Glossa Psycholinguistics

2.1 Previous research on masculine generics in German

The question whether masculine generics in Modern Standard German are truly gender-neutral has been investigated by a growing body of literature during the last decades. We aim at giving a cursory overview of this literature here, but also refer to Irmen and Linner (2005) and Gygax et al. (2009) for further concise overviews.

One of the earliest studies on the matter was conducted by Irmen and Köhncke (1996). In their study, participants were presented with sentences containing either a masculine or a feminine form. The masculine form could be understood as either generic or explicit. After sentence presentation, participants were asked to quickly indicate whether the pertinent sentence referred to a man or a woman. An analysis of overall decisions and the corresponding reaction times showed that masculine generics are less often interpreted as referring to a woman and if they are, reaction times are longer.

In a more subtle methodological approach by Braun et al. (1998), participants read a short text about either an ecotrophology (which was judged to be stereotypically female) or a geophysics conference (which was judged to be stereotypically male). Within the two texts, five phrases were either given as masculine generics, as Beidnennung,² or as a neutral noun.³ Participants were then to guess the percentage of female attendees. Results showed that the percentage of female attendees given for texts without masculine generics was higher than for those participants who read texts with masculine generics. Stereotypicality of the conferences’ fields did show an influence; however, masculine generics in both contexts elicited significantly higher percentages of male conference attendees.

Rothermund (1998) gave brief descriptions of situations to participants. The descriptions either contained an explicitly male or female referent or a masculine generic. After reading the description, participants were prompted to decide whether items in a list of words were part of the description. Half of such items were part of the description, while the other half were not. Some of the newly added items were stereotypically female and male distractor words. It was found that it took participants longer to decide that a stereotypically male distractor was not part of the original description if the description contained a masculine generic. The opposite effect, however, was found for the same setup but with plural instead of singular referents.

Providing their participants with a cloze task, Rothmund and Scheele (2004) found that clozes are more often resolved with male referents in contexts with masculine generics as compared to contexts with other forms, such as majuscule-I⁴ or neutral nouns.

Heise (2000) confronted participants with beginnings of stories which contained as protagonists either masculine generics, alternative forms, such as the majuscule-I or the slash-form,⁵ or neutral nouns. Participants then had to give names to the protagonists. It was found that for stories with masculine generics and neutral nouns, participants more often used typically male names for the protagonists.

Stahlberg and Sczesny (2001) asked participants to name their favourite painter, potential candidates for the German chancellery, and celebrities. Questions were formulated with either the masculine generic or alternative forms, such as the majuscule-I or the slash-form, or neutral nouns. The authors found that questions containing masculine generics led to significantly fewer answers containing female referents. In a very similar study by Stahlberg et al. (2001), participants filled in questionnaires asking for their favourite protagonists in novels, real life, and history, and for their favourite famous athletes, singers, and politicians, among other categories. Again, results showed that when presented with masculine generics, participants replied significantly less often with female individuals.

Gygax et al. (2008) asked participants to determine whether a presented sentence is a meaningful continuation of a previously shown sentence. Participants were to judge the meaningfulness by considering the masculine generic in the first sentence and the explicitly gendered noun in the second sentence. The authors found that the proportion of positive judgements was higher for male continuations and that there was no effect of stereotypicality. Additionally, reaction times for male continuations were significantly shorter.

Irmen and Kurovskaja (2010) had participants rate sentences in terms of correctness and customariness. Sentences contained either a masculine or feminine role noun as well as either an explicitly masculine or feminine form which referred to the preceding role noun. Sentences with feminine role nouns and gender incongruent referents were rated as less correct and less customary than those with masculine forms and incongruent referents. Additionally, reaction times were slower for sentences with feminine role nouns and gender incongruent referents.

Sato et al. (2016) confronted participants with either two male faces or with a female and a male face. As language stimuli, plural forms of generic masculines were presented. Participants were asked to judge whether a given word form referred to the given faces. The authors found that responses to two male faces were given more quickly than to faces of mixed sex. They concluded that this facilitation of reaction times reflected the ease in interpreting role nouns in the masculine form to be masculine explicit rather than generic.

Misersky et al. (2019) ran an ERP study with sentences in which a role noun introduced a group of people, followed by a congruent or incongruent continuation. Role nouns were either grammatically masculine or feminine; the continuation was congruent if its noun shared the grammatical gender of the preceding role noun. For both types of incongruent continuation (masculine > feminine and feminine > masculine), a P600 was observed. That is, even though the masculine form, in theory, is assumed to be generic, its female continuation led to the same effect as an incongruent continuation of a female form, which, in theory, is not considered to be generic.

In sum, previous research overall agrees on the nature of masculine generics. They show masculine biased readings, resulting in, among other things, a higher percentage of male responses, quicker responses for male continuations, and a lower level of female representation. However, most studies do not come without issues, of which we mention the two most crucial ones here. First, a non-negligible number of studies investigating the nature of the masculine generic make use of students as participants (e.g. Gygax et al., 2008; Heise, 2000; Stahlberg & Sczesny, 2001). Students are not only particularly prone to progressive change (e.g. Bailey & Williams, 2016), but make up a rather low percentage of all language users. Thus, including only students as participants might influence results to an unknown extent. Second, with a few exceptions, studies tend to ignore the potential influence of stereotypes, which might influence the nature of pertinent generic masculine forms.

The aim of the present study is therefore twofold. First, it is investigated whether a masculine bias in masculine generics is found when one’s method does not directly rely on participants and their language use specifically elicited for linguistic analysis. This not only allows for doing without the potential influence of specific social groups (e.g. students), but at the same time provides further insight into the semantic nature of masculine generics as well as of masculine and feminine explicits in a more general language use. Second, the potential influence of stereotypicality on the masculine bias is accounted for in our statistical analyses to ensure that said bias is not the result of stereotypes. The twofold aim is operationalised using the framework of the Discriminative Lexicon (Baayen, Chuang, Shafaei-Bajestan, et al., 2019; Chuang & Baayen, 2021) with its two computational implementations: naive and linear discriminative learning. The Discriminative Lexicon constitutes a framework which entails that linguistic knowledge and words’ features are a product of speakers’ experience, and, in turn, resonance processes between entries in the mental lexicon. The computational implementations are introduced in the following subsection.

2.2 Naive discriminative learning

Naive discriminative learning (henceforth NDL; Baayen et al., 2011; Baayen & Ramscar, 2015) is grounded in psychological theory on cognitive mechanisms (Pearce & Bouton, 2001; Rescorla, 1988), which has been shown to successfully model important learning effects in humans and animals (Kamin, 1969; Ramscar et al., 2010). Following the so-called Rescorla-Wagner rules (Rescorla & Wagner, 1972; Wagner & Rescorla, 1972), learning is understood as a result of informative relations within events, which in turn consist of cues and outcomes. The associations between cues and outcomes are constantly recalibrated when new events are encountered. At any stage of the learning process, the associations of a given outcome and all cues encountered thus far can be taken as the outcome’s relation to the world around the learning subject. Association weights are recalibrated in such a way that weights of an association increase every time the involved cue and outcome co-occur, while association weights decrease if a pertinent cue occurs without a given outcome. At the end of this process, a stable state with final association weights is reached. These final outcomes represent the interrelations of a pertinent outcome with all cues encountered during the learning process. Adopting this reasoning to language, cues and outcomes may, for example, be content and function words as well as inflectional and/or derivational functions (e.g. singular vs. plural, specific vs. generic; derivational suffixes like -ee, -ation, and -ment) found in a text corpus annotated according to the needs of the respective investigation. Once the stable end state is reached, each outcome’s association weights with all cues constitute the pertinent outcome’s semantic vector. In comparison to other models of semantic vector computation, e.g. fastText (Bojanowski et al., 2016) or Word2Vec (Mikolov, Chen, et al., 2013), the vectors computed by NDL are linguistically transparent. For German role nouns in the present investigation, this process is straightforward. For each role noun, vectors of its semantic and formal components, e.g. its base meaning, number, gender, and genericity, will be contained within the vector space computed by NDL. The resulting vector space can be made use of in statistical analyses and also in further computational implementations, such as described in the following subsection.

2.3 Linear discriminative learning

Just like NDL, linear discriminative learning (henceforth LDL; e.g. Baayen, Chuang, Shafaei-Bajestan, et al., 2019) is part of the Discriminative Lexicon. LDL simulates a mental lexicon by generating a system of form-meaning relations by discriminating between different forms and meanings. It allows the researcher to investigate in detail the relationship between entries, i.e. their forms and meanings, in the mental lexicon. Notably, as we will outline in the following paragraphs, LDL networks are simple two-layer networks which are linguistically transparent and interpretable.

In an LDL implementation, forms are represented by numerical vectors. Such form vectors typically consist of binary-coded information on whether certain n-gram or n-phone cues are contained within a given word form. For each word form’s individual form vector c, the presence of a n-gram/n-phone cue is marked with 1, while the absence of such a cue is marked with 0. The form vectors of all word forms of a given set of words constitute the so-called form or cue matrix C, with each row corresponding to the form vector of a pertinent word form and each column representing a unique form cue. As a toy example, let us assume that we have a small corpus of only three German words: Wind ‘wind’, Kind ‘child’, and Rind ‘bovine’. Using triphones, the corresponding C matrix then looks as follows:

Meaning is also represented by numerical vectors. Meaning vectors or semantic vectors can be incorporated from any model generating such vectors, for example, NDL, fastText (Bojanowski et al., 2016), or Word2Vec (Mikolov et al., 2013). The semantic vectors of all word forms and, if applicable, inflectional and derivational functions of a given set of words constitute the so-called meaning or semantic matrix S. In S, each row corresponds to the semantic vector s of a pertinent word form or function, and each column represents a semantic dimension. Most commonly, the semantic vectors of content words are the sum of the semantic vectors of their individual parts. For example, the semantic vector of the word form Kinder ‘children’ is the sum of the semantic vectors of Kind ‘child’ and PLURAL. For our toy example, let us assume the following semantic matrix S:

With both the form matrix C and the semantic matrix S available, one can compute comprehension and production by means of multivariate multiple regression. That is, comprehension and production are modelled by simple linear mappings from the form matrix C to the semantic matrix S, comprehension, and from the semantic matrix S to the form matrix C, production. For comprehension, thus, the following equation is solved:

Let C’ denote the Moore-Penrose⁶ generalised inverse of C. Then, solving for F:

F is the transformation matrix used to map C onto S. As a so-called comprehension weight matrix, F specifies how strongly nodes in the C and S matrix are associated. Similarly, for production, the following equation is solved:

For G, then

Accordingly, for our toy example, we can solve $F=C\prime S$ with

and $G=S\prime C$ with

For the present toy example, CF is exactly equal to S and SG is exactly equal to C. In full-sized implementations of LDL, however, CF and SG are approximations of the S and C matrix due to their high dimensionality. That is,

and

While LDL relies on only multivariate multiple regression, previous studies have found that such simple linear mappings result in high overall accuracies (e.g. Baayen, Chuang, Shafaei-Bajestan, et al., 2019; Baayen et al., 2018). Once comprehension is modelled, its accuracy is assessed by comparing a given word’s predicted semantic vector to all observed semantic vectors, commonly by using Pearson correlation. If a given word’s predicted vector is most highly correlated with its observed vector, the model’s prediction is taken to be correct. For production, an additional step is required, as predicted n-grams/n-phones need to be assembled into potential word forms. As the present study does not make use of the production part of LDL, we refer the interested reader to the detailed accounts in Baayen, Chuang, Shafaei-Bajestan, et al. (2019), Chuang et al. (2020), and Heitmeier et al. (2021).

Finally, LDL offers a variety of measures calculated via observed and predicted matrices which allow for insight into a variety of semantic features. Such measures take into account the predicted semantic vectors, as these vectors are the result of the mapping process. That is, these vectors are assumed to reflect the interrelations of the entries of the simulated mental lexicon. LDL measures have been shown to not only successfully model, e.g. acoustic duration (Chuang et al., 2021; Schmitz et al., 2021; Stein & Plag, 2021), but also real word and pseudoword semantics (Chuang et al., 2021; Schmitz et al., 2021). Because of their successful applications, measures derived from an LDL implementation will be made use of in the analysis of masculine generics as well as masculine and feminine explicits in the present paper.

2.4 Research questions

Because, as far as the authors know, there is no comparable work available on the semantics of role nouns in German in terms of distributional semantics and especially regarding discriminative learning and measures derived from an implementation of LDL, no informed predictions on how semantic vectors or LDL measures may differ between different paradigm member types (see Section 3.1) are given. Instead, the following research questions are investigated:

RQ1: Do semantic vectors computed via NDL show semantic (dis-)similarities between paradigm member types, in line with the masculine bias found in previous research?

RQ2: Do measures derived from an implementation of LDL reflect semantic differences between paradigm member types?

RQ3: Do measures derived from an implementation of LDL successfully predict paradigm member types, even when stereotypicality of paradigms is accounted for?

3.1 Target words

For the present investigation, a set of 120 target words was adopted from Gabriel et al. (2008). In their study, the authors investigated the influence of stereotypical and grammatical information on the presentation of gender in language. For their investigation, they chose roles and their pertinent role nouns which are, from a stereotypical perspective, rather strongly associated with either males or females (e.g. mason and beautician), as well as role nouns which are neither stereotypically male nor female (e.g. author). Thus, Gabriel et al.’s set of items presents the perfect selection of target words for the present paper. If all role nouns, independent of their stereotypical associations, show similarities in terms of their semantics, this makes any potential findings more robust.

As the present investigation is interested in the generic masculine as well as the explicit masculine and the explicit feminine, for each target item, there are three target forms: the generic masculine form, the explicit masculine form, and the explicit feminine form. We call these constellations target word triplets. As we include singular and plural forms in our analyses, two sets of triplets per target word are considered. We call these groups of six words target word paradigms. Table 1 illustrates some of the 120 target word triplets. A list of all triplets is part of the data available for this paper.

Accordingly, Table 2 illustrates what a complete target word paradigm looks like for the target word Kosmetiker ‘beautician’. Each cell of Table 2 is what constitutes a type; we will use this term in the remainder of this paper. Thus, there are six different types per paradigm, i.e. three per triplet.

3.2 Corpus

To investigate the research questions of the present paper, a text corpus of German was required in which explicit and generic masculine role nouns were sense disambiguated. To the authors’ knowledge, there is no such corpus available. Thus, such a text corpus of German was created.

To arrive at a feasible corpus, first, sentences were extracted from the Leipzig Corpora Collection’s news sub-corpus (Goldhahn et al., 2012). Sampling one million sentences for each year from 2010 to 2019, a total of ten million sentences were extracted. The news sub-corpus was chosen to account for general variations. That is, using only texts from news websites, it was ensured that there was no influence on the representations of any masculine or feminine forms due to variations of register or genre across the sampled sentences.

Second, a sample of 830,000 sentences was extracted from the ten million sentences sample. While working with a larger corpus is generally preferable, a huge number of sentences comes with extensive computational costs at later stages of the implementation of naive discriminative learning. To keep the required computational requirements viable, we aimed at a number of sentences close to similar implementations (cf. Baayen, Chuang, Shafaei-Bajestan, et al., 2019).

The 830,000 sentences consisted of two types of sentences. For the first type, 800,000 sentences without target words were sampled. For the second type, sentences containing target words were sampled. During this process, issues with several target items became apparent, which led to the exclusion of seven target word paradigms.⁷ To account for the different frequencies of target word paradigms within our general ten million sentences sample, the target word paradigms were binned into six groups, based on their frequencies within the ten million sentences sample corpus. For each group, then, a set number of attestations was randomly sampled for the final corpus. The numbers of attestations for all frequency groups are given in Table 3. Note that some target words showed fewer than 100 attestations. In these cases, all attestations were extracted.

These 830,000 sentences made up the initial version of the text corpus. While the 800,000 sentences without target words were kept as is, parts of the 30,000 sentences with target words underwent re-sampling during the annotation process. This is explained further in the following subsection.

3.3 Annotation

The text corpus introduced in the previous section was annotated in two ways. First, all sentences were annotated automatically using the RNNTagger software (Schmid, 1999). Using the RNNTagger, inflectional features such as case, number, and tense were annotated. As the present paper is not concerned with derivational processes, no annotation based on derivation was conducted.

Second, the 30,000 sentences containing target words were manually annotated by two authors and two assistants, since, as far as the authors know, there is no automatic annotation software available that successfully sense disambiguates between explicit and generic masculine readings. All annotators were native speakers of German with an educational level comparable to A-levels or higher. Taking into account the context of each target word, the following three features were annotated: gender (masculine vs. feminine), number (singular vs. plural), and genericity (explicit vs. generic). To ensure a high level of inter-annotator agreement, a training set of 300 randomly sampled sentences was annotated before the annotation of the corpus itself. Only in 3 cases, i.e. 1%, did annotators disagree. As a consequence, it was decided that similar and generally opaque cases were to be documented for discussion and decisions among all annotators. If, after discussion of a given sentence among annotators, it remained unclear whether a target word was used in an explicit or generic manner, this sentence was discarded and a new sentence for the pertinent target word was sampled.

Finally, for the sentences containing target words, the automatic and the manual annotations were brought together. For target words, the manual annotation was kept, while for their sentence surroundings, the automatic annotation was adopted.

3.4 Training semantic vectors

Applying NDL as implemented by the Python package pyndl (Sering et al., 2022), the semantic vector space that is used in the remainder of this paper was trained based on the corpus introduced in the previous subsections. Vectors were trained for content and function words as well as for inflectional functions. Crucially, the variable of interest, genericity, that is, its two values ‘generic’ and ‘explicit’, were treated as inflectional functions as well. Overall, the semantic vectors were trained on 830,000 sentences to a total of 49,044,960 tokens. Following Baayen, Chuang, Shafaei-Bajestan, et al. (2019), for each sentence of the corpus, each individual base, function word, and inflectional function within the sentence (outcomes) was predicted by the other bases, function words, and inflectional functions (cues) of the same sentence. As a result, semantic vectors not only for words but also for inflectional functions were obtained straightforwardly.

The resulting square matrix was of dimension 30,887 × 30,887. The diagonal of the matrix was then set to 0, as the present work focuses on semantic similarity (cf. Baayen, Chuang, Shafaei-Bajestan, et al., 2019). However, as a matrix of such dimensionality requires excessive computational power, the matrix was reduced before entering the next implementational step. Reduction took place by removing those columns whose variance was below the median variance of all columns. Such columns can be removed from the matrix without a loss of accuracy, as their discriminative power is negligible (cf. Baayen, Chuang, Shafaei-Bajestan, et al., 2019). The resulting matrix was of dimension 30,887 × 15,023.

3.5 Training a comprehension network

To train an LDL implementation using the WpmWithLdl package⁸ (Baayen, Chuang, & Heitmeier, 2019), the semantic vector space created by NDL was taken as a starting point. Based on the semantic vectors, a semantic matrix S was created. Following the reasoning introduced in 2.3, semantics of content words consisted of the sum of their pertinent parts, e.g. for Kinder ‘children’: Kinder = Kind+PLURAL. For the focus of the present paper, this meant that masculine generics such as Anwalt ‘lawyer’ are represented by their base meaning Anwalt_base as well as the function vectors for number (i.e. SINGULAR or PLURAL), gender (MASCULINE), and genericity (GENERIC). Masculine explicits, in contrast, contain for genericity the semantic vector of EXPLICIT, and feminine explicits consist of their base meaning, a number vector, FEMININE for gender, and EXPLICIT for genericity.

The semantic matrix was created for 10,222 word forms. We arrived at this number by combining our target paradigm members and their respective semantic vectors, and the semantic vectors for which entries in CELEX (Baayen et al., 1995) were found. The reason entries in CELEX were required is found in the construction of the form matrix. The present study makes use of triphones, as previous studies have found strings of three elements (i.e. phones or grams) to capture the variability of neighbouring phonological information well for a number of languages (e.g. Baayen, Chuang, Shafaei-Bajestan, et al., 2019; Chuang et al., 2021; Milin et al., 2017; Schmitz et al., 2021). Triphones were chosen over trigrams with follow-up research in mind, which requires phone representations (see the discussion for more on future research directions). Using triphones, phonological transcriptions of all word forms were required. These transcriptions were adopted from CELEX.

While the resulting cue matrix of dimension 10,222 × 9,320 on its own is still within reasonable size, e.g. concerning resulting computation times, the size of the semantic matrix of dimension 10,222 × 15,023 would have led to issues, especially concerning not only computation times but also the hardware resources required. Following Baayen, Chuang, Shafaei-Bajestan, et al. (2019), who found that working with at least 4,000 columns suffices, we reduced the dimensionality of the semantic matrix. We proceeded similarly to the reduction of the matrix given in 3.4. That is, checking all columns for their variance, we disregarded those below the median variance, as they overall contribute least to the accuracy and discriminatory features of vectors. The final semantic matrix was of dimension 10,222 × 7,511.

Using the semantic and form matrices, the comprehension part of the LDL network was modelled as introduced in Section 2.3. Then the following measures were extracted:

comprehension quality. Computing the correlation of a given word’s observed and predicted semantic vector, a measure of comprehension quality is obtained. Higher values indicate a higher comprehension quality.

semantic neighbourhood density. To compute a word’s semantic neighbourhood density, its predicted vector and the semantic vectors of its eight nearest neighbours⁹ were checked for their correlation coefficients. The mean of these coefficients is taken as the value of this measure. Higher values indicate denser semantic neighbourhoods.

semantic activation diversity. This measure consists of the square root of the sum of the squared values of a given word’s predicted vector, i.e. the Euclidean norm of that vector. Higher values imply stronger links to many other entries, indicating a word’s semantic activation diversity.

4.1 Semantic similarity across paradigm member TYPEs

To analyse the semantic similarity across paradigm member types, we made use of cosine similarity. Cosine similarity expresses the (dis-)similarity of two given vectors with values typically in a range of [–1,1]. Higher values indicate a high similarity, while lower values indicate a higher dissimilarity. As semantic vectors reflect words’ semantics, cosine similarity values allow for judgements concerning semantic similarities. As such, cosine similarity has been regularly used in the context of distributional semantics (e.g. Huyghe & Wauquier, 2020; Sitikhu et al., 2019). Cosine similarity was computed using the gdsm package (Schmitz & Schneider, 2022).

In the present case, cosine similarities were used to investigate how similar the semantics of two given paradigm member types are. For example, it was used to check how similar the set of vectors of singular masculine generics is to the set of singular masculine explicits. Such a comparison was conducted for all three possible combinations of types across all paradigm triplets within number. The vectors used in this analysis are those which were used as vectors in the observed S matrix in the LDL implementation in 3.5. The results of these comparisons are given in Table 4.

Vectors of masculine explicits are most similar to vectors of masculine generics, while vectors of feminine explicits are most similar to vectors of masculine explicits. While this overall pattern is true for both the singular and plural, differences are more pronounced in the latter. Using Wilcoxon-Mann-Whitney-Tests, it was found that the differences between types are highly significant, with p < 0.001 in all cases, indicating that masculine generics are most similar to masculine explicits.

While these results already provide a first insight into the semantic nature of the masculine generic, they consist of rather simple statistical analyses of bare semantic vectors. Hence, in the following subsections, the measures extracted from the LDL implementation as well as stereotypicality judgements are used to further analyse the semantic representations of masculine generics. Stereotypicality judgements are incorporated, as previous studies have shown that semantic vectors may be subject to biases as well (e.g. Bolukbasi et al., 2016; Caliskan et al., 2017). The stereotypicality judgements used in our analysis were taken from Gabriel et al. (2008), the same study the target word paradigms for the present investigation were adopted from. Stereotypicality here refers to the assumed extent to which given groups are made up of women or men, while groups were presented to participants by both masculine and feminine German role nouns.

4.2 LDL measures

Let us now have a look at the LDL measures extracted for the individual paradigm member types. The measures, comprehension quality, semantic neighbourhood density, and semantic activation diversity, are illustrated by Figure 1.

Figure 1: LDL measures per paradigm member type as computed by the LDL implementation. Panel A: comprehension quality; Panel B: semantic neighbourhood density; Panel C: semantic activation diversity.

Apparently, certain paradigm members show very similar values for certain measures. Applying Wilcoxon-Mann-Whitney-Tests, we took a closer look at the individual values. For all three measures, masculine generics and explicits are highly similar within number, with all p-values above 0.17. Feminine explicits, on the other hand, are significantly different to either type of masculine in either number, with all p-values below 0.001. Feminine explicits are significantly different across number for all measures, with all p-values below 0.001. In sum, the semantic measures apparently reflect semantic differences between paradigm member types.

4.3 Predicting paradigm member types

To obtain greater insight of how the three LDL measures and stereotypicality might influence the masculine bias found in 4.1, we tested whether the measures and ratings were able to successfully predict the six paradigm member types.

First, the independent variables under discussion were checked for their correlation. It was found that the LDL measures comprehension quality and semantic neighbourhood density showed a high correlation coefficient (ρ = 0.67). Using highly correlated variables within the same regression model may lead to issues of collinearity, rendering the estimates of the model unreliable (cf. Tomaschek et al., 2018). We thus decided to perform a principal component analysis (PCA; see e.g. Schmitz et al., 2021; Tomaschek et al., 2018). In such an analysis, the dimensionality of the data is reduced by transforming the included variables into principal components. This transformation results in linear combinations of the predictors that are orthogonal to each other, thus not correlated. Both highly correlated LDL measures entered the PCA. Once the PCA is computed, one may decide which principal components to retain for further analysis. For a meaningful decision, we followed three rules of thumb (cf. Baayen, 2008; O’Rourke et al., 2005). First, the eigenvalue of a component should be higher than 1, as an eigenvalue of 1 or more indicates that a component explains more variance than it introduces. Second, the cumulative variance explained by candidate components should at least be higher than 80 % to explain a sufficient amount of variance overall. Third, components are only useful for further analyses if their makeup is interpretable. Following these rules, we retained the first principal component. As for its interpretation, the component is highly positively loaded with both comprehension quality and semantic neighbourhood density. Thus, the component can be considered a measure of quality of comprehension and neighbourhood density, indicating that a higher degree of comprehension quality comes with denser semantic neighbourhoods. We will henceforth call this component semantic quality & density.

Then, type entered a multinomial regression analysis as dependent variable using the nnet package (Venables & Ripley, 2002), while stereotypicality ratings, semantic activation diversity, as well as semantic quality & density were included as predictor variables. Stereotypicality did not reach significance, while semantic activation diversity and semantic quality & density reached significance. The coefficients, standard errors, z-values, and p-values of the fitted model are given in Table 5. Effect sizes as well as confidence intervals are given in the OSF supplementary material.

The model fit is high, with an R² value of 0.32. This R² value is the so-called McFadden’s pseudo R² value, i.e. a value which indicates the goodness of fit of a multinomial regression model (McFadden, 1974). According to McFadden (1979), values between 0.2 and 0.4 represent excellent model fit.

Let us now take a closer look at the individual effects of semantic activation diversity and semantic quality & density. The effects of both predictor variables are illustrated in Figure 2. For semantic activation diversity, one finds that plural feminine explicits show the highest probability for lowest values (approx. 2.7), while singular feminine explicits behave contrarily, with the highest probability for highest values of semantic activation diversity (approx. 9). Plural masculine forms, that is, both generics and explicits, show a very similar pattern in terms of their probabilities. Their highest probability is reached at a semantic activation diversity level of approx. 4.8. Analogously, both singular masculine forms show a very similar pattern as well. Their highest probability is reached at a semantic activation diversity level of approx. 6.9.

Figure 2: Predicted probabilities of the six paradigm member types as modelled by semantic activation diversity (Panel A) and semantic quality & density (Panel B). Dashed lines = singular; solid lines = plural.

For semantic quality & density, masculine forms within number also display very similar patterns. Plural masculine forms show their highest probability at the lower end of semantic quality & density, at approx. –7.3. Singular masculine forms show their highest probability at the higher end of semantic quality & density, at approx. 1.3. The feminine forms here also show a similar pattern. However, their probabilities are below those of the masculine forms for all values of semantic quality & density. Their highest probability, which is only approx. 0.07, is reached at a semantic quality & density value of approx. 1.3.

Note that the multinomial regression analysis of type disregarded the interrelations of the six paradigm member types. Three types are singular, three types are plural. Four types are masculine, two types are feminine. Two types are generic, four types are explicit. Hence, the levels of type are not independent of each other but related, due to shared features. To check whether these relations show an influence on the results presented thus far and, if so, to see what the nature of these influences is, we fitted three separate logistic regression models. Each model was fitted to predict one of the three features: number, gender, and genericity. Analogously to the multinomial regression model, stereotypicality, semantic activation diversity, and semantic quality & density were included as predictor variables alongside the two features which were not the dependent variable of the pertinent logistic regression model. For instance, number was predicted by the three variables of interest and by gender and genericity.

For the prediction of number, it was found that the LDL measures, semantic activation diversity and semantic quality & density, show significant effects. The higher the values of these measures, the more likely a form is to be singular. For the prediction of gender, it was found that semantic quality & density shows a significant effect. The higher the value of this predictor is, the more likely a form is masculine. For the prediction of genericity, no significant effects were found. While this may seem surprising at first, a closer look at the paradigm member straightforwardly explains this finding. First, there are masculine generics but no feminine generics. Second, taking into account the observed values of the LDL measures, the two levels of genericity, explicit and generic, appear to be almost identical. Hence, these variables cannot help disambiguate explicit and generic forms. In sum, the three individual analyses of number, gender, and genericity are in line with the results of the multinominal regression analysis of type. The coefficients, standard errors, z-values, and p-values of the three fitted generalised linear models are given in Table 6; the effect sizes are part of the OSF supplementary material.

In sum, the present analyses found that stereotypicality does not have a significant influence on any type of paradigm member. The LDL measures, however, show significant effects. Concerning the quality of comprehension and semantic neighbourhood density, as entailed in semantic quality & density, singular masculine forms are found to have the highest values. Masculine plurals, however, show an opposite picture. Concerning semantic activation diversity, plural feminines are found to have the highest values. Feminine singulars, however, show an opposite effect. Thus, semantic quality & density, and hence its underlying measures, appear to modulate masculine forms more extensively than feminine forms, while semantic activation diversity clearly distinguishes feminine forms but masculine forms to a far lesser extent.