposure in the whole-cohort model (not reported here), we perform the threshold analysis, as explained in the following text.

The procedure for the threshold analysis consists in replacing the continuous SL exposure predictor with a binary one, for which the cutoff point would be determined objectively, based on Information Theory. To identify the optimal cutoff point, we refit the model recursively, using each time a different SL exposure value as the binary cutoff point. As the cumulative SL experience measure features 70 different values in the group under study, the model needs to be fitted 70 times. Plotting the AIC values for all the models (shown in Figure 12) shows the fluctuations in model fit depending on SL exposure threshold. The lowest AIC value identifies the model with the best fit. The cutoff point for that model is interpreted as the amount of exposure beyond which a bilingual child can be expected to perform within the monolingual range.

FIGURE 12.

Optimal threshold of cumulative SL exposure above which bilinguals perform within the monolingual range in the SRep task. The continuous line represents fluctuations in AIC (indicating model fit) depending on where the cutoff point is situated along the SL exposure continuum. The dashed line indicates the lowest AIC, corresponding to the best-fitting model, and hence the optimal cutoff point.

The optimal cutoff point on the continuum of SL cumulative exposure is at 33 months equivalent (where the dashed line falls in Figure 12). The model therefore predicts that a (5- to 7-year-old) bilingual child who has been exposed to the SL for the equivalent at least 33 months can be expected to perform within the monolingual range (after controlling for SES and memory abilities) in the SRep task.

The same procedure is then repeated for the other aspects of English proficiency we assessed in this study.^{Footnote 21} This results in the following thresholds of cumulative SL exposure: lexical semantics (composite DELV score): 44 months equivalent; discourse semantics: 32 months equivalent (see Figure 13).

FIGURE 13.

Optimal threshold of cumulative SL exposure above which bilinguals perform within the monolingual range in the lexical semantics and discourse-semantics tasks. The continuous lines represent fluctuations in AIC (indicating model fit) depending on where the cutoff point is situated along the SL exposure continuum. The dashed lines indicate the lowest AIC, corresponding to the best-fitting models.

The overall picture, when combining the information from the three preceding analyses, is that from 32 or 33 months equivalent of cumulative exposure to the SL, bilingual children (between 5 and 7 years of age) perform within the range of monolingual children in some aspects of language proficiency (indexed by the lexical semantics and the SRep tasks). The discourse semantics results suggest a more conservative threshold of 44 months equivalent (with respect to lexical semantics).

In the next section, we compare our threshold analysis to a more traditional approach based on language dominance.

LANGUAGE DOMINANCE THRESHOLDS

In the literature on bilingualism, it is common practice to consider that, below 20% of current exposure to an additional language, children should be considered “functionally monolingual” in their dominant language (e.g., Bedore et al., Reference Bedore, Peña, Summers, Boerger, Resendiz, Greene, Bohman and Gillam2012; Gutiérrez-Clellen and Kreiter, Reference Gutiérrez-Clellen and Kreiter2003; Pearson et al., Reference Pearson, Fernández, Lewedeg and Oller1997). As its name indicates, functional monolingualism implies that the child should perform within the monolingual range in terms of language proficiency.

Assuming that cumulative language exposure is a reliable proxy for language dominance (as demonstrated by Unsworth, Reference Unsworth, Silva-Corvalán and Treffers-Daller2015), we operationalized language dominance as the proportion of cumulative exposure to the SL out of the child’s lifetime (in months). We then replicated the threshold analyses above using that estimate of language dominance as our predictor of interest.

The threshold analysis of the SRep data using language dominance as predictor of interest suggests a cutoff point of 57% dominance in the SL (in 5 to 7 year olds).

Figure 14 compares the threshold based on the additive measure (corresponding to the horizontal line) with the threshold based on the proportional measure (cf. the vertical line). A number of data points are found in the top left quadrant, corresponding to the children that are predicted to perform within the monolingual range according to the additive threshold, but not according to the proportional threshold. The threshold analysis based on language dominance is therefore more conservative than that based on the cumulative measure of language exposure.

FIGURE 14.

Cumulative exposure to the SL expressed in months equivalent (y-axis) and as a proportion of total language exposure (x-axis). The lines indicate the threshold of exposure required for monolingual-like performance in the SRep test.

Figure 15 compares Bedore et al.’s categories with our objective threshold for monolingual-like performance.

FIGURE 15.

Comparison of Bedore et al.’s language dominance categories and a continuous measure of language dominance based on cumulative exposure to the SL (in months equivalent). The horizontal line indicates the threshold of exposure required for monolingual-like performance in the SRep test.