The complexity principle and the morphosyntactic alternation between case affixes and postpositions in Estonian

2.1 The alternation between exterior locative constructions in Estonian

Estonian has 14 nominal cases, both in singular and plural; three are called “exterior locative cases”: allative, adessive, and ablative. Estonian reference grammars usually make very general claims on the lines that the meaning of adpositions is more concrete and specific, while the meaning of locative cases is more abstract and their range of uses broader (Erelt et al. 1995: 33–34, 2007: 191; Veismann and Erelt 2017: 446). The only pair of alternations that has been studied quantitatively using state-of-the-art statistical analysis is the adessive ∼ peal alternation (Klavan 2012, 2020; Klavan et al. 2015; Klavan and Veismann 2017).

The three Estonian (exterior) locative case affixes fulfil many relatively abstract functions besides expressing spatial relations. For instance, it is more frequent for the case affix to express temporal relations or addressees, experiencers, possessors, agents, and sources than location (see Appendix A for examples; Klavan et al. 2020). The postposition peale is an acceptable alternative only for the allative functions of direction of location, time, object of action and object of emotion; the postposition peal is an acceptable alternative only for the adessive functions of location and instrument; and the postposition pealt is an acceptable alternative only for the ablative function of source of location. The domain of variation is the locative function, but the functional versatility of case affixes has implications for our quantitative analysis (as explained in Section 3.1).

The estonian postpositions peale, peal, pealt are complex adpositions: “a word-type in which one of the constituent parts is an adposition, and the other is a case affix, in a form required by the adposition” (Hagège 2010: 38). This particular make-up yields further support to our working assumption that the three relations (and their realisations) can perhaps be treated as constructions within a more general locative super-construction. The postpositions peale, peal, and pealt are linked to the governed term by a genitive case. Overall, complex adpositions are quite pervasive in Finnic languages. It is vital to remember that an adpositional phrase in Estonian typically does not consist of only an adposition and a noun but includes case affixes on the noun and very often on the adposition itself, e.g. the allative case affix on pea-le, the adessive case affix on pea-l and the ablative case affix on pea-lt.

Syntactically, the Estonian locative cases and postpositions typically take the role of an adverbial (as in laual/laua peal ‘on the table’ in example 4) or adverbial modifier (as vaas laual/vaas laua peal ‘the vase on the table’ in example 5) (Erelt et al. 1995: 58).

2.2 The Complexity Principle (CP)

The Complexity Principle (Rohdenburg 1996, 2002, 2021; henceforth: ‘the CP’) aims to establish a direct relationship between the cognitive complexity of a grammatical construction and morphosyntactic choices made in connection with it. We adopt the CP as a theoretical framework since it (i) is cognitively grounded, (ii) generates concrete, testable hypotheses and (iii) has been applied to phenomena broadly compatible with the alternations we look at. On the other hand, the CP was developed in English linguistics, and research based on it largely focuses on English. The transfer of CP-related principles and assumptions to Estonian – a language typologically remote from English – is probably not without its complications. However, the validity of the CP as a principle will have to depend on its cross-linguistic applicability or generality. Rohdenburg (1996: 151; also Mondorf 2009, Ch. 2) explains that the CP is an extension of theories proposed by Hawkins (e.g., 1990, 1992) but goes beyond Hawkins’s focus on the processability of word-order alternations. It is formulated thus (Rohdenburg 1996: 151): “In the case of more or less explicit grammatical options the more explicit one(s) will tend to be favoured in cognitively more complex environments.”

In a later re-statement (Rohdenburg 2002: 79), the CP is extended to ‘grammatical (or lexico-grammatical) options’. Two fundamental questions come with the CP: (i) What makes a construction cognitively complex, and (ii) which grammatical variants qualify as cognitively more or less explicit (or transparent)? Concerning the first question, Rohdenburg (2021: 771) lists several circumstances that make a construction more complex, for instance, passivisation, subordinate clause negation, longer clauses or more complex noun phrases, as well as the low frequency of items (and, by extension, constructions). Based on examples like these, it is evident that complexity is a flexible and general concept that can apply at different levels. In many cases, it correlates with length because heavy constructions tend to be more challenging to store in working memory during parsing. In other cases, there need not even be a direct link to structural properties, for instance, when we assume that more frequent items are more deeply entrenched, easier to access, and therefore less complex. Finally, general notions of markedness also play a role, although Rohdenburg does not state this explicitly. If passives and negated subordinate clauses are classified as more complex, as in Rohdenburg (2021), then this is neither based on the length/weight nor exclusively on the frequency of such constructions but on the fact that an alternative unmarked (e.g. active or affirmative) construction exists. The broad scope of ‘complexity’ is part of its appeal, but there is also some potential for overextending the notion to contexts in which it does not truly hold. In other words: Its flexibility also makes the CP intrinsically vague and dependent on other assumptions – for instance, the notion of markedness that underlies several of the examples above has itself not gone uncontested (e.g. Haspelmath 2006). We would also expect such issues to be aggravated when we take Rohdenburg’s CP beyond its original ‘habitat’ – the English language – to another, typologically different language like Estonian.

Rohdenburg (2021: 771) lists grammatical alternations regarded as more or less explicit, some of which we show in Table 1. Concerning this matter, Rohdenburg (1996: 151–152; cf. 2021: 771) generally focuses on “formal contrasts involving the deletion (or addition) and the substitution of grammatical (or closed-class) elements”, so that “the more explicit variant is generally represented by the bulkier element or construction”. Explicitness (or transparency) thus correlates with more substantial morphological material. As we will argue below, this relationship between morphological substance and explicitness/transparency works well for the cases adduced by Rohdenburg throughout his work. However, here, too, there is a danger of assuming that the relationship is a universal one.

Mondorf (2009) studies the English comparative alternation in English (heavier vs. more heavy) in a CP-based framework. Her expectation that more complex adjective phrases correlate with the use of analytic comparatives rests on the assumptions that (i) this provides an early indication that a comparative follows and thus makes it easier to identify phrase structure, (ii) morphological parsing is simplified by encoding the degree-marking morpheme as a free item rather than an inflectional affix, and (iii) the phrase-initial marker more alerts the parser not only to expect a comparative, but also to expect a relatively complex AdjP, and thus to activate a greater processing capacity (2009: 6–7). Mondorf (2009: 6) suggests that more-support in English comparatives “can most likely be extended to other kinds of variation phenomena that draw on the synthetic-analytic distinction” because it “merely represents one instance of a presumably universal tendency”. She calls this tendency periphrasis-support or analytic support and defines it thus:

In cognitively more demanding environments which require an increased processing load, language users – when faced with the option between a synthetic and analytic variant – tend to compensate for the additional effort by resorting to the analytic form. (Mondorf 2009: 6)

However, it is immediately clear that this new principle needs to be viewed critically in the context of Estonian exterior locatives. Here, the analytic variant hinges upon a postposition, which means that only the second point made by Mondorf (whereby free morphemes are generally more explicit than affixes) applies. In contrast, her first and third points do not. Moreover, as explained above, in the inflectional variants of Estonian exterior locative constructions it is not simply the headword in a complex Landmark phrase that gets inflected, but also its preceding modifiers. Thus, while the analytic variant of an Estonian exterior locative construction comes with a separate (and therefore, perhaps, maximally transparent) adposition, the inflections in a synthetic variant aid the parser even before the headword is reached. Mondorf’s (2009) derivation of an analytic-support principle from Rohdenburg’s CP works in English, where analyticity and anticipatory word order coincide. However, it is rather doubtful whether it can be transferred to Estonian.

2.3 Research questions and expectations

We treat the three semantic relations of lative, locative and separative as subordinate, more specific manifestations of a more general exterior locative concept. While they are characterised by different relations between Trajector and Landmark in terms of dynamics and direction, our working assumption still is that they are closely related enough to be governed by similar grammatical constraints. From a cognitive perspective, this kind of probabilistic uniformity is economical because it requires fewer ‘rules’. Beyond this expectation of relative homogeneity, we have more specific expectations motivated by the CP. We formulate the following hypotheses:

3.1 Data retrieval

Our data were extracted from the Estonian National Corpus (ENC 2017; 1.1 billion words, mainly web-based; Kallas and Koppel 2018) using SketchEngine (http://www.sketchengine.eu/). The corpus has been automatically tagged with the Estonian Filosoft part-of-speech tagset allowing for the automatic extraction of case forms and postpositions.

Subsampling was necessary because the manual annotation of occurrences is rather time-consuming (see Section 3.2). Due to the generally much lower frequency of the postpositional variant for all three constructions, we decided to take random samples of 1,000 cases for each of the three alternations, balanced by variant (with n = 500 synthetic and n = 500 analytic cases), which resulted in a total of n = 3,000 cases. Without this kind of balancing, the number of postpositional cases would have been too small for a statistical analysis involving the set of predictors we used. Table 2 documents the number of hits obtained for each of the three constructions and the steps we took in generating a manageable subsample. Since our approach has consequences for estimating the percentages in Section 4 below, we will briefly explain it here. Within the lative construction in Table 2, there were a total of F = 959,515 cases marked by the postposition peale. Inspecting a random sample of these, it took f = 2,142 cases before we arrived at the targeted number of s = 500 valid cases. The rejected 1,642 cases did carry the postposition peale but expressed a different semantic relation. False positives of this kind are often invariable – that is, they do not allow for the alternation between postposition and inflection. Our precision Pr for peale was, therefore, 500/2,142 = 0.233; thus, we concluded that only 23.3 % of instances of peale in the ENC express the lative relation, and this figure was used to calculate the adjusted absolute frequency F _a of peale. We finally arrived at adjusted proportions (p _a ) of postpositional and inflectional variants based on the pair of adjusted values within each of the three constructions. At this point, suffice it to say that these extrapolations are essential to our statistical analysis, as will be explained in Section 3.2.

From the overall frequencies of the three exterior locative cases and the corresponding adpositions in Table 2, it can be seen that the most frequent case in the trio is the adessive, followed by allative and ablative. The most frequent postposition is peale. The adessive has the lowest value for precision, since this case affix has other essential functions to fulfil in the language (e.g., possessor in the possessive construction; see Appendix A).

3.2 Annotation

All occurrences were coded by the first author for nine variables, as shown in Table 3. The outcome variable is postpos, with case as the reference level and postposition predicted by the regression model (see below). The other variables are discussed below.

The predictor position describes the arrangement of the Landmark phrase and Trajector relative to each other, with ‘pre’ standing for Landmarks preceding their Trajector (example 6) and ‘post’ for the inverse pattern (example 7). We treat as more complex the word order where Landmark phrases precede the associated Trajector phrase, and we predict that a Landmark preceding the Trajector favours postpositions (Hypothesis 2a).

In terms of topic-comment structure, Landmark preceding Trajector is more marked.^[1] The Trajector is considered to be the most prominent participant in locative expressions (Langacker 2008: 70), but it is in the relationship between Trajector and Landmark that new information is found. It stands to reason, therefore, that the preferred or canonical word order is such that the Trajector phrase precedes the Landmark phrase. Although Estonian is typically considered a language with a relatively free word order (Lindström 2005: 10), any (functionally oriented) linguist will agree that nothing is ever completely ‘free’. In Estonian, as in many other European languages, it is common to begin a clause with the information already known to the speaker/listener and provide new information at the end of a clause. According to Estonian reference grammars (e.g., Erelt 2003: 93–94), Estonian has two basic syntactic patterns of clauses: normal and inverted. The basic word order in the normal clause is SVA, where the subject (S) is morphologically unmarked, the verb (V) agrees with the subject in person and number, and the verb may be followed, for example, by a subject predicative and/or a locational adverb (A) (cf. example 8).

In the “inverted clauses”, it is not the subject that comes first in the clause, as in normal clauses, but an adverbial (A) or an oblique object (Obl) expressing location, time, possessor or experiencer (Erelt 2003: 93; cf. example 9). Lindström (2005: 10) refers to these clauses as specific clause types in which the word order sequence is conventionalised in Estonian. Such conventionalised word order sequences make it easier for the listener/reader to understand the clause since information structure plays a role in these clauses. What is already known comes at the beginning, and what is new at the end of the clause (Lindström 2005: 10).

Given that the adpositional variant is more explicit and specific than the case variant, it should be used at the end of clauses where new information is provided in Estonian. The case variant is predicted to be used at the beginning of a clause because it is shorter than the adpositional variant and less specific.

For the predictor length, the number of syllables in the Landmark phrase was counted. The binary logarithm (base = 2) was applied, and values were centred on the whole-number value closest to the mean, which happened to be 2 (corresponding to a length of 4 syllables). We regard relatively long Landmark phrases as more complex and therefore predict that they should favour postpositions (Hypothesis 2c). Length is one of the most crucial variables in numerous studies on various syntactic alternation phenomena (e.g., Hawkins 1994; Wasow 1997; Arnold et al. 2000; Wasow 2002; Wasow and Arnold 2003; Hawkins 2004). A critical methodological question concerns whether to include the adpositions peale, peal, pealt in the count as a separate word. Hinrichs and Szmrecsanyi (2007: 453) and Rosenbach (2005: 623) indicate in their studies on the English genitive alternation that the definite or indefinite articles determining the possessum phrase of an of-genitive were not included because they provide a natural imbalance and skew the results. For similar reasons, it was decided not to include the postpositions peale, peal, pealt in the counts. Hence, Landmark phrases such as laual [laud + ADE] and laua peal [laud + GEN peal] were considered disyllabic. It should be noted that with adjectival attributes, there is an agreeing case marker on the attribute, e.g., i-lu-sa-le lau-a-le (7 syllables) versus i-lu-sa lau-a peale (5 syllables), making the former phrase longer and hence more complex than the latter.

The predictor complexity takes the reference value simple if the Landmark lemma is not a compound (e.g., laud ‘table’ in example 10) and the value compound if it is (e.g., kirjutuslaud ‘writing desk’ in example 11). We treat compound Landmarks as more complex and, following the Complexity Principle, we predict that compound Landmarks favour postpositions (Hypothesis 2b).

frequency denotes the overall raw frequency of a Landmark form in combination with the respective semantic relation (lative, locative or separative) in the entire ENC. This, too, was logged (base = 2) and centred on the whole number closest to the mean, which happened to be nine (corresponding to an absolute f = 512). We treat less frequent combinations as more complex and predict that they will favour postpositions (Hypothesis 2d). This is based on the assumption that form-function combinations of lower frequency will be less entrenched, harder to access and therefore more complex, not in a formal but in a cognitive way.

The variable function denotes the grammatical function of the Landmark phrase: adverbial means that the Landmark is a sentence constituent in its own right, while modifier means that the Landmark modifies the Trajector within the same constituent. For example, both the adessive and the adpositional realisation with peal can fulfil two syntactic functions in a clause – that of an adverbial, as õue peal ‘on the yard’ in example 12, or an adverbial modifier as merel ‘on the sea’ in example 13. The variable has two levels: ‘adverbial’ and ‘modifier’. Although it may be presumed that the modifier function is more complex since it involves embedded modification, i.e. it is a type of environmental complexity that the CP addresses and hence the more explicit, postpositional variant should be more likely, we have no solid prior expectation as to which of them will favour the use of a postposition.

The two self-explanatory variables verb_lemma and lm_lemma were used as group variables in the random-effects part of our models (see below) and are not documented in detail, apart from the number of levels they take for each construction. Finally, sem_rel is classified as a ‘filter’ variable in Table 1: Its only function is to partition the data into three subsets, which were then used in the respective models, one for each construction.

3.3 Statistical modelling and visualisation

We worked in the R-environment (R Core Team 2019), using RStudio (RStudio Team 2009–2019). For each of the three constructions (lative, locative, separative), we fitted a Bayesian mixed-effects logistic regression model using the R-package ‘brms’ (Bürkner 2020), which is based on Stan (Stan Development Team 2019). Each model drew on a subset of the data defined by the variable sem_rel (see Table 1) and was specified as follows:

No interactions were included in the model, as we have no theoretical reason to assume any moderating effects among predictors. No random slopes were specified for the group variables verb_lemma and lm_lemma; thus, we decided against a maximised random part, as Barr et al. (2013) recommended. Weakly regularizing priors were specified for the fixed part, and given the estimated coefficients (which fell squarely within the prior distribution), we dispensed with a sensitivity analysis of alternative priors. Somewhat more restrictive priors were used for the random part. The model syntax and the priors were the same for all three models, but the number of levels for both group variables (verb_lemma and lm_lemma) differs between them, as documented in Table 2 and Appendix B.

Models were run with four chains of n = 3,000 iterations, each including a warmup phase of 1,000 iterations. The total number of posterior samples was thus n = 8,000. The convergence of chains was indicated by the R-hat diagnostic taking the value of 1.00 for all parameters in the model. A basic summary of model coefficients and priors is given in the appendix, but also see our discussion of Figure 1 below. A more comprehensive summary can be found in the online repository (see data availability statement). No model comparison or model selection process was conducted since it was considered essential to retain all theoretically important predictors in the model, irrespective of their estimated effects (cf. Heinze et al. 2018); we thus adopted the notion of the ‘deductive model’ as proposed by Tizón-Couto and Lorenz (2021).

Visualisations were done with functions in the R-package ‘lattice’ (Sarkar 2018). Plots show the median posterior probability (in %) of the postpositional variant under the respective condition and 50 % and 90 % percentile-based posterior uncertainty intervals. Such intervals will occasionally be reported in the text. For instance, in the third panel of Figure 2, the percentage of postpositions for the lative in connection with short LMs can be given as ‘15.2 % [11.7; 19.3]’, which means ‘a median posterior percentage estimate of 15.2 % with a 90 % uncertainty interval extending from 11.7 % to 19.3 %’. We also display the contrast between conditions (e.g., short Landmark phrases vs. long Landmark phrases) as an estimated difference in absolute percentage points with the respective uncertainty intervals. Comparing such intervals to the reference value of zero (= ‘no difference’) provides additional evidence for interpreting an effect beyond the effect size itself. The difference between short and long LM phrases was estimated with values of ±1 for the centred predictor length, which is the whole-number value closest to one standard deviation (SD) of this predictor across the data. The same approach was taken for frequency, in this case, predictor values of ±4 corresponded most closely to ±1 SD. Factors of no immediate interest in a given scenario are held constant. The exact routine is made transparent in the online material (see data availability statement below). For categorical variables like function or position, it may seem counterintuitive to assume normal (or average) values since, in reality, they take categorical values at any one time. However, this approach allows us to target specific effects and thus make results more accessible.

As explained in Section 3.1, the share of postpositional realisations in the ENC is much lower than the share of 50 % in our balanced dataset. For instance, we expect the actual proportion of peale within the targeted semantic context (lative) to be only 0.066 (or 6.6 %), not 0.5 (or 50 %) as in our data. In order to model the actual expected share of postpositions more realistically, we added a corrective intercept to our estimates, calculated as the log-odds of the ‘real’ proportion of the outcome variant.^[2] The values we used were log(0.0658/(1 − 0.0658)) = −2.65 for the lative, log(0.0324/(1 − 0.0324)) = −3.40 for the locative, and log(0.0936/(1 − 0.0936)) = −2.27 for the separative (see Table 2).

4.1 Model coefficients

We first turn to a short discussion of the coefficients in the fixed part of the statistical model, shown in Figure 1 (also see Appendix B). Four predictors appear in black. These correspond to the four hypotheses formulated as 2a–d in Section 2.3 above. The direction of an expected effect is indicated with the letter ‘H’ in the margin of the plotting region: If the respective predictor has the expected effect, its coefficient should be positioned between the vertical reference line at zero and this symbol. The fifth predictor, function, appears in grey and without the symbol ‘H’ because it does not come with a particular expectation but was included as a control. It will, therefore, not feature in the main discussion, although we will briefly return to it in Section 4.5. Note that the expected direction of the effect is negative for the predictor frequency, while for the other three, it is positive. Note further that we use stricter uncertainty intervals of 50 % and 95 % in this plot, while in the percentage plots below, we use 50 % and 90 % intervals, as discussed in Section 3.3.

Figure 1:

Coefficient estimates .

Results transformed into percentages will be discussed in more detail below. What we can see at a glance in Figure 1, however, is that for the predictors complexity and length, the effect we find in the data runs counter to our expectations (cf. Hypotheses 2b and c): Compound LMs as well as LMs of greater length disfavour the selection of the postpositional variant. LMs of higher frequency (in connection with the respective alternations) also disfavour the selection of the postpositional variant, but this is a pattern we expected in connection with Hypothesis 2d. The actual effects of length and frequency are larger than the figure suggests since we assume that it is not a unit change but a change of 1 SD that should be treated as a realistic change in the predictor value (see discussion in Section 3.3 above). The remaining theoretically motivated predictor, position, does not affect the variation of the lative; for the other two semantic categories, it tends to support our Hypothesis 2a (with a correlation between postpositions and LMs that precede the Trajector). However, the effect is not very pronounced and comes with a higher degree of uncertainty, with the 95 % intervals cutting across the zero reference value.^[3] While effect sizes are not equal, the general pattern is the same for all three semantic categories, which provides a first pointer to our first broad hypothesis concerning the uniformity of mechanisms of variation across all three semantic categories (also see 4.4 below). In the next section, we will unfold these relatively general and abstract findings into predicted percentages of the postpositional variant.

4.2 Average probabilities by individual factors

To facilitate the direct comparison of the predictors mainly of interest, all four are combined in Figure 2. The panel corresponding to each predictor breaks down into two parts: The bottom part shows estimated percentages of the postpositional variant under the two contrasting conditions (e.g., simple vs. compound LMs in the second panel) for the three semantic categories, while the top part shows the estimated absolute percentage-point difference between conditions. Both parts of each panel show 50 % and 90 % posterior uncertainty intervals. Despite the traditional criticism that lines should not be used to connect categorically different points, we still use them because they have considerable advantages for directly comparing the patterns (cf. Sönning forthcoming). The colour scheme is adjusted to make transparent whether or not our hypotheses are confirmed: In the bottom part of each panel, black points above grey points signal that the data support the respective hypothesis; this pattern would then result in points positioned above the grey reference line in the corresponding plot on top.

Figure 2:

Posterior probabilities and contrasts by individual factors .

When we average across the two contrasting conditions, irrespective of the panel we look at, it can be seen that separative constructions are generally most likely to be realised with a postposition (18.1 %), followed by locatives (14.8 %), while postpositions are least likely with the lative (9.9 %). This pattern is most clearly visible in the bottom part of panel one (position) because it holds true under both conditions and because the difference between LMs that precede and those that follow the Trajector is small. Secondly, each predictor’s effect has the same direction across all three constructions, although it differs in magnitude, as discussed in more detail below. This can be seen at a glance in the top panels, where all values for a given predictor are either above or below the reference line.

For separative meanings, an LM that precedes the Trajector is more likely to take a postposition than cases in which the LM follows the Trajector (+3.0 [0.1; 6.1]). This effect is in the expected direction, as we regarded the pattern LM → Trajector as the marked sequence that would require a more explicit (postpositional) signal. However, the effect is relatively small – for the locative, it must be called negligible, and for the lative it is virtually non-existent, with +1.6 [−0.9; 4.1] and +0.1 [−2.3; 2.4], respectively. There is thus only minimal support for our Hypothesis 2a.

Regarding our second main predictor, complexity, constructions with compound Landmarks are much less likely to be postpositional than inflectional in the separative (−15.3 % [−20.2; −10.9]) and the locative (−12.8 % [−17.2; −8.8]); in the lative, the effect is less pronounced but still very much visible – (−4.6 % [−7.7; −1.5]). These findings contradict expectations formulated as Hypothesis 2b: There is no evidence that compound LMs favour the postpositional variant, and the exact opposite pattern prevails.

The third panel of Figure 2 shows that the length of the LM substantially influences the selection of constructional variants. Longer LM phrases are less likely to combine with postpositions than constructions with shorter LM phrases. The general direction of this effect is the same for all three alternations, and it goes directly against our Hypothesis 2c: Since longer LMs involve a greater processing load, we argued that they should be more likely to combine with the more explicit (namely postpositional) markers. In this case, the effect is most pronounced with the locative (−22.6 % [−28.3; −17.8]), followed by the lative (−10.6 % [−14.3; −7.5]), while the separative is least affected (−6.1 % [−10.4; −2.1]).

Finally, constructions with LM forms that occur less frequently with the respective locative function are generally more likely to take postpositions than forms that are more frequently used. This effect is most pronounced with the locative (+18.0 [13.4; 23.3]), followed by the separative (+15.0 [10.8; 19.4]), while the lative is least affected (+5.0 [2.3; 8.2]). Thus, frequency is the only predictor that genuinely supports its associated hypothesis (2d).

There are two central conclusions from the above. Firstly, results broadly agree with our expectation that constructional variation in the categories (lative, locative, separative) should be conditioned along similar lines by our main predictors. The effect of any one predictor may differ in magnitude between semantic categories. However, it always carries the same sign – or, in other words, it never points in the opposite direction. We therefore regard our first hypothesis as confirmed. A subsidiary finding is that there is no obvious ranking of the three semantic relations based on their responsiveness to conditioning factors: Apart from the uniform direction of effects in Figure 2, the patterns we see in the top parts of the four panels are all different – except perhaps that the lative is least affected by three out the four predictors: position, complexity and frequency. The second major finding is that of our four specific hypotheses, only the one relating to frequency (hypothesis 2d) is strongly supported.

4.3 Percentages for specific factor combinations

While the preceding section isolated the effects of the four predictors associated with our Hypotheses 2a–d, we will look at specific combinations of factor settings in the following paragraphs. By not averaging across specific conditions, we will gain insights concerning the overall range of percentages predicted for each semantic category and, thus, the reality underlying the more generalised results presented above. The only predictor not considered in this approach is function; this we control for since it does not feature in our main assumptions.

Figure 3 shows sixteen specific conditions for each of the three constructions, arranged in descending order based on the estimated median percentages of postpositional variants. Since individual effects point in the same direction for all three alternations, the ranking is bound to be similar if, of course, not quite the same. To facilitate processing, no uncertainty intervals are shown in this plot. Conditions are identified by four columns of black and white circles on the right, corresponding to the four predictor variables position, complexity, length and frequency. Circles are labelled ‘1’ (LM precedes TR) versus ‘2’ (LM follows TR) for position, ‘S’ (simple/non-compound) versus ‘C’ (complex/compound) for complexity, ‘S’ (short) versus ‘L’ (long) for length: and ‘H’ (high) versus ‘L’ (low) for frequency. The colour coding again reflects our expectations: According to our Hypotheses 2a–d, black dots should be nearer the top and white dots should be nearer the bottom in each panel.

Figure 3:

Ranked median percentages for individual factor combinations by construction .

For the locative and lative, the top six and bottom six conditions are the same; furthermore, the top two and bottom two conditions are the same between all three semantic relations. These findings in themselves already indicate that there is a considerable degree of similarity between the different locative relations regarding their responses to the factors we included.

If we ignore position, which has only a minor effect (cf. Figure 2), simple, short and infrequent LMs are most strongly in favour of postpositional variants: If averaged across the two respective conditions for position, the expected percentages are 22.5 % in the lative, 40.5 % in the separative and 56.4 % in the locative. Naturally, the lowest values are found with LMs that are compound, long and frequent, with average percentages of 3.8 % (separative), 2.1 % (lative) and 0.2 % (locative), respectively. The lative displays the most moderate range of values, which agrees with the finding that it was also the least affected under most circumstances in Section 4.2. Separative and locative, conversely, are characterised by more variation between conditions, the latter with two rather extreme high values. Note that the specific scenarios pictured here are not necessarily frequent in natural language production in Estonian; the sometimes high percentages shown here do not conflict with the generally much lower frequencies of postpositions in the corpus.

4.4 The uniformity of effects across constructions

It was evident from Figures 1 and 2 that effects, if not equal in size and if not consistently ranked in the same way across semantic functions, nevertheless point in the same direction and that estimates for specific conditions should therefore be correlated across semantic types. We explore this finding more formally in Figure 4, which ranks the n = 16 specific conditions defined by binary values of position, complexity, length and frequency according to the average predicted frequency of the postpositional variant across the three semantic relations, in ascending order from left to right.

Figure 4:

Assessing the uniformity of effects across constructions .

A more or less regular upward slope can be observed in all three relations – more regular for the locative and the lative, less so for the separative. In other words: Conditions that result in a relatively high share of postpositional realisations on average tend to do so for all three semantic categories, which is confirmation of our most general first hypothesis (see Section 1.2). As mentioned above, this finding is not new at this point – it is merely shown from a different perspective. The (sometimes striking) contrasts between the separative and the other two categories at individual steps in the left-to-right progression of Figure 4 are due to different effect sizes, not to differences in the direction of effects (see Figure 1 and Appendix B).^[4]

Table 4 further confirms the broad correlation of the behaviours of lative, locative and separative under the four conditioning factors we consider here. We use one linear and one rank-based correlation coefficient.

While all three possible correlations are statistically significant, we can also see that, by far the strongest correlation is the one between the lative and the locative. The separative does not correlate as well, which agrees with its somewhat more erratic pattern in Figure 4. Our first hypothesis only addressed the expected general alignment of the three alternations regarding their responses to the different predictor variables; we had no theory to motivate why any of them should diverge from the average pattern.

4.5 Short comments on the grammatical status of Landmarks

This section highlights the difference between LMs that function as adverbials at the sentence level and those constructed as modifiers within a noun phrase. The discussion will be relatively brief: The predictor function, while included in our statistical model, is detached from our hypotheses – that is, we saw no reason to expect that either adverbials or modifiers should favour postpositional variants. However, find an effect we did, and while its theoretical implications remain opaque for now, we decided to include it in our presentation.

Figure 5 shows that LMs functioning as adverbials correlate with higher proportions of postpositions, with a percentage-point difference (relative to the modifier use) of +6.7 % [3.3; 9.8], +8.4 % [5.0; 11.8] and +3.7 % [−1.3; 8.3] for the lative, locative and separative, respectively. Although a higher degree of uncertainty comes with the result for the separative, this is a regular finding, and the differences are substantial. As to accounting for this effect, we can at present only make the informal observation that the co-occurrence of higher-order syntactic elements (i.e., adverbials as sentence-level constituents, not modifiers as phrase-level constituents) with higher-order grammatical markers (i.e., free postpositions, not bound case affixes) seems intuitively plausible.

Figure 5:

The effect of the predictor function .