Detecting direction in interaction evidence

IntroductionPaper (PDF)

I have previously argued (Wallis 2014) that interaction evidence is the most fruitful type of corpus linguistics evidence for grammatical research (and doubtless for many other areas of linguistics).

Frequency evidence, which we can write as p(x), the probability of x occurring, concerns itself simply with the overall distribution of a linguistic phenomenon x – such as whether informal written English has a higher proportion of interrogative clauses than formal written English. In order to calculate frequency evidence we must define x, i.e. decide how to identify interrogative clauses. We must also pick an appropriate baseline n for this evaluation, i.e. we need to decide whether to use words, clauses, or any other structure to identify locations where an interrogative clause may occur.

Interaction evidence is different. It is a statistical correlation between a decision that a writer or speaker makes at one part of a text, which we will label point A, and a decision at another part, point B. The idea is shown schematically in Figure 1. A and B are separate ‘decision points’ in a given relationship (e.g. lexical adjacency), which can be also considered as ‘variables’.

Figure 1: Associative inference from lexico-grammatical choice variable A to variable B (sketch).

Figure 1: Associative inference from lexico-grammatical choice variable A to variable B (sketch).

This class of evidence is used in a wide range of computational algorithms. These include collocation methods, part-of-speech taggers, and probabilistic parsers. Despite the promise of interaction evidence, the majority of corpus studies tend to consist of discussions of frequency differences and distributions.

In this paper I want to look at applications of interaction evidence which are made more-or-less at the same time by the same speaker/writer. In such circumstances we cannot be sure that just because B follows A in the text, the decision relating to B was made after the decision at A. Continue reading

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The replication crisis: what does it mean for corpus linguistics?

Introduction

Over the last year, the field of psychology has been rocked by a major public dispute about statistics. This concerns the failure of claims in papers, published in top psychological journals, to replicate.

Replication is a big deal: if you publish a correlation between variable X and variable Y – that there is an increase in the use of the progressive over time, say, and that increase is statistically significant, you expect that this finding would be replicated were the experiment repeated.

I would strongly recommend Andrew Gelman’s brief history of the developing crisis in psychology. It is not necessary to agree with everything he says (personally, I find little to disagree with, although his argument is challenging) to recognise that he describes a serious problem here.

There may be more than one reason why published studies have failed to obtain compatible results on repetition, and so it is worth sifting these out.

In this blog post, what I want to do is try to explore what this replication crisis is – is it one problem, or several? – and then turn to what solutions might be available and what the implications are for corpus linguistics. Continue reading

Adapting variance for random-text sampling

Introduction Paper (PDF)

Conventional stochastic methods based on the Binomial distribution rely on a standard model of random sampling whereby freely-varying instances of a phenomenon under study can be said to be drawn randomly and independently from an infinite population of instances.

These methods include confidence intervals and contingency tests (including multinomial tests), whether computed by Fisher’s exact method or variants of log-likelihood, χ², or the Wilson score interval (Wallis 2013). These methods are also at the core of others. The Normal approximation to the Binomial allows us to compute a notion of the variance of the distribution, and is to be found in line fitting and other generalisations.

In many empirical disciplines, samples are rarely drawn “randomly” from the population in a literal sense. Medical research tends to sample available volunteers rather than names compulsorily called up from electoral or medical records. However, provided that researchers are aware that their random sample is limited by the sampling method, and draw conclusions accordingly, such limitations are generally considered acceptable. Obtaining consent is occasionally a problematic experimental bias; actually recruiting relevant individuals is a more common problem.

However, in a number of disciplines, including corpus linguistics, samples are not drawn randomly from a population of independent instances, but instead consist of randomly-obtained contiguous subsamples. In corpus linguistics, these subsamples are drawn from coherent passages or transcribed recordings, generically termed ‘texts’. In this sampling regime, whereas any pair of instances in independent subsamples satisfy the independent-sampling requirement, pairs of instances in the same subsample are likely to be co-dependent to some degree.

To take a corpus linguistics example, a pair of grammatical clauses in the same text passage are more likely to share characteristics than a pair of clauses in two entirely independent passages. Similarly, epidemiological research often involves “cluster-based sampling”, whereby each subsample cluster is drawn from a particular location, family nexus, etc. Again, it is more likely that neighbours or family members share a characteristic under study than random individuals.

If the random-sampling assumption is undermined, a number of questions arise.

  • Are statistical methods employing this random-sample assumption simply invalid on data of this type, or do they gracefully degrade?
  • Do we have to employ very different tests, as some researchers have suggested, or can existing tests be modified in some way?
  • Can we measure the degree to which instances drawn from the same subsample are interdependent? This would help us determine both the scale of the problem and arrive at a potential solution to take this interdependence into account.
  • Would revised methods only affect the degree of certainty of an observed score (variance, confidence intervals, etc.), or might they also affect the best estimate of the observation itself (proportions or probability scores)?

Continue reading

Logistic regression with Wilson intervals

Introduction

Back in 2010 I wrote a short article on the logistic (‘S’) curve in which I described its theoretical justification, mathematical properties and relationship to the Wilson score interval. This observed two key points.

  • We can map any set of independent probabilities p ∈ [0, 1] to a flat Cartesian space using the inverse logistic (‘logit’) function, defined as
    • logit(p) ≡ log(p / 1 – p) = log(p) – log(1 – p),
    • where ‘log’ is the natural logarithm and logit(p) ∈ [-∞, ∞].
  • By performing this transformation
    • the logistic curve in probability space becomes a straight line in logit space, and
    • Wilson score intervals for p ∈ (0, 1) are symmetrical in logit space, i.e. logit(p) – logit(w⁻) = logit(w⁺) – logit(p).
Logistic curve (k = 1) with Wilson score intervals for n = 10, 100.

Logistic curve (k = 1) with Wilson score intervals for n = 10, 100.

Continue reading

Coping with imperfect data

Introduction

One of the challenges for corpus linguists is that many of the distinctions that we wish to make are either not annotated in a corpus at all or, if they are represented in the annotation, unreliably annotated. This issue frequently arises in corpora to which an algorithm has been applied, but where the results have not been checked by linguists, a situation which is unavoidable with mega-corpora. However, this is a general problem. We would always recommend that cases be reviewed for accuracy of annotation.

A version of this issue also arises when checking for the possibility of alternation, that is, to ensure that items of Type A can be replaced by Type B items, and vice-versa. An example might be epistemic modal shall vs. will. Most corpora, including richly-annotated corpora such as ICE-GB and DCPSE, do not include modal semantics in their annotation scheme. In such cases the issue is not that the annotation is “imperfect”, rather that our experiment relies on a presumption that the speaker has the choice of either type at any observed point (see Aarts et al. 2013), but that choice is conditioned by the semantic content of the utterance.

Continue reading

Binomial → Normal → Wilson

Introduction

One of the questions that keeps coming up with students is the following.

What does the Wilson score interval represent, and why is it the right way to calculate a confidence interval based around an observation? 

In this blog post I will attempt to explain, in a series of hopefully simple steps, how we get from the Binomial distribution to the Wilson score interval. I have written about this in a more ‘academic’ style elsewhere, but I haven’t spelled it out in a blog post.
Continue reading

EDS Resources

This post contains the resources for students taking the UCL English Linguistics MA, all in one place.

Session 15: Introduction to statistics

Sessions 18 and 19: Statistics Workshops

Suggested further reading