Are embedding decisions independent?

Evidence from preposition(al) phrases

Abstract Full Paper (PDF)

One of the more difficult challenges in linguistics research concerns detecting how constraints might apply to the process of constructing phrases and clauses in natural language production. In previous work (Wallis 2019) we considered a number of operations modifying noun phrases, including sequential and embedded modification with postmodifying clauses. Notably, we found a pattern of a declining additive probability for each decision to embed postmodifying clauses, albeit a pattern that differed in speech and writing.

In this paper we use the same research paradigm to investigate the embedding of an altogether simpler structure: postmodifying nouns with prepositional phrases. These are approximately twice as frequent and structures exhibit as many as five levels of embedding in ICE-GB (two more than are found for clauses). Finally the embedding model is simplified because only one noun phrase can be found within each prepositional phrase. We discover different initial rates and patterns for common and proper nouns, and certain subsets of pronouns and numerals. Common nouns (80% of nouns in the corpus) do appear to generate a secular decline in the additive probability of embedded prepositional phrases, whereas the equivalent rate for proper nouns rises from a low initial probability, a fact that appears to be strongly affected by the presence of titles.

It may be generally assumed that like clauses, prepositional phrases are essentially independent units. However, we find evidence from a number of sources that indicate that some double-layered constructions may be being added as single units. In addition to titles, these constructions include schematic or idiomatic expressions whose head is an ‘indefinite’ pronoun or numeral.

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.

EDS Resources

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

Session 15: Introduction to statistics

• Binomial – Normal – Wilson
• Binomial spreadsheet

Sessions 18 and 19: Statistics Workshops

• EDS example 1 (Levin 2013)
• EDS example 2 (Bowie et al 2013)
• 2 × 2 or 2 × 1 χ² tests

Suggested further reading

• Plotting confidence intervals (part 1) and part 2
• Robust and sound?
• Choosing the right test
• A statistics crib sheet
• z-squared: the origin and application of χ²
• Plotting the Wilson distribution
• Coping with imperfect data