On the utility and meaningfulness of variation

In many traditional dialectological surveys, linguistic variation has been explored primarily from a geographical angle (e.g., Nerbonne, Reference Nerbonne2010), the reason being that most atlas projects aimed to document old base dialects and their geographical distributions (e.g., Stoeckle, Reference Stoeckle, Côté, Knooihuizen and Nerbonne2016). What is more, many of these atlas projects have only considered one or a few select speakers at each location (e.g., NORMs/NORFs [i.e., nonmobile, older, rural males/females]). This, perhaps inadvertently, encourages a view toward one place = one variety. As Stoeckle (Reference Stoeckle, Côté, Knooihuizen and Nerbonne2016:196) pointed out, however, this view “does not correspond to linguistic reality” in which inter- and intra-speaker variation are the norm rather than the exception (see Bülow & Pfenninger, Reference Bülow and Pfenninger2021).

The concept of variation can be a crucial source of information about the individual and/or locality, and this idea is cultivated across disciplines. For example, in cognitive developmental research, larger intraindividual variation—that is “differences in the level of a developmental variable within individuals and between repeated measurements” (van Geert & van Dijk, Reference Van Geert and van Dijk2002:341)—in cognitive resources is associated with vulnerability or impairment and is often taken to be indicative of lower cognitive functioning (e.g., Fagot, Mella, Borella, Ghisletta, Lecerf, & De Ribaupierre, Reference Fagot, Mella, Borella, Ghisletta, Lecerf and De Ribaupierre2018). Relatedly, greater linguistic variation either at the level of the individual or of a locality may be an indicator of language change (e.g., Elspaß, Reference Elspaß, Neuland and Schlobinski2018), though it is not necessarily clear whether variation is a precondition of language change or a consequence thereof (e.g., Glaser, Reference Glaser2014). Given the idea that variation may carry information about impending cases of language change, recent years have seen an uptake in attempts to integrate the concept of variation into, for example, syntactic theory (e.g., Cornips & Corrigan, Reference Cornips and Corrigan2005). The idea here is that variation may be an inherent part of an individual’s or a locality’s grammar and provide the basis for dynamism and language change (e.g., Seiler, Reference Seiler, Valentin and Vinckel2008), as has also been argued in sociolinguistics since the field’s conception (e.g., Labov, Reference Labov1966).

Stoeckle (Reference Stoeckle, Côté, Knooihuizen and Nerbonne2016) investigated interpersonal variation in the Syntactic Atlas of German-speaking Switzerland to explore which regions of German-speaking Switzerland evince the most variation, and whether higher variability may be regarded as an indicator of dynamism and linguistic change. To this end, he introduced a “Variation Index,” which operationalizes variation as the degree of agreement between the informants regarding the locally dominant variant (i.e., the variant that was provided by the most informants, at each location). Localities in which all individuals reported only a single variant (i.e., the dominant variant) received a value of 0 indicative of no variation within the locality, whereas localities in which individuals reported multiple variants received higher scores indicative of higher locality-level variation. Stoeckle concluded from his analysis that the higher variability in certain dialect areas is a result of variants dominant in one dialect area becoming more widespread—in other words, certain local variants may be in the process of becoming more supra-regional variants.

Wirtz et al. (Reference Wirtz, Pickl, Niehaus, Elspaß and Möllerunder review) employed a similar measure of variation, the “Variation Intensity Index,” which takes into account frequency data concerning all variants and not just the dominant one, and conducted an apparent-time analysis in order to determine whether the degree of variation differs intergenerationally. Concerning generational differences in variation intensity, Wirtz et al.’s apparent-time analysis lends weight to the assumption that the younger generation of informants reported more familiarity with linguistic variants of a variable and thus a higher degree of variation than did the older generation. Specifically, these findings indicate that young adult informants consider a broad repertoire of variants to be common in their locality as compared to individuals from older age groups. These age effects necessitate analyses focusing on measures of variability as the response variable to consider, in addition to other predictor–outcome relationships, (chronological) age as a potential covariate. Additionally, their Variation Intensity Index was calculated at the locality level and disaggregated by two age cohorts—whether related measures of variation at the informant level (e.g., the diversity of linguistic variants an informant reports for a variable at a given locality) follows similar age-related patterns, and also between which age group(s) the diversity of reported linguistic variants is prone to substantial change, remains to be seen. Additionally, the aforementioned authors strictly explored the spatial clustering patterns in variation intensity of 15 variables, a comparatively small sample for an aggregate analysis. It thus remains an outstanding question whether the diversity of reported variants computed across a larger sample of variables is subject to spatial autocorrelation.

Career as a meaningful predictor for language variation

The idea of career as a potentially influential factor has not necessarily been left unattended, but empirical results attempting to disentangle how differential aspects of speakers’ primary occupation impact on their patterns of variation do not run rampant in the sociolinguistic literature. Traditionally, occupation has been treated as a class-related, economic variable, at least in Western societies. For example, Labov’s (Reference Labov1966) study of five phonological variables in the Lower East Side of New York City employed a class model that followed the model developed in 1961 by the Mobilization for Youth project. This included conceptualizing class as a 10-category linear scale (Warner & Lunt, Reference Warner and Lunt1942; Warner, Meeker, & Eells, Reference Warner, Meeker and Eells1949), which combined education level, family income, and occupational groupings. Such an operationalization was considered advantageous, as it would simultaneously tap into several dimensions of socioeconomic status (e.g., Labov, Reference Labov2001). Along similar lines, Trudgill (Reference Trudgill1974) drew on a combined class scale but weighted occupation as the most important component. This is based on the notion that class identity alongside the associated (linguistic) behaviors tends to remain constant, at least in Great Britain during the late 20^th century, such that “even the most affluent manual workers retain the values, ideas, behaviour patterns and general culture of the working class, and there has been little embourgeoisement of the British working class” (Trudgill, Reference Trudgill1974:34). Others (e.g., Macaulay, Reference Macaulay1977) rely exclusively on occupational groupings to operationalize a class scale, the rationale being ease of data collection and the fact that further class indicators such as income and education are typically strongly correlated with occupational groupings (see also Dodsworth, Reference Dodsworth2009).

Recently, starker occupation-centered scales have also emerged. Prediger (Reference Prediger2016), for example, classified the occupational status of his participants (second language learners of German) on a 5-point scale based on the degree of manual labor required, the goal being to approximate the intensity of exposure to vernacular speech in the workplace. Advocating for a more multidimensional approach to occupation, Wirtz (Reference Wirtz2024) proposed a measure of occupational complexity based on the DOT (U.S. Department of Labor, 1977). The goal herewith is to take a multifactorial perspective to the differential communicative and manual requirements of an occupation and how these are intertwined with patterns of varietal behavior. His rationale for a multifactorial approach to occupational status, explicitly not drawing on class-related covariates, was to circumvent spuriously drawing categorical lines or placing clear-cut thresholds on occupations. As Wirtz (Reference Wirtz2024) noted, occupations house diverse sociological phenomena and complexity dimensions (e.g., communicative, technical, and/or physical skills), which are interwoven with the extent to which speakers are exposed to diverse contextual environments and, by extension, locality- and population-level sociolinguistic variation. Thus, adhering to operational definitions of different complexity dimensions on continuous scales allows us to more faithfully capture the granularity in the effects of occupation.

Of course, as Sankoff & Laberge (Reference Sankoff, Laberge and Sankoff1978) also noted, even the most carefully conceptualized scales and operationalized variables fall short at capturing the sociohistorical features of occupational factors. Sankoff & Laberge (Reference Sankoff, Laberge and Sankoff1978) proposed focusing on the linguistic market, that is, a domain in which (non-)standard language forms are regarded as useful and desirable capital for particular economic roles. However, as Dodsworth (Reference Dodsworth2009:1318) noted, the index measured standard language competence and ignored possible alternative linguistic markets (as well as alternative cultural settings with different or no linguistic standardization) which do not orientate toward a prestigious standard variety. Given this, we must consider approaches that take into account the influence of occupational complexity on a speaker’s linguistic repertoire. Additionally, as lifespan perspectives (e.g., Riverin-Coutlée & Harrington, Reference Riverin-Coutlée and Harrington2022) have exemplified, shifts in job-related complexity may be strong predictors of differences in linguistic variation, in addition to classic sociolinguistic factors (e.g., Labov, Reference Labov1966, Reference Labov2001; Trudgill Reference Trudgill1974). This necessitates the additional inclusion of changes in job complexity and/or age as potential moderating covariates when examining the relationship between occupation and linguistic outcomes (e.g., the linguistic repertoire may change more for people who switch careers often, or occupation may have a stronger impact on the language use of young adults recently joining the workforce as opposed to working midlife and older adults).

Finally, whereas previous investigations have explored whether economic factors and differences in occupational status impact, for example, speakers’ (socio-stylistic) differential use of sociolinguistic variables, there are no investigations attending to whether the diversity of reported linguistic variants per informant at a given locality relates to career-specific variables such as occupational complexity. This is a desideratum insofar as the range of an informant’s reported variants can provide meaningful information on an individual’s knowledge of linguistic variation, and whether this diversity can be predicted by career-related complexity metrics.

Research questions

The main goal of this article is to analyze the association between the diversity of an informant’s reported variants and occupational complexity, and whether age moderates this relationship—while also attending to potential issues of spatial autocorrelation. To this end, we address the following research questions:

1. (1) To what extent is the diversity of individual informants’ reported variants spatially clustered?

2. (2) To what extent does occupational complexity with data, people, and things predict differences in the diversity of reported variants (when controlling for locality-related variation as a potential confound)?

3. (3) To what extent is the relationship between occupational complexity and the diversity of reported variants moderated by chronological age?

As detailed above, occupational complexity with data, people, and things may play a role in influencing the range of an individual informant’s reported variants, but empirical evidence along these lines is lacking. From a variationist sociolinguistic angle, the hypothesis stands that the career of a speaker may indeed hold high predictive power when it comes to, for instance, their own linguistic behavior (e.g., Steinegger, Reference Steinegger1998). This is because an individual’s career is complexly interwoven with the extent to which they are exposed to the linguistic behavior of others, a diversity in contextual environments, and, consequently, the locality- and community-level (socio-)linguistic variation. Given the exploratory nature of the present analyses, we refrain from any a priori hypotheses concerning the (directionality of the) effects of occupational complexity. In light of Wirtz’ et al. (Reference Wirtz, Pickl, Niehaus, Elspaß and Möllerunder review) findings, however, it does appear plausible that there may be age-related effects on informants’ familiarity with different variants at a given locality—specifically, with younger adults reporting familiarity with more variants. What is more, since occupational complexity may change (and likely increase, at least in certain domains) throughout the lifespan (e.g., in relation to work-related milestones such as taking on management positions and/or engaging in more cognitively complex careers due to increased experience), it seems additionally necessary to incorporate age as a moderating covariate of occupational complexity.

Atlas of Colloquial German

The data for the present study result from the Atlas zur deutschen Alltagssprache ‘Atlas of Colloquial German’ (AdA; Elspaß & Möller, Reference Elspaß and Möller2003; see also Pickl, Pröll, Elspaß, & Möller, Reference Pickl, Pröll, Elspaß, Möller, Bülow, Fischer and Herbert2019), the largest and longest running linguistic atlas of contemporary colloquial German in the German-speaking world. The data are collected in approximately annual to biannual intervals via online surveys in German-speaking regions (i.e., Germany, Austria, Switzerland, Liechtenstein, Luxembourg, and the German-speaking parts of northern Italy, eastern Belgium, and the Alsace and Lorraine regions in eastern France).

In the AdA questionnaires, informants are asked to identify local variants in lexis, pronunciation, grammar, phraseology, and pragmatics, and in some cases also to declare how common/uncommon a certain variant or construction is for the “everyday colloquial speech” in their respective locality. The informants are usually presented with a brief concept in the form of a picture and/or description along with a list of potential variants from which they are then requested to choose the expression(s) “normally” used in their locality, or otherwise to provide a variant not listed (for examples from the current round, see https://www.atlas-alltagssprache.de). In the AdA, participants act as informants and are thus requested not to indicate their own personal use, but are rather instructed to name variants that are used in the colloquial speech of their hometown/city, that is, the kind of speech one would normally hear, be it more closely oriented toward a dialect or standard German. Importantly, given the heterogeneity in potential varietal spectra in the German-speaking realm (e.g., diaglossic and diglossic settings, see Auer, Reference Auer, Delbecque, van der Auwera and Geeraerts2005), the concept of “everyday colloquial speech” can range from local dialects (e.g., in German-speaking Switzerland) over intermediate varieties (e.g., in some areas of Bavarian-speaking Austria) to different regional forms of standard German varieties (e.g., in northern Germany and metropolitan areas).

In the AdA, the localities are not predefined, and participation is not constrained by any social-specific factors, which facilitates a more realistic portrait of colloquial language variation by way of capitalizing on informants’ “expertise of the local language use” (Pickl et al., Reference Pickl, Pröll, Elspaß, Möller, Bülow, Fischer and Herbert2019:41, our translation). Such crowdsourcing data collection methods necessarily result in socially very diverse datasets (see Leemann, Derungs, & Elspaß, Reference Leemann, Derungs and Elspaß2019), particularly as concerns variables relating to, for example, age, gender, mobility, socioeconomic status and, importantly for this contribution, occupational status.

Informants

The present study draws on data from Round 11 of the AdA, and we concentrate on Germany, Austria, Switzerland, and German-speaking northern Italy, as these countries evinced the highest response rates. In terms of data cleaning, we excluded participants who (a) did not provide a postal code and/or place of residence, and thus could not be categorized in terms of regional location; (b) did not provide information on their age; (c) did not provide information on their occupation; or (d) for whom no occupational complexity measure could be determined. For 9,173 informants—the main sample pool for the present study—it was possible to link their main occupation to an occupational complexity measure in accordance with the DOT (see the section, Occupational Complexity, for more details on the categorization process). As concerns the nationality distribution of informants, we received the most responses from individuals in Germany (n = 7563), followed by Austria (n = 1156), Switzerland (n = 390), and the German-speaking parts of northern Italy (n = 64). These quantities are approximately proportional to the German-speaking populations of the respective countries and thus the four countries were sampled at a consistent rate.

Participation was comparatively balanced in terms of gender (men = 4276, women = 4897), but there was an uneven distribution of age cohorts (10–19 = 743; 20–29 = 3276; 30–39 = 2168; 40–49 = 1324; 50–59 = 1,117; 60+ = 545), with adolescents and older adults being the most underrepresented age cohorts. Note that data on informants’ chronological age were collected categorically, which is why age is entered a categorical rather than as a numeric predictor in the following analyses.

Following Wirtz et al. (Reference Wirtz, Pickl, Niehaus, Elspaß and Möllerunder review), localities were determined by using the first two digits of the participant-reported postal code in Germany, and, in light of their drastically smaller geographical size, the first digit of the participant-reported postal code in Austria, Switzerland, and northern Italy. This resulted in 114 localities and allowed us to examine a geographically large area, but which was condensed enough to still capture areal variation (note that, for the AdA maps published on the internet, the data are grouped according to a fixed network of locality points).

Quantifying the diversity of reported linguistic variants

In order to capture the diversity of reported variants in the AdA data quantitatively, we employed a standardized measure of the number of reported variants of a variable for each informant, averaged across the 62 variables detailed in the following section. Specifically, a variable with n variants was assigned a value of 1 − (1/n) (e.g., a single variant reported yields a measure of 0, two variants reported yield a measure of 0.5, etc.). In other words, the integer value of the number of variants informants report being familiar with was scaled to the interval [0, 1) and the scores were subsequently averaged across 62 variables. While from a purely computational perspective it makes no difference to use the scaled measure of diversity of reported variants as opposed to the number of reported variants for each informant, the scaled measure functions as an intuitive standardized measure of variation in terms of the informants’ familiarity with linguistic variants. Additionally, since this measure of variation was adapted from Wirtz et al.’s (Reference Wirtz, Pickl, Niehaus, Elspaß and Möllerunder review) Variation Intensity Index, the aforementioned scaling procedure also ensures that measures of variation at the informant-level and locality-level can be more readily compared across studies. Furthermore, the aggregate approach (i.e., a single measure of informants’ familiarity with linguistic variants) is in line with operationalizations of intraindividual variation, which often encapsulate task-specific individual-level variation in a single measure (e.g., from developmental psychology the “intra-individual standard deviation” score [Fagot et al., Reference Fagot, Mella, Borella, Ghisletta, Lecerf and De Ribaupierre2018]).

Table 1 provides the descriptive statistics for the scaled measure of the diversity of reported variants across the six age cohorts (see also Figure A2 in the online Appendix for a visual overview, and also Figure A3 for a visual overview in relation to gender).

Table 1.

Descriptive statistics of the scaled measure of the diversity of reported variants across age cohorts

Variables

The scaled measure of the diversity of reported variants was calculated based on 62 variables from Round 11 of the AdA (for the variables in Round 11, see https://www.atlas-alltagssprache.de/elfte-runde/). Items requiring informants to declare whether a certain variant or construction is common/uncommon were excluded from analysis, as these inherently result in single-answer responses and thus leave no room for informants to indicate familiarity with multiple variants of the variable. The variables included were mainly lexical in nature, though select morphological, phonological, and syntactic variables were also included. Table 2 provides several examples of the variables from which the scaled measure of the diversity of reported variants was derived.

Table 2.

Examples of variables from which the scaled measure of the diversity of reported variants was derived

Figure A1 in the online Appendix illustrates the raw number of reported variants by individual informants for each of the 62 variables and illustrates that participants typically did not report more than two, three, or four variants of a variable.

Note that the different linguistic domains mentioned prior were collated in the final measure of the diversity of reported variants. This is in line with previous dialectometric work which emphasizes aggregation as a way to smooth over the noise of individual variables and linguistic architecture and produce a more representative measure. For instance, in his dialectometric analysis of the Sprachatlas von Bayerisch-Schwaben (‘Language Atlas of Bavarian Swabia’), Pröll (Reference Pröll2015) examined different linguistic domains both separately and in an aggregated manner and found that, on the whole, the overall picture was more representative and more than the sum of the individual parts (i.e., linguistic domains). Moreover, in their pilot study, Wirtz et al. (Reference Wirtz, Pickl, Niehaus, Elspaß and Möllerunder review) found no difference between the locality-level variation intensity in lexical, morphological, and phonetic variables.

Occupational complexity

In each AdA round, informants were asked to provide their current primary occupation. Main occupation was then matched with the best fitting category listed in the fourth edition of the United States DOT (U.S. Department of Labor, 1977), which comprises more than 12,000 occupations that have been evaluated based on observations by job analysts. Of the 9-digit classification code listed for each occupation, the middle three digits represent occupational complexity with data, people, and things respectively. This measure reflects the notion that each occupation requires workers to function in relation to these three complexity dimensions.

Table 3 indicates the dimensions used to classify occupations. To facilitate interpretive ease, scores were recoded so that for each dimension a higher value was indicative of higher occupational complexity (ranges for complexity with data: 0–6; for complexity with people: 0–8; and for complexity with things: 0–7, and in the statistical models, occupational complexity was z-scored). For example, the occupation “Automobile Mechanic” is assigned scores of 4 for complexity with data, 2 for complexity with people, and 6 for complexity with things. This indicates that the occupation involves “analyzing” data (i.e., “examining and evaluating data; presenting alternative actions in relation to the evaluation is frequently involved”), “speaking-signaling” people (i.e., “talking with and/or signaling people to convey or exchange information”), and “precision working” with things (i.e., “using body members and/or tools or work aids to work, move, guide, or place objects or materials in situations […] [in which the] selection of appropriate tools, objects, or materials, and the adjustment of the tool to the task require exercise of considerable judgment”). As another example, the occupation “Pastor” is assigned scores of 5 with data, 8 with people, and 0 with things, which implies that the job components involve “coordinating” data (i.e., “determining time, place, and sequence of operations or action to be taken”), “mentoring” people (i.e., “dealing with individuals in terms of their total personality in order to advise, counsel, and/or guide them”), and “handling” things (i.e., “involves little or no latitude for judgment with regard to attainment of standards or in selecting appropriate tool, object, or materials”) (for more extensive descriptions of the occupational complexity metrics, see the Explanation of Data, People, and Things: https://www.dol.gov/agencies/oalj/PUBLIC/DOT/REFERENCES/DOTAPPB). Importantly, the occupational complexity measure does come with several caveats, the most notable one being that no occupational complexity measure for “Student” (neither school pupils nor university students) exists. However, based on the guidelines for occupational complexity classification outlined in the DOT, we assigned a value of 3 to the complexity measure with data (i.e., “gathering, collating, or classifying information about data, people, or things”), and following Wirtz (Reference Wirtz2024), a value of 2 for complexity with people and a value of 0 for complexity with things. This was rationalized by the fact that occupations with arguably similar complexity, activities, and cognitive requirements such as administrative assistants (complexity = 320) and researchers (complexity = 420) are coded in the DOT with similar complexity values. Importantly, an individual’s occupation was only coded for the aforementioned complexity measures when a direct translation of the occupation was evident in the DOT (apart from students). This was done to ensure comparability between (a) occupations in the German-speaking countries and the DOT measures developed for the US marketplace and (b) modern occupations and complexity measures developed for occupations in the late 20^th century.

Table 3.

Dimensions used in the rating of occupations into complexity of working with data, people, and things

While the O*Net program (https://www.onetonline.org/) is now the primary source of occupational information in the United States, the occupational complexity measure remains in use in, for example, cognitive psychology (e.g., Smart et al., Reference Smart, Gow and Deary2014), as it is nevertheless useful for broadly classifying occupational requirements.

Table 4 lists the descriptive statistics for the three complexity dimensions in informants’ primary occupation disaggregated by age cohort. As Figure 1 additionally illustrates, the younger cohort unsurprisingly evinced comparatively homogeneous complexity scores across data, people, and things, largely given their status as students (either as school pupils or university students). The remaining age cohorts were more heterogeneous in terms of their respective occupational complexity. As concerns complexity with things, we note the surplus in zeros, that is, informants practicing occupations with little to no manual labor demands, which is likely an artifact of the crowdsourcing method and its tendency toward sampling bias (Leemann, Kolly, Purves, Britain, Glaser, Reference Leemann, Kolly, Purves, Britain and Glaser2016), for instance, in terms of socioeconomic status and education. Along similar lines, the people domain of occupational complexity evinces an excess of twos (“Speaking-Signaling”), illustrating that occupations involving an expressly high degree of communicative competence are also a minority in this sample.

Figure 1.

Distributions of occupational complexity measures across the domains of data, people, and things.

Table 4.

Descriptive statistics of occupational complexity with data, people, and things across age cohorts

Statistical analyses

Given the scaling of the diversity of reported variants as the outcome variable—that is, strictly bounded by [0, 1)—and additionally in light of the surplus of zeros in the data (i.e., informants who reported familiarity with a single variant across all variables), we employed zero-inflated beta models (Markl, Reference Markl2023). Zero-inflated beta models are tailored to handle datasets that (a) contain many zeros and (b) are bounded by [0, 1), which makes them an optimal choice for current data distribution of the outcome variable.

The zero-inflated beta models were fitted using a Bayesian approach with the brms package (version 2.20.4, Bürkner, Reference Bürkner2017) in R (version 4.2.2, R Core Team, 2020). Bayesian models can estimate generalized (non)linear multivariate models using the probabilistic programming language Stan (version 2.32.3, Carpenter, Gelman, Hoffman, Lee, Goodrich, Betancourt, Brubaker, Guo, Li, & Riddell, Reference Carpenter, Gelman, Hoffman, Lee, Goodrich, Betancourt, Brubaker, Guo, Li and Riddell2017). The Bayesian framework allows us to investigate the absence of “null effects.” The focus of the analyses is directed toward the distributions of the inquired effects (i.e., the posterior distributions) rather than on point estimates. By doing this, we effectively avoid asking questions strictly relating to whether there is an effect of a variable (null hypothesis significance testing) but rather ask what the most probable direction and magnitude of an effect is. (For variationist accounts of the conceptual advantages of Bayesian methods, we refer interested readers to Markl [Reference Markl2023], and for tutorials on Bayesian inferential statistics for the language sciences, see Vasishth, Nicenboim, Beckman, Li, and Jong Kong [Reference Vasishth, Nicenboim, Beckman, Li and Jong Kong2018]).

In this paper, we fitted two models to investigate the relationship between occupational complexity with data, people, and things (note that the occupational complexity measures were z-scored before being entered into the respective models), and the diversity of reported variants as a dependent variable. The first model was fitted with solely the occupational complexity predictors, which provides an unadjusted estimate of the effect of complexity of primary occupation on the diversity of individual informants’ reported variants. In this model, we also included an interaction effect between occupational complexity with people and things. Given that previous research has shown that individuals in manual professions tend toward dialectal variants, while individuals in communicatively oriented professions tend toward standard language (e.g., Chambers & Trudgill, Reference Chambers and Trudgill1998:57–59; Niebaum & Macha, Reference Niebaum and Macha2014:211–212), individuals in occupations requiring a combination of higher complexity in both domains may be more likely to report familiarity with a wider range of variants. In line with our interest in age as a potential moderator variable—age may affect the strength of the relationship between diversity of reported variants and occupational complexity—we fitted a second model including age as an interaction effect with the three occupational complexity measures. The age cohort 20–29 being the largest informant group was entered as the reference level, such that the model compares all other age groups with the 20–29 cohorts. Due to reasons of computational feasibility and comprehensibility, we did not include a three-way interaction effect between occupational complexity with people and things and age cohort—we found this to be rational also because the interaction effect in the first model, though theoretically justified, did not robustly predict differences in informants’ familiarity with a wider range of variants, as the Results section will show.

Given that the diversity of reported variants per variable was averaged across the 62 variables in Round 11 of the AdA for each informant—resulting in a single value per informant—there was no need to include by-person random intercepts. However, in order to control for spatial autocorrelation as a potential confounder (see the first Results section for the rationale) when not being entered into the model as a fixed effect, we introduced by-locality random intercepts into the models. The model formulas are detailed in the online Appendix.

In interpreting the effects, we established a region of practical equivalence (ROPE) of ±0.05 around the point null value 0, which is a region/interval that is practically equivalent to zero (Kruschke, Reference Kruschke2018). The underlying idea of the ROPE is that although the coefficient may not precisely equal zero, the effect size may potentially be so small that it holds little practical importance. We judge there to be compelling evidence for a given effect when 95% of the highest density interval (HDI, a type of credible interval, basically the Bayesian analog to the frequentist confidence interval) of the posterior predictive distribution for a parameter β falls outside the ROPE, and when the maximum probability of effect (MPE, the proportion of the posterior distribution that is of the median’s sign, indicating whether the probability of the effect is positive or negative) is close to 1 (i.e., 100%). In other words, when the ROPE = 0% and MPE = 100%, we judge the respective effect to be significant.

Model convergence was assessed using the Rhat statistic, which was at the ideal value of 1 for each parameter. For each parameter, the effective sample sizes, which are an estimate of the number of independent draws from the posterior distribution, were also at sufficiently high values (>1000, i.e., larger than 10% of the total number of post-warmup draws [Vasishth et al., Reference Vasishth, Nicenboim, Beckman, Li and Jong Kong2018]).