Towards a Synergetic Statistical Model of Language Phonology

^*Address correspondence to: Germán Coloma, Universidad del CEMA, Córdoba 374, C1054AAP, City: Buenos Aires, Argentina. E-mail: [email protected]

Abstract

¹

¹ I thank Reinhard Köhler, Mariano Fernández and two anonymous referees for their extremely useful comments and suggestions to a previous version of this article.

This paper proposes a method to analyse linguistic data using simultaneous equation regressions, and applies that method to a database of 100 languages and four phonological variables (consonant inventory size, vowel inventory size, stress distinctiveness and tone distinctiveness). The proposed method is based on some principles of synergetic linguistics, since its equations can be derived from an optimization problem that assumes that the levels of the phonological variables are chosen to maximize decoding ease and to minimize production effort. It is also good to replicate the most significant correlation coefficients of the database, and to solve a puzzle concerning the sign of some of those coefficients. With the aid of this method, we build a linear statistical model of phonological structure, according to which consonants, vowels and tone are all negatively related to stress distinctiveness. This result can be related to some findings of the literature about quantitative phonological typology.

Notes

^* Address correspondence to: Germán Coloma, Universidad del CEMA, Córdoba 374, C1054AAP, City: Buenos Aires, Argentina. E-mail: [email protected]

¹ I thank Reinhard Köhler, Mariano Fernández and two anonymous referees for their extremely useful comments and suggestions to a previous version of this article.

² For illustrations of these applications, see Johnson (2008), chapter 3.

³ The linear shape that we assume when writing Equation (1) is, of course, only one of the many possible functional relationships that we can postulate. In this paper, however, we will always use linear relationships, basically because our aim is to illustrate a methodology whose properties are much easier to explain and to analyse in this context than in any alternative non-linear one. Besides, as our main concern will be to interpret the sign and magnitude of the relationships that we find between different sets of variables (and not the actual behaviour or evolution of those variables), the coefficients obtained can be seen as “linear approximations” of possibly non-linear relationships between the variables.

⁴ For an explanation of the logic behind this method, see Kennedy (2008), chapter 10.

⁵ The procedure that makes use of those correlation coefficients is known as “seemingly unrelated regression equations’ method” (SUR), and is the one that we will use in our estimations in Section 5. For an explanation of this procedure, see Greene (2011), chapter 10.

⁶ For a good summary of this literature, see Altmann et al. (2012).

⁷ For an explanation of the procedure used in this maximization problem, and the properties implicit in its first-order conditions, see Sundaram (1996), chapter 4.

⁸ Note that in system (6)–(9) we make the implicit assumption that a₁ = 1. This is a convention that implies using that parameter as a numéraire in the whole system, which means that all the other benefits and costs are expressed in terms of that parameter.

⁹ Other authors have also found some evidence against a negative correlation hypothesis of language structure. In a study about Indo-European languages, for example, Silnitsky (2003) finds no significant correlation between phonological variables and grammatical variables.

¹⁰ In the description of the languages, we tried to use the most reliable source that was available to us. Most of those descriptions come from sources such as IPA (1999), Gary and Rubino (2001), Brown (2006), Comrie (2009), and the articles published by the Journal of the International Phonetic Association in its section known as “Illustrations of the IPA”.

¹¹ In fact, the only statistically significant coefficients of the table are the ones that correspond to the Stress/Tone correlation (p = 0.0029) and to the Consonants/Stress correlation (p = 0.024), whereas the one that corresponds to Vowels/Stress (p = 0.1317) barely fails to be statistically significant at a 10% probability level. The three positive coefficients, moreover, are not significant at all, since their probability values are equal to 0.2507, 0.2674 and 0.4543.

¹² All the regressions whose results are reported in this paper were performed using the software package EViews 3.5.

¹³ This model is good to interpret the phonological structure of most Romance languages, in which stress is generally contrastive. Those languages tend to have fewer consonant and vowel phonemes than the average, and have not developed tone distinctions.

¹⁴ That would be the general case for Niger-Congo languages, where stress contrasts are not common but tone distinctions are, together with relatively large numbers of consonants and vowels.

¹⁵ For a discussion concerning these conceptions, see Bickel (2013).