Glossa Psycholinguistics

2.1 Syntactic approaches

From a syntactic identity perspective, a possible explanation for acceptable mismatches is that they are only apparent mismatches on the surface, but that the underlying structure conforms to syntactic identity. This has been explicitly proposed for voice mismatches under VPE by Merchant (2013) and for VPE with nominal antecedents by Johnson (2001).

For the former case, Merchant (2013) argues that mismatches like (1b,c) are acceptable under VPE, because voice is encoded in a VoiceP dominating the target of VPE (which Merchant identifies as vP), as (2) shows. Since the Voice head survives ellipsis, under this analysis, the elided constituent has an identical antecedent (3).¹

Johnson (2001) proposes a similar analysis for acceptable instances of VPE with nominal antecedents, like (4). By contrasting the acceptable (4a) with the ungrammatical (4b), he argues that deverbal nouns are the result of syntactic derivation and that they contain a verbal head which can serve as an antecedent (unlike infidelity in (4b)). As Merchant (2013) assumes for voice mismatches, there is no actual syntactic mismatch involved in (4a), according to Johnson (2001).

Merchant (2013) or Johnson (2001) predict categorical acceptability differences between grammatical apparent mismatches like (3) and (4a), on the one hand, and genuine mismatches, on the other hand: Only the latter should be ungrammatical, because they violate syntactic identity. More gradual acceptability patterns, like the one investigated in this article, therefore challenge these approaches, unless additional effects of processing, repair or discourse structure (which I discuss in what follows) are assumed. However, in that case, it would have to be shown that syntactic approaches have additional and independent explanatory power.

2.2 Parsing heuristics

C. S. Kim et al. (2011) explain observed acceptability contrasts among voice and category mismatches like (1b), (1c), and (4) with processing principles. Similarly to Merchant (2013) and Johnson (2001), C. S. Kim et al. (2011) also analyze these mismatches as, in principle, grammatical, but they argue that they can still be heavily degraded if they are hard to process, due to violations of parsing principles. C. S. Kim et al. (2011) investigate the effects of two parsing principles experimentally. First, they observe a tendency to omit the highest verbal projection possible under identity (MaxElide, Merchant, 2008). Second, arguments seem to be aligned in canonical order, depending on their thematic role: complements of transitive verbs are expected to appear to the right of their heads. Their rating studies show that voice mismatches, which require higher verbal projections like VoiceP to survive ellipsis, are degraded as compared to matching instances of VPE, which allow for the omission of these projections and hence conform to MaxElide.

The account of C. S. Kim et al. (2011) makes less categorical predictions than syntactic accounts, since the penalties for violating heuristics can be additive. It should also be noted that they tested only for the potential effects of two principles, and the account could be extended to other acceptability contrasts if further heuristics are assumed.

2.3 Accommodation and reconstruction

In contrast to C. S. Kim et al. (2011), who analyze acceptable (apparent) mismatches as grammatical but possibly degraded, accommodation and reconstruction accounts view them as ungrammatical, but possibly acceptable when it is relatively easy to accommodate or reconstruct the missing antecedent.

Under an accommodation account (Thoms, 2015; van Craenenbroeck, 2012), VPE requires syntactic identity, but the identity constraint can be satisfied not only by overtly present antecedents, but also by accommodated antecedents. Which antecedents can(not) be accommodated is subject to further constraints: For instance, van Craenenbroeck (2012) argues that the accommodated antecedent cannot contain material which is focused or has been extracted from the ellipsis site and that it may include additional pronouns and copulas, which can be freely accommodated (Merchant, 2004). Under this view, mismatches can still conform to syntactic identity conditions, as long as accommodation is possible.

Arregui et al. (2006) take a similar approach, but they argue that the missing antecedent is syntactically reconstructed, instead of being accommodated. According to their VP recycling hypothesis, hearers apply syntactic derivation to the available linguistic material to construct a matching antecedent. The effort required for this varies as a function of the number of derivation steps required. Since great processing effort results in degraded acceptability (see e.g Hofmeister et al., 2013), VPE mismatches which involve more derivation steps are predicted to be more strongly degraded.

The main difference between their VP recycling hypothesis and the accommodation accounts is that the latter propose specific rules restricting what can be accommodated, whereas reconstruction is not guided by ellipsis-specific rules. Relying on more general syntactic mechanisms also distinguishes the VP recycling hypothesis from the processing account of C. S. Kim et al. (2011), who attribute the acceptability of mismatches to particular parsing heuristics like MaxElide.

Arregui et al. (2006) present data from a rating study which shows an acceptability decrease from (5a) through (5d), taken from Arregui et al. (2006, p. 234), in support of their account. The idea is that the number of derivation steps required to reconstruct a matching antecedent increases accordingly: In (5a), a VP identical to the omitted one is contained in the first conjunct, so there is no mismatch. In (5b), the VP is nominalized and embedded. In (5c), the subject the comet is additionally extracted out of the VP. Finally, in (5d), there is no verbal head of to see at all, but only an adjective. Consequently, VPE is predicted to be acceptable in (5a) and gradually degraded from (5b) (embedding) and (5c) (embedding + extraction) through (5d), where syntactic reconstruction is impossible.

Even though Arregui et al. (2006) agree with C. S. Kim et al. (2011) on the relevance of parsing principles, the former assume that all of the mismatches in (5) are ungrammatical and that the repair mechanism is specific to VPE, whereas the latter view at least some mismatches as grammatical and resort to more general parsing heuristics.

2.4 Memory retrieval

Parker (2018) pushes in a similar direction as the VP recycling hypothesis by providing a processing-based explanation for the acceptability cline observed by Arregui et al. (2006). His proposal agrees with the VP recycling hypothesis in viewing VPE mismatches as ungrammatical, yet sometimes acceptable, but Parker (2018) derives the pattern from memory retrieval mechanisms, which are required to resolve ellipses and other filler-gap dependencies. As with other dependencies, he argues that the processing of ellipsis involves searching for an antecedent from working memory when the hearer encounters the ellipsis site (in the case of VPE, the auxiliary or modal). Antecedents which agree with the ellipsis site to a larger extent in terms of morphosyntactic properties, like voice or syntactic category, are more strongly activated in this search process. The higher activation facilitates their retrieval, which results in reduced processing effort and leads to higher acceptability. Parker (2018) supports his account of the acceptability cline with a computational model of working memory.

The central empirical prediction of the memory retrieval account with respect to VPE mismatches is that mismatches are more acceptable the more syntactically similar the antecedent and target are, because the activation of the antecedent in memory is stronger when it matches more features with the ellipsis site. This predicts the same pattern that Arregui et al. (2006) found, but the explanations differ. Furthermore, the quantitative predictions of both approaches can differ, depending on the amount and type of derivation steps and the set of distinctive features predicting activation in working memory which are assumed.

2.5 Information- and discourse-structural approaches

The accounts discussed so far predict and explain effects of the form of the antecedent and its similarity to the potential target of ellipsis, which will be also investigated in this article. However, there is experimental evidence that the acceptability of VPE mismatches is also determined by discourse, information structure and even extralinguistic context. These factors do not explain the acceptability cline reported by Arregui et al. (2006) (because there is no context manipulation in their experiments), but since context can affect the acceptability of mismatches, an empirically appropriate account of VPE mismatches should also take this into account.

Kehler (2000, 2002) emphasizes the importance of discourse relations between the conjuncts containing the antecedent and target for the acceptability of VPE mismatches: Mismatches are degraded when a connective like and (. . . too) suggests that a parallel relation holds between antecedent and target (6a), but not in the case of other discourse relations, like (6b), involving a cause-effect relation (more specifically, a violated expectation in Kehler’s terminology).

Kertz (2013) reanalyzes the data in Kehler (2000, 2002) in terms of information structure: She argues that degraded VPE mismatches in Kehler’s parallel relations contain contrastive topics, which raise the expectation of further parallel structure. Furthermore, Kertz finds similar effects for nonelliptical utterances, and concludes that mismatches are not degraded due an ellipsis-specific mechanism.

Miller and Hemforth (2014) find an effect of implicit Questions under Discussion (QuDs), which can be triggered by the antecedent, on the acceptability of VPE with a nominal antecedent. The contrast in (7) shows that VPE is more acceptable when the antecedent raises an implicit polar question which is picked up in the target of ellipsis (7a), than when it does not (7b).

Similarly, Grant et al. (2012) show that the inclusion of non-actuality implicature triggers, like certain modals (8a), which raise the inference that the event described in the antecedent did not occur, improves the acceptability of mismatches as compared to the same mismatches without the trigger (8b).²

Finally, Geiger and Xiang (2021) show that the resolution of VPE is affected not only by linguistic context, but also by extralinguistic context, which they model with graphical stimuli consisting of comic strips. Their experiments do not explicitly deal with mismatches, but in some of their conditions, they tested instances of discourse-initial VPE, which clearly lack an overt linguistic antecedent. The data indicate that extralinguistic context is taken into account also when linguistic context is present, and not only as a last resort strategy applied in its absence.

2.6 Summary

The accounts of VPE mismatches discussed in this section differ along various dimensions, even though not all of the theories are committed to particular assumptions about each of these: (i) the grammaticality of mismatches, (ii) the content of the ellipsis site, (iii) ellipsis-specific or general mechanisms determining acceptability, and (iv) pragmatic vs. psycholinguistic mechanisms.

While the syntactic accounts discussed in 2.1 imply a grammaticality split between acceptable (grammatical) and ungrammatical mismatches, the other proposals do not make this distinction. The VP recycling hypothesis (Arregui et al., 2006) and the memory retrieval account (Parker, 2018) view all mismatches as ungrammatical, but possibly acceptable, whereas these mismatches are grammatical, but possibly degraded, according to the processing account of C. S. Kim et al. (2011). The information- and discourse-structural accounts are not committed to either of these perspectives.

The accounts also disagree with respect to the question of whether or not there is unarticulated structure at the ellipsis site. On the one hand, the syntactic, reconstruction and accommodation accounts, as well as the processing account of C. S. Kim et al. (2011), assume that there is unarticulated structure at the ellipsis site, which is what requires a syntactically identical (possibly reconstructed) antecedent. On the other hand, the information- and discourse-structural accounts are also compatible with the assumption that there is no structure or just a null anaphor at the ellipsis site. However, they do not speak against unarticulated syntactic structure, since an appropriate antecedent might also become salient through discourse or context.³

Beyond the question of what the ellipsis site looks like and whether acceptable mismatches are grammatical, the accounts propose different mechanisms to account for their acceptability. The information- and discourse-structural approaches operate on pragmatic concepts, whereas the accounts based on memory retrieval, processing constraints and reconstruction rely on processing mechanisms. Additionally, the reconstruction accounts propose a mechanism specific to VPE, whereas the others rely on more general principles.

From an empirical perspective, the studies discussed in this section show that the acceptability of mismatches is affected not only by syntactic factors, but also by linguistic and extralinguistic context. This suggests that listeners regularly take into account different sources of information when processing VPE. Purely syntactic theories of VPE mismatches or those assuming a syntactic reconstruction mechanism cannot account for this observation.

4.1 Materials

The materials were identical to those used by Arregui et al. (2006) in the ellipsis conditions (10). In the nonelliptical conditions, the auxiliary did was replaced by an overt VP (11).

4.2 Procedure

The web-based acceptability rating study was conducted using the LimeSurvey presentation software (LimeSurvey GmbH, 2012). 64 self-reported native speakers of American English were recruited on the crowdsourcing platform Prolific (http://prolific.co) and rewarded with £2.50 for participating. Participants were asked to rate the naturalness of each of the sentences on a 7-point Likert scale with labeled endpoints (1 = completely unnatural, 7 = completely natural). They were assigned to one of eight lists, in which the materials were distributed so that each participant saw each of the 16 token sets once and each of the four Antecedent conditions in (10) equally often (n = 4). Completeness (ellipsis/complete) was tested as a between-subjects variable in order to keep the ellipsis study comparable to the one by Arregui et al. (2006). The stimuli were mixed with 60 fillers, which included instances of gapping, sentences with possible subject gaps and garden path sentences with reduced complement and relative clauses. These materials were presented in individual pseudo-randomized order, ensuring that no two stimuli of the same type (e.g. items of Experiment 1 or gapping fillers) immediately followed each other.

4.3 Results

Figure 2 provides an overview of the mean ratings across the eight conditions. The data were analyzed with Cumulative Link Mixed Models for ordinal data (Christensen, 2022) in R, using a backward model selection procedure: Starting from a full model containing fixed effects for all predictors and their interactions as well as the maximal random effects structure supported by the data, I subsequently removed fixed effects that did not significantly improve model fit (starting with the interactions), as evidenced by Likelihood Ratio tests calculated using the anova function (R Core Team, 2022), to find the simplest model capable of appropriately explaining the data. The p-values reported for the final model were also obtained with this method, that is, by comparing a model containing the predictor in question to a model without it. This model selection approach was used in all analyses reported in this article.

Figure 2: Mean ratings for the eight conditions tested in Experiment 1. Error bars indicate 95% confidence intervals.

In order to keep the analysis comparable to Arregui et al. (2006), I first analyzed the data sets for VPE and nonelliptical controls separately. I then conducted an analysis of the complete data set, in order to test for interactions between Antecedent and Completeness, which would evidence effects that are ellipsis-specific. Completeness was deviation-coded (ellipsis = 0.5, complete VP = –0.5), whereas I used forward coding for Antecedent, in order to test the hypothesis of a gradual acceptability decrease from (11a) to (11d): As Table 1 shows, the factor was transformed to three variables comparing (i) Available VP vs. the rest, (ii) Available/embedded VP vs. VP trace/Neg. Adjective, and (iii) Neg. Adjective vs. the rest. In what follows, I use the labels in Table 1 to refer to these predictors. In addition to the predictors of theoretical interest, the scaled and centered Position of the trial in the experiments was considered in the analyses to quantify and factor out potential familiarization effects with the materials or the task.

4.4 Discussion

Experiment 1 replicated and extended the second experiment of Arregui et al. (2006), using a different statistical analysis technique; it confirms that the gradual acceptability cline they report is ellipsis-specific. In addition to Arregui et al. (2006), who showed that the acceptability of VPE is not driven by the acceptability of the first conjunct alone, my data suggest that it cannot be explained by the interaction between the first and the complete second conjunct. The data for the nonelliptical controls do not show the gradual pattern found for the ellipsis conditions, which is reflected in highly significant Condition:Completeness interactions for all three contrasts. The next two experiments turn to investigating whether the effect observed for the ellipsis conditions can be explained by the information-theoretic account.

5.1 Materials

The materials were based on the stimuli of Arregui et al. (2006), tested in Experiment 1. For the production task, the materials were cut off after the subject of the second conjunct, as shown in (12) for the sample item in (5).

5.2 Procedure

The production study was conducted over the Internet, using the LimeSurvey presentation software. 120 self-reported native speakers of American English, recruited on Prolific, participated in the experiment. Subjects who had completed the rating study were blocked from participating. Each participant was rewarded with £2.50. Subjects were asked to provide the most natural continuation to stimuli like (12). They were explicitly instructed not to be creative or funny, but to produce the continuation that they considered to be the most likely one. This was intended to counterbalance the possibility that participants might actually avoid highly predictable continuations, because they did not consider them interesting or newsworthy. The materials were distributed across eight lists, so that each participant saw each of the 16 token sets once and each of the four conditions equally often.¹⁰ The 16 stimuli were combined with 16 items from another experiment and presented in individual fully randomized order. The items from the other study also consisted of conjoined sentences to be completed after the subject of the second conjunct.

5.3 Annotation

The production data were annotated for a series of variables on which the predictors in the statistical analyses reported below were based. These variables concern three properties of the participants’ responses: first, whether the continuation produced is identical to the VP expected, given the antecedent, i.e. saw the comet in the case of (12); second, whether this VP was complete or somehow reduced (and, if so, how); and, third, whether the VP appeared immediately after the subject of the second conjunct. Responses which consisted in obvious errors or which were not meaningful continuations of the utterance were excluded before annotation. This involved 4 data points (0.2% of the complete data).

5.4 Results

The analyses of the annotated production data addressed the two research questions introduced above: First, does the predictability of a potentially reduced VP gradually decrease across conditions, just as the perceived acceptability of VPE does? And, second, does the likelihood of these potentially reduced VPs actually being elided by participants also decrease accordingly?

The left panel of Figure 3 provides an overview of the ratio of potentially reduced VPs to the total responses (after the exclusion of nonsense responses). The set of potentially reduced VPs comprises all complete VPs classified as parallel (see 5.3.1) and all instances of VPE. The right panel of Figure 3 shows the ratio of VPE to this set of potentially reduced VPs. VPs that cannot be reduced are excluded here, in order to consider only utterances where VPE is an option. Both plots suggest that there is at least a gradual tendency in the expected direction, i.e. that both the potentially reduced VP is more predictable, and its omission more likely, in those conditions in which VPE is more acceptable.

Figure 3: Ratio of parallel continuations that could be reduced by VPE (i.e. instances of VPE, parallel complete VPs, do so, do it and do that constructions) to the total responses (left) and ratio of VPE to the potentially reducible responses, i.e. parallel complete VPs and VPE (right). Error bars indicate 95% confidence intervals.

The analyses reported in this section operate on the stricter of the two notions of identity discussed above, that is, lexical identity between the VP derived from the antecedent in the first conjunct and the one produced by the participant. For these responses, it is definitely the case that the VP can be omitted without a change in meaning. Applying the same set of analyses to the data set relying on the classification of synonym VPs as parallel yields very similar results.¹³

The data were analyzed with mixed effects logistic regressions (Bates et al., 2015) in R (R Core Team, 2022), which model the outcome of a binary dependent variable from a series of predictors. Again, likelihood ratio tests calculated with the anova function (R Core Team, 2022) were used to establish whether including a predictor in the model significantly improved model fit. I conducted two series of analyses to investigate the two research questions that motivated the experiment: first, whether the VP produced by participants is parallel to the one expected given the antecedent, and, second, whether this VP is reduced by VPE.

5.5 Discussion

Experiment 2 had two main goals: First, to test whether the target VP differed in predictability across conditions, in line with the rating data, which would provide an information-theoretic explanation for the acceptability pattern. Second, to investigate whether the ratio of VPE produced by participants also varies as a function of the likelihood of the potential target VP.

The first analysis of the production data showed that the target VP is, overall, more likely in those conditions where its omission is more acceptable. Even though not all of the contrasts between the four conditions were significant, the gradual decrease in the predictability of the target VP (quantified as the ratio of full or reduced parallel VPs) resembled the one found in the rating data. This supports the hypothesis that the gradual pattern in the rating data is actually driven by an overall tendency to reduce predictable expressions and to encode unpredictable ones more redundantly.

The second analysis showed that the production data are not only in line with the rating data, but that there is a similar gradual effect in the likelihood of subjects actually producing an instance of VPE, provided that this is possible. Participants also produced some instances of other VP reduction strategies (do so, do it and do that), but their low number did not allow for a systematic investigation of their distribution in comparison with VPE and complete VPs. The analysis also suggested that embedding the target VP under a modal increases the preference for VPE. This finding might also follow from an information-theoretic account, if the presence of an embedding expression like a modal or auxiliary increases the likelihood of the target VP.

The production data also show that participants produce antecedent-target mismatches in all conditions to some extent. From the perspective of the VP recycling hypothesis (Arregui et al., 2006) and the memory retrieval account (Parker, 2018), this is unexpected, because mismatches are analyzed as ungrammatical. These theories account for the observation that some presumably ungrammatical mismatches are perceived as relatively acceptable, but this does not explain why speakers would produce ungrammatical utterances on purpose. In contrast, under the information-theoretic account, there is no reason to assume that antecedent-target mismatches are ungrammatical; in fact, it implies that all utterances which are systematically produced by speakers are grammatical (leaving production errors aside). The observations that (i) participants systematically produced VPE mismatches, and that (ii) their ratio decreases with the predictability of the target are thus expected under the information-theoretic account.

An anonymous reviewer pointed out that the gradually decreasing ratio of VPE across conditions might be observed because the rarer mismatches violate more grammatical constraints. This could potentially reconcile the production of presumably ungrammatical structures with accounts which do not predict this. While it is possible that subjects randomly violate grammatical constraints and that the violation of more constraints in one utterance is less likely, the data speak against this. In the production data, there were no other violations of grammaticality beyond VPE, which suggests that the production of mismatches is more systematic than the result of random errors. Furthermore, the VP recycling hypothesis, in particular, is motivated by gradual differences between utterances which Arregui et al. (2006) view as categorically ungrammatical. If grammaticality were gradual, e.g. in an optimality-theoretic framework (Müller, 1999), where it decreases as a function of the number of constraints violated, there is no need to assume a processing component, because the grammar alone already predicts the observed pattern.

A further option is that the mismatch conditions do not gradually differ in acceptability, but that speakers deliberately produce ungrammatical ellipses because they are shorter, at least as long as the listener can still recover the intended meaning (Bergen & Goodman, 2015). If successful communication becomes less likely the more difficult it is to reconstruct (Arregui et al., 2006) or retrieve (Parker, 2018) the antecedent, a trade-off between the likelihood of success and the loss in efficiency would also predict a gradual pattern in the production data. However, Bergen and Goodman (2015) would predict other ungrammatical omissions, which also shorten the utterance and are easy to reconstruct (e.g. omissions of perfectly inferable articles or prepositions), but this is not attested in the data.

In sum, the production study confirms the central prediction of the information-theoretic account that the ratio of VPE varies as a function of the likelihood of the potential target of ellipsis. This supports an explanation of the pattern in the rating data observed by Arregui et al. (2006) and in Experiment 1 in terms of probability-driven reduction.

6.1 Materials

The stimuli in (16) were, in principle, identical to those tested in Experiment 1. The only modification was the addition of a spillover region after the auxiliary did, which consists of a temporal clause introduced by after or a causal clause headed by because. Without a spillover region, the auxiliary did would be the last word of the utterance, so that there would be no possibility of measuring the effort associated with its processing, which often is reflected in the reading times for words following a target word (Mitchell, 1984). Specifically for VPE, processing difficulty has been evidenced in the region past the auxiliary (Parker, 2022). The spillover region for (16) is given in (17).

6.2 Procedure

48 self-reported native speakers of American English, recruited on Prolific, participated in the web-based self-paced reading experiment, which was conducted using PCIbex (Zehr & Schwarz, 2018). None of them had participated in the previous experiments. Each participant was rewarded with £2.50. The participants read the sentences word by word by pressing the space bar in a centered self-paced reading paradigm. The stimuli were presented in black 20 pt Courier font on a white background. Before each trial, there was a separator allowing the participants to take a short break between trials, which they also could end by pressing the space bar. Each sentence was followed by a speeded binary acceptability judgment task. Subjects were asked to reply to the question “Is this sentence acceptable?” by pressing the Y(es) or the N(o) keys, respectively. This task had a 2000 ms timeout to ensure that subjects answered intuitively. In the instructions, participants were asked to answer quickly and notified about a time limit for answering. The participants were assigned to one of four lists in which the materials were distributed so that each subject saw each token set once and each condition equally often (n = 4). The 16 stimuli were mixed with 24 stimuli from an unrelated experiment on sluicing and 36 filler sentences. 24 of the filler sentences were coordinated structures, half of which involved subject gaps. The remaining 12 fillers were garden path sentences, half of which contained reduced relative clauses. The other half contained complementizer-less complement clauses. The stimuli were presented in individual pseudo-randomized order, ensuring that no trials of the same category (VPE, sluicing, filler) immediately followed each other. Four of the garden path and eight of the subject gap fillers were followed by an additional polar comprehension question presented after the acceptability judgment task, which was used as an attention check. The correct answer was “Yes” for half of the questions and “No” for the other half. 6 participants who responded correctly to less than 75% of the comprehension questions were excluded from further analysis.

6.3 Preprocessing of the reading time data

The reading time data analyses investigated the possible effects of increased effort of ellipsis processing in two regions: (i) on the auxiliary did itself, where readers become aware of VPE, and (ii) in the spillover region, where delayed effects of processing effort are expected to occur. I looked into effects at the onset of the spillover region, i.e. the first three words of the causal or temporal clause following the auxiliary.¹⁸ Reading times faster than 90 ms and slower than 3000 ms (by word) were excluded from further analysis. This resulted in a loss of 0.45% of the total data points.

For the spillover region, the raw reading times for the first three words were first summed and then log-transformed using the natural logarithm. Regions with at least one missing data point, due to the removal of excessively fast and slow reading times described above, would have been excluded from further analysis, but none of the data points in the spillover region was affected. The log cumulated reading times were then residualized with a linear model (R Core Team, 2022) predicting the log cumulated reading time from the logarithmized position of the trial in the experiment and the cumulated length of the spillover region onset (measured in the number of characters). The residuals of this model were used as the dependent variable in the analysis of the spillover reading times.

The data for the auxiliary region were logarithmized using the natural logarithm. Since reading times were always measured on the same word (did), it was not necessary to factor out word length by residualizing response times.

6.4 Results

6.4.1 Self-paced reading data

Figure 4 provides an overview of the average reading times in the two critical regions (Auxiliary and Spillover onset). The data were analyzed with linear mixed effects regressions (Bates et al., 2015) in R (R Core Team, 2022), following a backwards model selection procedure as in the previous analyses described.

Figure 4: Mean reading times by condition in the auxiliary region (left) and the onset of the spillover region (right). Error bars indicate 95% confidence intervals.

6.4.1.1 Auxiliary region

I first investigated possible effects of the experimental manipulation in the auxiliary region, in which participants might become aware of the omission of a VP. The full model¹⁹ contained fixed effects for the three contrasts of Antecedent, which was forward-coded as in the analyses of Experiments 1 and 2 (see Table 1), the scaled and centered Position of the trial in the experiment and their interactions. Furthermore, a by-subject random intercept was included. The model did not converge when a by-item intercept or higher-order random effects were included. The final model (see Table 7) contains only a theoretically uninteresting position effect, which reflects a general speed-up in the course of the experiment. None of the three Antecedent contrasts was significant: AVP v EVP (χ² = 2.0, p > 0.1), EVP v Trace (χ² = 0.09, p > 0.7), Trace v Adj (χ² = 0.85, p > 0.3).

Table 7: Final model for the reading times on the auxiliary.

Predictor	Estimate	SE	χ 2	p
Intercept	5.86	0.03	310.97	<0.001
Position	–0.06	0.01	73.59	<0.001

6.4.1.2 Spillover region

The analysis for the spillover region used the residual log cumulated reading time for the first three words of the spillover region, which was computed as described in 6.3, as the dependent variable. Otherwise, the procedure was identical to the analysis of reading time on the auxiliary. Again, the full model contained the three Antecedent contrasts, the scaled and centered Position of the trial in the experiment and their interactions as well as a by-subject random intercept.²⁰

The final model is summarized in Table 8, and shows that VPE is processed significantly more slowly with a negative adjective antecedent than in the other conditions. Further simplifying this model was not possible, because removing either of the other two predictors basically pools two of the remaining conditions and results in the remaining additional contrast becoming significant: If AVP v EVP is removed, these two conditions taken together are significantly faster than the VP with trace condition (χ² = 4.91, p < 0.05); if EVP v Trace is removed, the available VP condition is read significantly faster than these two conditions taken together (χ² = 5.1, p < 0.05).

Table 8: Fixed effects in the spillover region reading times model.

Predictor	Estimate	SE	χ 2	p
Intercept	0.00	0.5	0	1.0
AVP v EVP	–0.02	0.02	1.58	>0.2
EVP v Trace	–0.02	0.02	1.77	>0.1
Trace v Adj	–0.05	0.02	9.3	<0.01

The analysis using the forward coding scheme shows that the reading time data also exhibit a gradual pattern, and it confirms slower reading times for adjectival antecedents, but it does not allow one to determine which of the two other predictors should be removed. I therefore conducted a second analysis to test whether – within this gradual pattern – the available VP condition was read significantly faster than the VP with trace condition. For this purpose, I dummy-coded the Antecedent predictor by setting the VP with trace condition as the reference level, and looked for significant pairwise differences between this predictor and the other ones (see Table 9). Except for the different coding scheme used, the full model in this analysis was identical to the one using the forward-coded predictor.

Table 9: Dummy coding scheme for Antecedent.

Predictor	Available VP	Embedded VP	VP with trace	Neg. adjective
AVP v Trace	1	0	0	0
EVP v Trace	0	1	0	0
Adj v Trace	0	0	0	1

The final model (see Table 10) shows that besides the significant difference between the VP with trace and the negative adjective conditions (χ² = 18.22, p < 0.001) there is also a significant difference between the available VP and the VP with trace conditions (χ² = 4.91, p < 0.05).

Table 10: Fixed effects in the spillover region reading times model with Trace as baseline level.

Predictor	Estimate	SE	χ 2	p
Intercept	–0.01	0.04	0.05	>0.8
AVP v Trace	–0.03	0.02	4.91	<0.05
ADJ v Trace	0.07	0.02	18.22	<0.001

6.4.2 Speeded acceptability judgment

Figure 5 provides an overview of the binary acceptability judgments and the mean response times to the judgment task across conditions. The judgments indicate that participants, overall, accepted all conditions except the negative adjective condition, which was rejected about half of the time. The response times suggest that positive responses were faster than negative responses, but there does not seem to be a systematic effect across conditions which is in line with the judgments.²¹

Figure 5: Ratio of positive judgments (left) and mean response times (right) across conditions in the binary acceptability judgment task. The error bars indicate 95% confidence intervals.

I used mixed effects logistic regressions to test whether the ratio of positive and negative judgments varies across conditions and whether it is related to the reading time on the spillover region, which indicates gradually increasing processing difficulty. Since the information-theoretic account predicts that VPE is degraded when it is hard to process, I expected the ratio of negative judgments to increase as a function of reading time. In addition to the categorical differences between conditions, including the actual reading time for individual stimuli might indicate differences between stimuli and individual participants.

The analysis investigated the effects of the Antecedent (forward-coded), the scaled and centered Position of the trial in the experiment, the residual log Reading Time for the spillover region (which was the dependent variable in the reading time analysis, continuous) and their interactions with mixed effects logistic regressions predicting the outcome of a binary dependent variable Judgment. Timed-out trials (n = 22) were excluded from the data set for this analysis, because their overall number was relatively small and the analysis with logistic regressions requires a binary dependent variable (in this case, positive and negative judgments). The full model contained fixed effects for the three Antecedent contrasts and Position and Reading Time, their interactions, and by-subject and by-item random intercepts. Models with a more complex random effects structure did not converge. Otherwise, the procedure was identical to the logistic regression analyses of the production data.²²

The final model is summarized in Table 11. The main effect of Trace v Adj confirms that VPE was significantly more likely to be rejected with an adjectival antecedent than in any of the other conditions (χ² = 83.54, p < 0.001). The effect of AVP v EVP suggests that VPE with available antecedents was less often rejected than in the other conditions (χ² = 8.3, p < 0.01). The EVP v Trace contrast comparing the medial levels was not significant (χ² = 1.79, p > 0.1). This supports a gradual acceptability cline across the four conditions, which has been found in the previous experiments. The significant effect of Reading Time shows that VPE is perceived as more acceptable when it is easier to process. This effect is driven by individual differences between subjects and differences between token sets, since the gradually increasing processing effort between conditions, which has been evidenced by the reading time data analysis, is already explained by the Antecedent effects included in the model.

Table 11: Final model for the binary acceptability judgment data.

Predictor	Estimate	SE	χ 2	p
Intercept	1.89	0.25	32.76	<0.001
AVP v EVP	0.96	0.35	8.3	<0.01
Trace v Adj	0.96	0.25	83.54	<0.001
Reading Time	–1.64	0.49	11.56	<0.001

6.5 Discussion

Experiment 3 used a combined self-paced reading and binary acceptability judgment paradigm to investigate whether VPE is harder to process in those conditions in which the omitted VP is less predictable and VPE more strongly degraded. The results confirm a crucial prediction of the information-theoretic account of antecedent-target mismatches, given the differences in VP predictability observed in the production study: Speakers avoid utterances which induce excessively high peaks of processing effort, and hearers perceive these as more heavily degraded. The self-paced reading study was supplemented with a speeded binary acceptability rating task in order to relate processing effort to the perceived acceptability of VPE.

7.1 Does VP predictability predict acceptability?

The first analysis investigates the information-theoretic account’s prediction that the omission of more predictable expressions is perceived as more acceptable. The production data from Experiment 2 already showed that the gradual acceptability pattern between conditions can be attributed to a difference in likelihood, but not whether acceptability differences between stimuli can, too. To investigate this, I aggregated the acceptability ratings from Experiment 1 and the ratios of parallel continuations from Experiment 2 by item and condition and performed a linear regression analysis (R Core Team, 2022) to test whether the production data predict ratings.

The full model predicted the mean Acceptability (numeric, aggregated by item and condition) from the likelihood of a Parallel Continuation (numeric), the three Antecedent contrasts (forward-coded) and all two-way interactions.²⁵ The Antecedent contrasts were included to factor out the differences between conditions found in Experiment 1 and distinguish additional effects of Parallel Continuation from the overall pattern. The final model (see Table 12), which was obtained by backward model selection, as in previous analyses, contains significant main effects of all three Antecedent contrasts, which replicate the pattern found in the rating study. The additional Parallel Continuation effect (F = 7.69, p < 0.01) shows that the likelihood of the target additionally increases the acceptability of VPE. This indicates that VPE is more acceptable when the target is likely, not only between conditions, but also within a single condition.

7.2 Does reading time predict acceptability?

The analysis of the binary judgment data already showed that reading time has an effect on acceptability beyond the gradual difference between conditions in the spillover region, which was revealed by the reading time data analysis. The analysis in this subsection investigates whether the same holds for the Likert scale acceptability ratings for VPE collected in Experiment 1.

The full model predicted the mean acceptability by token set and condition from the three forward-coded Antecedent contrasts, the aggregated residual log Reading Time in the spillover region for each token set and condition and all interactions between the predictors.²⁶ The final model (see Table 13) shows that acceptability gradually decreases across conditions (all contrasts are significant). Additionally, a main effect of Reading Time (F = 4.65, p < 0.05) reveals that sentences which are read more slowly are perceived as less acceptable. This shows that not only the binary judgments but also the Likert scale ratings for VPE improve when processing the ellipsis is easier.

7.3 Does VP predictability predict reading time?

A third analysis investigated whether the predictability of the target VP has an effect on reading time in the spillover region. It is a well-established finding that cloze probability predicts reading times (see e.g. Smith & Levy, 2011) and my Experiments 2 and 3 support such an effect at the condition level, but not for individual stimuli.

The analysis started from a full model predicting the mean Reading Time (numeric, aggregated by item and condition) from the likelihood of a Parallel Continuation (numeric), the forward-coded Antecedent contrasts and all two-way interactions.²⁷ The final model is summarized in Table 14. Like in the analyses of the reading time data in 6.4.1, VPE is processed significantly more slowly in the negative adjective condition. The other contrasts between conditions are not significant in this analysis (for AVP v EVP, F = 3.04, p = 0.09, for EVP v Trace, F = 0.67, p > 0.4). The significant effect of Parallel Continuation (F = 4.65, p < 0.05) suggests that in addition to the Antecedent effects, which resemble the pattern found in Experiment 3, there is an item level effect suggesting that VPE is processed more slowly when the target is predictable. This is unexpected under the information-theoretic account, which predicts the opposite.

7.4 Discussion

The analyses in this section investigated to what extent the acceptability, predictability and processing effort measures collected in the experiment are related not only in the gradual pattern across conditions, but also at the level of individual stimuli, in the way the information-theoretic account predicts. This was investigated with regression analyses testing for effects of continuous reading time and predictability predictors beyond the contrasts between the four conditions, which have been established in the analyses of the experiments in Sections 4–6.

The predictions of the information-theoretic account are supported by two of the three analyses: First, VPE is perceived as more acceptable when the potential target VP is more predictable. From the information-theoretic perspective, this evidences a tendency to reduce predictable VPs and to use more redundant encodings for unpredictable VPs. Second, acceptability also decreases as a function of processing effort, indexed by reading times. This holds both for the binary judgments collected in Experiment 3 and the Likert scale data from Experiment 1. The expectation that a greater VP predictability similarly leads to reduced processing effort was not confirmed. Note that the inverted effect of VP predictability on reading times does not indicate that there is no effect at all of VP predictability on reading times, but that in this analysis, there is no additional effect of VP predictability beyond the differences between conditions. Since the materials were not designed to perform the analyses reported in this section, future research might look further into this by employing of stimuli that systematically vary VP predictability beyond the Antecedent condition.²⁸

Except for the unexpected effect of VP predictability on reading times, these results are in line with the information-theoretic account. The effect of reading times on acceptability might also be expected under the VP recycling hypothesis (Arregui et al., 2006) and the memory retrieval account (Parker, 2018), because they derive acceptability from processing effort: Whatever makes certain stimuli difficult to process in addition to the reconstruction or memory retrieval effort will also result in degraded acceptability. However, neither of these accounts predicts that VP predictability affects acceptability. The predictability effect does not falsify their predictions, but they do not provide an explanation for it, while the information-theoretic account does.

8.1 Implications for other theories of VPE mismatches

The results of the experiments are also partially in line with some of the other accounts of VPE mismatches discussed in Section 2. In what follows, I discuss the implications of my findings with respect to the theories discussed there.

8.2 Conclusion

The experiments and analyses presented support the main predictions of an information-theoretic account of antecedent-target mismatches under VPE: VPE is more acceptable when the potential target VP is more predictable and processing the ellipsis requires less processing effort. This provides an account of the acceptability cline reported by Arregui et al. (2006) in terms of an independently evidenced processing mechanism, which has also been shown to account for other omission and reduction phenomena.