1 Introduction

The present paper investigates the English construction with help followed by the infinitive with or without to, as in (1):

The construction help + (to) Infinitive is a rare case when this choice is possible in Present-Day English. Different factors have been proposed to explain when one or the other variant is preferred. Some of them are related to the universal functional principles of iconicity, minimization of cognitive complexity and avoidance of identity (also known as horror aequi). Other factors include register, morphological form and the presence or absence of the Helpee. Lohmann’s (2011) quantitative study of help in British English showed that the variation is multifactorial and probabilistic.

Moreover, it has been observed that American English has a particularly strong preference for the variant without to, although the bare infinitive is more common than the to-infinitive in both British and American varieties (e.g. Biber et al. 1999: 735). In addition, the bare infinitive has been gradually replacing the to-infinitive in the constructions with help in both varieties, so that one can speak of a parallel diachronic development (Mair 2002). As shown in a corpus study by Rohdenburg (2009: 318–319), the infinitive marker to was dropped very rarely in British and American English with the authors born to the end of the 18^th century, but there was a significant increase in the drop of the marker by the end of the 19^th century. This tendency continued in American English also in the 20^th century, with British speakers following the suit with some delay, which supports Mair’s (2002) claim of Americanization cum grammaticalization of help.

The aims of the paper are twofold. First, I want to investigate whether the quantitative differences in the use of the bare and to-infinitive are also accompanied by the differences in probabilistic constraints. The paper compares the impact of the above-mentioned factors in the use of the bare and to-infinitive after help in seven varieties of online English from Australia, Ghana, Great Britain, Hong Kong, India, Jamaica and the USA, using the data from the Global Web-based English corpus, or GloWbE (Davies 2013).

The second goal is to investigate to what extent the use or omission of to before the infinitive can be explained by the universal tendency to use less coding material when the information is predictable, which can be seen as a manifestation of the speaker’s bias towards efficient, or economical communication (e.g. Haiman 1983; Aylett & Turk 2004; Levy & Jaeger 2007; Haspelmath 2008). Here, I will focus on constructional predictability. The main hypothesis of this study is that the longer variant (i.e. with to) is preferred when a specific infinitive is less expected to appear as a part of the construction with help. This hypothesis will be tested when the other relevant factors, which are known from previous research, are controlled for in a multiple regression analysis. Importantly, the present study explores these effects in two opposite directions, testing both the predictability of the infinitive given HELP and the predictability of HELP given the infinitive, which are similar to Schmid’s (2000) measures of Attraction and Reliance. As will be shown below, this approach yields some unexpected results, which open new opportunities for information-theoretic studies of morphosyntactic variation.

Methodologically, this paper employs Bayesian regression analysis, which is still novel in linguistics (but see one of the first attempts in Levshina 2016). More exactly, I use generalized additive mixed-effects regression in order to model non-linear effects of constructional predictability.

The paper is organized as follows. Section 2 discusses some of the recent studies of morphosyntactic variation, which suggest an inverse correlation between predictability and formal length. Section 3 introduces the main factors that have been discussed in previous research on the alternation. Section 4 describes the data source and the process of data extraction. In Section 5 one can find the variables that are tested in this study. Section 6 introduces the statistical method and reports the results of the quantitative analyses. Finally, a discussion of the findings is offered in Section 7.

2 Communicative efficiency and constructional predictability

Communicative efficiency can be achieved in different ways, from choosing an appropriate politeness marker, to omission of redundant information. Iconicity and minimization of cognitive complexity (see Section 2) can also be regarded as devices for maximization of communicative efficiency. In the centre of the present discussion, however, is a specific case when less predictable elements, which carry more information, get more formal coding, and more predictable elements, which carry less information, get less coding.

The inverse correlation between formal length and frequency has been known since Zipf’s (1935) seminal work. However, recently it has been shown that word length is even more strongly correlated with the average predictability of words based on context than with their context-free frequency (Piantadosi et al. 2011). There is ample evidence that more expected words, syllables or phonemes are more likely to undergo length reduction and loss of articulatory detail than less expected ones (e.g. Jurafsky et al. 2001; Aylett & Turk 2004; Bell et al. 2009; Mahowald et al. 2013).

This correlation inspired Aylett and Turk’s (2004) smooth signal redundancy hypothesis, which says that information content should be spread evenly across the signal. A similar idea has also been expressed as the hypothesis of Uniform Information Density (see Levy & Jaeger 2007). These proposals involve concepts from Shannon’s (1948) information theory. Information content, or surprisal, is based on the conditional probability of a unit given its context, e.g. n words on the right or left. It is the opposite of predictability. That is, the less predictable a unit is from its context, the more informative it is.

Of particular relevance for the present study are the studies of grammatical alternations with optional markers, which tend to be omitted when the structures that they introduce are predictable from the context, e.g. the relativizer that in English relative clauses after definite NPs (Wasow et al. 2011), the object marker in Japanese in typical agent-patient configurations (Kurumada & Jaeger 2015), or head-marking of the subject of the relative clause in Yucatec Maya after definite NP heads (Norcliffe & Jaeger 2016).

As far as help + (to) Infinitive is concerned, one can expect that the particle to will be more frequently used in the situations when the information content is higher. Information content is defined in the present study in two ways: a) based the predictability of the infinitive given HELP and b) based on the predictability of HELP given the infinitive.¹ These two measures have analogues in usage-based construction linguistics, which are known as Attraction, i.e. the conditional probability of a word given a construction, and Reliance, i.e. the conditional probability of a construction given a word (Schmid 2000). Although many corpus linguists find it useful to compute one bidirectional measure that represents the association between a construction and one of its collexemes (e.g. Stefanowitsch & Gries 2003), Schmid has been arguing that Attraction and Reliance represent two different types of information, each valuable on its own (e.g. Schmid & Küchenhoff 2013). To the best of my knowledge, these two types of predictability – predictability of a collexeme given the construction and the other way round – have not been previously taken into account in the previous studies of predictability effects in morphosyntactic alternations.

In speech, the use of additional coding material may give the speaker and the listener more time to plan and process the utterance. The predictability effects have been observed in writing, as well. As Wasow et al. (2015) hypothesize, this may happen because the speech habits are carried over to writing, or because of temporal pressures on readers. Still, the predictability effects found in writing are robust enough to test the main hypothesis of the present study on data from a written corpus.

3 Factors known from previous research

4 Corpus and the procedure of data extraction

The data used in the present study come from the Corpus of Global Web-based English (GloWbE) created by Davies (2013). This large corpus contains 1.9 billion words and represents online English from twenty countries. For this case study, seven geographic varieties were chosen from different parts of the world: Australia, Ghana, Great Britain, Hong Kong, India, Jamaica and the USA. The choice for this corpus was motivated primarily by its size. One needs large corpora in order to compute reliable information-theoretic measures, especially if the construction of interest is not very frequent. I used a part of the corpus with eighteen million words per country, nine million from the General subcorpus and nine million from the Blog subcorpus.

The data extraction procedure was as follows. First, I used a Python script to collect all instances of help in any inflectional form followed by an infinitive somewhere in the sentence. If there were finite verb forms, clause-combining conjunctions like because, or subject pronouns like I, he and she between help and the infinitive, the instance was discarded. A quality check based on one hundred manually extracted examples from five subcorpora revealed that this approach was quite successful in recognizing the instances of the construction: The recall was 86%, and the precision was 93%. Only active uses were collected because the bare infinitive can be used only in active sentences (Huddleston & Pullum 2002: 1244), as shown in (6):

The spelling variants of the verbs were normalised, so that the pairs like maximize and maximise, fulfil and fulfill were treated as one word.

In spite of the fact that the corpus compilers performed some cleaning, there were still quite a few duplicate sentences in the data. They were removed with the help of a script. Another problem were nonsense sentences, which were probably machine-generated or contained advertising information (cf. similar problems reported in Mair 2015: 31–32). However, they were not numerous and were removed during the process of variable coding.

Finally, I cleaned the data manually from the instances of a formally similar but functionally different construction with the dummy it-subject, where the to-infinitive is always used (McEnery & Xiao 2005). An example is shown in (7).

After the data collection and cleaning, I obtained the frequencies shown in Table 1. Since the sizes of the subcorpora were identical (18 million words), the “raw” frequencies are directly comparable between the varieties. One can see that Hong Kong has the highest total frequency of the constructions, and Jamaica the lowest. However, the differences are not very large. As for the relative frequencies of the variants, the variant with the bare infinitive is the more frequent one in all countries. The USA subcorpus displays the highest relative frequency of help followed by the bare infinitive (84.9%), whereas the Jamaican subcorpus has the lowest one (60.8%), followed by Great Britain (70.3%) and the other countries.

The next section describes the predictor variables, which represent the factors mentioned in Sections 2 and 3. The Helper’s animacy is not taken into account because it was very difficult to automate the annotation procedure. The parser returned very poor results due to highly complex syntactic structures, e.g. when help was itself part of an infinitival clause. Note that the effect of animacy in Lohmann’s (2011) study was rather weak. Prosodic factors (in particular, stress clash) are not tested, either, due to the practical difficulties in obtaining the stress patterns from the written data of such a large size. I added one new variable, the valency of the infinitive.

5 Predictors for regression analysis

6 Bayesian generalized additive mixed-effect models: Characteristics and results

6.1 Bayesian inference and characteristics of the models

To test the effect of the predictors on the use of bare and to-infinitives, I used Bayesian mixed-effects generalized additive models. For this purpose, I employed Stan, a programming language and platform for Bayesian inference (Stan Development Team 2015) and the package brms (Bürkner 2017), which provides an R interface to Stan (R Core Team 2017).

Seven Bayesian logistic regression models were fitted, one for each variety. The response variable was the use of the bare or to-infinitive. The predictors described in Section 5 were treated as fixed effects. The individual websites and the verbs that fill in the infinitive slot were treated as random effects (more exactly, random intercepts). Sum contrasts were used with all categorical and binary variables, so that zero represents the grand mean (i.e. the unweighted mean of means) of the categories. The numeric variables were centred around the mean. Two interaction terms were modelled after diagnostic tests. One interaction is between linguistic distance and the horror aequi variable, which was found to be significant by Lohmann (2011). The other is the interaction between the form of help and the presence or absence of the Helpee. In addition, an interaction between the two information-theoretic measures was taken into account by introducing bivariate smoothing terms (see below). The discriminating power of the models was excellent (all concordance indices C were greater than 0.9).

Bayesian regression allows the researcher to test directly the research hypothesis. In our case, we can obtain the probability of a predictor having a positive or negative effect on the presence or absence of the particle to. In Bayesian inference, such probabilities are called posterior probabilities, or posteriors, because they are computed after the data have been taken into account. They also depend on prior probabilities, or priors, which represent the researcher’s prior beliefs in the probability of some parameters before the data are taken into account. If one provides non-informative priors (e.g. uniform ones, where any value is equally probable), this will result in posteriors that are influenced only by the data, as in frequentist statistics. As recommended by the Stan developers, I used the default weakly informative priors, which only help to constrain the posteriors to reasonable values, i.e. those to be normally found in logistic models. Bayesian regression is a perfect match for probabilistic grammar because posterior probabilities can be easily compared cross-lectally. They also allow us to study a continuum of credibility without forcing us to make binary decisions based on p-values. For more information about the technical details of Bayesian modelling, one can be referred to Kruschke (2011). In what follows, I focus on the results.

The algorithm returns 6000 posterior estimates of each regression parameter (1500 estimates in four Markov chains per each model). These probability distributions can be represented in a histogram which displays our posterior beliefs after the data have been taken into account. An example is provided in Figure 1. It shows the effect of average word length on the chances of the bare and to-infinitive in the websites from Great Britain. The numeric values on the horizontal axis are the log-odds ratios. A positive log-odds ratio means that the odds of the to-infinitive increase with average word length, whereas a negative value means that the odds of the to-infinitive decrease (and, conversely, the odds of the bare infinitive increase). From the posterior distribution one can compute the posterior mean, which is displayed as a dot in Figure 1, as well as 95% credible intervals, which show the region between the 2.5% and the 97.5% percentiles, where the 95% of the posterior distribution lies. Credible intervals thus span the most believable posteriors. If one has to make a categorical judgment of the type “Does the variable increase the chances of one or the other outcome?”, one can use this criterion. If a credible interval does not include zero, as in this illustration, one can say that the effect is credibly nonzero.

Figure 1

Posterior probability distribution of the effect of average word length in a text on the presence or absence of to in the subcorpus representing Great Britain.

The posterior distribution can also help us assess the probability of observing the positive and negative effect of a given predictor on the chances of the to-infinitive by computing the proportions of the posteriors that are greater and less than zero. In our example, the proportion of the posteriors greater than zero is 100%. This information allows us to test directly the alternative hypothesis.

Additional diagnostic tests with polynomials suggested that some of the effects of the predictability variables are non-linear. To take that into account, I used the methods of generalized additive modelling (Wood 2006), which applies smooth functions to model non-linear relations between predictors and the response. More exactly, I used bivariate smoothing terms, which take into account possible non-additive effects of two predictors. Using the LOO criterion for model comparison, I chose isotropic smooths, which are appropriate when variables are on similar scales. As for the other continuous variables, no convincing non-linearity was detected.

6.2 Results of Bayesian modelling

6.2.1 Predictability-related variables

The marginal effects of the information content of a verb given HELP are displayed in Figure 2. They are based on the predicted probabilities of the to-infinitive. Recall that the hypothesis was as follows: The greater the information content, the higher the chances of the marked form. Although some of the plots point in the right direction (e.g. the data from Ghana, Hong Kong and the USA), the 95% credible bands are very broad in comparison with the magnitude of those effects, which means that the latter are marginal at best.

Figure 2

Marginal effects of information content of a verb given the construction with help (the horizontal axis) on the probability of the to-infinitive (the vertical axis).

In contrast, the marginal effects of the information content of the construction given a verb are more robust, as shown in Figure 3. In the USA data, the effect is the weakest. In Australia, Great Britain, India and Jamaica, we also observe some non-monotonicity, with a small dip in the centre.

The effects of both information-theoretic variables in interaction are displayed in Figure 4. The lighter areas (from violet to blue and then to green and yellow) indicate the information content values where the chances of the to-infinitive increase, while the darker areas show the values with a higher preference for the bare infinitive. When the information content of HELP given a verb is very high (see the top part of the plots), the chances of the to-infinitive tend to increase. There is also a slight increase in the bottom right part of the plots in some of the varieties. This is a region with with high information content of a verb given HELP (the horizontal axis) and low to middle information content of HELP given a verb (the vertical axis). This increase explains the non-linear patterns discovered in Figure 3.

Figure 3

Marginal effects of information content of the construction with help given a verb (the horizontal axis) on the probability of the to-infinitive (the vertical axis).

Figure 4

Non-linear effects of information-theoretic measures in seven varieties. Horizontal axis: information content of a verb given the construction; vertical axis: Information content of the construction given a verb. Lighter shades (yellow): Higher predicted probability of the to-infinitive. Darker shades (violet): Lower predicted probability of the to-infinitive.

6.2.2 Cognitive complexity, horror aequi and their interaction

The effects of cognitive complexity and horror acqui are as expected in all countries. Table 2 displays the effects of linguistic distance. With each word between help and the infinitive, the odds of the to-infinitive credibly increase. There is some variation in the strength of this effect, with the American variety displaying the smallest value, and the Indian one the largest.

Table 2

Bayesian regression results for linguistic distance (log-odds ratios).

Country	Posterior mean	2.5%	97.5%	P(β > 0)
Australia	0.46	0.3	0.63	100%
Ghana	0.7	0.57	0.84	100%
Great Britain	0.56	0.41	0.71	100%
Hong Kong	0.69	0.56	0.83	100%
India	0.82	0.66	0.99	100%
Jamaica	0.48	0.3	0.65	100%
USA	0.38	0.22	0.54	100%

Table 3 shows the effects of the presence of to before help for mean linguistic distance. The chances of the to-infinitive decrease if there is to before help. There is some variation, again. The Hong Kong data display the weakest effect, and the Jamaican subcorpus shows the strongest effect.

Table 3

Bayesian regression results for the presence of to before help (log-odds ratios).

Country	Posterior mean	2.5%	97.5%	P(β > 0)
Australia	–1.33	–1.51	–1.15	0%
Ghana	–1.29	–1.46	–1.14	0%
Great Britain	–1.24	–1.4	–1.09	0%
Hong Kong	–1.13	–1.27	–0.98	0%
India	–1.35	–1.54	–1.17	0%
Jamaica	–1.62	–1.82	–1.44	0%
USA	–1.3	–1.52	–1.09	0%

The positive interaction terms (see Table 4) indicate that the odds of the to-infinitive become higher, as the linguistic distance between help and the infinitive increases. The US data display the weakest effect, while the Jamaican variety has the strongest effect, closely followed by several others.

Table 4

Bayesian regression results for the interaction term between linguistic distance and the presence of to before help (log-odds ratios).

Country	Posterior mean	2.5%	97.5%	P(β > 0)
Australia	0.28	0.14	0.41	99.98%
Ghana	0.28	0.17	0.38	100%
Great Britain	0.37	0.24	0.5	100%
Hong Kong	0.38	0.27	0.49	100%
India	0.39	0.24	0.54	100%
Jamaica	0.4	0.27	0.54	100%
USA	0.22	0.08	0.35	99.9%

6.2.3 The form of help, the presence or absence of the Helpee and their interaction

The results are best represented visually. Figure 5 displays the mean posteriors and the 95% credible intervals. In all varieties, the form helping without the Helpee has the highest chances of being used with the to-infinitive. With the exception of the Indian variety, the base form help is the most likely to be followed by the bare infinitive. However, when the Helpee is present, the difference between the forms is small. Normally, the presence of the Helpee increases the chances of the bare infinitive, although its effect is quite small after the base form help, where the credible intervals largely overlap (see especially the US variety). In the Ghanaian variety, we even see a small increase in the chances of the to-infinitive.

Figure 5

Posterior means and 95% credible intervals of the interaction between the form of help and the presence or absence of the Helpee. The vertical axis represents the probability of to-infinitive.

6.2.4 Valency of the infinitive

Table 5 shows the numbers that represent the effect of transitivity of the infinitive on the presence of to. One can see that high probabilities (greater than 90%) are observed in the data from Hong Kong, India and Jamaica, followed by the USA (almost 87%). In the other countries, there is no strong bias in either direction. A separate check (not shown here) reveals that the presence of clause complements has no highly credible effects (close to 100%) in any of the varieties. In the USA, there is 92.3% probability that the clausal complements increase the chances of the bare form, followed by Jamaica (85.1%) and Hong Kong (84.2%).

Table 5

Bayesian regression results for transitive vs. intransitive infinitive (log-odds ratios).

Country	Posterior mean	2.5%	97.5%	P(β > 0)
Australia	0	–0.16	0.17	49.5%
Ghana	–0.03	–0.21	0.16	38.7%
Great Britain	–0.01	–0.18	0.15	44%
Hong Kong	0.18	0.01	0.34	98.5%
India	0.13	–0.05	0.31	92.5%
Jamaica	0.16	–0.05	0.37	93.4%
USA	0.12	–0.09	0.33	86.6%

6.2.5 Formality (average word length)

Finally, let us consider the degree of formality represented by the average word length of the text presented at an individual website. The posteriors in Table 6 show the effect of adding one letter on the log-odds of the to-infinitive vs. the bare infinitive. In most countries the average word length has positive effect on the chances of the to-infinitive, as predicted. The strongest effect is observed in Great Britain. The Ghanaian and US data display very weak positive effects. The Indian data show, surprisingly, the opposite effect: the longer the words in a text, the higher the chances of the bare infinitive.

Table 6

Bayesian regression results for the average word length (log-odds ratios).

Country	Posterior mean	2.5%	97.5%	P(β > 0)
Australia	0.3	0.04	0.57	98.9%
Ghana	0.1	–0.17	0.36	76.1%
Great Britain	0.59	0.33	0.86	100%
Hong Kong	0.27	0.03	0.52	98.7%
India	–0.35	–0.63	–0.07	0.8%
Jamaica	0.3	–0.02	0.64	96.8%
USA	0.12	–0.2	0.44	76.6%

7 Summary and discussion of the results

In general, the bare infinitive is the preferred variant in all varieties discussed here. The highest proportion of the bare infinitive is observed in the US data, whereas the lowest proportion is found in the Jamaican subcorpus, followed by the British data. The remaining countries exhibit proportions very similar to the British one.

The results of the previous studies are largely corroborated, although there are also quite a few new details.

• The variables related to horror aequi and the principle of cognitive complexity behave in accordance with the expectations in all varieties. They interact, such that the effect of to before help weakens with linguistic distance between help and the infinitive. Here, the models reveal no surprises.

• The varieties also behave similarly with regard to the form helping, which substantially increases the chances of the to-infinitive. It is followed by helps in most varieties. However, the models demonstrate that this contrast is strong only in the absence of the Helpee. When the Helpee is explicit, the differences between the forms are small. For the base form help, the chances of the bare infinitive tend to be the highest, with or without the Helpee (except for the Indian variety, where helped is also very likely to be followed by the bare infinitive).

• As expected, the presence of the Helpee increases the chances of the bare form in all forms, with the exception of the base form help, when the presence of the Helpee makes little difference.

• There is a positive effect of the average word length, which serves as a proxy of formality, on the probability of the to-infinitive in most varieties, although it has low credibility in the Ghanaian and US subcorpora. Surprisingly, one finds a credible reverse effect in the Indian variety.

• There is also some evidence that transitive infinitives increase the chances of the to-infinitive in the varieties of Hong Kong, India, Jamaica and the USA, although this effect is only sufficiently credible in the data from Hong Kong. There are also some indications that the clausal complements play a role in some of the varieties, but these indications are very weak.

To summarize, there are very strong cross-lectal similarities with regard to the factors of horror aequi and cognitive complexity. As far as the other contextual factors (stylistic, morphological and syntactic) are concerned, most varieties behave in a similar way, but there are also exceptions. Interestingly, the US model often exhibits relatively weak effects in comparison with the other models. This may be due to the fact that the to-variant is the closest to extinction in that variety. The competition between the variants gradually disappears.

Let us now turn to the second question of the present study. The aim was to find out if constructional predictability determines the use of the bare or to-infinitive in the varieties of English and whether these effects (or lack thereof) are consistent. The generalized additive models show that there are some common effects in the expected direction in all seven varieties, but their directionality, strength and shape vary. The main conclusion one can draw is that the information content of HELP given a verb displays stronger and more systematic effects in the expected direction than the information content of a verb given the constructions. The infinitives that are associated with high information content of HELP are, as a rule, highly frequent verbs, such as be, have, do, say, ask, try and use.⁵ These verbs appear in many diverse constructions, which explains the high information content of HELP. A few examples are provided in (12).

To support this conclusion, Figure 6 displays the differences between the percentages of to in all examples and in those where HELP is highly informative given the infinitive (top 5% of all scores in each variety). One can see that the proportion of to-infinitives is greater in the highly informative contexts than on average across all varieties.

Figure 6

Percentages of to-infinitives in all contexts and in those where help given the infinitive is highly informative (top 5% of the scores).

These findings are rather unexpected. Most information-theoretic studies of grammatical alternations show that speakers tend to provide extra marking on unexpected units, such as the more frequent use of that before relative clauses (e.g. I like the book (that) you gave me) that are less predictable from the lexical properties of the noun phrase (Wasow et al. 2011), or the more frequent use of the case marker on semantically untypical direct objects in Japanese (Kurumada & Jaeger 2015). Unlike in those studies, the stronger predictability effect found here explains the marking on the infinitive, but the infinitive is not surprising itself. What is unexpected, is the construction in which it appears. Still, this effect can be considered a manifestation of the general tendency to maximize communicative efficiency. The speaker or writer provides an additional clue (i.e. the particle to) in those contexts when the infinitive is more difficult to recognize as a part of the construction with help. That makes the parsing of the utterance easier for the hearer or reader.

These findings open a new perspective for studies of constructional predictability in language. They show that predictability effects can go in different directions, which need to be examined separately. Moreover, it is important that the effects found in the present study are non-linear, which has not been addressed before, to the best of my knowledge. The results also demonstrate the importance of examining cross-lectal data when searching for universal functional principles of human language.

Competing Interests

The author has no competing interests to declare.