 Research article
 Open Access
 Published:
Capturing multiple interaction effects in L1 and L2 objectnaming reaction times in healthy bilinguals: a mixedeffects multiple regression analysis
BMC Neuroscience volume 21, Article number: 3 (2020)
Abstract
Background
It is difficult to set up a balanced higherorder fullfactorial experiment that can capture multiple intricate interactions between cognitive and psycholinguistic factors underlying bilingual speech production. To capture interactions more fully in one study, we analyzed objectnaming reaction times (RTs) by using mixedeffects multiple regression.
Methods
Ten healthy bilinguals (median age: 23 years, seven females) were asked to name 131 colored pictures of common objects in each of their languages. RTs were analyzed based on language status, proficiency, word choice, word frequency, word duration, initial phoneme, time series, and participant’s gender.
Results
Among five significant interactions, new findings include a facilitating effect of a crosslanguage shared initial phoneme (mean RT for shared phoneme: 974 ms vs. mean RT for different phoneme: 1020 ms), which profited males less (mean profit: 10 ms) than females (mean profit: 47 ms).
Conclusions
Our data support languageindependent phonological activation and a gender difference in inhibitory cognitive language control. Single word production process in healthy adult bilinguals is affected by interactions among cognitive, phonological, and semantic factors.
Background
Bilinguals and the language phenomena specific to them have long puzzled researchers, due to their deviation from monolinguals in multiple regards. For the process of word production in monolinguals, there is a general understanding of a sequential process that a person performs when naming an object. After first defining the concept to be expressed, a lemma is selected, a phonological code is retrieved, syllabified, and phonetically encoded before articulation ensues. This model was derived from a body of research that has identified specific time windows for each single step in word production [1, 2]. However, there are competing hypotheses to the proposed serial models. Indeed, some studies argued for cascade models in which a set of semantic candidates unselected could enter into the phonological stage and the corresponding multiple phonological codes are activated [3, 4].
Bilinguals show behavior yet to be fully explained by the current models. Compared to monolinguals, they possess a slower reaction time (RT) when confronted with an objectnaming task, both in their first language (L1) and their second language (L2). Also, responses given in the L1 generally happen faster than in the L2 when L1 is of currently dominant use, but the reverse pattern has also been observed [5,6,7]. By now, a multitude of competing explanation attempts focusing on different specific steps of the word production process exist [5, 8].
Regarding the selection of the taskrelevant language, phonological activations were shown to occur both in L1 and L2, suggesting that taskrelevant language selection does not occur in the semantic/lemma selection stages [9, 10]. The inhibitory control (IC) model introduced the selection of taskrelevant language earlier at the stage of semantic/lemma selection [11]. Herein, lexical representations are equipped with a mark indicating the corresponding language. A higherlevel control system would then, depending on the task, inhibit all representations with the L1 or L2 mark respectively (resulting in effectively a L1 vs. a L2mode), allowing for the correct lexical route to be taken [11]. Because these language modes would hardly ever be used equally, different levels of basal activation would result and make activation of one of the two languages more timeconsuming.
Concerning variables related to the semantic/lemma selection stage, both language proficiency and age of acquisition of L2 have been shown to impact the RT. At present, it has been hypothesized that both earlier acquisition and higher proficiency can lead to stronger activation levels of lemmas and thereby faster RT, and that this effect may arise out of a modulation of cortical activity patterns, making the L2 activity progressively more (or less) similar to the L1 activity [5, 12, 13]. Because these findings stress the influence of lemma activation level on RT, we formed the hypothesis that obvious responses to a given stimulus (the modal response) should be given faster than less obvious responses (the nonmodal response), due to the latter case reflecting a conflict in lemma selection, which would add time to the RT.
At the stage of phonological code retrieval, the word frequency (WF) effect must be mentioned. This phenomenon describes the tendency that the RT length diminishes when the target word is a commonly used one [14]. Currently, research indicates that the WF effect occurs relatively late in the word production process and at least partly reflects the process of phonological code retrieval [15]. A hypothesis on bilingual wordproduction delay focused on the WF effect is represented by the weakerlinks hypothesis, which will be examined more closely later.
For an effect again more exclusive to bilinguals, we have to consider the languageindependent, simultaneous activation of L1–L2 phonological representations that multiple studies point to [9, 10]. Such an activation implies a conflict having to be resolved between the L1 and L2 in choosing the phonological code in the task language. This would then impact the RT. In contrast, a shared initial phoneme increases the activation of the target phonological code, yielding a facilitating effect on RT. As a result, another hypothesis was formed for our present paper: analogous to one of the experiments performed by Colomé and Miozzo, we would expect a facilitating effect on RT when comparing target words that share the same initial phoneme between both their L1–L2 translations with target words that do not, arising out of an additive activation of the shared phoneme [10].
After the phonological code is retrieved and syllabification and phonetic encoding are applied, articulation ensues. Bilinguals herein commonly deal with differences in articulation efforts, because many times the different translations of a given target word contain varying numbers of syllables or even just differences in pronunciation, which impact the plan for forming the corresponding sound sequences. For example, German target words include more complex affricate “pf” or “ts” sounds that take longer than a simple obstruent “p”, which is rather prevalent in other languages. These and similar duration differences among phonemes in speechmotor planning influence the effort of articulation and cannot be captured by the number of phonemes, but could be assessed by measuring the actual word duration (WD).
Furthermore, we may not forget the importance of higherlevel executive functions. New meta analyses seem to indicate that the widely presumed bilingual advantage over monolinguals for executive functions may in fact be less powerful than previously assumed, or even an artifact due to publication bias [16]. Considering this, findings suggesting such a possible positive effect of bilingualism on executive function should be reconsidered [17]. This justifies investigating the possibility of a bilingual disadvantage in some regards. As has been previously put forth, bilingualism may be connected to the expenditure of additional cognitive resources due to a higher need for selfmonitoring during speech compared to monolinguals [18]. This might enable a fatigue effect, slowing down RT over time. Our study’s specific setup allowed for not only an analysis of such a fatigue effect, but also a learning effect and a possible interaction of both. Moreover, we formulated the hypothesis that due to motivational factors, an inverse relationship between accuracy in an objectnaming task and RT is possible. This is based on the scenario of a speedaccuracy tradeoff that participants face when making the decision of either putting sustained effort into finding the correct response or, instead, focusing on minimizing the respective RT.
Another way in which the effects of bilingualism on higher cognitive functions have been evaluated is with the Simon task. Recently, a genderdependent executive effect has been pointed out, with females being more easily distracted by the unnecessary spatial information presented during the task [19]. Translating this finding to a withinbilingual framework, it remains to be seen whether a similar gender effect can be shown in the context of bilingual language control regarding the suppression of taskirrelevant language. The respective hypothesis we defined in the current study was based on the previously mentioned effect of a crosslinguistically shared initial phoneme. If a genderdependent cognitivecontrol advantage of suppressing the phonological information in the taskirrelevant language exists for males, they should profit less from the facilitating effect of a crosslinguistically shared initial phoneme compared to females.
Other important variables modulating cognitive control in different tasks are represented by age and age of L2 acquisition [5, 20]. Bilingualism has been linked to improved retention of cognitive skills in later life periods compared to monolingualism [21]. Furthermore, inhibitory cognitive control decreases with age as shown by the existing literature [21, 22]. This decrease would take effect in tasks relying on inhibitory control, such as finding appropriate nonmodal responses when no modal response is present. Thus, one would therefore expect an increase in the difference in RT between modal and nonmodal responses with age. Regarding age of L2 acquisition, studies have struggled to clearly identify both the locus of influence as well as the mechanism of mediation [5]. Its connection to cognitive control mechanisms has hardly been explored, even though it is argued that there is a fundamental difference in network organization based on this variable [23]. Furthermore, age of L2 acquisition has been theorized to determine the size of phonological representations, with earlier learned words saved as blocks and expressions acquired later being deconstructed into phonological elements [24]. Thus, we hypothesize that the influence of the initial phoneme status (shared or different between L1 and L2) on RT would be stronger the later the L2 was acquired.
Importantly, there is not only the possibility of these factors acting isolated, but rather in combination with one another. Here one has to point toward the weakerlinks hypothesis, according to which bilinguals possess a weaker connection between their semantic and phonological representations when compared to monolinguals. This is believed to occur due to the former having to split their phonological activations between two different sets of representations due to language specificity of phonological codes, while the latter are able to focus the entire activation on one single set [8, 25]. The hypothesis in this regard bears similarities to the theoretical underpinnings of the WF effect, but with the degree of the WF effect varying with language use. WF initially benefits highfrequency words, but eventually the lowfrequency words catch up. Thus, it is hypothesized that RT difference between the highfrequency words and the lowfrequency words would be smaller for the language of longer use than for the language of shorter use, and RTs would be shorter for the language of the currently dominant use than for the language of the currently nondominant use. With regards to this theoretical construct, we set out to investigate the interaction between language dominance and WF on one hand and participant age and WF on the other hand.
In addition to the predictions we derived so far from the serial model extended to bilinguals, testing an interaction effect between word choice (WC; semantic/lemma selection) and phonological encoding in a single language (German) could distinguish the purely serial model, in which phonological encoding occurs only after semantic/lemma selection, from cascade models, in which a set of unselected semantic/lemmata activates phonological codes of these candidate lemmata [4]. Cascade models typically predict that WF effects increase when multiple lemma candidates remain unselected, which may be the case when nonmodal word response is made, compared to when a modal word response is made [3]. To investigate the influence of the mentioned variables, the present study uses mixedeffects multiple regression and intends to test the effects of various established psycholinguistic and cognitive factors and new twoway interactions between these established factors in one statistical approach [26].
Methods
Participants and study design
The entire data used was collected from twenty healthy volunteers (median age: 24 years, 10 females; Table 1), 10 of which were collected in the context of a study on cortical language representations investigated by navigated transcranial magnetic stimulation (nTMS) [27]. The additional 10 volunteers were collected for analyses 3 and 4 (see below). The participants confirmed to the Kohnert definition of bilingualism, as each of them reported regular exposure to both L1 and L2 before the age of 10 years [28]. The following inclusion criteria were considered: age of at least 18 years, righthandedness according to the Edinburgh Handedness Inventory, and acquisition of two languages before the age of 10 years [27]. The data collection took place on two appointments separated by at least 14 days to exclude nTMS aftereffects [27]. In the present study, we utilized the data taken as “baseline”, meaning that objectnaming performance prior to nTMS application was analyzed.
Objectnaming task
The same objectnaming task was carried out on both appointments (one per language, two consecutive runs per appointment) using a NexSpeech module (version 4.3; Nexstim Plc., Helsinki, Finland) [27]. It consisted of 131 colored pictures of different concrete animate and inanimate objects (such as “baby”, “rake”, or “orange”) in a sequence randomized for each run [27, 29,30,31].
During each appointment, the language used in the task was invariant. The sequence of languages was counterbalanced. Each participant was instructed to name the pictured object as simply, quickly, and plausibly as possible [27, 29,30,31]. One initial objectnaming run was followed by another containing only the objects that the investigator deemed correctly named in the first run. The objects were displayed for 700 ms each, with an interval of 2500 ms between the display of two consecutive objects [27, 29,30,31].
Audio extraction and measurement of reaction times
We used the builtin report mechanism of the NexSpeech module to get information on when each single trial began (trial start time). The recorded video files of .asf data type were copied to an external computer, where an inhouse Matlab script was used that first separated the audio track from the video and then saved each audio track in the form of a .wav file. Subsequently, we performed RT measurements on the audio tracks using Praat (version 6.0.28; http://www.fon.hum.uva.nl/praat/; Fig. 1).
The respective response to each object was documented for each trial, and both voice onset (time at which the response to a given trial began) and voice offset (time at which the response was finished) were measured and noted. This allowed for immediate calculation of both WD and RT by subtraction of voice onset from voice offset (for WD) and subtraction of trial start time from voice onset (for RT), respectively.
Different categories of possible errors were defined to characterize incorrect responses. There was a no response (NR) when the participant did not give any response or audibly indicated not knowing a proper response (e.g., “ehh…”), a performance error (PE) if the word was articulated in a flawed way such as by distorted pronunciation or through the interjection of inappropriate utterances (e.g., “teaehhhpot”), and a semantic error (SE) if the given response was correctly articulated, but from a semantic point of view not adequate to describe the pictured object (e.g., “tomato” as a response to a picture of an orange) [27, 29,30,31].
Data analyses
Statistical method
We performed confirmatory forward mixedeffects multiple regression analysis on the RTs of the L1 and L2. We used a mixedeffects multiple regression analysis, a method introduced into RT analyses of psycholinguistic studies to overcome problems regarding factorial study designs [26]. Mixedeffects multiple regression allows (1) to analyze all observations without averaging, (2) to test multiple, possibly interacting nominal and continuous factors, and (3) to estimate the genuine effect of each factor by partialling out the information common between fixedeffects factors and the random effects of participants and objects. In other words, mixedeffects regression allows to partial out the idiosyncrasies that participants and objects brought with them into the objectnaming datasets in one model. Moreover, if the byparticipant random intercept and the bypicture random intercept are significant, it means that the studied sample is diverse enough in terms of participants and objects. The significant diversity of the sample data, in turn, allows to generalize the results of the significant fixedeffects factors beyond the sample of participants and objects used in the present study.
Our approach is confirmatory in the sense that we tested preselected factors known to influence the RT according to previous studies as aforementioned. However, past studies have not shown the individual degree to which each factor accounts for the variance in its corresponding level of word production. Therefore, we performed a forward stepwise model comparison instead of a hierarchical model comparison.
Factors
Regarding the random effects, we tested the byparticipant random intercept and the bypicture random intercept. Regarding the fixedeffects factors, we tested five types of variables. These variables include factors related to cognitive states (practice effect and/or fatigue effect) that would change over time (run numbers 1 vs. 2; trial numbers in each run from 1 to maximum 131), a factor related to language status (L1 vs. L2), factors related to semantic/lemma selection (test language run 1 percent correct [L1: 0.73–0.93; L2: 0.65–0.94]; taskrelevant German run 1 percent correct [0.65–0.95]; WC: modal word vs. others), factors related to phonological code retrieval (log10 WF; first phoneme difference: same vs. different), factors related to articulatory load such as WD for included objects (ranging from 159 ms for “bi” in L1 Chinese [”fountain pen”] to 2165 ms for “panchina” in L2 Italian [”bench”]) and WD difference (L2–L1: ranging from − 1520 ms for “Mais” in L2 German [“corn on the cob”] to 1924 ms for “Trommel”, a nonmodal name in L2 German for “Fass” [“barrel”]), as well as other demographic factors (age: 19 to 27 years; age of L2 acquisition: 0 to 10 years; gender: female vs. male). For the grouping factors, the slope was calculated as the change from the subgroup listed first to the subgroup listed second.
Regarding the fixedeffects interactions, we tested four interaction effects motivated by the current literature: language status × log10 WF interaction, age × log10 WF interaction, gender × first phoneme difference, and run number × trial number interaction. The factors of each interaction term are ordered so that the coefficient estimated for the interaction term is used to adjust the coefficient of the second factor for the first factor’s second subgroup. The information about the log10 WF for the object target names for the picture set used in the present study was taken from the SUBTLEXDE [32].
Because our ultimate goal was to identify the contexts in which longer RTs are likely to occur during the objectnaming task, instead of removing outlying longer RTs, the positivelyskewed RT distribution was corrected by inversetransforming the RT. Moreover, because WD and WD difference were also positively skewed, they were log10 transformed.
Local purposes
We planned two analyses for different foci. Analysis 1 was intended to compare the RTs of L1 and L2, with special attention to the first phoneme difference factor (same vs. different) and the WD difference factor. Analysis 2 was intended to compare only German RTs, with special attention to the WC factor (modal word vs. others) in addition to the first phoneme difference factor and the WD difference factor.
Data selection
We took three steps to select trials from the baseline datasets. First, we selected trials for which verbal responses were made in the 2500 ms time window and for which we were able to measure the RT properly. For Analysis 1, we paired up L1 and L2 trials for each object in each run of each participant, enabling us to calculate WD differences for each pair. We further grouped the paired words into one set in which the L1 and L2 translation did share the same first phoneme and one set in which they did not (3506 trials). Then, for Analysis 2, we selected German trials (1448 trials) from the trials selected for Analysis 1 and divided them according to whether or not the specific response was a modal or nonmodal response.
Statistical procedures
Prior to the regression analysis, we corrected the positive skewness of the RT distribution by inverse transformation, in addition to log10 transformation of WD and WD difference mentioned earlier. We performed a forward model comparison, selecting at each step the factor that reduced the variance most among the factors that independently significantly reduced the variability in objectnaming RT, with the threshold set at 0.05 for alpha.
For the forward model comparison, the empty model with only the fixed intercept was calculated first. Against this empty model, byparticipant random intercept was tested. Next, the bypicture random intercept was tested. Then, the preselected fixed effects factors were tested one by one. Afterwards, the byparticipant random slopes for fixedeffects factors and bypicture random slopes for fixedeffects factors were tested. Then, the twoway interaction effects between fixed factors were tested. The final model was rerun by using the restricted maximum likelihood method to obtain the unbiased variance components. In the final model, the order of factors in the regression equation was rearranged so that the analysis program forms the interaction terms consistent with the interaction hypotheses of the fixed effects. When a theoretically motivated 2way interaction was significant, atheoretic 3way interactions were additionally tested to see if there was a significant 3way interaction that would make the 2way interaction nonsignificant and reduce the remaining variance significantly. It was also used to help localize the source of the effect of interest.
The assumptions for multiple regressions were examined for each final model, following Baayen [33]. To see if the residuals are normally distributed, standardized residuals were calculated and a density plot was generated for visual inspection. The skewness of the distribution was calculated to see if it would fall in the normal range between − 0.5 and + 0.5. To check the homoscedasticity assumption by visual inspection, fitted values are plotted along the horizontal axis and the corresponding standardized residuals were plotted along the vertical axis with the reference lines drawn at ± 2.5 for the standardized residuals. Trials with residuals that fell outside the ± 2.5 standard deviation (SD) were identified and tagged with actual reaction times and participants in order to find where in the range of reaction times the deviated residuals lay and see if they exclusively belonged to one or two participants.
For the final mixedeffects model, because there is no agreedupon way of determining the degrees of freedom to translate the obtained tvalues for the coefficient of each factor into pvalues, pvalues based on degrees of freedom returned by statistical programs may be misleading [34, 35]. Therefore, to complement the information, we provide the bootstrap confidence intervals (CIs) of each factor’s coefficient obtained by 10,000 times of bootstrapping in addition to providing the pvalues determined by using the degrees of freedom calculated by Kenward and Roger’s method [36,37,38]. Additionally, the proportion of variance accounted for was calculated for the final model, the fixed effects, and the random effects.
In the results section, we report means and CIs of the backtransformed fitted RTs indicated by the subscript btf. To perform this series of statistical analysis, we used R (version 3.1.1; The R Foundation for Statistical Computing, Vienna, Austria) in combination with the lme4 package, the nlme package, lmerTest, krbttest, the MuMIn package, and the effects package [34, 36, 37, 39,40,41,42].
Analyses extended with a larger more representative and genderbalanced sample
Irreproducibility of results is a recently surging concern in neurobiology of language. The male sample (n = 3, contributing 561 trials) may not be representative to claim the gender effect and/or the first phoneme difference × gender effect even if 10,000times bootstrap replications confirmed them. To address this concern, additional data were collected to see if the results of the first sample could be replicated with a larger, more representative, and more genderbalanced sample (n_{female} = 10, n_{male} = 10, in 7145 trials in total). With the time constraints imposed on the study 2 completion, the data were collected with a simplified procedure, scheduling the L1 and L2 sessions on the same day without the nTMSrelated steps. In addition, the two samples differ in gender composite (7:3 vs. 3:7). Here, our report focuses on the replicability test of the effects detected in the sample that may be less representative and genderimbalanced. At the end of the result section, a brief report was added to mention two of the interactions that were part of the decomposition of sample difference and relevant to the presenttheory testing investigation.
The data from the previous analysis was combined with the new data set. Using this larger, more representative, and genderbalanced data set, the final models of analysis 1 and analysis 2 were tested. Where applicable, the hypothesized effects that were not significant in sample 1 were added to the final model to see if they would become significant with a larger, more representative, genderbalanced sample. These hypotheses included word frequency × age (or age of L2 acquisition) for the Weaker Links hypothesis from Analysis 1 and word frequency × word choice interaction for the Cascade model from analysis 2. Because the first replicability test asks if there are noncontributing terms in the proposed final model, backward model comparisons for elimination was performed instead of forward model comparison. To be consistent, subsequent testing of the previously nonsignificant terms was also performed by backward model comparison. The threshold for elimination was set at α = 0.05. As the model increases its complexity with the doubled sample size, calculating the Kenward and Roger degrees of freedom became impractically timeconsuming. The default method of calculating the degrees of freedom (Satterthwaite method) was used. The bootstrap test was performed with 10,000 replications as was done in the previous analyses. When the effects package did not generate the plot to show the specific aspect of the interaction between a continuous variable and a categorical variable or between continuous variables, the fitted means and confidence intervals were calculated in the effect package and the result was reorganized and plotted by our custom scripts.
Results
Analysis 1: Analysis including L1 vs. L2 comparisons
Analysis 1: Overview
3506 trials from 10 participants in responses to 131 objects were analyzed. As shown by the model comparison (Table 2), the forwardmodel comparisons arrived at the final model that consisted of the byparticipant random intercept, the bypicture random intercept, five fixedeffects factors (run number, trial number, first phoneme difference, language status, and log10 WF), and three twoway interactions (run number × log10 WF, language status × log10 WF, and run number × trial number). The final model accounted for 34.91% of the variance. The byparticipant random intercept and the bypicture random intercept jointly accounted for 22.38% of the variance. The five fixedeffects terms and the three interaction terms jointly accounted for 12.53% of the variance. The variables related to the articulatory effort were not contributing factors.
For the verbal summary about the continuous variable factors (log10 WF and trial numbers), means and CIs of the RTs are represented at log10 WF = 1 (10 occurrences per million) as low frequency, log10 WF = 4 (10,000 occurrences per million) as high frequency, trial number 20th as earlier trials and trial number 120th as later trials. For an overview, see Tables 2, 3 and 4 and Fig. 2.
The skewness of the distribution of the residuals fell in the range of normal distribution (skewness − 0.49). Homoscedasticity assumption was not violated by visual inspection. Residuals outside 2.5 SD occupied 1.96% of the trials (69 out of 3506) and all participants in the analysis contributed 3–14 trials (median = 5.5). The 10,000 times bootstrap test showed that all the significant factors and interactions were stable.
Analysis 1: Random effects
Regarding the random effects, adding the byparticipant random intercept first (χ^{2}(1) = 439.51, p < 0.0001) and adding the bypicture random intercept second (χ^{2}(1) = 325.41, p < 2.2e−16) both significantly reduced the variance (Table 2). These results suggest that for the final model reported, by partialling out the idiosyncrasies of the participants and the objects in the sample, significant effects of the fixedeffects factors and their interactions are generalizable beyond the participants and the objects employed in the present study. Regarding the byparticipant random intercept (SD = 6.603e−05, 95% CI 3.590e−05, 9.617e−05), the backtransformed adjusted random intercepts ranged from 936 to 1162 ms. Regarding the bypicture random intercept (SD = 5.566e−05, 95% CI 4.678e−05, 6.414e−05), the backtransformed adjusted random intercepts ranged from 938 ms for “Schlange” (”snake”) to 1211 ms for “Kommode” (”dresser”).
Analysis 1: Fixed effects
Fixedeffects factors related to phonological code retrieval
First phoneme difference The firstphoneme difference factor was significant (b = − 4.571e−05, t(3399) = − 7.113, p = 1.37e−12) and did not interact with other factors (Table 3). More specifically, RT was, on average, shorter for the trials with the same first phoneme (M_{btf} = 974 ms, 95% CI_{btf} 935 ms, 1017 ms) than for the trials with the different phonemes (M_{btf} = 1020 ms, 95% CI_{btf} 977 ms, 1066 ms; Fig. 2a, Table 4).
Language status × log10 word frequency degree interaction The log10 WF factor was significant (b = 3.331e−05, t(216) = 4.225, p = 3.52e−05) but more important, there was a significant degree interaction effect between the language status factor and the log10 WF factor (b_{interaction} = 2.148e−05, t(3361) = 3.692, p = 2.26e−04; Table 3). Due to this interaction, although adding the language status factor significantly reduced the variance earlier in the forward model comparison (χ^{2}(1) = 26.78, p = 1.827e−06; Table 2), the coefficient of the language status factor was nonsignificant in the final model (b = − 2.117e−05, t(3361)= − 1.578, p = 0.1147; Table 3).
More specifically, RTs were, on average, shorter for the highfrequency words (log10 WF = 4) than for the lowfrequency words (log10 WF = 1), but the difference between the highfrequency words and the lowfrequency words was greater for L2 (L2 high: M_{btf} = 916 ms, 95% CI_{btf} 875 ms, 960 ms; L2 low: M_{btf} = 1043 ms, 95% CI_{btf} 996 ms, 1095 ms) than for L1 (L1 high: M_{btf} = 973 ms, 95% CI_{btf} 927 ms, 1024 ms; L1: low M_{btf} = 1044 ms, 95% CI_{btf} 996 ms, 1096 ms) and the L2 highfrequency words received the shortest RTs (Fig. 2b, Table 4). The RTs were, on average, shorter during L2 object naming than during the L1 object naming in the present sample. Now even though the L2 may thus be the language of currently dominant use, the hypothesis that the difference between the highfrequency words and the lowfrequency words being greater in the L2 than in the L1 nevertheless correctly distinguished the L2 from the L1 in the present sample.
None of the additional atheoretical 3way interactions (language status × word frequency × run number, or × trial number, or × first phoneme difference) were significant, made the significant twoway interaction nonsignificant, or significantly reduced the variance at the same time.
Factors related to cognitive states
Run number × log10 word frequency degree interaction There was a significant effect of the runnumber factor (b = 1.467e−04, t(3405)= 8.991, p < 2e−16) in addition to the significant effect of the log10 WF factor reported earlier. More importantly, there was a significant degree interaction effect between the run number factor and the log10 WF factor (b_{interaction} = − 2.257e−05, t(3389)= − 3.837, p = 1.27e−04; Table 3). More specifically, RT was, on average, shorter for the highfrequency words than for the lowfrequency words. Besides, RT was shorter in run 2 than in run 1, which suggests a practice effect. Furthermore, the RT difference between the highfrequency words and the lowfrequency words was smaller in run 2 (Run 2 high: M_{btf} = 929 ms, 95% CI_{btf} 887 ms, 976 ms; Run 2 low: M_{btf} = 989 ms, 95% CI_{btf} 946 ms, 1036 ms) than in run 1 (Run 1 high: M_{btf} = 956 ms, 95% CI_{btf} 912 ms, 1004 ms; Run 1 low: M_{btf} = 1094 ms, 95% CI_{btf} 1042 ms, 1151 ms), possibly due to fatigue effects depriving the highfrequency words of their advantage (Fig. 2c, Table 4).
None of the additional atheoretical 3way interactions (run number × word frequency × trial number, or × first phoneme difference, or × language status) were significant, made the significant twoway interaction nonsignificant, or significantly reduced the variance at the same time.
Run number × trial number degree interaction There was a significant effect of the runnumber factor and a significant effect of the trialnumber factor (b = − 5.155e−07, t(3425) = − 5.827, p = 6.17e−09). More important, there was a significant degree interaction effect between the runnumber factor and the trialnumber factor (b_{interaction} = − 4.414e−07, t(3418)= − 2.951, p = 0.0032, Table 3). More specifically, RT was, on average, shorter in run 2 than in run 1, suggesting a practice effect. Also, RT was shorter for the earlier trials than for the later trials, suggesting a fatigue effect developing over 131 trials. Furthermore, the RT difference between the earlier trials and the later trials was greater for run 2 (Run 2 20th trial: M_{btf} = 930 ms, 95% CI_{btf} 894 ms, 969 ms; Run 2 120th trial: M_{btf} = 1021 ms, 95% CI_{btf} 976 ms, 1071 ms) than for run 1 (Run 1 20th trial: M_{btf} = 1014 ms, 95% CI_{btf} 927 ms, 1061 ms; Run 1 120th trial: M_{btf} = 1070 ms, 95% CI_{btf} 1023 ms, 1123 ms) depriving the later trials in run 2 of the practice effect advantage (Fig. 2d, Table 4).
None of the additional atheoretical 3way interactions (run number × trial number × first phoneme difference, or × language status, or × word frequency) were significant, made the significant twoway interaction nonsignificant, or significantly reduced the variance at the same time.
Analysis 2: German object naming only
Analysis 2: Overview
1448 trials from eight participants in responses to 131 objects were analyzed. The forwardmodel comparisons arrived at the final model that consisted of the byparticipant random intercept, the bypicture random intercept, seven fixedeffects factors (run number, trial number, log10 WF, first phoneme difference, WC, German run 1 percent correct, and participant’s gender) and two twoway interactions (gender × first phoneme difference, German run 1 percent correct × log10 WF).
The skewness of the distribution of the residuals fell in the range of normal distribution (skewness − 0.49). Homoscedasticity assumption was not violated by visual inspection. Residuals outside 2.5 SD occupied 2.14% of the trials (31 out of 1448) and all participants in the analysis contributed 1–9 trials (median = 3.5). The 10,000 times bootstrap test showed that all the significant factors and interactions were stable.
The final model accounted for 48.41% of the variance. More specifically, the byparticipant intercept and the bypicture intercept jointly accounted for 20.99% of the variance, while the seven fixedeffects terms and the two fixedeffects interaction terms jointly accounted for 27.42% of the variance. The variables related to the articulatory effort were not contributing factors. For an overview, see Tables 5, 6, 7 and Fig. 3.
Analysis 2: Random effects
Regarding the random effects, adding the byparticipant random intercept first (χ^{2}(1) = 292.27, p < 0.0001) and adding the bypicture random intercept second (χ^{2}(1) = 159.41, p < 2.2e−16) both significantly reduced the variance (Table 5). These results suggest that, for the final model reported below, by partialling out the idiosyncrasies of the participants and the objects in the sample, significant effects of the fixedeffects factors and their interactions are generalizable beyond the participants and the objects employed in the present study. Regarding the byparticipant random intercept (SD = 5.878e−05, 95% CI 2.143e−05, 9.512e−05), the backtransformed adjusted intercepts ranged from 722 ms to 811 ms. Regarding the bypicture random intercept (SD = 6.634e−05, 95% CI 5.418e−05, 7.790e−05), the backtransformed adjusted intercepts ranged from 692 ms for “Schreibtischstuhl” (”desk chair”) to 858 ms for “Kamera” (”camera”).
Analysis 2: Fixed effects
Fixedeffects factors related to semantic or lemma selection
Word choice The wordchoice factor was significant (b = − 2.916E−05, t(1434) = − 2.688, p = 0.0073) and did not interact with other factors. More specifically, RT was, on average, longer for the naming responses of nonmodal words (M_{btf} = 1012 ms, 95% CI_{btf} 966–1062 ms) than for the naming responses of modal words (M_{btf} = 983 ms, 95% CI_{btf} 942–1027 ms), regardless of other factors (Fig. 3c).
German run 1 percent correct × log10 word frequency degree interaction There was a significant degree interaction (b_{interaction} = − 1.295e−04, t(1342) = − 2.193, p = 0.0285) between the German run 1 percent correct factor and a factor related to phonological code retrieval (log10 WF) (b_{log10WF} = − 1.548e−04, t(1402) = 2.938, p = 0.0034). Due to this interaction, although the German run 1 percent correct factor significantly reduced the variance earlier in the forward model comparison (χ^{2}(1) = 6.40, p = 0.011383, Table 5), the coefficient of the German run 1 percent correct factor was nonsignificant in the final model (b = − 3.631e−04, t(8.1) = − 1.280, p = 0.2359, Table 6).
More specifically, RT was, on average, shorter for higherfrequency words than for lowerfrequency words. Furthermore, the difference between the highfrequency words and the lowfrequency words was greater for the participants with lower German run 1 percent correct (70% correct, high frequency: M_{btf} = 803 ms, 95% CI_{btf} 741 ms, 878 ms; 70% correct, low frequency: M_{btf} = 950 ms, 95% CI_{btf} 869 ms, 1049 ms) than for the participants with higher German run 1 percent correct (95% correct, high frequency: M_{btf} = 976 ms, 95% CI_{btf} 915 ms, 1047 ms; 95% correct, low frequency: M_{btf} = 1076 ms, 95% CI_{btf} 1008 ms, 1154 ms), with the advantage associated with higher frequency words attenuated for those high in German run 1 percent correct (Fig. 3e, Table 7).
None of the additional atheoretical 3way interactions (German run 1 percent correct × word frequency × run number, or × trial number, or × first phoneme difference, or × word choice, or × gender) were significant, made the significant twoway interaction nonsignificant, or significantly reduced the variance at the same time.
Factors related to phonological code retrieval
In addition to the log10 WF factor reported earlier, the firstphoneme difference factor was significant (b = − 5.199e−05, t(1410) = − 4.281, p = 1.98e−05). Moreover, there was a significant degree interaction between the gender factor and the firstphoneme difference factor (b_{interaction} = 4.277E−05, t(1388) = 2.302, p = 0.0215, Table 6). The RT was, on average, shorter for the trials of L1–L2 target words sharing the same first phoneme than for the trials in which L1–L2 target words started with different phonemes. More importantly, the RT difference between the trials of the L1–L2 target words starting with different first phonemes and the trials of the L1–L2 target words sharing the same first phoneme was smaller for male participants (male, first phoneme diff: M_{btf} = 1041 ms, 95% CI_{btf} 971 ms, 1122 ms; male, first phoneme same: M_{btf} = 1031 ms, 95% CI_{btf} 959 ms, 1115 ms) than for female participants (female, first phoneme diff: M_{btf} = 976 ms, 95% CI_{btf} 926 ms, 1032 ms; female, first phoneme same: M_{btf} = 929 ms, 95% CI_{btf} 882 ms, 981 ms, Fig. 3d, Table 7).
Four of the additional atheoretical 3way interactions (first phoneme difference × gender × trial number, or × word frequency, or × word choice, or × German run 1 percent correct) were nonsignificant and did not significantly reduced the remaining variance. First phoneme difference × gender × run number was significant (p = 0.003) and significantly reduced the remaining variance jointly with the other two automatically added atheoretical twoway interactions (p = 0.008). The theoretically motivated twoway interaction (first phoneme difference × gender) became nonsignificant, whereas one of the automatically added atheoretic twoway interaction run number × gender was significant (p = 0.0006). The first phoneme factor remained significant with the benefit by the same first phonemes. These results together showed that the significant run number × gender interaction depended on the first phoneme difference factor (Fig. 4). Female participants benefitted from the second run regardless of the first phoneme difference factor. In contrast, male participants benefitted in the second run when the first phonemes were different, whereas they did not benefit from the second run when the first phonemes were the same. Therefore, the source of the lack of languageindependent phonological activation in male participants was localized in this condition (Fig. 4, right bottom panel).
Factors related to cognitive states
Run number The runnumber factor was significant (b = 9.064e−05, t(1329) = 12.053, p < 2e−16, Table 6) and did not interact with other factors. More specifically, RT was, on average, shorter in run 2 (M_{btf} = 942 ms, 95% CI_{btf} 904 ms, 982 ms) than in run 1 (M_{btf} = 1029 ms, 95% CI_{btf} 985 ms, 1078 ms), regardless of other factors (Fig. 3 panel a, Table 7). The result suggests a robust practice effect.
Trial number The trialnumber factor was significant (b = − 6.108E−07, t(1376) = − 5.598, p < 2.61e−08, Table 6) and did not interact with other factors. More specifically, RT was, on average, longer for later trials (trial number 120th M_{btf} = 1024 ms, 95% CI_{btf} 979 ms, 1074 ms) than for earlier trials (trial number 20th M_{btf} = 964 ms, 95% CI_{btf} 924 ms, 1007 ms), regardless of other factors (Fig. 3b, Table 7). The result suggests a robust fatigue effect building up steadily during each run for the 5 min 30 s.
Analysis 3 (Analysis 1 extended with n = 20)
Analysis 3 Overview
7145 trials from 20 participants in responses to 131 objects were analyzed. The data set consisted of 3471 trials from 10 female participants and 3674 trials from 10 male participants, and thus, it was genderbalanced. The final model consisted of the fixed intercept, the byparticipant random intercept, the bypicture random intercept, six fixedeffects factors and four 2way interactions (Tables 8 and 9, Fig. 5). First phoneme difference, word frequency × language status, word frequency × run number, and trial number × run number were replicated. Word frequency × age became significant with this large sample. The 2way interaction was predicted by the Weaker Links hypothesis. However, contrary to the prediction, the advantage of the higher frequency words over lower frequency words was greater for older participants than for the younger participants.
The extended model accounted for 40.79% of the variance. The byparticipant random intercept and the bypicture random intercept jointly accounted for 29.42% of the variance. The six simple fixedeffects terms and the four interaction terms jointly accounted for 11.36% of the variance. The skewness of the distribution of the residuals fell in the range of normal distribution (skewness − 0.428). Homoscedasticity assumption was not violated by visual inspection. Residuals outside ± 2.5 SD occupied 1.89% of the trials (135 out of 7245) and 19 out of 20 participants in this larger data set contributed 1–23 trials (median = 3.5). When these 135 trials with outlying residuals were removed, all the significant terms remained significant and all the nonsignificant terms remained nonsignificant. Therefore, none of the results were driven by these trials. Moreover, the 10,000times bootstrap test showed that all the significant factors and interactions were stable (Tables 8, 9 and 10; Fig. 5).
Random effects
Regarding the random effects of the combined data set, the byparticipant random intercept was significant (χ^{2}(1) = 1630.89, p ~ 0, SD = 1.058e−04, 95% CI 7.147e−05, 1.398e−04). Likewise, the bypicture random intercept was significant (χ^{2}(1) = 796.17, p = 3.664e−175, SD = 6.61505, 95% CI 5.687e−05, 7.543e−05). Regarding the representativeness of each gender group, the byparticipant random intercept of the female sample was significant (χ^{2}(1) = 971.7911, p = 2.431e−213. Likewise, the byparticipant random intercept of the male sample was significant (χ^{2}(1) = 604.61, p = 1.662e−133. These results suggest that each gender group consisted of sufficiently diverse participants, and thus, for the final model reported below, significant effects of the gender factor and their interactions as well as other significant effects are generalizable beyond the participants in the present study.
Fixed effects
First phoneme difference
First phoneme difference was significant. It did not interact with gender or age. Reaction times were shorter for names with the same first phoneme (M_{btf} = 935 ms, 95% CI_{btf} 895 ms, 979 ms) than for those with the different first phonemes (M_{btf} = 992 ms, 95% CI_{btf} 947 ms, 1042 ms), (b = − 6.144e−04, t(7053) = − 11.291, p = 2.593e−29; Tables 8, 9 and 10, Fig. 5a). The direction of the difference was the same as observed in analysis 1. Thus, the effect of first phoneme difference was replicated.
Word frequency × language status
The word frequency × language status interaction was significant. Reaction times were shorter for high frequency names than for low frequency names. However, the advantage of higher frequency names over lower frequency names was greater in L2 (typically currently dominantuse) (L2, high frequency: M_{btf} = 875 ms, 95% CI_{btf} 833 ms, 920 ms; L2, low frequency: M_{btf} = 1074 ms, 95% CI_{btf} 1011 ms, 1145 ms) than in L1 (typically currently nondominant use) (L1, high frequency: M_{btf} = 904 ms, 95% CI_{btf} 859 ms, 953 ms; L1, low frequency: M_{btf} = 1064 ms, 95% CI_{btf} 1002 ms, 1134 ms), (b_{interaction} = − 1.148e−05, t(6984) = 2.226, p = 0.026; Tables 9, 10, Fig. 5b). The pattern of the directions of the reaction time difference was the same as observed in analysis 1. Thus, the effect of the word frequency × language status interaction was replicated.
Word frequency × run number
The word frequency × run number interaction was significant. Reaction times were shorter for higher frequency names than for lower frequency names. However, the advantage of higher frequency names over lower frequency names was greater in run 1 (run 1, high frequency: M_{btf} = 919 ms, 95% CI_{btf} 873 ms, 970 ms; run 1, low frequency: M_{btf} = 1143 ms, 95% CI_{btf} 1072 ms, 1225 ms) than in run 2 (run 2, high frequency: M_{btf} = 858 ms, 95% CI_{btf} 818 ms, 902 ms; run 2, low frequency: M_{btf} = 998 ms, 95% CI_{btf} 943 ms, 1060 ms), (b_{interaction} = − 1.273e−05, t(7002) = − 2.456, p = 0.014; Tables 9, 10, Fig. 5c). The pattern of the directions of the reaction time difference was the same as observed in analysis 1. Thus, the effect of the word frequency × run number interaction was replicated.
Trial number × run number
The trial number × run number interaction was significant. Reaction times were longer for later trials than for earlier trials. However, the advantage of earlier trials over later trials was greater in run 2 (run 2, early trial: M_{btf} = 881 ms, 95% CI_{btf} 844 ms, 921 ms; run 2, later trial: M_{btf} = 966 ms, 95% CI_{btf} 921 ms, 1015 ms) than in run 1 (run 1, early trial: M_{btf} = 989 ms, 95% CI_{btf} 943 ms, 1039 ms; run 1, later trial: M_{btf} = 1040 ms, 95% CI_{btf} 989 ms, 1096 ms), (b_{interaction} = − 3.935e−07, t(7023) = − 3.172, p = 0.002; Tables 9, 10, Fig. 5d). The pattern of the directions of the reaction time difference was the same as observed in analysis 1. Thus, the trial number × run number interaction was replicated.
Word frequency × age
The trial number × age interaction was significant. It was a degree interaction. Reaction times were shorter for higher frequency names than for lower frequency names. This advantage of high frequency names over lower frequency names was greater for older participants (age 32, high frequency: M_{btf} = 857 ms, 95% CI_{btf} 787 ms, 941 ms; age 32, low frequency: M_{btf} = 1088 ms, 95% CI_{btf} 787 ms, 941 ms) than for younger participants (age 19, high frequency: M_{btf} = 921 ms, 95% CI_{btf} 842 ms, 1016 ms; age 19, low frequency: M_{btf} = 1051 ms, 95% CI_{btf} 949 ms, 1179 ms), (b_{interaction} = 2.193e−06, t(7020) = − 2.893, p = 0.004; Tables 9, 10, Fig. 5e). Thus, the word frequency effect was replicated. However, the pattern of the directions of the reaction time difference was not consistent with the prediction derived by the Weaker Links hypothesis. Thus, the Weaker Links hypothesis was not supported.
Analysis 4 (Analysis 2 extended with n = 18)
Analysis 4 Overview
The data set of analysis 4 consisted of 3267 German trials from the data set of analysis 3. The data consisted of 1430 trials from eight female participants and 1837 trials from 10 male participants, and thus, it was genderbalanced.
The final model consisted of the fixed intercept, the byparticipant random intercept, the bypicture random intercept, eight fixedeffects factors, five 2way interactions, and one 3way interaction (Tables 11, 12 and 13, Figs. 6 and 7). Among the terms that were significant in sample 1, run number, trial number, and word frequency × German run 1 percent correct remained significant, without changing the direction of reaction time difference. Thus, each of their effects were replicated (Tables 11, 12 and 13; Fig. 6a–c). In contrast, word choice interacted with word frequency. The advantage of modal names over nonmodal names was replicated. However, the reaction time difference was not greater for nonmodal names than for modal names. Thus, the Cascade hypothesis was not supported (Tables 11, 12 and 13; Fig. 6d). First phoneme difference × gender interacted with age (Tables 11, 12 and 13; Fig. 7e1–e5). The superior inhibitory control of male participants decreased with the increase of age (Tables 12, 13, Fig. 7e1–e5). The pattern of first phoneme difference × gender in analysis 1 was replicated among younger participants (Tables 12, 13; Fig. 7e1, e2) but it was not replicated among the older participants (Tables 12, 13; Fig. 7e3–e5).
The extended model accounted for 47.90% of the variance. The byparticipant random intercept and the bypicture random intercept jointly accounted for 33.76% of the variance. The fixedeffects terms jointly accounted for 14.14% of the variance. The skewness of the distribution of the residuals fell in the range of normal distribution (skewness − 0.335). Homoscedasticity assumption was not violated by visual inspection. Residuals outside ± 2.5 SD occupied 1.87% of the trials (61 out of 3267) and 17 out of 18 participants in the data set contributed 1–10 trials (median = 2.5). When these 61 trials with outlying residuals were removed, all the significant terms remained significant and all the nonsignificant terms remained nonsignificant. Therefore, none of the results were driven by these trials. Moreover, the 10,000times bootstrap test showed that all the significant factors and interactions were stable (Table 12).
Random effects
The byparticipant random intercept was significant (χ^{2}(1) = 791.39, p = 4.023e−174, SD = 1.200e−04, 95% CI 7.395e−05, 1.662e−04). Likewise, the bypicture random intercept was significant (χ^{2}(1) = 396.02, p = 4.04576e−88, SD = 7.021e−04, 95% CI 5.916e−05, 8.132e−05). Regarding the representativeness of each gender group, the byparticipant random intercept of the female sample was significant (χ^{2}(1) = 456.26, p = 3.128e−101). Likewise, the byparticipant random intercept of the male sample was significant (χ^{2}(1) = 291.9298, p = 1.888e−65). These results suggest that each gender group consisted of sufficiently diverse participants, and thus, for the final model reported below, significant effects of the gender factor and their interactions as well as other significant effects are generalizable beyond the participants in the present study.
Analysis 4 Fixed effects
Run number
The effect of run number was significant. Reaction times were shorter in run 2 (M_{btf} = 920 ms, 95% CI_{btf} 879 ms, 964 ms) than in run 1 (M_{btf} = 1013 ms, 95% CI_{btf} 964 ms, 1067 ms) (b = 1.023e−04, t(3120) = 16.615, p = 1.802e−59; Tables 12, 13; Fig. 6a). The direction of the reaction time difference was the same as observed in analysis 2. Thus, the effect of run number was replicated.
Trial number
The effect of trial number was significant. Reaction times were longer for later trials (trial 130th: M_{btf} = 982 ms, 95% CI_{btf} 929 ms, 1043 ms) than for earlier trials (trial number 2nd: M_{btf} = 918 ms, 95% CI_{btf} 871 ms, 970 ms) (b = − 5.613e−07, t(3172) = − 6.370, p = 2.614e−10; Tables 12, 13, Fig. 6b). The direction of the reaction time difference was the same as observed in analysis 2. Thus, the effect of run number was replicated.
Word frequency × German run 1 percent correct
The effect of word frequency × German run 1 percent correct was significant. Reaction times were longer for lower frequency words than for higher frequency words. This difference was greater for participants with lower German run 1 percent correct (70% correct, high frequency: M_{btf} = 830 ms, 95% CI_{btf} 756 ms, 920 ms; 70% correct, low frequency: M_{btf} = 1062 ms, 95% CI_{btf} 942 ms, 1217 ms) than for those with higher German run 1 percent correct (90% correct, high frequency: M_{btf} = 880 ms, 95% CI_{btf} 827 ms, 941 ms; 90% correct, low frequency: M_{btf} = 1050 ms, 95% CI_{btf} 974 ms, 1139 ms), (b_{interaction} = − 1.003e−04, t(3158) = − 2.470, p = 0.014; Tables 12, 13, Fig. 6c). The direction of the reaction time difference was the same as observed in analysis 2. Thus, the effect of word frequency × German run 1 percent correct was replicated.
Word choice and word choice × word frequency
Word choice × word frequency was significant. Reaction times were shorter for modal names than for nonmodal names. The advantage of higher frequency words over lower frequency words was greater for modal names (modal, high frequency: M_{btf} = 851 ms, 95% CI_{btf} 806 ms, 903 ms; 70% correct, modal, low frequency: M_{btf} = 1053 ms, 95% CI_{btf} 983 ms, 1135 ms) than for the nonmodal names (nonmodal, high frequency: M_{btf} = 951 ms, 95% CI_{btf} 888 ms, 1023 ms; nonmodal, low frequency: M_{btf} = 1050 ms, 95% CI_{btf} 975 ms, 1138 ms), (b_{interaction} = − 3.185e−05, t(3239) = − 3.276, p = 0.001; Tables 12, 13, Fig. 6d). Thus, the effect of word choice was replicated. The word choice × word frequency interaction became significant in this larger sample. However, the pattern of the directions of the reaction time difference was not consistent with the prediction by the Cascade hypothesis. Thus, the Cascade hypothesis was not supported.
First phoneme difference × gender × age
The effect of first phoneme difference × gender was qualified by age. Among younger participants (e.g., below 26 years old), the advantage of the same first phoneme over the different first phonemes was smaller for males (male, age 19, same first phoneme: M_{btf} = 965 ms, 95% CI_{btf} 808 ms, 1147 ms; male age 19, different first phonemes: M_{btf} = 976 ms, 95% CI_{btf} 814 ms, 1160 ms) than for females (female, age 19, same first phoneme: M_{btf} = 871 ms, 95% CI_{btf} 683 ms, 1049 ms; female, age 19, different first phonemes: M_{btf} = 924 ms, 95% CI_{btf} 714 ms, 11,217 ms, b_{2wayInteraction} = 2.253e−4, t(3167) = 2.111, p = 0.035; Tables 12, 13, Fig. 7e1, e2). However, among older participants (e.g., over 26 years old), the advantage of the same first phoneme over the different first phonemes increased in males (male: age 32, same first phoneme: M_{btf} = 931 ms, 95% CI_{btf} 853 ms, 1093 ms; male age 32, different first phonemes: M_{btf} = 1012 ms, 95% CI_{btf} 916 ms, 1204 ms; female: age 32, same first phoneme: M_{btf} = 925 ms, 95% CI_{btf} 813 ms, 1127 ms; female age 32, different first phonemes: M_{btf} = 946 ms, 95% CI_{btf} 830 ms, 1156 ms; b_{3wayInteraction} = − 8.966e−06, t(3166) = − 2.198, p = 0.028; Tables 12, 13; Fig. 7e3–e5). These results were consistent with the prediction by the decrease of the inhibitory cognitive control with the increase of age.
Sample difference and theoreticallyrelevant participantrelated variables
Part of the sample difference was the increase of the age range. Here we briefly report two of the agerelated results that were significant in a separate comprehensive study of sample difference decomposition.
First phoneme difference × age of L2 acquisition
In a complex model to systematically decompose the sample difference present in analysis 3, first phoneme difference × age of L2 acquisition was one of the significant interactions that involved participantrelated variables. The advantage of the same initial phoneme across both languages was smaller as the age of L2 acquisition was earlier (Fig. 8a). This result was consistent with the prediction derived by the different phonological encoding hypothesis.
Word choice × age
In a complex model to systematically decompose the sample difference present in analysis 4, word choice × age was one of the significant interactions that involved participantrelated variables. The advantage of the modal names over nonmodal names was smaller as the participants were younger (Fig. 8b). This result was consistent with the prediction by the decline of cognitive control with the increase of age.
Discussion
The present study investigated in what context longer RTs for object naming are likely to occur along the various stages of singleword production in healthy proficient bilingual adults. We tested preselected factors wellestablished in bilingual cognition and general psycholinguistic word production theories. We also tested interactions between these factors. This could help to gain a better in toto understanding of the interlanguage competition processes.
We have found that longer RTs of our proficient bilingual adults were associated with factors taken to reflect the difficulty in the semantic/lemma selection stage and the phonological code retrieval stage of singleword production interacting with cognitive states changing over trials and runs. These factors include (1) the fatigue effect building over the 131 trials for about 5 min 30 s and over 2 runs, (2) the difficulty in the semantic/lemma selection reflected in nonmodal WC and the German run 1 naming accuracy, (3) the difficulty in phonological code retrieval associated with lowfrequency words and words with the nonoverlapping initial phoneme in the two languages, and (4) the reduced advantage of the run 2 practice effect due to the increasing fatigue effect in later trials and the minimal advantage of practice effect on highfrequency words in the second run. These findings would imply the same phenomenon to occur in settings not confined to the frame of study. Prolonged word production could, for example, play a role in the increased frequency of tipoftongue states for bilinguals, or possible involuntary switches between L1 and L2 partly due to exhausted executive functions [43]. This hypothesis should however be considered tentatively, because it is unclear whether exhaustion similar to the one in a test setting tends to occur outside of long and strenuous study tasks.
The most intriguing interaction was observed where phonological factors interacted with other aspects of cognitive control. The gender difference in the inhibitory control of taskirrelevant information interacted with the bilingual advantage of enhanced phonological activation from L1 to L2 shared initial phonemes, which adversely affected the male speakers. Here, their presumed superior inhibitory control suppressed the facilitative phonological activation associated with the taskirrelevant language. The female speakers on the other hand benefitted from the doubled phonological activation regarding their presumed inferior inhibitory control of the taskirrelevant information.
Another important interaction concerned the speedaccuracy tradeoff. Speakers with higher accuracy in German object naming were associated with longer RTs. Also, an interaction with WF was observed. The WF effect was smaller for slower but highly accurate participants than for quick but less accurate participants. The accuracy difference likely arises at the stage of phonological code retrieval.
Theoretical implications
Support of languageindependent phonological activation
In the present study, a facilitatory effect on RTs was demonstrated when both the L1 and the L2 target word shared the same initial phoneme. The presence of this effect confirms our initial hypothesis. Herein, we suspected a possible increased activation of the initial part of the target word building up by both languages providing a converging access on the level of phonological representations. As a result, a faster phonologicalcode retrieval process occurs compared to cases not sharing the initial phoneme. In this line, our findings support the hypothesis established by Colomé and Miozzo, which argues that during bilingual speech production, phonological representations of a given concept are activated in both languages [9, 10]. Additionally, an influence of task language status was not shown. Therefore, the lack of the languagestatus effect in this dataset cannot be taken as evidence for languagespecific activation or the inhibitory control model [4, 11]. We suspect the lack of the languagestatus effect to be due to the high proficiency that our participants possess.
Additionally, we observed a significant interaction of first phoneme status with age of L2 acquisition. This falls in line with the discussion on languageindependent phonological activation above, but more importantly supports the notion that age of L2 acquisition plays a role in organizing phonological representations as postulated before [24]. We can, however, make no claims regarding whether there are additional loci influenced by age of acquisition.
Gender difference in inhibitory control
Our working hypothesis with regards to a gender difference in inhibitory control in bilingual object naming was built on previous findings implying such a difference for certain processes relying on selfmonitoring. The measure previously used was the Simon task, which requires suppressing taskirrelevant location information to correctly process taskrelevant direction information and at which females were shown to perform worse [19]. While a very recent study provides compelling evidence for the case that bilingual language control is in fact isolated from other inhibitory control, such as tested in the Simon task, the possibility of an unrelated yet analogous influence of gender on language control was not addressed [44]. Thus we extended the gender difference in suppressing taskirrelevant information from the spatial domain to the language domain. Here we would, therefore, expect a genderdependent difference in profit from other facilitating effects, such as the shared initial phoneme facilitation.
For our primary sample, the facilitatory effect of a crosslinguistically shared initial phoneme occurred in females, but not in males to the same extent. A confirmatory analysis with our secondary sample however revealed a slightly different finding, namely an interaction between first phoneme status, gender, and age. While for ages below 26 years, same initial phonemes across languages did shorten RT in women and not in men, the same was not true for ages above 26 years. We interpret this difference to signify a stronger basal level of selfmonitoring about task relevance in language that is prominent in bilingual males compared to bilingual females, but is notably influenced by the worsening of cognitive control during the ageing process [21, 22]. One possible mechanism could be a stronger a priori inhibition of the nontarget language, which would render any facilitation on RTs by means of a cumulative activation of phonological representation null. However, a priori inhibition of the taskirrelevant language already from the semantic process on is not consistent with our data that showed the simultaneous bilingual phonological activation.
Support for the weakerlinks hypothesis
In our findings, the L2 responses were generally given faster than the L1 responses. This finding stands in contrast with frequent reports of the L2 being slower in word production than the L1 [5, 6]. A similar situation was reported by Christoffels and colleagues, where behavioral data showed a faster RT for the L2 than for the L1 [7]. In this study, however, the effect only occurred in languagemixed settings, whereas it disappeared in samelanguage block design such as the one used by us.
A possible explanation might be found in the weakerlinks hypothesis, which stresses the importance of differences in WF as a highly relevant factor leading to different RTs [5, 8]. Since 75% of our participants reported German, presumably the dominant language at the time of the experiment, as their L2, the higher WF gained through the German language dominance might lead to a situation in which this paradoxical RT effect occurs. It did no escape our view however, that the WF effect showed to be stronger for the L2 as well. This in turn conflicts, on first view, the weakerlinks hypothesis, which predicts that language dominance should be related to a smaller WF effect [25]. This interaction effect could be explained in two different ways.
First, it should be reminded of how the smaller WF effects is achieved along the time course of language development: WF first benefits highfrequency words in reducing RTs before lowfrequency words catch up [25]. Therefore, following this line and counterfactually going back the timeline, if L1 had been the language of dominant use and L2 had been the language of nondominant use until a point in time, RTs would have been, on average, shorter for L1 than for L2 and the WF effect would have been smaller for L1 than for L2 at that time point. Then, as L1 became the language of nondominant use as with the bilinguals in the present study, RT increased on average for L1, keeping the previously achieved smaller WF effect for L1 but increasing the L1 RTs until RTs for L1 lowfrequency word match RTs for L2 lowfrequency words.
An alternative possible explanation for the conundrum of the interaction effect could come in the consideration of not only ceiling effects playing a role in activation, but also floor effects, affecting highfrequency words of nondominant L1 adversely. There is the possibility of L1, being the predominantly nondominant language in our dataset, summarily having reached an activation floor level through continued nonuse. If in such a scenario even words with a relatively high frequency are rarely used simply due to them belonging to the L1, this attenuated activation would mean that even these highfrequency words rest on a, compared to the much more dominant L2, minor level of activation. The L2, which is summarily more activated due to its dominance, could in this context profit far more from the WF effect: only lowfrequency words would rest at an activation floor, while the more often used words would experience the usual acceleration in RTs via the WF effect. This difference could explain a stronger WF effect for a dominant language; it is however a highly speculative hypothesis deserving of further critical thought.
Distinguishing word choice, proficiency and age of L2 acquisition
WC, proficiency in terms of naming accuracy and age of L2 acquisition are variables shown to affect semantic/lemma selection in the aforementioned studies. We intended to distinguish these variables. The choice of modal vs. nonmodal responses reflects semantic decision processes at the start of word production. As expected, analysis demonstrated a significant effect of WC on RTs. Responses containing nonmodal words arguably involve a more difficult semantic decision for the participant than trials in which the modal word is the obvious choice. This process of decisionmaking seems to take up enough time to impact the resulting RTs (by 100–200 ms on depending on word frequency). While WC does therefore still seem to be a viable measure of processing difficulty at the semantic/lemma selection stage, this study identified age as a factor that has to be taken into account. As previous studies have pointed out, bilinguals do seem to possess distinct advantages in retaining agedependent loss of cognitive ability compared to monolinguals [21]. In this withingroup setting the effects of age are still detectable, and awareness of possible confounding effects via this interaction is important.
Regarding the speedaccuracy tradeoff, our initial hypothesis concerning the inverse relationship between naming accuracy and RT speed was confirmed. As a significant main effect, a higher percentage of initially correctly named objects went in conjunction with slower RTs. In contrast to the factor of WC, naming accuracy did interact with another factor, namely WF, a variable of phonological code retrieval. Naming accuracy therefore seems to be less suited as a reflection of a purely semantic/lemma selection level than WC. This interaction could however be related to cascade models, which predict a semanticphonological interaction. For instance, the size of the unselected semantic/lemma candidates interact with WF, which indexes phonological code retrieval. The more limited the set of candidates is, the smaller the WF effect will be [3]. Therefore, naming accuracy might be connected to a higher, taskcontrolling level rather than to the purely semantic/lemma selection level. From there, it would be possible for naming accuracy to influence the efficacy of word production via modulation of internal monitoring, effectively creating internal constraint on semantic/lemma selection.
This additional hypothetical link is further confirmed by the direction of the significant interaction effect that the WF effect was stronger for lower accuracy naming than for higher accuracy in our dataset. Less selfmonitoring means relying more on the established activation patterns given by the WF effect, while a stronger monitoring results in a stricter internal constraint with less reliance on established activation levels. This pattern falls in line with previous research, showing an inverse relationship between semantic constraint and WF effect in object naming predicted by cascade models [3]. If we hypothesize that naming accuracy is part of the higherlevel constraint generating system, it remains to be seen, in future studies, specifically on what aspect the naming accuracy variable imposes a topdown constraint. Here, the soon to be made available name and imageagreement rating scores specific to our set of objects will certainly prove to be helpful.
Age of acquisition did not turn out to be a significant factor on the level of semantic/lemma selection in our study. We conclude that for the purpose of reflecting semantic processing, WC is the most wellsuited variable in the present study [5].
Limitations
Data analysis under factorial study designs with analysis of variance without the use of mixedeffects multiple regression usually requires a very extensive set of data. Considering the huge sample sizes common for variancebased analyses, we have to acknowledge that our small sample size limits our interpretations.
We circumvented this by taking advantage of the flexibility that the mixedeffects multiple regression analysis offers but that the conventional analysis of variance does not. By using mixedeffects multiple regression, the present study detected the effects of 10 theoretically motivated categorical factors and continuous factors and their interactions on trialbytrial RT measured for 7145 trials for analysis 1 and 3267 trials for analysis 2. In addition to the advantage of multiple regression analysis that is able to compute the effects of fixedfactors, controlling for all other factors in the model, mixedeffects multiple regression performs byparticipant analysis and byitem analysis standardly required from psycholinguistic study in one analysis and partialled out the significant participantrandom effect (idiosyncrasy of the study participants) and the significant itemrandom effect (idiosyncrasy of objects used in the study); thus, the significant effects of the fixed factors should be generalizable to people and stimuli outside the samples used in the study.
Furthermore, our data is subject to an imbalanced language distribution. 75% of our participants reported German as their L2, which may be enough to heavily influence the results, but not enough to clearly attribute any specific observations to. This imbalance would pose a problem if the statistical method was insufficient to partial out the effects of other fixed factors and random effects of participants and items. The consequences might include:
25% nondominant L2 masking an even stronger WF effect for L2, which could, if present, be interpreted to disconfirm the weakerlinks hypothesis.
15% dominant L1 feigning a bigger WF effect for the L1. If this were the case, it might also be interpreted against the weakerlinks hypothesis.
Skewing of RT towards a German languagespecific average, weakening the potential for generalization of our data interpretations [45].
Outside statistics, regarding language dominance, we assume German language dominance due to the experiment taking place in a Germanspeaking frame, yet there was no specific data lifted regarding the amount of usage of each participant’s languages.
Similarly, because the source study for which we measured object naming RT does not have supplementary language proficiency scores measured on established batteries in languages of the participants (German, English, French, Italian, Luxembourgian, Slovakian, Chinese, Bosnian, Croatian, Spanish, and Cantonese) beyond object naming accuracy, we can make no hard statements regarding individual language proficiency, a factor that has been suspected to strongly influence bilingual word production peculiarities [7, 46].
Lastly, we have to concede that for variables such as gender, it is impossible for us to control for any unknown third factors across the grouping variable. To solve this problem, a much bigger sample size across many different personal backgrounds would be required, which we unfortunately did not have access to.
Conclusions
Our mixedeffects multiple regression analysis of bilingual object naming RT revealed that the single word production process in healthy adult bilinguals is affected by interactions among cognitive, phonological, and semantic factors. Bilingual phonological activation interacted with gender in the inhibitory control of taskirrelevant language. Phonological code retrieval interacted with language status, language dominance, practice effect and speedaccuracy tradeoff. The practice and fatigue effects interacted as well. Age of acquisition appears to modulate phonological word representations. Our analysis revealed that WC stands out as a robust predictor, unaffected by other factors, to detect failures in semantic/lemma selection. Taken together, dense interactions between phonological factors and other factors revealed in the present study have confirmed that meaningsound mappings are arbitrary within and across different languages and bilingual brains orchestrate cognitive, psycholinguistic, and functional components to enable speedy and accurate single word production.
Availability of data and materials
The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.
Abbreviations
 CI:

confidence interval
 NR:

no response
 nTMS:

navigated transcranial magnetic stimulation
 L1:

first language
 L2:

second language
 PE:

performance error
 RT:

reaction time
 SD:

standard deviation
 SE:

semantic error
 WC:

word choice
 WD:

word duration
 WF:

word frequency
References
 1.
Levelt WJ, Roelofs A, Meyer AS. A theory of lexical access in speech production. Behav Brain Sci. 1999;22(1):1–38.
 2.
Indefrey P. The spatial and temporal signatures of word production components: a critical update. Front Psychol. 2011;2:255.
 3.
Griffin ZM, Bock K. Constraint, word frequency, and the relationship between lexical processing levels in spoken word production. J Mem Lang. 1998;38(3):313–38.
 4.
Costa A, Caramazza A, SebastianGalles N. The cognate facilitation effect: implications for models of lexical access. J Exp Psychol Learn Mem Cogn. 2000;26(5):1283.
 5.
Hanulová J, Davidson DJ, Indefrey P. Where does the delay in L2 picture naming come from? Psycholinguistic and neurocognitive evidence on second language word production. Lang Cogn Process. 2011;26(7):902–34.
 6.
Ivanova I, Costa A. Does bilingualism hamper lexical access in speech production? Acta Physiol. 2008;127(2):277–88.
 7.
Christoffels IK, Firk C, Schiller NO. Bilingual language control: an eventrelated brain potential study. Brain Res. 2007;1147:192–208.
 8.
Gollan TH, Montoya RI, FennemaNotestine C, Morris SK. Bilingualism affects picture naming but not picture classification. Mem Cogn. 2005;33(7):1220–34.
 9.
Colomé À. Lexical activation in bilinguals’ speech production: languagespecific or languageindependent? J Mem Lang. 2001;45(4):721–36.
 10.
Colomé À, Miozzo M. Which words are activated during bilingual word production? J Exp Psychol Learn Mem Cogn. 2010;36(1):96.
 11.
Green DW. Mental control of the bilingual lexicosemantic system. Bilingualism Lang Cogn. 1998;1(2):67–81.
 12.
Nichols ES. The influence of proficiency and age of acquisition on second language processing: an fMRI study of MandarinEnglish bilinguals. 2013.
 13.
Brysbaert M, Ghyselinck M. The effect of age of acquisition: partly frequency related, partly frequency independent. Vis Cogn. 2006;13(7–8):992–1011.
 14.
Oldfield RC, Wingfield A. Response latencies in naming objects. Q J Exp Psychol. 1965;17(4):273–81.
 15.
Jescheniak JD, Levelt WJ. Word frequency effects in speech production: retrieval of syntactic information and of phonological form. J Exp Psychol Learn Mem Cogn. 1994;20(4):824.
 16.
Lehtonen M, Soveri A, Laine A, Järvenpää J, de Bruin A, Antfolk J. Is bilingualism associated with enhanced executive functioning in adults? A metaanalytic review. Psychol Bull. 2018;144(4):394–425.
 17.
Bialystok E, Craik FI, Klein R, Viswanathan M. Bilingualism, aging, and cognitive control: evidence from the Simon task. Psychol Aging. 2004;19(2):290.
 18.
Parker Jones Ō, Green DW, Grogan A, Pliatsikas C, Filippopolitis K, Ali N, Lee HL, Ramsden S, Gazarian K, Prejawa S. Where, when and why brain activation differs for bilinguals and monolinguals during picture naming and reading aloud. Cereb Cortex. 2011;22(4):892–902.
 19.
Stoet G. Sex differences in the Simon task help to interpret sex differences in selective attention. Psychol Res. 2017;81(3):571–81.
 20.
Grady CL, Springer MV, Hongwanishkul D, McIntosh AR, Winocur G. Agerelated changes in brain activity across the adult lifespan. J Cogn Neurosci. 2006;18(2):227–41.
 21.
Bak TH, Nissan JJ, Allerhand MM, Deary IJ. Does bilingualism influence cognitive aging? Ann Neurol. 2014;75(6):959–63.
 22.
Persson J, Lustig C, Nelson JK, ReuterLorenz PA. Age differences in deactivation: a link to cognitive control? J Cogn Neurosci. 2007;19(6):1021–32.
 23.
Ellis AW, Ralph L, Matthew A. Age of acquisition effects in adult lexical processing reflect loss of plasticity in maturing systems: insights from connectionist networks. J Exp Psychol Learn Mem Cogn. 2000;26(5):1103.
 24.
Brown GD, Watson FL. First in, first out: word learning age and spoken word frequency as predictors of word familiarity and word naming latency. Mem Cogn. 1987;15(3):208–16.
 25.
Gollan TH, Montoya RI, Cera C, Sandoval TC. More use almost always means a smaller frequency effect: aging, bilingualism, and the weaker links hypothesis. J Mem Lang. 2008;58(3):787–814.
 26.
Harald Baayen R, Milin P. Analyzing reaction times. Int J Psychol Res. 2010;3(2):12–28.
 27.
Tussis L, Sollmann N, BoeckhBehrens T, Meyer B, Krieg SM. Identifying cortical first and second language sites via navigated transcranial magnetic stimulation of the left hemisphere in bilinguals. Brain Lang. 2017;168:106–16.
 28.
Kohnert K. Bilingual children with primary language impairment: issues, evidence and implications for clinical actions. J Commun Disord. 2010;43(6):456–73.
 29.
Krieg SM, Sollmann N, Tanigawa N, Foerschler A, Meyer B, Ringel F. Cortical distribution of speech and language errors investigated by visual object naming and navigated transcranial magnetic stimulation. Brain Struct Funct. 2016;221(4):2259–86.
 30.
Sollmann N, Tanigawa N, Ringel F, Zimmer C, Meyer B, Krieg SM. Language and its righthemispheric distribution in healthy brains: an investigation by repetitive transcranial magnetic stimulation. NeuroImage. 2014;102(Pt 2):776–88.
 31.
Sollmann N, Tanigawa N, Tussis L, Hauck T, Ille S, Maurer S, Negwer C, Zimmer C, Ringel F, Meyer B, et al. Cortical regions involved in semantic processing investigated by repetitive navigated transcranial magnetic stimulation and object naming. Neuropsychologia. 2015;70:185–95.
 32.
Brysbaert M, Buchmeier M, Conrad M, Jacobs AM, Bölte J, Böhl A. The word frequency effect. Exp Psychol. 2011;58:412–424.
 33.
Baayen H. Analyzing linguistic data: a practical introduction to statistics using R. Cambridge: Cambridge University Press; 2008.
 34.
Bates D, Maechler M, Bolker B, Walker S. lme4: linear mixedeffects models using Eigen and S4. R package version. 2014; 1(7):1–23.
 35.
Bates D, Maechler M, Bolker B, Walker S, Christensen RHB, Singmann H, Dai B, Scheipl F, Grothendieck G, Green P. Linear mixedeffects models using ‘Eigen’ and S4. R package version 1.117. 2018.
 36.
Halekoh U, Højsgaard S. A kenwardroger approximation and parametric bootstrap methods for tests in linear mixed models—the R package pbkrtest. J Stat Softw. 2014;59(9):1–30.
 37.
Kuznetsova A, Brockhoff PB, Christensen RH. lmerTest package: tests in linear mixed effects models. J Stat Softw. 2017;82(13):1–26.
 38.
Kenward MG, Roger JH. Small sample inference for fixed effects from restricted maximum likelihood. Biometrics. 1997;53(3):983–997.
 39.
R Core Team. R: a language and environment for statistical computing. 2013.
 40.
Pinheiro J, Bates D, DebRoy S, Sarkar D, R Core Team. nlme: linear and nonlinear mixed effects models. R package version 3.1117. 2014. http://CRAN.Rproject.org/package=nlme. Accessed 24 Apr 2018.
 41.
Barton K. Multimodel Inference. R package version 1.13. 4. 2015.
 42.
Fox J. Effect displays in R for generalised linear models. J Stat Softw. 2003;8(15):1–27.
 43.
Pyers JE, Gollan TH, Emmorey K. Bimodal bilinguals reveal the source of tipofthetongue states. Cognition. 2009;112(2):323–9.
 44.
Paap KR, AndersJefferson R, Mikulinsky R, Masuda S, Mason L. Language: on the encapsulation of bilingual language control. J Mem Lang. 2019;105:76–92.
 45.
Bates E, D’Amico S, Jacobsen T, Székely A, Andonova E, Devescovi A, Herron D, Lu CC, Pechmann T, Pléh C. Timed picture naming in seven languages. Psychon Bull Rev. 2003;10(2):344–80.
 46.
Costa A, Santesteban M. Lexical access in bilingual speech production: evidence from language switching in highly proficient bilinguals and L2 learners. J Mem Lang. 2004;50(4):491–511.
Acknowledgements
We would like to thank Mr. Axel Schroeder for his support during data acquisition and storage.
Funding
The study was completely financed by institutional grants from the Department of Neurosurgery.
Author information
Affiliations
Contributions
SS performed data handling, data analysis, data interpretation, literature research, and drafted the manuscript. NT conducted data handling, data analysis including statistics, data interpretation, literature research, and supported the drafting of the manuscript. LT performed data acquisition and data handling. BM was involved in the conception of the experimental design of the study, data acquisition, data handling, and was responsible for study supervision. NS was involved in designing the study, performed data acquisition, data handling, data analysis, data interpretation, literature research, and assisted during the drafting of the manuscript. SK was involved in the conception of the experimental design of the study, data acquisition, data handling, data interpretation, literature research, and drafting of the manuscript and supervised the study. All authors read and approved the final manuscript.
Corresponding author
Correspondence to Sandro M. Krieg.
Ethics declarations
Ethics approval and consent to participate
The study was approved by the local ethics committee (Institutional Review Board of the Technical University of Munich; Registration number: 222/14) and was conducted in accordance with the Declaration of Helsinki. Written informed consent was obtained from all subjects prior to study inclusion.
Consent to publish
Not applicable.
Competing interests
NS received honoraria from Nexstim Plc (Helsinki, Finland). SK is consultant for Nexstim Plc (Helsinki, Finland) and received honoraria from Medtronic (Meerbusch, Germany) and Carl Zeiss Meditec (Oberkochen, Germany). SK and BM received research grants and are consultants for Brainlab AG (Munich, Germany). BM received honoraria, consulting fees, and research grants from Medtronic (Meerbusch, Germany), Icotec ag (Altstätten, Switzerland), and Relievant Medsystems Inc. (Sunnyvale, CA, USA), honoraria and research grants from Ulrich Medical (Ulm, Germany), honoraria and consulting fees from Spineart Deutschland GmbH (Frankfurt, Germany) and DePuy Synthes (West Chester, PA, USA), and royalties from Spineart Deutschland GmbH (Frankfurt, Germany). However, all authors declare that they have no competing interests regarding the materials used or the results presented in this study.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.
About this article
Cite this article
Schramm, S., Tanigawa, N., Tussis, L. et al. Capturing multiple interaction effects in L1 and L2 objectnaming reaction times in healthy bilinguals: a mixedeffects multiple regression analysis. BMC Neurosci 21, 3 (2020). https://doi.org/10.1186/s128680200549x
Received:
Accepted:
Published:
Keywords
 Bilinguals
 Language
 Object naming
 Voice latency
 Voice onset measurements
 Word production