2.1 Grammar, graphemics, and usage

In this paper, we apply usage-based grammar to a graphemic alternation phenomenon in German, arguing that properties of a probabilistic grammatical system can be inferred by examining written usage, i.e., from a graphemic perspective. Usage-based Grammar (UBG; e.g., Tomasello 2003; Bybee & Beckner 2009; Kapatsinski 2014) is based on two core assumptions: (i) grammar is acquired using only general cognitive devices, (ii) grammar is determined only by general cognitive constraints and by the input. Since the input is always rife with variation, which is intrinsically probabilistic, a third assumption is crucial to some researchers: (iii) grammars are learned as probability distributions over possible forms, meanings, and form-meaning pairs. We embrace all three assumptions and apply them to a graphemic alternation phenomenon. UBG is rarely extended to graphemics in such a way, but we view graphemics as a component of the language faculty on a par with components such as phonetics and phonology, and we consequently believe that graphemics should be viewed under the usage-based umbrella.⁵ Much like the phono-component comprises regularities about how grammar is encoded in speech sounds, graphemics comprises regularities about how grammar is encoded in written symbols. For writing systems like German, the mappings to be learned include sounds to letters, parts of speech to spellings (e.g., capitalisation of nouns), syntactic categories to spaces and punctuation marks, etc. (Primus 2010).⁶

In UBG, corpus data (i.e., production data) are often used as evidence, sometimes cross-validated in behavioural experiments (see, for example, Arppe & Järvikivi 2007; Bresnan et al. 2007; Ford & Bresnan 2013; Dąbrowska 2014; Divjak 2016; Divjak, Dąbrowska & Arppe 2016; Schäfer 2018; Schäfer & Pankratz 2018; Pankratz & Van Tiel 2021). This is justified because the usage-based (hence probabilistic) nature of the acquisition process should be reflected in the output of competent adult speakers/writers as captured in corpora, and not just in the acquisition process itself. Consequently, it should also be reflected in production data obtained from competent adults, and we should be able to uncover the probabilistic mappings of lexical-grammatical categories to written forms from such data. We consequently use corpus data as well as data elicited in controlled experiments, both being forms of production data. However, there is a difference between using production data as evidence and assuming that they directly mirror cognitive reality. While it is generally assumed that corpora represent a valid source of data in cognitively oriented linguistics (e.g., Newman 2011), it is also known that there is no straightforward correspondence between corpus data and cognitive reality (e.g., Gries 2003; Dąbrowska 2016). What we hope to recover from corpus data are major abstractions learned by a majority of speakers, uncovering general cognitive principles that ideally go far beyond individual acquisition careers and idiosyncrasies of single languages.

A convenient framework to formulate such abstractions is Prototype Theory (Rosch 1973; 1978). As a cognitive theory of classification, it is compatible with probabilistic views since it allows for fuzzy category membership (e.g., Sutcliffe 1993; Murphy 2002: 11–16). Grammatical units can thus be modelled as belonging to multiple categories to different degrees or—in our case to be introduced immediately below—as alternating between a morphological and a syntactic realisation.⁷ Prototype Theory is also intrinsically compatible with UBG as it assumes just a very general mechanism of classification whereby newly encountered objects are classified by similarity to a prototypical exemplar. In most versions of Prototype Theory, these prototypes are identified by (weighted) features or cues, and unseen exemplars are categorised depending on how many of those features they share with the prototype. We use Prototype Theory as a suitable framework in our analysis. Grammatical prototypes are mapped onto graphemic realisations (e.g., spellings), and the more strongly a unit matches the prototype, the more likely it is to be realised as the variant mapped to that prototype.

One caveat that is specific to graphemics needs to be mentioned before we proceed to the description of the concrete phenomena. The acquisition of the writing system involves explicit instruction and is thus more strongly imposed by prescriptive norms. However, we expect writers to learn grammar-graphemics mappings primarily from their realisations in the input, especially whenever the norm is unspecific or unclear (especially as it has changed back and forth over the past three decades), a situation which provides ideal test cases for our view of graphemics. Variation and alternations in the written input shape the acquired probability distribution, and conditioning factors are acquired to the degree that they can be retrieved from the type and the frequency of the input.⁸ We are convinced that graphemics is a field in its own right which deserves attention in any grammatical/linguistic framework. See Berg (2016) for a compatible fundamental argument independent of a concrete grammatical framework.

2.2 Spaces, words, and univerbation

As explained in Section 2.1, we use graphemic evidence from corpora and controlled experiments, and we argue that it indirectly allows us to draw conclusions about writers’ cognitive grammars. More specifically, we assume that compound spellings of N+V units indicate that writers conceive of those units as single syntactic words, whereas disjunct spelling indicates that they conceive of the unit as two syntactic words. Therefore, we briefly introduce the status of the space in German writing and how it pertains to N+V units.

German writing uses an alphabetic script with a strong correlation between underlying phonological forms (the phonemic level) and characters (graphemes). A common fundamental principle of such scripts is the separation of syntactic words by spaces (Jacobs 2005: 22). Also, stems and their affixes are never separated from one another, which reinforces the status of the space as a demarcation of syntactic words.⁹ These factors facilitate the reader’s ability to decode the sequence of syntactic words, and they constitute a crucial principle in the encoding and conventionalisation of meanings associated with word forms (Jacobs 2005: 22).

Unlike in English, German has regular compound spelling of syntactic words comprising more than one stem, especially for the case of the highly productive noun+noun (N+N) compound pattern (Jacobs 2005: 34; Fuhrhop 2007: 182), for which compound spelling is the dominant graphemic realisation. However, there is a heterogeneous group of multi-word constructions for which only tendencies towards compound spelling can be observed (Wurzel 1998: 335; Szczepaniak 2009: 95). As opposed to N+N compounds, these constructions typically consist of words with different parts of speech, such as mithilfe (von) (‘with the help (of)’) from mit der Hilfe (von) or zuhause (‘at home’) from zu Hause. For such cases, Lehmann (2020: 206) posits a “downgrading of a syntactic to a morphological boundary” between the two words. When writers use compound spelling in these cases, they choose to encode the construction as a single word with a morphological boundary instead of a sequence of words with a syntactic boundary. If many speakers consistently make this choice over a significant period of time, the unit might become lexicalised as a single word (Lehmann 2020: 212). Until such a diachronic process is complete and one of the spellings has become clearly dominant, the item alternates between a syntactic and a morphological realisation. For many of these constructions, this is the case both in non-standard as well as standard written German, albeit to different degrees.

N+V units with different affinities towards compound spelling like Rad fahren (‘bike riding’, often also spelled radfahren) and eislaufen (‘ice skating’, infrequently also spelled Eis laufen) often represent different levels of diachronic re-conventionalisation as single words.¹⁰ This indeterminacy means that speakers have both the syntactic realisation (disjunct spelling) and the morphological realisation (compound spelling) in their graphemic input, which subsequently leaves them with quite a free choice to be made based on how a concrete item is classified according to their individual grammar. It is the task of usage-based probabilistic graphemics to uncover factors influencing such decisions and decode the principles at work in speakers’ internal grammar by analysing their writing habits (see Schäfer & Sayatz 2016).

2.3 The status of noun+verb units in German

In this section, we explain why the existence of this alternation is not surprising considering the morphosyntactic system of German. Furthermore, we argue that in each concrete case where an N+V unit is written, the strength of the tendency towards either compound or disjunct spelling can be derived from the overall syntactic and morphological patterns available in present-day German. These patterns are shown to have prototypical properties which are matched more or less well by individual N+V units and their syntactic contexts, which leads to either compound or disjunct spelling being the preferred realisation.¹¹ To this end, we will shed some light on particle verbs as a target class for N+V units in Section 2.3.1, on N+V units as structures involving incorporation in Section 2.3.2, before turning to the influence of nominal compounds (of the N+N type) in Section 2.3.3. We sum up our arguments and derive our hypotheses for the empirical studies in Section 2.3.4.

3.1 Choice of corpus, sampling, and annotation

As a first step, we adopted a data-driven approach in order to find nearly all N+V units in contemporary written usage. In a second step, we counted their occurrences in compound and disjunct spelling in four relevant morphosyntactic contexts: fully nominalised as the heads of noun phrases, in am progressives, as participles in analytical verb forms, and as infinitives in a range of verbal constructions).

Clearly, we required a large corpus with rich morphological and morphosyntactic annotations containing texts written in a broad variety of registers and styles (including ones written under low normative pressure). We chose the DECOW16B corpus (Schäfer & Bildhauer 2012) because it fulfils all the aforementioned criteria.²⁴ Much like the SketchEngine corpora (Kilgarriff et al. 2014), the COW corpora contain web documents from recent years. However, the German DECOW (containing 20.5 billion tokens in 808 million sentences and 17.1 million documents) offers a much wider range of annotations compared to SketchEngine corpora, including morphological annotations and several levels of syntactic annotation (dependencies and topological parses). For our purpose, the complete internal analysis of nominal compounds described in Schäfer & Pankratz (2018) was particularly of interest. This level of analysis allows for corpus searches of roots within nominal compounds.

The list of actually occurring N+V units was obtained by querying for compounds with a nominal non-head and a deverbal head. The rationale behind this approach is that any N+V unit of interest should occur at least once in compound spelling as a fully nominalised compound. Since this step relied on automatic annotation already available in the corpus, the results contained erroneous hits which we removed manually. The resulting list contained 819 N+V units.²⁵

In the second step, we created lists of all relevant inflectional forms of the verb in each N+V unit and used these to query all possible compound and disjunct spellings (including variance in capitalisation) of each of the 819 N+V unit types. In total, 28,665 queries were executed to create the final data set used here. The queries retrieved 958,118 compound spellings and 1,288,768 separate spellings, which results in a total sample size of 2,246,886 tokens.

For each N+V unit in the sample, the following variables were annotated automatically: (i) the verb lemma, (ii) the noun lemma, and (iii) the overall frequency in the corpus. The morphosyntactic contexts could be annotated semi-automatically, because separate queries were executed for each context anyway. Additionally, we manually coded all 819 N+V units for the relation that holds between the verb and the noun. The codes used in clear-cut cases were Argument (441 N+V units) and Oblique (286 N+V units). For 92 units, both relations were conceivable, and those cases were coded as Undetermined.

The data thus obtained were analysed in two ways. First, we report the results of a collexeme analysis in Section 3.2, which quantifies how strongly individual N+V units tend to be written as one word or two words. Second, in Section 3.3 we report a full statistical model of the alternation.

3.2 Results: association strengths

In this section, we report an analysis of the item-specific affinities of N+V units towards univerbation. The method we use is similar to collocation analysis (see Evert 2008 for an overview) and derives from Collostructional Analysis (Stefanowitsch & Gries 2003). More specifically, the method is called distinctive collexeme analysis (Stefanowitsch & Gries 2009).²⁶

Our goal was to quantify how strongly each N+V unit tends towards univerbation vis-a-vis all other N+V units. Thus, we need to compare the counts of cases with and without univerbation of the unit in question with the total counts for all other N+V units. Such comparisons must be made relative to the overall number of the specific N+V unit as well as the number of all other N+V units. The counts needed for each N+V unit are nicely summarised in a 2×2 contingency table as shown in Table 1.

With these counts, we are able to quantify how strongly the proportions in the first row differ from those in the second row, and there is a range of statistical measures that assess the magnitude of this difference. For example, one could use odds ratios or effects strengths from frequentist statistical tests.²⁷ We chose Cramér’s v derived from standard χ² scores $(v=\sqrt{{\chi }^2/n})$ .²⁸ Cramér’s v (also called ϕ in the case of two-by-two tables) measure quantifies for each individual N+V unit how strongly its observed counts (cells c₁₁ and c₂₁) deviate from the counts that we would expect if there were no difference between this unit and all other N+V units (cells c₂₁ and c₂₂) with respect to their tendency to univerbate. Since Cramér’s v normalises the χ² scores to the range between 0 and 1, it allows us to compare analyses where the sample sizes differ. In itself, v does not tell us whether the deviation is negative (for a N+V unit with fewer than average compound spellings) or positive (for a N+V unit with more than average compound spellings). The information about the direction of the deviation is added by multiplying v with the sign of the upper left cell of the residual table of the χ² test. Thus, the signed Cramér’s v measures how strongly individual N+V units are attracted or repelled by univerbation (positive and negative values, respectively). Measures with such properties are often called ‘attraction strengths’ or ‘association scores’.

We calculated the signed v for each of the 819 N+V units. The distribution of these scores is plotted in the form of a density estimate in Figure 1.²⁹ The graph shows the distribution of the attraction strengths for N+V units with argument and oblique relations separately. While there is variation in both directions in both cases, the argument relation tends more towards disjunct spelling (lower/more negative scores), and the oblique relation favours compound spelling more (higher/more positive scores). The number of units close to 0 (i.e., without a clear tendency) is notable with the argument relation. For example, a N+V unit strongly attracted by univerbation is Zeitreisen (‘time travel’, oblique relation) with an attraction score of 0.125. An example with a strong tendency against univerbation is Fehlermachen (‘mistake make’, argument relation) with an attraction score of –0.088. Finally, Haareschneiden (‘hair cut’, argument relation) shows no clear tendency towards or against univerbation, having an attraction score of –0.007. The results of the association analysis will be corroborated by the subsequent analysis in Section 3.3, and we will use the attraction scores to control for item-specific tendencies in the experiment in Section 4.

Figure 1: Density estimate of the distributions of the association scores, separately for the two semantic relations; the x-axis was truncated at –0.05 and 0.05 where the curves are essentially flat.

3.3 Results: full statistical model

In this section, we present the parameter estimates for a binomial multilevel model (or generalised linear mixed model, GLMM) which models the relevant factors influencing writers’ choice of the compound and the disjunct spelling.³⁰ The results of the method used in Section 3.2 and the GLMM presented here converge. However, the GLMM has a more standard interpretation and allows for finer-grained data analysis. Also, it has long been accepted that combining several methods strengthens the analysis when the results converge (e.g., Arppe & Järvikivi 2007).

Given the grand total of 2,246,886 observations in the sample (see Section 3.1), we will completely refrain from an interpretation of the GLMM in terms of frequentist inferential statistics. For samples of such magnitude in data-driven approaches, frequentist significance tests are the wrong tool, because it is so easy to achieve significance with such large sample sizes that conclusions based on this criterion become practically meaningless. Therefore, we provide standard likelihood ratio confidence intervals for parameter estimates and prediction intervals for conditional modes as an approximate measure quantifying the precision of the parameter estimates and predictions. The models we specify reflect theoretically motivated decisions, and we therefore reject all types of model selection by means of step-up or step-down procedures.

As argued in Section 2.3, we expect the probability of the univerbation of N+V units to depend on the morphosyntactic context, the relation holding between the verb and the noun, and on the specific N+V unit (a lexical tendency). Accordingly, the response variable was chosen to be the proportion of compound spellings among all the spellings of the N+V unit. In the input data provided to the estimator, the response variable was thus a vector of 819 proportions, one for each N+V unit.³¹

The two important fixed effects in the model are the morphosyntactic context and the internal relation (see Section 3.1). With 819 N+V units, the lexical indicator variable for the individual N+V unit should not be used as a fixed effect, because there would be too many levels (Gelman & Hill 2006: 244–247; Schäfer 2020). Thus, we specified a generalised linear mixed model with the N+V unit variable as a random effect.³² In lme4 notation, the specification is shown in (15).

The estimated parameters of the model are given in Table 2. Additionally, effect plots for Context and Relation are given in Figure 2.³³ As expected, the prototypically verbal contexts (infinitives and participles) are associated with a low probability of compound spelling (the infinitive is on the intercept, which is estimated at –4.685, and participles have a coefficient of 1.054). NPs and progressives as prototypically nominal contexts clearly favour compound spelling (coefficients of 3.886 and 4.907, respectively). Both the coefficients and the effect plot (right panel in Figure 2) show a low probability of compound spelling when an argument relation holds between the verb and the noun (on the intercept), and a high probability when the relation is oblique (coefficient 3.085). The undetermined cases are in between the two clear-cut cases (coefficient 1.344).

Figure 2: Effect plots for the regressor encoding the morphosyntactic context of the N+V unit and the regressor encoding the syntactic relation within the N+V unit in the GLMM modelling the corpus data.

Given the narrow confidence intervals and the high marginal measure of determination $R_m^2=0.576$ , we consider the hypotheses regarding fixed effects to be well corroborated by the data. The differences between specific N+V units already shown in Section 3.2 show up in the model as the residual variance in the random effects (in the form of the conditional modes). The conditional modes have a standard deviation of 2.108. The relatively high standard deviation is a sign that there is considerable variation across the individual N+V units. Furthermore, the conditional $R_c^2$ is as high as 0.999. This is commonly interpreted as saying that the fixed effects and the idiosyncratic effect of concrete N+V units almost fully explain the variance in the data. A random selection of 20 conditional modes, which illustrates the relevance of lexical idiosyncrasies through obvious differences with mostly very narrow prediction intervals, is shown in Figure 3. The individual N+V unit thus plays a major role in writers’ tendency to univerbate N+V units, which matches the results from Section 3.2.

Figure 3: A random selection of conditional modes with 95% prediction intervals for the levels of the random effect in the GLMM modelling the corpus data.

4.1 Design and participants

The goal of the experiment was to replicate the findings from the corpus study in another empirical paradigm and to test whether writers’ behaviour under controlled experimental conditions is similar to the behaviour of writers under circumstances without experimental control as found in corpora. We used pre-recorded auditory stimuli in order to elicit spellings of given N+V units. The stimuli were chosen based on theoretically motivated criteria and the information about item-specific tendencies obtained from the exploratory part of the corpus study in Section 3.2. We constructed eight sentences instantiating the four morphosyntactic contexts described in Section 3.3 crossed with the two semantic relations.

An overview of the item design is shown in Table 3, where each line represents the features of one of the eight items. The low number of eight target items will be motivated below (see Footnote 34). In order to control for differences in lexical preferences, the concrete pairs of N+V units used in each context were chosen such that the contrast in lexical preference (see Section 3.2) for and against univerbation was as substantial as possible. As expected, units with an argument relation have negative attraction scores, and ones with an oblique relation have positive scores (see column ‘Attr. score’ in Table 3). For each context, we selected pairs where the difference between the scores was larger than 0.05. Except for the infinitive context (difference 0.063), we managed to find pairs for which the difference is actually above 0.1 (NP: 0.197, Participle: 0.124, Progressive: 0.124). In the spirit of Footnote 28, it should be kept in mind that the v scores have no interpretation independently of their specific distribution. They were merely used here to maximise the differences between the corresponding N+V units with argument and oblique relation. They are an exploratory tool, and nothing substantial in the design of this experiment hinges on their concrete numerical values.

The sentences were constructed in a way such that all N+V units were the predicate of a subordinate clause. This consistently ensured verb-last constituent order and avoided interfering verb-second effects, which are typical of independent sentences in German. The stimuli with full glosses are given in Appendix 5. Furthermore, we added 32 fillers, resulting in a total of forty sentences being read to the participants. Of the forty sentences, twenty (including the target items) had to be written down by the participants. The order of the target items was randomised, but it was ensured that there were at least three sentences in between two target stimuli. There were nine distractors in the form of yes–no questions related to random sentences previously heard by the participants.

In total, 61 participants took part in the experiment. All of them were first-semester students of German Language and Literature at Freie Universität Berlin. They were between 18 and 44 years old with a median age of 22 years. There were two separate groups (of 32 and 29 participants), and the randomisation of the order of stimuli was different between the two groups.³⁴

4.2 Results

In this section, we report the parameter estimates of a GLMM modelling the behaviour of the participants in our experiment. The model specification in lme4 notation is given in (16). The coefficient estimates for the GLMM are reported in Table 4.³⁵

There is some variation between writers as captured in the standard deviation of the conditional modes (1.648), but the small difference between the marginal $R_m^2(0.836)$ and the conditional $R_c^2(0.910)$ suggests that speaker variation does not explain much of the variance in the data. This demonstrates that the phenomenon cannot be reduced to individuals mastering the norm to different degrees or having different preferences when it comes to univerbation. Instead, the major deciding factors are the ones predicted by our theoretical model.

There seems to be only weak evidence that the participle has a different effect than the infinitive (which is on the intercept) given the large confidence interval ([1.966, 4.643]). On the other hand, progressives (10.667) and NPs (8.962) clearly have a much more positive effect on the probability of univerbation. We do not see evidence for any difference between NP and progressive contexts given the large and overlapping confidence intervals. The oblique relation favours univerbation as predicted (6.951) compared to the argument relation (which is modelled by the intercept), and despite a quite large confidence interval ([5.054..10.078]), the effect is clearly positive.

Figure 4: Effect plots for the regressor encoding the morphosyntactic context of the N+V unit and the regressor encoding the syntactic relation within the N+V unit in the GLMM modelling the experimental data.

The effect plots in Figure 4 (left panel) provide a visual interpretation of the coefficient table. The prototypically verbal contexts are associated with low probabilities of univerbation, the two prototypically nominal ones with high probabilities of univerbation. Judging by the large and overlapping confidence intervals, there is no support for assuming a substantial difference between infinitives and participles. The same can be assumed for NPs and progressives. The two semantic relations are correlated with the probability of univerbation as expected (right panel of Figure 4).

In sum, the experiment supports our theoretically motivated hypotheses, and it corroborates the results from the corpus study. We proceed to a final analysis of the phenomenon in light of our findings in Section 5.