A corpus (plural corpora) is a large-scale collection of texts sampled from genuine linguistic productions by native speakers. From a statistical viewpoint, a corpus is a sample drawn from the true, unknown law of a given language. Corpus linguistics consists in digging into corpora to better understand the rules governing the language under study. This is why Gries  describes corpus linguistics as a “distributional science”, a science that infers knowledge from data. Often, corpus linguists focus on the frequencies of occurrence of various elements in corpora, their dispersion, and their co-occurrence properties. Baayen  argues that “corpus linguistics should be more ambitious”. Focusing on a classification problem, he compares the performances of different classifiers based either on the principle of parametric regression or on more data-adaptive algorithms gathered under the banner of machine learning, both in terms of accuracy of prediction and of quality of the underlying models for human learning. Following Baayen , we also advocate for ambitious corpus linguistics drawing inspiration from the latest developments of semiparametrics for a modern targeted learning.
We break free from artificial discipline-specific boundaries, as we benefit from the lessons of state-of-the-art causal analysis and biostatistics to address a long-standing issue in linguistics. Our guiding principle is the following: predicting is not explaining. It conveys the idea that one should always carefully cast the questions at stake as statistical parameters of the true, unknown law of the data. Once this is done, we suggest the two-step procedure known as targeted minimum loss estimation (TMLE [3, 4]). The first step takes advantage of the power of machine learning, while acknowledging its limits in terms of inference. To overcome these limits, the second step consists in bending the initial estimators by targeting them toward the parameters they are meant to capture.
For the paper to be accessible to non-linguists, Section 2 introduces keys notions and issues in linguistics. In Section 3, we briefly introduce the dative alternation, the theoretical issues it raises, and a summary of recent corpus-based, statistics driven investigations. In Section 4, we lay out our plan for the prediction and explanation of the dative alternation based on corpus data. We claim that these two tasks differ substantially. Our approach is motivated by causal considerations. Section 5 is a concise presentation of the statistical apparatus that we elaborate to tackle the statistical problems defined in Section 4. We present and comment on the results in Section 6. Additional material is gathered in the appendix. In particular, details on the machine learning and on TMLE procedures are given in Sections A.2 and A.3, respectively. These are the most technical parts of the article.
2 A brief introduction to linguistics
2.1 What linguistics is about
Like biologists studying the structure, function, growth, evolution, distribution, and taxonomy of living cells and organisms, linguists study language. In this respect, doing linguistics means investigating the cognitive system which we identify as the knowledge of a language. This knowledge takes the form of a mental grammar. Therefore, understanding what it means to know a language is to understand the nature of such a grammar.
Despite aiming at an objective description of language, linguists have their theoretical preferences, depending on what they believe the true essence of mental grammar is. In this regard, two competing theories have shaped contemporary linguistics.
As described by Chomsky [5–7], transformational-generative grammar (henceforth “Chomskyan grammar/linguistics”) is based on the assumption that, like formal languages, the grammars of natural languages consist of (a) a set of abstract algebraic rules and (b) a “lexicon” that contains meaningful linguistic elements. The algebra is the innate core of grammar. It constitutes what Chomskyans call the “universal grammar”, common to all natural languages. It is therefore what Chomskyans truly look for. The lexicon is relegated to the periphery of grammar, along with what makes a language idiosyncratic (e.g. inter-speaker variation, cultural connotations, stylistic mannerism, non-standard usage, etc.). Central to Chomskyan grammar is the opposition between deep structure and surface structure. This opposition hinges on syntax, i.e. the way in which words are combined to form larger constituents such as phrases, clauses, or sentences. The deep structure of a sentence is its abstract syntactic representation. The surface structure of a sentence is its final syntactic representation in speech or text. For instance, the sentence students hate annoying professors has one surface structure but two alternative interpretations at the level of the deep structure: (a) students hate to annoy professors and (b) students hate professors who are annoying. Derivation is the process whereby a sentence is generated from abstract operations in the deep structure to a string of words in the surface structure. To sum up, Chomskyan grammar is a “top-down” approach to language: linguists study how algebraic rules “at the top” generate an infinite number of sentences “at the bottom”. One major problem with this approach is that by focusing on the top, linguists tend to look down upon the bottom.
Conversely, usage-based linguistics is a “bottom-up” approach. Its tenet is that actual language usage shapes the structure of language [8–11]. From a usage-based viewpoint, grammar is the product of usage varying from speaker to speaker and there are no hard and fast rules. Grammar is therefore derivative, not generative. It does not have a core and a periphery. It is instead a structured inventory of symbolic units. Not only does the inventory of a native speaker of English contain highly schematic constructions (the past tense, the ditransitive construction, the active construction, etc.), concrete words or phrases such as ritualized or formulaic expressions (double whammy, hang in there!), idioms (that didn’t go down well with the editor, he kicked the bucket, etc.), or non-canonical phrasal collocations (you’re getting to me these days), but also mixed constructions having both abstract and concrete elements (the more you drink, the smarter you think you are). We adopt the viewpoint of usage-based linguistics because (a) we believe it offers a psychologically realistic view of grammar and (b) such a view, unlike Chomskyan grammar, can be operationalized.
2.2 Corpus linguistics
Linguists must rely on the native speakers of a language acting as informants and providing data such as sentences. On the basis of such data, linguists test their hypotheses about the cognitive systems of native speakers. Chomskyans have relied heavily on introspecting judgments for data collection. Their motivation may date back to de Saussure, the father of modern linguistics, who delimited the object of study (langue) as a structured system disconnected from the vagaries of place and time wherein it is deployed. However, the method has been called into question because linguists’ intuitions are not always consonant with what they observe in the data.
With the rise of massive digital collections of texts, linguists who have been dissatisfied with the practice of using themselves as informants have found corpora to be far more useful than introspective judgments to test their hypotheses. Unsurprisingly, these linguists, who consider that genuine language use in all its complexity should be at the center of linguistic research, share the main tenets of the usage-based model.
Note that the above definition covers general corpora as opposed to, say, language acquisition corpora or convenience corpora such as the Guardian data, as pointed out by one anonymous reviewer. Arguably, a combination of the usage-based methodology and corpus-driven research has led to a paradigm shift in linguistics.
A corpus is a machine-readable collection of (spoken or written) texts that were produced in a natural communicative setting, and the collection of texts is compiled with the intention (a) to be representative and balanced with respect to a particular linguistic variety or register or genre and (b) to be analyzed linguistically .
Corpora have their limitations. One of the most frequent criticisms leveled against corpus linguistics by Chomskyans is that corpora do not indicate whether a given expression or use of an expression is impossible. From our usage-based perspective, the response to this critique is simple: because grammatical rules are mere generalizations about actual usage, negative evidence is of limited importance. A more serious criticism is the following: no corpus – however large and balanced – can ever hope to be representative of a speaker, let alone of a language. Supporters of introspective linguistics might argue that a corpus should not be a basis for linguistic studies if it cannot represent language in its full richness and complexity. Most corpus linguists rightly counter that they do not aim to explain all of a language in every study . In this paper, we take a slightly different stance. While we acknowledge that no corpus can provide access to the true, unknown law of a language, we firmly believe that a corpus is a sample drawn from this law. We consider that ambitious corpus linguistics consists in bridging the gap between what we can observe and measure from a corpus, and what we do not know about a language. To achieve this, ambitious statistics is needed.
2.3 Why alternations matter to linguists
Verbs express events. Events involve participants. Participants occupy “places” in the clauses that verbs control. These places are called arguments. The verb drink, for example, is a two-argument verb because in a drinking event there is at least a drinker and a liquid that is drunk. In the active voice, the drinker occupies the subject position and the liquid the object position as in (i):
Suppose Bob wants to brush the whiskey off his breath before setting off to the linguistics lab. He is now holding his toothbrush in one hand and a tube of toothpaste in the other. Four participants are involved: Bob, his teeth, his toothbrush, and the toothpaste. In sentence (ii), three participants are assigned a semantic role by the verb: Bob is the agent (the initiator of the event), toothpaste is the theme (an inanimate entity undergoing a change of location from the brush to the teeth), and his teeth is the goal (the end-point of a motion). The toothbrush is not syntactically realized. The ensuing scene can be described using either (ii a) or (ii b):
|Bob||is brushing||his teeth||with||toothpaste.|
|Bob||is brushing||toothpaste onto||his teeth.|
In (ii a), his teeth is the object of the verb and toothpaste is the object of the preposition with. In (ii b), toothpaste is the object and his teeth is the object of the preposition onto. This means that our attention is brought to his teeth in (ii a) and to toothpaste in (ii b). The phenomenon of a verb exhibiting variation in its syntactic realization is called an alternation. Each alternating form is called an alternant.
Linguists have long believed that alternations were conditioned by verb meaning, two verbs with identical or similar meaning displaying similar alternating behavior . To illustrate this, suppose now that Bob proceeds to shaving. The verb slather involves three participants: Bob, his face, and the shaving cream. Again, the scene can be described using either alternant in (iii):
- a.Bob is slathering his face with shaving cream.
- b.Bob is slathering shaving cream onto his face.
Given that brush and shave are close in meaning (both associated events imply that a ‘thick mass’ is transferred from a container to a body part), we should not be surprised to see that they display the same alternation. Linguists might be enticed to include brush and slather in the same typological verb class, e.g. the class of “grooming verbs”. However, they are somehow different. For example, even though neither verb allows the theme argument to stand alone, as shown in (iv), only brush allows the goal to stand alone, as evidenced in (v): 1
- a.*Bob is brushing toothpaste.
- b.*Bob is slathering shaving cream.
- a.Bob is brushing his teeth.
- b.*Bob is slathering his face.
The question remains open as to whether one should (a) include both verbs in the same class, acknowledging that the class is heterogeneous, or (b) assign them to related but distinct classes, at the risk of demultiplying classes and blunting Ockham’s razor.
Such puzzles are central in an area of linguistics called argument realization, i.e. the study of the syntactic patterns that the arguments of a verb may enter . In (ii) and (iii), the challenge is to explain why two apparently similar verbs display diverging behaviors and why the divergences takes these forms. Addressing these issues matters because of their far-reaching implications for our understanding of language. From a cognitive perspective, one may wonder how speakers classify store verbs in their mental inventories of linguistic units.
3 The dative alternation
Well known to linguists is the dative alternation, which consists of the prepositional dative (henceforth PD) and the ditransitive constructions (or double-object construction, henceforth DO), as exemplified in (vi) and (vii) respectively:
|John||gave||the book||to Mary.||(PD)|
The dative event involves three participants: a giver (John), someone who receives something (Mary), and an entity transferred from the giver to the recipient (the book). In terms of semantic roles, the giver is an agent, the participant receiving something is the recipient, and the entity transferred from the agent to the recipient is a theme. What alternates in this case is the realization of the recipient and the theme, one of which must be an object while the other can be either a direct object or a prepositional object. Levin and Rappaport Hovav  describe the dative alternation as a case of object alternation.
3.1 Theoretical issues
The dative alternation has been a fruitful research topic in many different theories. Substantial accounts of past research can be found for instance in Levin , Krifka  and Levin and Rappaport Hovav [15, chapter 7].
Chomsky [5, 6] suggests that an alternating verb has a single lexical entry for both forms. These forms have the same deep syntactic structure. Differences visible at the sentence level are explained by the fact that the surface structure of the basic form is a direct projection of the deep structure, whereas the surface structure of the derived form is the product of a transformation.
Subsequent Chomskyan studies holding a distinction between deep and surface structures debate over which variant of the dative alternation is transformationally derived from the basic argument realization. Conclusions differ. On the one hand, Fillmore , Hall , and Emons  contend that PD is basic whereas DO is derived. On the other hand, Burt  and Aoun and Li  argue for the opposite pattern of transformation: DO is basic whereas PD is derived.
Semantic restrictions to the dative alternation have challenged Chomskyan accounts. One restriction is that certain verbs alternate while others readily enter only one variant: 2
- a.Anthony gave $100 to charity.
- b.Anthony gave charity $100.
- a.Anthony donated $100 to charity.
- b.?Anthony donated charity $100.
- a.??The bank denied a checking account to me.
- b.The bank denied me a checking account.
Proponents of the Localist Hypothesis , according to whom locative expressions are seen as the source from which all more abstract expressions derive, construe the recipient as a spatial goal. They further argue that DO is possible in (xi b) if London refers metonymically to a person or an institution, in which case it differs from (xi a) where London is clearly a place:
- a.She sent a parcel to London.
- b.She sent London a parcel.
- a.Will taught linguistics to the students.
- b.Will taught the students linguistics.
DO conveys a sense of completion in such a way that the teaching is successful in (xii b). Example (xii a) is more neutral in this respect. However, more recent studies warn that these semantic differences are intuitive and may be subject to contextual modulation [15, 25, 26].
Despite continuous efforts to maintain that alternating verbs have a single meaning underlying both formal variants [27–29], there is now cross-theoretical consensus that the two variants of the dative alternation have distinct semantic representations. According to Pinker  and Rappaport Hovav and Levin , caused motion underlies PD, whereas caused possession underlies DO, as schematized in (xiii):
- a.John gave the book to Mary.X cause Z to be at Y (caused motion, Y is a goal)‘John causes the book to go to Mary’
- b.John gave Mary the book.X cause Y to have Z (caused possession, Y is a recipient)‘John causes Mary to have the book’
In a similar fashion, Speas [32, pp. 88–89] schematizes the semantic representations of both variants as follows:
- a.X cause [Y to be at (possession) Z] (PD)
- b.X cause [Z to come to be in STATE (of possession)] by means of [X cause [Y to come to be at (poss) Z]] (DO)
In the Construction Grammar framework, Goldberg  posits that PD is a subtype of the more general caused-motion construction (cf. the Localist Hypothesis), whereas DO expresses a transfer of possession:
- a.X cause Y to move Z (PD)
- b.X cause Y to receive Z (DO)
The above finds empirical support in Gries and Stefanowitsch .
Given that the distribution of verbs across the dative variants is semantically constrained, and given the frequent lack of semantic equivalence between PD and DO for a given verb, a set of semantic factors have been recognized to influence the choice of PD vs. DO. Among the known lexical semantic restrictions applying to verbs in the dative alternation are the following:
- –Movement (PD) vs. possession (DO): in PD, the theme undergoes movement (literal or figurative) from an origin to a goal, whereas in DO the agent possesses the theme via the verb event.
- –Affectedness: as seen in (xii), the recipient of a dative verb is more likely to receive an affected interpretation when expressed as the first object in DO than in PD;
- –Continuous imparting of force: in PD, the verb can express a continuous imparting of force (e.g. haul, pull, push). DO shows a dispreference for such verbs (??Will pushed Anthony the biscuits). Under certain conditions, exceptions occur .
- –Communication verbs: as opposed to speech act verbs (tell, read, write, cite, etc.) and verbs derived from nouns expressing communication means (fax, email, phone), which can occur in PD or DO, verbs that denote a manner of speaking (shout, yell, scream, whisper, etc.) have a strong dispreference for DO. Exceptions are listed in Gropen et al. .
- –Verbs of impeded possession: such verbs (deny, spare, cost) have a preference for DO.
- –Latinate verbs: due to their morphophonology, such verbs (donate, explain, recite, illustrate, etc.) disprefer DO, except when they express a future possession (guarantee, assign, offer, promise), as pointed out by Pinker [30, p. 216].
Lexical semantic restrictions are sometimes overridden by information-structure factors (interalia [36–38]). Such factors have to do with how information is formally packaged in a sentence. The first factor is discourse givenness, that is to say the fact that the reference of an expression is present in the minds of speakers. In general, given material precedes new material. PD is expected when the theme is more given than the recipient, as in (xvi a), whereas DO is more likely when the recipient is more given than the theme, as in (xvii b):
- a.Will gave his manuscript to a first-year student. (PD)
- b.??Will gave a first-year student his manuscript. (DO)
- a.??Will gave a manuscript to his best student. (PD)
- b.Will gave his best student a manuscript. (DO)
The second factor is a corollary of the first: because recipients are typically human and themes typically inanimate, they are more likely to be given and thus to occur before themes. In this respect, DO is more frequent than PD. Bresnan and Nikitina  find empirical support for this, but they also find exceptions such as (xviii a):
- a.It would cost nothing to the government. (PD)
- b.It would cost the government nothing. (DO)
Although peripheral, the third factor, heaviness, is correlated with information-structure considerations. Heaviness is characterized by the complexity and/or length of sentence constituents. Heavy material comes last, as exemplified below:
- a.??Anthony gave a bottle of his favorite red wine to Will. (PD)
- b.Anthony gave Will a bottle of his favorite red wine. (DO)
Because given material is generally shorter than non-given material (e.g. given recipients will generally occur in the form of pronouns), DO is the preferred realization of the dative alternation due to the last two factors.
Which factor(s) take(s) precedence over the other(s) is still theoretically unclear. Snyder  claims that information-structure factors are more important than heaviness, whereas Arnold et al.  treat all factors on equal footing. What is clearer is that what determines the dative alternation is a multifactorial problem whose full understanding is best resolved empirically. This is why we now turn to recent corpus-based, statistics-driven investigations of the dative alternation.
3.2 Corpus-based answers
Since Williams , the dative alternation has become a model construction for benchmarking predictive methods [2, 36, 42–44]. Focusing on DO, Williams  uses the logistic procedure to test on a two-part but limited data set (original data set, sample size is 168; aggregate data set, sample size is 59). The model construction includes 8 variables: syntactic class of verb, register, modality, givenness of goal, prosodic length of goal vs. theme, definiteness of goal, animacy of goal, and specificity of goal. Williams  finds that not all independent variables are predictors of the position of the goal. Only three reach a relatively high level of significance in the model: the prosodic length of goal vs. theme (the length of the goal is shorter than the length of the theme), syntactic class of verb (ditransitive), and register (informal).
Arnold et al.  investigate the effects of newness and heaviness on word order in the dative alternation. Their data consists of debate transcriptions from the Canadian parliament (the Aligned-Hansard corpus). Utterances are manually annotated for: constituent order (non-shifted vs. shifted; prepositional vs. double object), heaviness (three categories of relative length measured as follows: number of words in the theme minus number of words in the recipient), and newness (given, inferable, or new). Arnold et al.  conclude that heaviness and newness are significantly correlated with constituent order. DO is preferred when the theme is (a) newer and (b) heavier than the goal.
Gries  uses linear discriminant analysis to investigate the effect of multiple variables on the choice of PD vs. DO. in the British National Corpus. Gries observes that all properties of NPgoal along with morphosyntactic variables have the highest discriminatory power. However, (a) discriminant analysis makes distributional assumptions that are seldom satisfied by the data, and (b) Gries  concedes that the data set is limited: being part of a larger project, it consists of only 117 instances of the dative alternation.
To circumvent assumptions about the data distribution and to control for the influence of multiple variables on a binary response, Bresnan et al.  use (mixed-effects) logistic regression, like Williams  and Arnold et al. . Unlike those previous works, Bresnan et al.  predicting’s data set is relatively large, consisting of 2,360 dative observations from the 3M-word Switchboard collection of recorded telephone conversations. More importantly, the authors also address the question of circular correlations, which are largely ignored in former statistical models, e.g.:
- –personal pronouns are short, definite and have animate, discourse-given referents;
- –animate, discourse-given nominals are often realized as personal pronouns, which are short and definite.
Bresnan et al.  ’s dative data set is annotated for 14 explanatory variables whose influence on the choice of the dative variants is considered likely: modality, verb, semantic class of verb use, and length, animacy, 3 definiteness, 4 pronominality, and accessibility of recipient/theme; see also Section 4.1. One of their logistic regression models predicts which variant of the dative alternation is used with high accuracy.
Using Bresnan et al.’s data set, Baayen  tests naive discriminative learning (henceforth NDL) on the dative alternation. Baayen compares NDL to other well-established statistical classifiers such as logistic regression [42, 45], memory-based learning [44, 46], analogical modeling of language , support vector machines , and random forests . He addresses two questions:
- –how can statistical models faithfully reflect a speaker’s knowledge without underestimating or overestimating what a native speaker has internalized?;
- –how do occurrence and co-occurrence frequencies in human classification compare to such frequencies in machine classification?
Like memory-based learning, NDL stands out because it reflects human performance. Unlike parametric regression models, it is unaffected by collinearity issues. When two or more predicting variables are highly correlated, multiple regression models may indicate how well a group of variables predicts an outcome variable, but may not detect (a) which individual predictor(s) improve the model, and (b) which predictors are redundant. Unlike memory-based learning however, NDL does not need to store exemplars in memory to capture the constraint networks that shape linguistic behavior. Such exemplars are merged into the weights [54, p. 320].
Baayen  corpus fits a NDL model with the following predictors: verb, semantic class of verb use, and length, animacy, definiteness, accessibility, and pronominality of recipient and theme. NDL provides a very good fit to the dative data set, which compares well to predictions obtained with other classifiers such as memory-based learning, mixed-effects logistic regression and support vector machine.
The prediction of the dative alternation is now a well-travelled path in quantitative linguistics, as evidenced by the high accuracy of the most recent methods. Yet, the community is in midstream. There is far more to the dative alternation than its prediction, since predicting is not explaining. We believe that this distinction is worth maintaining both at the conceptual and the operational levels. This idea is the backbone of our article.
4 Targeting the dative alternation in English
- –speaker, a categorical variable with 424 levels, including NAs;
- –modality, a categorical variable with 2 levels: spoken vs. written;
- –verb, a categorical variable with 75 levels: e.g. accord, afford, give, etc.;
- –semantic class, a categorical variable with 5 levels: abstract (e.g. give in give it some thought), transfer of possession (e.g. send), future transfer of possession (e.g. owe), prevention of possession (e.g. deny), and communication (e.g. tell);
- –length in words of recipient, an integer valued variable;
- –animacy of recipient, a categorical variable with 2 levels: animate vs. inanimate;
- –definiteness of recipient, a categorical variable with 2 levels: definite vs. indefinite;
- –pronominality of recipient, a categorical variable with 2 levels: pronominal vs. nonpronominal;
- –length in words of theme, an integer valued variable;
- –animacy of theme, a categorical variable with 2 levels: animate vs. inanimate;
- –definiteness of theme, a categorical variable with 2 levels: definite vs. indefinite;
- –pronominality of theme, a categorical variable with 2 levels: pronominal vs. nonpronominal;
- –realization of recipient, a categorical variable with 2 levels: PD vs. DO;
- –accessibility of recipient, a categorical variable with 3 levels: accessible, given, new;
- –accessibility of theme, a categorical variable with 3 levels: accessible, given, new.
We considered speakers coded NA as mutually independent speakers, also independent from the set of identified speakers. About 80% of the identified speakers contribute more than one construction. This is a source of dependency between observations.
The approach we develop below takes this dependency into account. For the sake of clarity, we describe our approach in the context of independent observations. However, our results were obtained considering dependency.
4.2 Predicting and explaining the dative alternation
Our goal is to both predict and explain the dative alternation in English. In the next two subsections, we rephrase these two challenges in statistical terms. In a unifying probabilistic framework reflecting subject-matter knowledge, we specifically elaborate two statistical parameters targeted toward the above two goals. By “subject-matter knowledge” we mean what has been operationalized from what linguists know about the dative alternation and, more specifically, our data set. The parameters differ substantially because the two goals are radically different.
Predicting the dative alternation in English means building an algorithm that poses as a native speaker of English when she formulates a construction involving a dative alternation. The objective could be to deceive a native English speaker sitting in front of a computer and trying to figure out whether his or her interlocutor is also a native English speaker. To do so, the player can only rely on limited information, namely a transcribed construction involving a dative alternation with contextual information. The algorithm does not need to tell us how the dative alternation works. Telling us how the alternation works falls within the scope of explaining it. It is the topic of Section 4.2.2.
For us to learn how to build such an algorithm based on experimental data, a random experiment ideally follows these steps:
- 1.randomly sample a generic member from the population of native English speakers;
- 2.observe her until she formulates either in thoughts, orally, or in writing, a construction that involves a dative alternation;
- 3.record the construction with all the available contextual information;
- 4.repeat the three above steps a large number of times.
- 1.randomly sample a document that contains at least one dative alternation;
- 2.randomly sample a dative alternation from it;
- 3.record the specific construction with all the available contextual information;
- 4.repeat the three above steps a large number of times.
The random experiment
One may want to minimize the overall probability to wrongly predict the dative alternation. In this case, one may choose the loss function
The second statistical parameter
It is important now to emphasize what the notation only suggests. The statistical parameters
In contrast, explaining the dative alternation in English means uncovering what drives the choice of one dative form over the other. This is certainly a multi-faceted challenge, one that cannot be exhausted and yet is worth being taken up for itself through a specifically designed analysis. To the best of our knowledge, however, such a targeted approach has not yet been carried out. It is indeed through the back-door that explanations have been sought so far, typically by (a) predicting the dative alternation, and (b) extracting features of the resulting estimator
In Section 4.2.1, we imagined an ideal random experiment for the sake of learning to predict the dative alternation. What could an ideal experiment be for the sake of explaining it? More precisely, what could such an experiment be to assess the effect of each component of the contextual information on the dative alternation? We draw our inspiration from a common reasoning in the design and statistical analysis of randomized clinical trials for the sake of evaluating the effect of a drug on a disease. The interested reader will find an accessible review on this topic, presented as a trialogue between a philosopher, a medical doctor and a statistician, in (see Sections 3, 8, and 9 in particular . We consider in turn how to proceed with a categorical component as opposed to a non-categorical component.
4.2.3 Assessing the effect of a categorical contextual variable on the dative alternation
First, let us clarify what we mean by the importance of
- 1.randomly sample a generic member from the population of native English speakers;
- 2.randomly sample some contextual information W, and a message to convey;
- 3.give her all this information except
, some partial contextual information, which we denote ;
- 4.ask her to formulate a construction involving a dative alternation to convey the message under the constraint
- 5.record the resulting form of the alternation, which we denote
- 6.take her back in time and ask her to formulate a construction involving a dative alternation to convey the message under the constraint
- 7.record the resulting form of the alternation, which we denote
- 8.repeat the seven above steps a large number of times.
If we denote
It turns out that
Let us now describe a system of structural equations that encapsulates both
Assume that there exist two deterministic functions F and f, taking their values in
Let us now introduce the functional which maps the set
The fact that
4.2.4 Assessing the effect of an integer valued contextual variable on the dative alternation
We now turn to the elaboration of a notion of the importance of
We rely again on eq. (4) to carve out a new system similar to systems (5) and (7). The resulting statistical parameter is tailored to the fact that the importance we wish to quantify is that of a non-categorical variable. Let
The first ingredient is a so-called marginal structural model, a statistical model for the function
As opposed to the previous parameters
Often, users of logistic regression models take for granted that their model assumptions are met by the true, unknown law of their data. They are unaware of the precautionary measures required when assessing the results of a fit. This is especially true for the interpretation of the pointwise estimates, and for the reliability of the confidence intervals, which comes at a high price in terms of untestable assumptions about the true, unknown law of the data. We refer the reader to the discussion about the effect of definiteness of theme in Section 6 to hammer home this important point.
Because the set
By analogy, it is now time to characterize a statistical parameter of
5 Statistical apparatus
Now that the parameters we wish to infer are specified, we turn to their targeted estimation. The targeted estimation relies on machine learning prediction, see Section 5.1, followed by targeted minimum loss explanation, see Section 5.2.
5.1 Machine learning prediction
We consider first the inference of
We now give a nutshell description of the super-learning methodology. Say that we have n independent observations
Recall that the risk
5.2 Targeted minimum loss explanation
We now turn to the estimation of
It is apparent in eqs (6), (8) and (12) that the parameters
Taking a closer look at eqs (6), (8) and (12), we see that it is easy to estimate
[Correction added after online publication 11 December 2015: “Substituting the empirical marginal law of..” should read “Substituting the empirical marginal law of
Likewise, the parameter
Targeting is made possible because
The above estimators satisfy
We consider in turn every component of the contextual information variable W and estimate its effect on the dative alternation as defined in Section 4.2.2 along the lines presented in Section 5. We systematically report 95%-confidence intervals and p-values when testing whether the parameter is equal to 0 or not. We emphasize that these are not simultaneous 95%-confidence intervals. It is possible, however, to use the p-values to carry out a multiple testing procedure, controlling a user-supplied type-I error rate such as the familywise error rate.
6.1 Categorical contextual information variables
Let us now comment on the results of Table 1. We disregard the estimates whose p-values are large, because they correspond to insignificant results. We arbitrarily set our p-value threshold to 1%. An estimate
- –a 38.24% decrease when accessibility of recipient switches from accessible to new;
- –a 16.57% increase when semantic class switches from abstract to communication meaning;
- –a 14.71% decrease when semantic class switches from abstract to future transfer of possession meaning;
- –a 13.98% decrease when pronominality of recipient switches from nonpronominal to pronominal;
- –a 11.68% decrease when pronominality of theme switches from nonpronominal to pronominal, see examples (xxii) and (xxiii);
- –a 11.52% increase when semantic class switches from abstract to transfer meaning;
- –a 9.38% increase when animacy of recipient switches from animate to inanimate, see example (xx);
- –a 9.28% decrease when semantic class switches from abstract to prevention of possession meaning;
- –a 8.43% increase when animacy of theme switches from animate to inanimate;
- –a 7.82% decrease when accessibility of theme switches from accessible to new;
- –a 5.68% decrease when definiteness of theme switches from definite to indefinite, see example (xxi);
- –a 3.95% increase when definiteness of recipient switches from definite to indefinite.
Consider for instance example (xx): under the constraint “set the animacy of recipient to inanimate”, the speaker selects either (xx a) or (xx b); under the constraint “set the animacy of recipient to animate”, she selects either (xx c) or (xx d). What matters is the extent to which the probability to select the PD construction is altered when one switches from one constraint to the other. Even if linguists might find (xx d) slightly more natural than (xx c), (xx a) is undoubtedly more natural than (xx b). This is consonant with our result, which states that the probability of the PD construction increases when the animacy of recipient is set from animate to inanimate.
- a.Anthony gave $100 to charity.
- b.Anthony gave charity $100.
- c.Anthony gave $100 to Will.
- d.Anthony gave Will $100.
Illustrating the inferred statement about the effect of definiteness of theme is challenging. We see this as a welcome opportunity to emphasize the singularity of our statistical approach. To produce a convincing example, we have to choose a longer theme than before. Indeed, linguists know for a fact that when the theme is long, PD is dispreferred. In example (xxi), one can conceive that the preference of (xxi d) over (xxi c) is slightly stronger than that of (xxi b) over (xxi a). This is consonant with our result, which states that the probability of the PD construction decreases slightly when the definiteness of theme is set from definite to indefinite.
- a.Anthony bought the incredibly good cake for Will.
- b.Anthony bought Will the incredibly good cake.
- c.Anthony bought an incredibly good cake for Will.
- d.Anthony bought Will an incredibly good cake.
Example (xxi) is clearly counterintuitive to linguists used to interpreting results from logistic regression models. This is a common pitfall. It is due to the belief that the interpretation of a fitted logistic regression still holds even when the true law does not belong to the logistic model. This is never the case. From a mathematical point of view, the parameter matching definiteness of theme in a logistic regression model is a very awkward function of the true law. No matter how awkward the function is, no sensible interpretation can be built without it. In contrast, the parameter we define and estimate to assess the effect of definiteness of theme is a rather simple function of the true law. Moreover, its simple statistical interpretation is buttressed by a causal interpretation, at the cost of untestable assumptions. The above lines epitomize the approach defended in this article.
How do statisticians intuit then? Denote
Here, for a given context, PD is 1% more likely to occur when definiteness is switched from definite to indefinite and when the theme is short. Concomitantly, PD is 8.54% less likely to occur when definiteness is switched from definite to indefinite and when the theme is long. In addition, assume that
Now that the reader is more familiar with the statistical reasoning underlying our approach, let us consider one last example. Intuitively, when the theme is pronominal, PD is largely preferred:
- a.Anthony sent it to you.
- b.??Anthony sent you it.
Yet, Table 1 shows a 11.68% decrease of the probability of obtaining a PD construction when pronominality of theme switches from nonpronominal to pronominal. This is a consequence of averaging out the context, which is reminiscent of what happens with definiteness of theme. Indeed, the intuition at work in example (xxii) holds when the theme is indefinite. If the theme is definite, then the preference for PD is not so marked anymore:
- a.Anthony sent this to you.
- b.Anthony sent you this.
A reader can only be surprised by our finding if she is lulled into believing that examples such as (xxii) are as a rule more frequent in the data set than those such as (xxiii). It is immensely difficult to apprehend the variety of contexts where speakers choose to use a pronominal theme as opposed to a nonpronominal one, even in the limited context of our data set. We do not embark on this impossible task. We leave that to our method, through the definition of the effect of pronominality of theme and the power of our statistical apparatus.
Estimated effects of the categorical information variables.
6.2 Simpson’s paradox
Because we are concerned with the difference between predicting and explaining the outcomes of dative alternations, one of the reviewers rightly points out that the article should benefit from a realistic linguistic example where the effect of a contextual variable on the dative alternation is confounded.
We already argued in the first paragraph of Section 4.2.2 that predictions do not readily lend themselves to explanations. As discussed when commenting on example (xxi), even if we had relied solely on a logistic regression model to make predictions (we chose to rely on machine learning prediction), the estimated parameters could not have been interpreted as measures of the effects of the contextual information variables on the dative alternation. Therefore, we shall not illustrate confusion by opposing numerical predictions to numerical explanations.
Instead, confusion can simply be assessed by comparing estimates of naive measures of statistical association to estimates of the parameters introduced in Section 4.2.2. For simplicity, we focus on the effect of a binary contextual information variable. Among other choices, we oppose
Let us resume the discussion closing Section 6.1 on the definiteness of theme, denoted by
[Correction added after online publication 11 December 2015: “The estimator..” should read “The estimator
The above illustrates Simpson’s paradox. Well-known to epidemiologists and statisticians, it states that a trend appearing in different data groups may disappear or even reverse once these groups are combined.
Contingency table summarizing the count of each stratum of
6.3 Integer valued contextual information variables
The left panel represents the effect of length of theme on the alternation. It shows how the probability of PD (y-axis) evolves as a function of w when length of theme (x-axis) is set to w, all other things being equal. The weight values are the values of the function h appearing in eq. (12) when evaluated at the integers
The right panel represents the effect of length of recipient on the alternation. It shows how the probability of PD (y-axis) evolves as a function of w when length of recipient (x-axis) is set to w, all other things being equal. Again, the weight values are the values of the function h appearing in eq. (12) when evaluated at the integers
Estimated effects of the integer valued information variables.
Source: For each such contextual information (named in the first column) and each component of the related parameter (identified in the second column), we report the corresponding estimated effect(s), 95%-confidence interval(s) and p-value(s) when testing whether the parameter is equal to 0 or not (in the third, fourth and fifth columns, respectively).
If any, the lessons of this article are about crafting parameters to capture the essence of what one looks for, the merits of scaffolding a thought experiment yielding the ideal data one would have liked to work on, and targeting the above parameters. Using a well-travelled case-study in linguistics, we have adapted and benchmarked a combination of concepts and methods that has already proven its worth in biostatistics.
What is the take-away message on the dative alternation? We cannot answer this question by providing a fitted prediction model, as linguists would expect from a typical statistical study involving, for instance, logistic regression or naive discriminative learning. Prediction is at the core of our approach, but only as a means to an end. Our answer is two-fold: (a) we framed our account of the dative alternation in a causal model, as opposed to a prediction model, and (b) we investigated the effect of each available, contextual information variable on the choice of PD over DO, resulting in a table of estimates, confidence intervals, and p-values. In comparison with past findings, we found surprising results. For instance, we observed a significant decrease of the probability of obtaining PD when the theme is switched from nonpronominal to pronominal. A crude measure of statistical association such as the excess risk would have indicated a significant increase. This is an illustration of Simpson’s paradox.
We showed how to operationalize the effect of any given element of context on the dative alternation as a functional evaluated at the true, unknown law
Our method can be applied to an array of linguistic topics. In particular, all case-studies involving alternations such as
- –the choice of the predeterminer vs. preadjectival position of intensifiers (e.g., quite and rather),
- –the choice of one word over a near-synonym (e.g., almost/nearly, big/large, broad/wide, freedom/liberty),
As pointed out by one anonymous reviewer, the causal methods discussed here were pioneered for observational epidemiological studies where randomized interventions would be unethical or infeasible. In contrast, there are very few ethical or logistical challenges to designing randomized experiments to approximate the steps of the ideal study discussed in Section 4.2.2. For instance, a group of volunteers could perfectly read a corrupted, randomly selected corpus sample, with the contextual information in a sentence randomized to
We acknowledge that the reasoning underlying the approach advocated in this article is demanding. However, linguistics is at a quantitative turn in its history. Graduate programs throughout the world dramatically improve their offer in statistical training. Junior researchers are more eager than ever for statistics. Massive data sets are piling up. To achieve far reaching results, the discipline needs state-of-the-art theoretical statistics and robust statistical tools. We believe that after the heyday of logistic regression, linguists are now ready to embrace the distinction between predicting and explaining.
The authors wish to express their deep gratitude to the anonymous reviewers for their insightful comments. Special thanks also go to the editor, Michael Rosenblum. His suggestions helped greatly improve the manuscript. The authors gratefully acknowledge that this research was partially supported by the French National Center for Scientific Research (CNRS) through the interdisciplinary PEPS-HuMaIn-2013 initiative.
A.1 A lemma
We claimed in Section 4.2.2 that
Assume that eq. (4) can be extended to eq. (5). Assume moreover that
The conditional independence of
A.2 A few details on the super-learner
A.2.1 The super-learner performs almost as well as the best algorithm in the library
The theoretical study of the super-learner’s performances is easier when using the loss L characterized by
A.2.2 Specifics of our super-learner
The inference of
Incidentally, the minimizer
A.3 A few details on TMLE
A.3.1 Differentiability of the parameters
Let us consider
A.3.2 Fluctuating the initial estimators
Let us first describe here the different fluctuations that we use to target
The fluctuations for
Let us now turn to the next fundamental issue, which pertains to estimating the specific elements
A.3.3 Solving eqs (15) and (19)
The numerical computation of the substitution estimators
A.3.4 Including speaker-related dependency
The key to including speaker-related dependency is weighting.
We attach a weight to each observation. This weight is the inverse of the number of constructions contributed by the same speaker in the data set. The observations that we originally noted
We may now assume that
A.3.5 Confidence intervals
We build our confidence intervals by relying on the assumed asymptotic normality of our targeted estimators and their limit standard deviations inferred as the standard deviations of the corresponding efficient influence curves, see eqs (21)–(23). The theory provides us with a set of mathematical assumptions which guarantee that this approach does yield conservative confidence intervals. Some of them can be checked as they only depend on choices we make, such as the algorithms which join forces in the super-learner, see Section A.2.2. Some of them cannot, as they depend on the true, unknown distribution
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The asterisk “*” marks ungrammatical sentences.
A question mark “?” indicates that the example is relatively unacceptable. Two question marks “??” indicate that the example is definitely unacceptable.
If the referent of a noun is sentient or alive, it is animate, otherwise it is inanimate.
A noun phrase is definite when its referent is identified or identifiable in context. It is indefinite otherwise.