535 Studies in Second Language Learning and Teaching Department of English Studies, Faculty of Pedagogy and Fine Arts, Adam Mickiewicz University, Kalisz SSLLT 7 (3). 2017. 535-556 doi: 10.14746/ssllt.2017.7.3.9 http://www.ssllt.amu.edu.pl L2 irregular verb morphology: Exploring behavioral data from intermediate English learners of German as a foreign language using generalized mixed effects models Thomas Wagner University College of Education, Linz, Austria thomas.wagner@ph-ooe.at Abstract This paper examines possible psycholinguistic mechanisms governing stem vowel changes of irregular verbs in intermediate English learners of German as a foreign language (GFL). In Experiment 1, nonce-infinitives embedded in an authentic fictional text had to be inflected for German preterite, thus test- ing possible analogy-driven pattern associations. Experiment 2 explored the psycholinguistic reality of the so-called apophonic path by prompting two in- flections for one given nonce-word. Data were analyzed using generalized mixed effects models accounting for within-subject as well as within-item var- iance. The results of Experiment 1 and 2 support the notion of a pattern asso- ciator and yield only scarce evidence for the psycholinguistic reality of a uni- versal apophonic path. Therefore, the organization of irregular verb morphol- ogy in the mental lexicon of intermediate GFL learners might best be captured by the linguistic notion of structured lexical entries as well as the psycholin- guistic mechanism of an analogy-based pattern associator. Keywords: mental lexicon; irregular verb morphology; analogy; pattern asso- ciator; apophony Thomas Wagner 536 1. Introduction After around 130 years of research into the human mental lexicon (Whitaker, 2006), the semi-regular paradigm of German irregular verbs, combining rule-like as well as idiosyncratic processes, has become the fruit fly in psycholinguistic research. It is thought to offer invaluable insights into storage and retrieval of words in the human mental lexicon. In fact, these insights promise to shed light on the nature of human cognition in general. Over the last two decades, German irregular verb morphology has been explored from various perspectives. Data come from behavioral L1 studies of both children and adult speakers (Clahsen, Hadler, & Weyerts, 2004; Smolka, Zwitserlood, & Rösler, 2007), impaired speakers studies (Marusch, von der Mals- burg, Bastiaanse, & Burchert, 2012; Penke, Wimmer, Hennies, Hess, & Roth- weiler, 2014), electrophysiological studies (Smolka, Khader, Wiese, Zwitserlood, & Rösler, 2013), neuroimaging (Lück, Hahne, & Clahsen, 2006), constructivist neural network modelling (Ruh & Westermann, 2008) and corpus studies (Kö- pcke, 1998). The above studies focus on processing differences, reporting and discussing possible evidence for qualitatively distinct mechanisms of inflection. While some findings suggest that all German verbs are inflected by the same psycholinguistic mechanism, there is evidence pointing towards two qualita- tively distinct processing routes in the speakers’ mental lexicon. Overall, current findings appear to remain inconclusive in this respect. Most studies concur, though, that some sort of pattern- and analogy-driven mechanisms would be necessary to handle a key component of German verb in- flection, namely vowel change, a systematic stem vowel alternation in verbal in- flection. Like in English, a lot of irregular German verbs exhibit such stem vowel alternations when inflected for the German past tense and past participle, such as singen-sang-gesungen ‘sing-sang-sung.’ Modern single-route approaches model vowel change through analogical or connectionist networks, while the dual-route model accounts for vowel change by means of a so-called pattern as- sociator. The psycholinguistic reality of such a pattern associator has been ex- plored in L1 speakers in a number of studies (Bybee & Moder, 1983; Bybee & Slobin, 1982; Prasada & Pinker, 1993), but, unlike English, German as a foreign language (GFL) behavioral evidence is scarce. While recent studies focus on pro- cessing differences (Hahne, Müller, & Clahsen, 2006; Neubauer & Clahsen, 2009; Pliatsikas & Marinis, 2013; Strobach & Schönpflug, 2011), the intricacies of Ger- man vowel change remains largely unexplored. In a similar vein, Strobach and Schönpflug (2011) concluded that prior behavioral evidence appears inconclusive at best, suggesting further research was needed especially with regard to L2. L2 irregular verb morphology: Exploring behavioral data from intermediate English learners of. . . 537 The present study tries to fill this gap. It reports findings from two well-es- tablished nonce-word research designs in which 82 intermediate English GFL learners provided preterite, participle, and infinitive formations to given German nonce-words. The rationale behind this study was to test in how far GFL vowel change was governed by a pattern associator, operating on prototypical schemas (Bybee & Slobin, 1982; Köpcke, 1998; Pinker, 1999), or by the so-called universal apophonic path (Ségéral & Scheer, 1998). If universal apophony were psycholin- guistically real, GFL interlanguage patterns could not be attributed to transfer phe- nomena but would instead be the result of universal developmental effects. 2. German irregular verb morphology and models of inflection There are about 160 simplex irregular verbs in modern German, although, depend- ing on the choice of reference corpora, counts vary considerably. While Middle High German exhibited about 400 irregulars, the number decreased steadily, yielding to- day’s moderate type-frequency of roughly 4% of all verbs (Köpcke, 1998; Bittner, 1996). Their token-frequency, however, is remarkable, and roughly resembles that of the regulars (Clahsen, 1997; Clahsen, Eisenbeiß, & Sonnenstuhl-Henning, 1997). The verbal paradigm in German is traditionally categorized as consisting of regular (weak) and irregular (strong) forms, combining rule-based affixation with irregular stem vowel changes. German participles, for instance, involve three mor- phological processes: a prosodically constrained ge- prefixation, optional stem vowel allomorphy, as well as -(e)n or -t suffixation, both occurring with roughly the same token frequency in adult and child corpora (Clahsen, 1997). Recently, however, analyses have become more complex with regard to form and function of stem vowel change or apophony within the paradigm (Trompelt, Bordag, & Pechmann, 2013; Wiese, 2008), resulting in regular, hybrid, and irregular classes. Table 1 illustrates the most common inflectional patterns. Table 1 German vowel change patterns Regular, one stem vowel only Hybrid, change in participle and pret- erite Irregular, change in pre- sent, preterite, and par- ticiple Mixed, vowel change + suffix Infinitive spiel-en ‘to play’ trink-en ‘to drink’ sprech-en ‘to speak’ renn-en ‘to run’ Present tense 3rd person spiel-t ‘plays’ trink-t ‘drinks’ sprich-t ‘speaks’ renn-t ‘runs’ Preterite 3rd person spiel-te ‘played’ trank ‘drank’ sprach ‘spoke’ rann-te ‘ran’ participle ge-spiel-t ‘played’ ge-trunk-en ‘drunk’ ge-sproch-en ‘spoken’ ge-rann-t ‘run’ German stem vowel alternations for preterite and participle inflection form a patterned semi-regular paradigm. From a diachronic perspective, these patterns are a mere artefact of older variants (Bybee & Newman, 1995) and appear opaque Thomas Wagner 538 and unpredictable (Nübling, Dammel, Duke, & Szczepaniak, 2006), once even apostrophized as “one of the classic chestnuts of morphological analysis” (Ander- son, 1988, p. 157). Due to this unpredictability, German irregular verbs exhibit restricted gen- eralization properties, and there is little consensus about the distinctiveness of attested vowel change classes. The phonological patterns, for example, are nei- ther necessary nor sufficient to predict to which class a verb should conform. A verb such as sinken ‘to sink,’ for instance, readily joins the irregular pattern dis- played by trinken ‘drink’ (trinken : trank : getrunken :: sinken : sank : gesunken), while winken ‘to wave’ and blinken ‘to blink’ do not. Accordingly, attempts to define vowel change categories vary considerably, ultimately treating almost each and every variant of vowel change as a class of its own. German verb morphology has been a controversial object of enquiry in psy- cholinguistics. Studies throughout the last 30 years have resulted in the long-stand- ing past-tense-debate (Pinker & Ullman, 2002; Wagner, 2010). From this debate, two approaches emerged. Single-route models suggest one mechanism to account for storage and retrieval of both regular and irregular forms in the mental lexicon. Such mechanisms are either symbolic or non-symbolic in nature. Symbolic models (Albright & Hayes, 2003; Bittner, 1996) are inherently rule-based and deterministic, which creates a number of disadvantages: They are not, for instance, convincing in capturing vowel change as a concatenative process, they do not allow for a gradual transition between regular and irregular mechanisms, and they often lack the psy- cholinguistic underpinning from behavioral data (Becker, 1990). Analogical learners and connectionist networks, in contrast, model both regular and irregular verbal inflection entirely rule-free, conceiving linguistic representations in the mental lexi- con as graded and domain-general phenomena (Eddington, 2000; Goebel & Inde- frey, 2000; Westermann, Willshaw, & Penke, 1999). Connectionist models do this by cyclically building and relating weighted connections of parallelly distributed phonological and semantic information about verb infinitives and their inflections. Analogical learners store huge databases of individual exemplars and calculate gen- eralization properties among these on the basis of near-neighbourhood similarities. Trying to synthesize symbolic and associationist processing, the dual-route model assigns different mechanisms to regular and irregular morphology. Regular verbs would be processed by abstract symbolic rules, while irregular and thus lex- icalized German verbs would be stored undercomposed in memory and pro- cessed by associative patterning, not unlike what Ullman (2001) called declarative knowledge. Such an architecture would, as proponents of this approach claim, represent the two core characteristics of human cognition (Clahsen, 1999; Lück, Hahne, & Clahsen, 2006; Pinker, 1999). L2 irregular verb morphology: Exploring behavioral data from intermediate English learners of. . . 539 3. German irregular verb morphology in L2 acquisition German verb morphology has not only been controversial in psycholinguistics, but it has also been the bane of countless language learners (Neubauer & Clah- sen, 2009; Pinker, 1999). In order to trace possible difficulties in the acquisition of German irregular verb morphology, studies looked at processing differences. However, as with L1 speakers, there is conflicting evidence. Advanced Greek learners of German, for instance, employed two different mechanisms for regu- lar and irregular inflection (Pliatsikas & Marinis, 2013), while Polish learners re- lied more on lexical storage and retrieval compared to German L1 speakers (Neubauer & Clahsen 2009). And Strobach and Schönpflug (2011) report that their data from English learners of German were consistent with a single-route connectionist account. GFL vowel change, however, has not been examined in detail yet. For English L2, there is evidence in favour of an analogical or proto- typical organization in the mental lexicon of advanced German learners of Eng- lish (Wagner, 2010). At the heart of such prototype models are output-oriented morphophonological schemas, governing each vowel change class. Such classes emerge through exemplars sharing various morphophonological properties to varying degrees, thus following the principles of family resemblance (Rosch, 1975). For German L1, prototypical schemas have been suggested, too (Bybee, 1995; Wagner, 2010), but there is evidence that, contrary to English, analogical formations in German rely almost exclusively on a verb’s rhyme (Penke, 2006). An intriguing alternative to prototypical schemas comes from Ségéral and Scheer’s (1998) universal apophonic path. They claim that apophony across all types of languages followed a unidirectional five-part vowel change sequence [Øàiàaàuàu], providing all the necessary information in order to predict German stem alternations. This is possible only because the authors sophisticat- edly reanalyze the German verb paradigm as consisting of an infra-segmental level. The alleged universality of their path is challenging, though, especially since both English and German provide additional supportive evidence from children’s nursery rhymes, onomatopoeic expressions, and expletives. Amongst these, apophonic vowel changes such as [ɪ-ʌ] are remarkably frequent. The pat- tern [ɪ-a-ʊ] is, in fact, the most frequent type of a three-vowel-change pattern in German. If this apophonic path were to be psycholinguistically real, it would seriously challenge both single- and dual-route-models. The two nonce-word elicitation experiments reported in this paper are supposed to test these competing approaches. If a universal vowel change mechanism were psycholinguistically real, we should see learners of German (a) predominantly, or even exclusively, use vowel changes faithful to the apophonic path, and (b) adhere to its mono-directionality, thus rejecting vowel-changes Thomas Wagner 540 prompted in the reverse direction. If German verb morphology were governed by prototypical schemas, we should expect (a) a strong influence of the verb’s constituents on vowel change, (b) a complete overlap of the prototypical test item with the statistically most effective constituents, and (c) an insensitivity towards directionality effects. 4. General method 4.1. Overview Both experiments employed a repeated measure elicitation task, using nonce- words either embedded in an authentic fictional text or as part of a sentence completion frame. Although nonce-word elicitation cannot be controlled as thoroughly as, for instance, priming, lexical decision or eye-movement experi- ments, this research paradigm was used because of its natural setting and its long history in psycholinguistics (Berko, 1958; Bybee & Moder, 1983; Lemhöfer & Radach, 2009). In Experiment 1, 34 participants inflected 28 nonce infinitives and 15 distractors for preterite. In Experiment 2, 48 participants inflected either 28 irregular nonce-infinitives for preterite and participle, or 28 nonce preterites for infinitive and participle. The order in which items were presented varied across the test questionnaires in both experiments, thus helping counterbalance possible sequence effects (Prasada & Pinker, 1993; Ramscar, 2002). 4.2. Stimuli Based on the lexical statistics reported in Köpcke (1998), the 28 most prototypical vowel change triggering nonces were filtered out of 344 phonotactically well- formed constituent combinations. A subset of Experiment 2 used preterite forms by transposing the infinitive stems [i:] and [ɪ] into [a]-, [o:]-, or [ɔ]-vowel-change preterites, depending on the most frequent analogies to existing verbs. Thus, a nonce like strießen would result in stross by analogy to schließen ‘to close, to lock;’ schloss ‘closed, locked.’ In both experiments, test items’ constituent variants in- cluded onset structures C, CC, [ʃ], [ʃ]C, and [ʃ]CC, as well as coda variants [g], [m/m], [ŋ], [ŋk], and [s/ç]. All stimuli can be found in the appendix to this paper. 4.3. Participants Data for Experiment 1 came from randomly recruited GFL speakers of the Uni- versity of Maynooth, University of Edinburgh, and University of Leicester (N = 34). Data for Experiment 2 were randomly sampled among GLF speakers from L2 irregular verb morphology: Exploring behavioral data from intermediate English learners of. . . 541 Dublin City University, Trinity College Dublin, the University of Manchester, and University of Hull (N = 48). Random sampling was done within one cohort of the respective study programs involving German, and participants were not nested within classes. The test questionnaires were administered in small groups. Among the 82 participants, there were 42 females and 40 males. They were all Irish or British citizens, their L1 was English, there were no bilinguals, and they had been residents in their respective countries from birth. The mean age of the participants was 19 years (SD = 1.19), with a range from 17 to 21 years. They all had been learning German in instructional settings as part of their school cur- ricula for more than 4 years and approached intermediate level B1 (Council of Europe, 2001). They all studied German as part of their respective undergradu- ate degree programs. All subjects were unimpaired speakers. They did not re- ceive any remuneration for their participation. 4.4. Procedure For Experiment 1, participants were told that their data would feed into a new trans- lation of Burgess’ classic novel A clockwork orange (Burgess, 1962). The introduction pretended that the learners’ intuition was deemed instrumental in finding adequate translations of the notorious Nadsat-slang verbs. Using such a real novel extract, rid- dled with artificial slang, was meant to avoid unwanted semantic associations and distract the attention away from the linguistic details. Overall, great care was taken to leave subjects in Experiment 1 deliberately naïve to the real purpose of the exper- iment. After two items for practice, an audio CD provided the text with the intended pronunciation of the nonces as well as the timing for the gap-filling. Contrary to Pra- sada and Pinker (1993), and following Orsolini and Marslen-Wilson (1997), it was deemed appropriate to present the stimuli only once and elicit only one response to a particular test item in both experiments. This was supposed to discourage strategic approaches and tap into retrieval processes as directly as possible. The questionnaire of Experiment 2 informed participants that they were taking part in a genuine linguistic experiment about how German verbs are stored and or- ganised in the mental lexicon. Then they were told that, in order to make the experi- ment more interesting, they would be asked to creatively inflect non-existing forms; thus, they were encouraged to rely on their linguistic intuition about the appropriate sound of the inflection. One subset of the participants in Experiment 2 were asked to inflect given infinitives for preterite and participle, while the other one was prompted to inflect given preterite forms for infinitive and participle. Prompting one subset to inflect backward was supposed to test directionality effects. Recall that the apophonic path defines rule-like input-output derivations of one vowel quality out of another. Such derivations are assumed to be directional, and hence they are not expected to Thomas Wagner 542 work in the reverse order. In other words, if the apophonic path was real, English learners of German should prove to be able to complement a fragmentary apophonic path such as [iàx] with ease, whereas the reverse direction such as in [xßa] should prevent speakers from systematic vowel change inflections. Using nonce participles for testing the apophonic path’s directionality proved inadequate since, contrary to English, in German the choice of possible preterite inflections from a given participle in a reverse order is rather restricted. A given [ʊ] as a participle stem, for instance, would almost automatically elicit [a] in the preterite, since [i-a-ʊ] is the by far the most predominant German pat- tern. In order to test possible learners’ preferences, German preterites and not participles were given. After two items for practice, a CD provided all sentence frames, thereby timing the filling of the gaps and controlling potential confusion about the pronunciation of a verb (like [ɔ] or [o:] in an item such as plog). 4.5. Data coding and analysis Test items in both experiments were coded for onset, nucleus, and coda variants, covering onset structures C, CC, [ʃ], [ʃ]C, and [ʃ]CC, two nuclei, [i:] and [ɪ], as well as codas [g], [m/n], [ŋ], [ŋk], and [s/ç]. After inspection of frequency tables, on- set was collapsed into [ʃ] with optional consonant versus consonant only, and coda into consonant, velar, and fricative. Responses in Experiment 1 were coded for vowel changes in [a], [o], and [u], mixed inflections, and the residual category others. Wherever ATR contrasts were irrelevant for the present analyses, vowel variants such as [a:] versus [a], [i:] versus [ɪ], [o:] versus [ɔ], and [u:] versus [ʊ] were collapsed into [a], [i], [o], and [u] (Wiese, 2000). Responses in Experiment 2 were coded according to the type of vowel change series they produced as well as their well-formedness. Data were analyzed using generalized mixed regression models as well as non-parametric, conditional inference trees built through recursive partitioning. Both analyses were done using the statistical software R, version 3.3.1 (R Core Team, 2016). Mixed modelling was done using the package lme4 (Bates, Maechler, Bolker, & Walker, 2015), and recur- sive partitioning employed the party package (Hothorn, Hornik, & Zeileis, 2006). Although multifactorial ANOVAs appear to have been the predominant tool of choice in numerous L1 and L2 studies related to the past tense debate, mixed models are much more suited to the present data (Cunnings & Finlayson, 2015; Cunnings & Linck, 2015; Gries, 2015; Jaeger, 2008). They can, for instance, handle non-orthog- onal, unbalanced, and nested designs, typical of repeated measure experiments. They can also directly model dichotomous dependent variables and avoid unwar- ranted assumptions about sphericity, and they simultaneously incorporate random variance of test item and subject (Baayen, Davidson, & Bates, 2008). L2 irregular verb morphology: Exploring behavioral data from intermediate English learners of. . . 543 5. Results and discussion of Experiment 1 In Experiment 1, participants produced, apart from regular inflections (41%), three vowel change patterns. The most prominent one was [i-a], with more than 28%, followed by [i-o] with around 15%, and vowel changes in [u] with 4%. Mixed inflections also covered around 4%. Overall, less than 50% of the responses follow the default, and only 7% of the responses are random. Both the high amount of non-default responses and the high amount of attested vowel changes are re- markable. The nonces spingen, stingen, and schingen attracted the highest vowel change response frequencies, producing predominantly [a]-vowel-change. This could be taken as a first indication of a schema with the form [ʃ (C)_ɪ_ŋ] being prototypical for the most productive vowel change class. In order to investigate whether this overall schema did in fact contain the most prototypical constitu- ents, we first looked at the influence of each constituent on the choice between regular and vowel-changing preterites (excluding the residual others). The mosaic plot in Figure 1 illustrates the distribution of all preterites by constituents. Figure 1 Mosaic plots of two log-linear independence models illustrating the choice of preterite by onset and coda (left panel), and preterite by nucleus and coda (right panel) In the mosaic diagrams, both horizontal and vertical asymmetries indicate significant partial effects of the constituents on the type of preterite formation (p < .001). Size and shading of each tile in the diagrams represent frequencies as well as direction and significance of effects. The darkest grey shade indicates more ob- servations than expected. In the left panel, the dark tiles in the middle and top- right illustrate significant effects for the schemas [ʃC_ŋ(k)] and [C_fricative]. Onset Thomas Wagner 544 has almost no effect. In the right panel, effects for [#_i:_ ŋ(k)] and [#_ɪ_fricative] are visible (middle and top-right dark tiles). In order to explore the above effects in more detail, we performed a general linear mixed effects analysis of the rela- tionship between the constituent variants and the binary choice of preterite. To estimate parameters, restricted maximum likelihood was used instead of penal- ized quasi-likelihood since the latter is reported to produce biased estimates with binary response variables (Thiele & Markussen, 2012). As fixed effects, we en- tered nucleus and coda without interaction term into the model. Their factor lev- els were treatment-coded, so coefficients in the model correspond to simple ef- fects. Nucleus and coda were not crossed since some combinations, due to pho- notactic reasons, were not represented with data points. As random effects, we included intercepts for subjects and items as well as by-subject and by-item random slopes for coda since the effect of coda seemed to significantly vary across subjects and items, too. Moreover, including random slopes renders mixed models conservative and minimises α-errors. The dependent varia- ble was coded binary (regular vs. irregular). Main effect p values were obtained by likelihood ratio tests (all p values < .005). It was also tested if both fixed and random effects were highly correlated, and if the model was overdispersed; neither was the case. Scaled residuals were distributed fairly symmetrically. Table 2 Table of coefficients of the final model, estimated using Laplace approx- imation as well as the optimiser bound by quadratic approximation (bobyqua) instead of the heuristic default Nelder-Mead method Logits SE z p Intercept 0.19 0.35 0.52 .60*** Nucleus (effect size = 0.06) i: -0.25 0.30 -0.82 .41*** Codas (effect size = 0.28) ŋ(k) -1.04 0.31 -3.39 < .001*** s/ç -0.59 0.43 -1.36 .17*** Note. Logits are the log-odds of the parameter estimations; SE is the standard error; z-values come from the corresponding Wald statistics. When building the final model, we first followed Barr, Levy, Scheepers, and Tilly (2013) and therefore tried to include all fixed effects with their interac- tions as well as all random intercepts and slopes. However, adding interactions and random slopes other than coda prevented models from converging, most likely because there were too little data for the number of parameters to be estimated. Given that there still is little consensus as to how to deal with con- vergence problems (Barr et al., 2013; Cunnings & Finlayson, 2015), these terms were dropped again. Table 2 summarises the partial main effects of the constit- uents’ variants of the final model with a pseudo conditional R2 of 0.62. L2 irregular verb morphology: Exploring behavioral data from intermediate English learners of. . . 545 Table 2 illustrates a highly significant main effect for coda (χ2(2) = 14.28, p < .001), and a significant partial effect for codas with the velar nasal plus op- tional obstruent. In other words, [ŋ(k)] significantly affects the choice of preter- ite formations, decreasing the log odds for regulars by -1.04 (SE = 0.31), resulting in a decreased probability for regular responses of p = .30. Compared to nucleus, coda has a substantial effect size (range) of 0.28. Other than that, there are no significant partial effects. However, if we plot nucleus and coda as interactions, we can see the results presented in Figure 2. When looking at the simple main effects (left panel), we can see that the probability of regulars slightly decreases when we go from short (0.41) to long (0.35) nucleus. As for codas, probabilities of regulars decrease for velars (0.28) and fricatives (0.37) compared to other consonants (0.52). Note, though, the overlap of the error bars in both panels, indicating that we are dealing with merely mild effects. In the right panel we can see a substantial decline in probability for regulars (down to 0.30) for short nu- cleus [ɪ] followed by velars (solid line). Similar, but less pronounced, is the de- cline for long nucleus [i:] followed by fricatives (0.34, dashed line). In sum, the mixed effects analysis revealed effects for [#_ɪ_ŋ(k)] as well as [#_i:_fricative]. Figure 2 Effects plots for the individual partial effects in the final model (left panel) and the interaction of nucleus and coda (right panel) The choice between the different vowel changes in the preterites the learn- ers produced was modelled using conditional inference trees built through recur- sive partitioning. Figure 3 shows such a tree model for the different types of vowel change by onset, nucleus, and coda. The tree in Figure 3 is the result of a split algorithm. Unlike traditional classifica- tion and regression tree modelling, however, in which algorithms attempt to increase information gain measures, conditional inference tree modelling uses inferential test statistics in order to retain significant predictors only. As a consequence, the above tree model does not contain any covariates that are independent of the choice of vowel change patterns. Tree growth is thus based on statistical stopping rules, so that neither pruning nor cross-validation are required, and the data cannot be overfitted. Thomas Wagner 546 Figure 3 Conditional inference tree for the types of vowel change by onset, nu- cleus, and coda The algorithm finds only one significant predictor, namely coda (topmost split in the tree, Node 1). This is in line with the mixed model above, where the only significant main effect occurred with coda, too. In the tree diagram, we can see that the distinction between nasal coda structures on the one hand (Node 2 on the left) and the fricatives and the velar obstruent on the other is highly signif- icant (p < .001). The final level of the tree provides the proportional frequencies for the four kinds of vowel change. We find the highest proportion of regular re- sponses for fricatives and the velar obstruent (Node 7) as well as codas [m] and [n] (Node 3). In contrast, most of the vowel change responses can be found for [ŋ(k)], favoring [a] (Node 4), and [s/ç], favoring [o] (Node 6). Overall, the tree model suggests a highly significant influence for coda on the choice between dif- ferent vowel changes, with velar nasals favoring [a], and fricatives favoring [o]. To sum up, the nonces producing most vowel changes had the schema [ʃ(C)_ɪ_ŋ ]. For vowel change versus the default, an independence model showed significant effects for [ʃC_ŋ(k)], [C_fricative], [#_i:_ŋ(k)] and [#_ɪ_fricative], while the generalized mixed model yielded a significant effect for the rhymes [#_ɪ_ŋ(k)] and [#_i:_s/ç]. When predicting the types of vowel change, coda was the only significant predictor, with [ŋ(k)] favoring vowel changes in [a] and fricatives favoring [o]. 6. Results and discussion of Experiment 2 In Experiment 2, conditional inference trees modelling the type of vowel change also showed effects for coda, with [ŋ(k)] favoring [i-a-u] patterns, and fricatives favoring [i-o-o]. Recall, though, that Experiment 2 was supposed to test whether the participants’ vowel changes were faithful to the predictions made by the coda p < 0.001 1 {m,n, ng, nk} {g, s,ch} coda p < 0.001 2 m,n {ng, nk} Node 3 (n = 198) a mix o reg u 0 0.2 0.4 0.6 0.8 1 Node 4 (n = 291) a mix o reg u 0 0.2 0.4 0.6 0.8 1 coda p = 0.034 5 s,ch g Node 6 (n = 296) a mix o reg u 0 0.2 0.4 0.6 0.8 1 Node 7 (n = 96) a mix o reg u 0 0.2 0.4 0.6 0.8 1 L2 irregular verb morphology: Exploring behavioral data from intermediate English learners of. . . 547 apophonic path. Although there is a good deal of consistency between expected and elicited patterns (χ2 (10) = 146.27, p < .001 for given infinitives, χ2 (10) = 270.43, p < .001 for given preterites), there are quite a few inconsistencies. 1st response vowel change preterite 2nd response vowel change participle 1st response vowel change infinitive 2nd response vowel change participle [a] (231) Ö [a-o] (59) [i-a-o] (144) Ö others (20) Ò Ò [a-u] (62) Ò Ò regular (60) Ò [a-a] (48) Ò [e-a] (36) Ø others (62) Ø [i-a] (28) mixed (14) Ò Ò various (15) [i-a-u] (216) Ò Ö others (13) [o] (85) Ò Ò [o-o] (57) Ò regular (72) Ò others (33) Ò [e-a] (44) [u] (21) Ò Ö [u-u] (16) Ø [i-a] (87) Ò [i:-ɔ-ɔ] (240) Ò Ö others (25) Ò regular (71) Ò [i-o] (81) Ò [e-o] (58) Ø [a-u] (5) [i:-o:-o:] (72) Ò various (72) Figure 4 Interaction between preterite and participle response (left) and infini- tive and participle responses (right), excluding regular first responses, with ar- rows marking the various paths of inflectional combinations First, the learners produced 38% unattested vowel changes. For responses starting from a given infinitive, this is evidence against the apophonic path. More- over, 32% of the responses to given nonce preterites were regular. While it is un- derstandable for given infinitives to prompt learners to apply the default and not inflect it by analogy to a phonologically nearest neighbor, it is surprising when it comes to the nonce preterites. Those preterites, such as schoch, stang, or schnoss obviously lack regular suffixes. The 32% regular responses indicate either that the nonce’s obvious irregular phonological shape must have been inaccessible to quite a few learners, or that the directionality of the apophonic path rules out reverse ablaut. However, more than 50% of the responses to a given nonce pret- erite show vowel change commensurate with attested patterns. This, in turn, is evidence against a directional apophonic path since, clearly, a lot of learners de- veloped grammatical vowel change sequences starting backwards from a given nonce preterite. Figure 4 illustrates inconsistencies in further detail. What we can see in Figure 4, left panel, is an erosion from [a]-vowel-chang- ing patterns in the first (preterite) to the second (participle) response. 231 preter- ites branch out to four different participle patterns. And both [a]- and [o]-vowel- changes create unorthodox forms in the participle (others). On the right, we can see that given preterites prompted four different infinitive patterns, which, too, branch out heavily into various attested and unattested vowel changes (others). Thomas Wagner 548 In sum, evidence against the apophonic path lies in the inconsistencies when pro- ducing vowel change from nonce infinitive to preterite and participles, as well as in the analogically formed irregular infinitives from given nonce preterites. In order to model the relationship between the nonce given, the two re- sponses, and the overall grammaticality of the vowel change series, generalized mixed models with restricted maximum likelihood were fitted to the data. In all models, random intercepts were included for subject and items. Factor levels of predictors were treatment-coded. A maximal random-effects-structure with all random slopes as well as interactions of fixed effects prevented models from converging, so terms were dropped whenever this happened. First of all, the tense given turned out to be a significant predictor for the first (χ2 (1) = 9.57, p < .005) and second response (χ2 (1) = 4.76, p < .03), but, interestingly, not for the grammaticality of the overall vowel change pattern (χ2 (1) = 0.04, p = .84). In contrast, in a model with the two responses as fixed ef- fects, both are highly significant (p < .001). It thus appears as though it was not the given nonce verb as such that predicted the grammaticality of the overall patterns, but the interplay between the two inflections the learners produced. This is again evidence against the apophonic path since the stimulus repre- sented the directionality dimension of the apophonic path and should have re- sulted in well-formed vowel change patterns for given infinitives only. The final model included both the tense given and the two responses as fixed effects. Fixed and random effects were tested for multicollinearity. The predictors’ inflation factor was below 2.5, and the model was not overdispersed. Scaled residuals were distributed fairly symmetrically. Table 3 summarises the final model, with a pseudo conditional R2 of 0.78. Table 3 Table of coefficients of the final model, estimated using Laplace approx- imation as well as the optimizer bound by quadratic approximation (bobyqua) instead of the heuristic default Nelder-Mead method Logits SE z p Intercept -3.25 0.41 -7.96 < .001*** Nonce given (effect size = 0.13) Preterite 0.63 0.48 1.31 .19*** 1st response (effect size = 0.85) Ungrammatical 2.65 0.39 6.85 < .001*** 1st response (effect size = 0.01) Regular -3.76 0.45 -8.41 < .001*** 2nd response (effect size = 0.80) Ungrammatical 5.60 0.44 12.66 < .001*** 2nd response (effect size = 0.02) Grammatical 0.28 0.95 0.29 .077*** Note. Logits are the log-odds of the parameter estimations; SE is the standard error; z-values come from the corresponding Wald statistics; *** p < .001. Table 3 shows that the given tense is again insignificant. Ungrammatical first responses, compared to grammatical ones (mapped onto the intercept), result, however, in a significant increase of log odds by 2.65, and thus in a probability for L2 irregular verb morphology: Exploring behavioral data from intermediate English learners of. . . 549 ungrammatical patterns of 0.93. Likewise, ungrammatical second responses show an increase in log odds by 5.6 and a probability of 0.99 for ungrammatical overall pat- terns. The ungrammatical second response has the largest effect size in this model. In sum, the faithfulness to attested patterns is the result of the interplay between first and second response and not of the directionality prompted by the nonce verbs. It can therefore be concluded that the apophonic path cannot convincingly account for the present data. 7. Conclusion How far do the data of the two experiments support a schema-based or universal apophonic organization of vowel change in GFL speakers? First of all, we do see certain constituent combinations, such as [ʃC_ŋ(k)] and [C_fricative], triggering non-default inflections. This observation is by no means trivial since apparently even a restricted, classroom-based exposure to German makes analogical for- mations possible already in intermediate learners (Murphy, 2004; Gor & Cherni- govskaya, 2005 for similar results for learners of Russian). The learners’ L1 could, though, have a positive effect, since English and German irregular verb morphol- ogy are not all that different (Clahsen, Felser, Neubauer, Sato, & Silva, 2010). Second, there is an almost complete overlap between the nonces produc- ing most of the attested vowel changes in Experiment 1 (spingen, stingen, and schingen) and the most effective constituent combinations, thus having the cue- validity one would expect from a prototype (Rosch & Mervis, 1975). However, contrary to English (Bybee & Moder, 1983; Bybee & Slobin, 1982), it is predom- inantly the verbs’ rhymes, such as [#_ɪ_ŋ(k)] and [#_i:_s/ç], which account for vowel change patterns. So far, these findings are only partly in line with proto- typical schemas. Instead, as Penke (2006) already suggested, the internal organ- ization of irregular German verb schemata might rely solely on the rhyme. Third, the double inflections in Experiment 2 illustrate processes incom- patible with the apophonic path. Instead, they reveal a certain analogical productivity in a reverse fashion (Becker, 1990). It remains unclear, though, why there were so many default responses to given irregular nonce preterites. This is indeed surprising since both beginning and advanced learners are reported to pay considerable attention to stem-changes (Godfroid & Uggen, 2013), are less sensitive to a verb’s morphological structure (Neubauer & Clahsen, 2009), and prefer declarative memory over symbolic processing. Overall, the present Ger- man L2 data support the notion of an analogical pattern associator, either as part of a dual-route model or as an analogy-based single mechanism. From a theoretical point of view, it seems as though structured lexical entries from minimalist morphology might best provide a theoretical account for German Thomas Wagner 550 L2 vowel change (Clahsen, 1999; Wunderlich, 1996; Wunderlich & Fabri, 1995). Structured lexical entries are organized as hierarchical trees, with nodes and sub- nodes relating underspecified grammatical features to each other. However, those trees might not just organise individual underspecified entries, but the entire par- adigm, or verb classes, as such. Therefore, inflectional classes, and even regular verb morphology, would have a psycholinguistic reality and would not merely be the by-product of their members (Trompelt, Bordag, & Pechmann, 2013). From a processing point of view, promising avenues for further research could lie in micro-rules, analogical learners, connectionist networks, and probabil- istic models. The efficiency of so-called micro-rules has been proven for English past tense (Albright & Hayes, 2003). They argue for a model inductively creating micro- rules for both regular and irregular verbs. It is difficult, though, to qualitatively dis- tinguish instance-based input-output rules and analogical formations. Both pro- cesses might ultimately be just the two sides of the same coin. On the one hand, the entirety of exemplars and their related forms create patterns and thus facilitate new analogical formations, but, on the other hand, provide the basis for abstract micro-level subregularities and thus facilitate deterministic rules with the extent of one exemplar (Becker, 1990). In other words, rules could be interpreted as highly reinforced representational patterns and schemas (Bybee, 1988). Appropriate alter- natives to such symbolic approaches might lie in analogical learners (Aha, Kibler, & Albert, 1991; Daelemans, Zavrel, van der Sloot, & van den Bosch, 1999; Eddington, 2004, Skousen, 1989), connectionist networks (Westermann, Willshaw, & Penke, 1999) or probabilistic models (Albright, 2009; Baayen, 2003; Baayen & Hay, 2005; Gor & Chernigovskaya, 2005). Probabilistic models might, in fact, turn out to be par- ticularly suited since they can incorporate gradience and learning experience. From an acquisitional perspective, the most important finding in this study is probably that verb inflections by analogy to existing patterns appear to be pos- sible even at an intermediate learner level. The present GFL learners have, despite limited classroom-based exposure to the foreign language, accumulated enough exemplars of the verbal paradigm in their mental lexicons to generalise patterns, enabling them to productively handle new linguistic experiences. What, however, does this mean for the acquisition of German in instructional settings? On the one hand, if learners generally turned out to prefer lexical retrieval by means of ana- logical generalization, instructions revolving around morphological analyses of verb forms would be of little help; instead, massive exposure facilitating analogical inference would be called for. In that respect, further research should look into possible constraints and threshold levels for such generalization properties. On the other hand, English speaking learners of German, in particular, could benefit from a crosslinguistic focus on forms in order to make them aware of both the similarities and differences between the two verbal paradigms. L2 irregular verb morphology: Exploring behavioral data from intermediate English learners of. . . 551 References Aha, D. W., Kibler, D., & Albert, M. K. (1991). Instance-based learning algorithms. Machine Learning, 6, 37-66. doi: 10.1007/BF00153759 Albright, A. (2009). Modeling analogy as probabilistic grammar. In J. P. Blevins & J. Blevins (Eds.), Analogy in grammar. Form and acquisition (pp. 185-204). New York: Oxford University Press. Albright, A., & Hayes, B. (2003). Rules vs. analogy in English past tenses: A com- putational/experimental study. Cognition, 90(2), 119-161. doi: 10.1016/S 0010-0277(03)00146-X Anderson, S. R. (1988). Morphological theory. In F. J. Newmeyer (Ed.), Linguis- tics: The Cambridge survey. Vol. I. Linguistic theory: Foundations (pp. 146- 191). Cambridge: Cambridge University Press. Baayen, R. H. (2003). Probabilistic approaches to morphology. In R. Bod, J. B. Hay, & S. Jannedy (Eds.), Probabilistic linguistics (pp. 229-287). Cambridge, MA. Baayen, R. H., & Hay, J. B. (2005). Shifting paradigms: Gradient structure in morphology. Trends in Cognitive Sciences, 9(7), 342-348. doi: 10.1016/j.tics.2005.04.002 Baayen, R. H., Davidson, D. J., & Bates, D. M. (2008). Mixed-effects modeling with crossed random effects for subjects and items. Journal of Memory and Language, 59(4), 390-412. doi: org/10.1016/j.jml.2007.12.005 Barr, D. J., Levy, R., Scheepers, C., & Tily, H. J. (2013). Random effects structure for confirmatory hypothesis testing: Keep it maximal. Journal of Memory and Language, 68(3), 255-278. doi: 10.1016/j.jml.2012.11.001 Bates D., Maechler, M., Bolker, B., & Walker, S. (2015). Fitting linear mixed-ef- fects models using lme4. Journal of Statistical Software, 67(1), 1-48. doi:10.18637/jss.v067.i01 Becker, T. (1990). Analogie und morphologische Theorie. München: Wilhelm Fink. Berko, J. (1958). The child’s learning of English morphology. Word, 14, 150-77. doi: http://dx.doi.org/10.1080/00437956.1958.11659661 Bittner, A. (1996). Starke ‘schwache’ Verben, schwache ‘starke’ Verben. Deutsche Verbflexion und Natürlichkeit. Tübingen: Stauffenburg. Burgess, A. (1972). A clockwork orange. London: Penguin. Bybee, J. (1988). Morphology as lexical organisation. In M. Hammond & M. Noonam (Eds.), Theoretical approaches to morphology (pp. 119-141). San Diego: Academic Press. Bybee, J. (1995). Regular morphology and the lexicon. Language and Cognitive Pro- cesses, 10(5), 425-455. doi: http://dx.doi.org/10.1080/01690969508407111 Bybee, J., & Newman, J. (1995). Are stem changes as natural as affixes? Linguis- tics, 33(4), 633-654. doi: 10.1515/ling.1995.33.4.633 Thomas Wagner 552 Bybee, J., & Moder, C. L. (1983). Morphological classes as natural categories. Language, 59, 251-270. doi: 10.2307/413574 Bybee, J., & Slobin, D. I. (1982). Rules and schemas in the development and use of the English past tense. Language, 58, 265-289. doi: 10.2307/414099 Clahsen, H. (1997). The representation of German participles in the German mental lexicon: Evidence for the dual-mechanism model. In G. Booij & J. v. Marle (Eds.), Yearbook of morphology 1996 (pp. 73-96). Dodrecht: Kluwer Academic. Clahsen, H. (1999). Lexical entries and rules of language: A multidisciplinary study of German inflection. Behavioral and Brain Sciences, 22, 991-1060. doi: 10.1017/S0140525X99002228 Clahsen, H., Eisenbeiß, S., & Sonnenstuhl-Henning, I. (1997). Morphological structure and the processing of inflected words. Theoretical Linguistics, 23, 201-249. doi: 10.1515/thli.1997.23.3.201 Clahsen, H., Felser, C., Neubauer, K., Sato, M., & Silva, R. (2010). Morphological structure in native and nonnative language processing. Language Learn- ing, 60, 21-43. doi: https://doi.org/10.1017/S1366728912000648 Clahsen, H., Hadler, M., & Weyerts, H. (2004). Speeded production of inflected words in children and adults. Journal Child Language, 31(3), 683-712. doi: http://dx.doi.org/10.1017/S0305000904006506 Council of Europe (2001). Common European framework of reference for languages: Learning, teaching, assessment. Cambridge: Cambridge University Press. Cunnings, I., & Finlayson, I. (2015). Mixed effects modeling and longitudinal data analysis. In L. Plonsky (Ed.), Advancing quantitative methods in second language research (pp. 159-181). New York: Routledge. Cunnings, I., & Linck, J. A. (2015). The utility and application of mixed-effects models in second language research. Language Learning, 65(1), 185-207. doi: 10.1111/lang.12117 Daelemans, W., Zavrel, J., van der Sloot, K., & van den Bosch, A. (1999). TiMBL: Til- burg Memory Based Learner, version 2.0, reference guide. Induction of lin- guistic knowledge technical report. Tilburg, Netherlands: ILK Research Group. Eddington, D. (2000). Analogy and the dual-route model of morphology. Lingua, 110(4), 281-298. doi: 10.1.1.123.9060 Eddington, D. (2004). Issues in modelling language processing analogically. Lin- gua, 114(7), 849-871. doi: 10.1016/S0024-3841(03)00063-9 Godfroid, A., & Uggen, M. S. (2013). Attention to irregular verbs by beginning learners of German. Studies in Second Language Acquisition, 35(2), 291- 322. doi: 10.1017/S0272263112000897 Goebel, R., & Indefrey, P. (2000). A recurrent network with short-term memory capacity learning the German s-plural. In P. Broeder & J. Murre (Eds.), L2 irregular verb morphology: Exploring behavioral data from intermediate English learners of. . . 553 Models of language acquisition. Inductive and deductive approaches (pp. 177-200). Oxford: Oxford University Press. Gor, K., & Chernigovskaya, T. (2005). Formal instruction and the acquisition of verbal morphology. In A. Housen & M. Pierrard (Eds.), Investigations in instructed second language acquisition (pp. 131-166). Berlin: Mouton de Gruyter. Gries, S. T. (2015). The most under-used statistical method in corpus linguistics: Multi-level (and mixed-effects) models. Corpora, 10(1), 95-125. doi: 10.3366/cor.2015.0068 Hahne, A., Müller, J., & Clahsen, H. (2006). Morphological processing in a second language: Behavioural and event-related potential evidence for storage and decomposition. Journal of Cognitive Neuroscience, 18, 121-134. doi: http://dx.doi.org/10.1162/089892906775250067 Hothorn, T., Hornik, K., & Zeileis, A. (2006). Unbiased recursive partitioning: A con- ditional inference framework. Journal of Computational and Graphical Statis- tics, 15(3), 651-674. doi: http://dx.doi.org/10.1198/106186006X133933 Jaeger, T. F. (2008). Categorical data analysis: Away from ANOVAs (transfor- mation or not) and towards logit mixed models. Journal of Memory and Language, 59(4), 434-446. doi: 10.1016/j.jml.2007.11.007 Köpcke, K.-M. (1998). Prototypisch starke und schwache Verben in der deut- schen Gegenwartssprache. Germanistische Linguistik, 141-142, 45-60. Lemhöfer, K., & Radach, R. (2009). Task context effects in bilingual nonword pro- cessing. Experimental Psychology, 56(1), 41-47. doi: http://dx.doi.org/10.1027 /1618-3169.56.1.41 Lück, M., Hahne, A., & Clahsen, H. (2006). Brain potentials to morphologically complex words during listening. Brain Research, 1077, 144-152. doi: http://dx.doi.org/10.1016/j.brainres.2006.01.030 Marusch, T., von der Malsbur, T., Bastiaanse, R., & Burchert, F. (2012). Tense mor- phology in German agrammatism. The production of regular, irregular and mixed verbs. The Mental Lexicon, 7(3), 351-380. doi: 10.1075/ml.7.3.05mar Murphy, V. A. (2004). Dissociable systems in second language inflectional mor- phology. Studies in Second Language Acquisition, 26(3), 433-459. doi: https://doi.org/10.1017/S0272263104263033 Neubauer, K., & Clahsen, H. (2009). Decomposition of inflected words in a second language: An experimental study of German participles. Studies in Second Language Acquisition, 31, 403-435. doi: http://dx.doi.org/10.1017/S027226 3109090354 Nübling, D., Dammel, A., Duke, J., & Szczepaniak, R. (2006). Historische Sprach- wissenschaft des Deutschen: Eine Einführung in die Prinzipien des Sprach- wandels. Tübingen: Gunter Narr. Thomas Wagner 554 Orsolini M., & Marslen-Wilson, W. D. (1997). Universals in morphological repre- sentation: Evidence from Italian. Language and Cognitive Processes, 12, 1-47. doi: http://dx.doi.org/10.1080/016909697386899 Penke, M. (2006). Flexion im mentalen Lexikon. Tübingen: Max Niemeyer. Penke, M., Wimmer, E., Hennies, J., Hess, M., & Rothweiler, M. (2014). Inflec- tional morphology in German hearing-impaired children. Logopedics Pho- niatrics Vocology, 41(1), 9-26. doi: 10.3109/14015439.2014.940382 Pinker, S. (1999). Words and rules. The ingredients of language. London: Phoenix. Pinker, S., & Ullman, M. T. (2002). Combination and structure, not gradedness, is the issue. Trends in Cognitive Sciences, 6, 472-474. doi: http://dx.doi.org/ 10.1016/S1364-6613(02)02013-2 Pliatsikas, C., & Marinis, T. (2013). Processing of regular and irregular past tense mor- phology in highly proficient L2 learners of English: A self-paced reading study. Applied Psycholinguistics, 34, 943-970. doi:10.1017/S0142716412000082 Prasada, S., & Pinker, S. (1993). Generalization of regular and irregular morpho- logical patterns. Language and Cognitive Processes, 8, 1-56. doi: http://dx. doi.org/10.1080/0169096930840694 R Core Team (2016). R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing. Retrieved from https://www.R-project.org/ Ramscar, M. J. A. (2002). The role of meaning in inflection: Why the past tense does not require a rule. Cognitive Psychology, 45, 45-94. doi: 10.1016/S001 0-0285(02)00001-4 Rosch, E. (1975). Cognitive representations of semantic categories. Journal of Experimental Psychology: General, 104(3), 192-232. doi: doi.apa.org/jour- nals/xge/104/3/192.pdf Rosch, E., & Mervis, C. B. (1975). Family resemblance: Studies in the internal structure of categories. Cognitive Psychology, 7, 573-605. doi: 10.1016/00 10-0285(75)90024-9 Ruh, N., & Westermann, G. (2008). A Single-mechanism dual-route model of German verb inflection. In B. C. Love, K. McRae, & V. M. Sloutsky (Eds.), Proceedings of the 30th annual conference of the cognitive science society (pp. 2209-2214). Austin, TX: Cognitive Science Society. Ségéral, P., & Scheer, T. (1998). A generalized theory of ablaut: The case of mod- ern German strong verbs. In R. Fabri, A. Ortmann, & T. Parodi (Eds.), Mod- els of inflection (pp. 28-59). Tübingen: Niemeyer. Skousen, R. (1989). Analogical modeling of language. Dordrecht: Kluwer Academic. L2 irregular verb morphology: Exploring behavioral data from intermediate English learners of. . . 555 Smolka, E., Khader, P. H., Wiese, R., Zwitserlood, P., & Rösler, F. (2013). Electro- physiological evidence for the continuous processing of linguistic catego- ries of regular and irregular verb inflection in German. Journal of Cognitive Neuroscience, 25(8), 1284-1304. doi: 10.1162/jocn_a_00384 Smolka, E., Zwitserlood, P., & Rösler, F. (2007). Stem access in regular and irreg- ular inflection: Evidence from German participles. Journal of Memory and Language, 57(3), 325-347. doi: dx.doi.org/10.1016/j.jml.2007.04.005 Strobach, T., & Schönpflug, U. (2011). Can a connectionist model explain the processing of regularly and irregularly inflected words in German as L1 and L2? International Journal of Bilingualism, 15(4), 446-465. doi: 10.1177/ 1367006911403205 Thiele, J., & Markussen, B. (2012). Potential of GLMM in modelling invasive spread. CAB Reviews, 7, 1-10. doi: 10.1079/PAVSNNR20127016 Trompelt, H., Bordag, D., & Pechmann, T. (2013). (Ir)regularity of verbs revisited: Evidence for lexical entry complexity. The Mental Lexicon, 8(1), 26-52. doi: 10.1075/ml.8.1.02tro Ullman, M. T. (2001). A neurocognitive perspective on language: The declara- tive/procedural model. Nature Reviews. Neuroscience, 2(10), 717-726. doi: 10.1038/35094573 Wagner, T. (2010). Interlanguage morphology. Irregular verbs in the mental lexicon of German-English interlanguage speakers. Tübingen: Narr-Francke-Attempto. Westermann, G., Willshaw, D., & Penke, M. (1999). A constructivist neural net- work model of German verb inflections in agrammatic aphasia. In Pro- ceedings of ICANN99 (pp. 916-921). Edinburgh: IET Publishing. Whitaker, H. A. (2006). Words in the mind, words in the brain: Preface to inau- gural issue of The Mental Lexicon. The Mental Lexicon, 1(1), 3-5. doi: 10.1075/ml.1.1.02wh Wiese, B. (2008): Form and function of verbal ablaut in contemporary standard German. In R. Sackmann (Ed.), Explorations in integrational linguistics. Four essays on German, French, and Guaraní (Current Issues in Linguistic Theory 285) (pp. 97-151). Amsterdam: John Benjamins. Wiese, R. (2000). The phonology of German. Oxford: Oxford University Press. Wunderlich, D. (1996). Minimalist morphology: The role of paradigms. In G. Booij & J. van Marle (Eds.), Yearbook of morphology 1995 (pp. 93-114). Dodrecht: Kluwer Academic. Wunderlich, D., & Fabri, R. (1995). Minimalist morphology: An approach to in- flection. Zeitschrift für Sprachwissenschaft, 14(2), 236-294. doi: 10.1515/ zfsw.1995.14.2.236 Thomas Wagner 556 APPENDIX Table of test items and distractors of Experiment 1 and 2 No. Experiments 1 2a 2b Test items Distractors Test items Distractors Test items Distractors 1. knießen knießen knoss 2. schrimmen schrimmen schramm 3. luschen nisseln nisselte 4. spinken spinken spank 5. grießen grießen gross 6. rabotten pieben piebte 7. stinnen stinnen stann 8. biechen biechen boch 9. govoriten witten wittete 10. strinken strinken strank 11. vidden stiemen stiemte 12. loviten stitzen stitzte 13. schiechen schiechen schoch 14. schringen schringen schrang 15. sotteln miegeln miegelte 16. stiechen stiechen stoch 17. schmatten hitteln hittelte 18. strimmen strimmen stramm 19. spingen spingen spang 20. pitschen sicken sickte 21. schliegen schliegen schlog 22. kritschen pitschen pitschte 23. schingen schingen schang 24. fießen fießen foss 25. sprinken lichsen lichste 26. boppen liepen liepte 27. schlippen sprinken sprank 28. fiechen fiechen foch 29. stingen stingen stang 30. triechen triechen troch 31. krasen bristen bristete 32. strießen strießen stross 33. schinnen schinnen schann 34. pliegen pliegen plog 35. dengen fritteln frittelte 36. kingen kingen kang 37. friegen friegen frog 38. wetschen krietschen krietschte 39. linnen linnen lann 40. schnießen schnießen schnoss 41. harrken fietzen fietzte 42. schminnen schminnen schmann 43. frinken frinken frank