1What the method is for
Asking whether a dialect word is being lost, from a single cross-sectional survey.
To measure language change directly, one would survey the same population of speakers at times \(t_1\) and \(t_2\). This is a real-time study. As a design it is the most straightforward, but it requires waiting decades, during which respondents move away and die. As a matter of research design it is almost never feasible.
The apparent-time method substitutes a generational axis for the time axis. A single survey measures older and younger cohorts at once; the language of the older cohort is taken as an approximation of an earlier state, and that of the younger cohort as an approximation of the present or the future. The difference between cohorts is then interpreted as a difference in elapsed time.
Whether this move is legitimate is not settled by the observations. It lays a second interpretation — change over time — on top of a single observation of cohort difference, and in speaking of the direction of change from observational data it is a problem of causal inference. As Section 6 sets out, the limits of the method follow from exactly that.
2Origin
A framework William Labov built in order to catch a change in progress.
In 1963 Labov reported that the first element of the diphthongs /aɪ/ and /aʊ/ was shifting on Martha's Vineyard, Massachusetts. By dividing the island's residents by district, age group, occupation and ethnicity and examining the distribution of the variants, he argued that the recent history of this sound change could be reconstructed (Labov 1963). The idea of reading a distribution across age groups as a time axis begins here.
Labov went on to found variationist sociolinguistics as a field, through the 1966 study of sound change in New York City and the three volumes of Principles of Linguistic Change published between 1994 and 2010. The apparent-time method became its central instrument and is now in wide use in dialect research.
The claim that a change in progress can be observed
What the method presumes is a view in which language change does not advance uniformly through a population but advances in layers, the layers being generations. If a change has run to completion, the cohort difference disappears; if it has not begun, no cohort difference appears. On this reasoning, a cohort difference is observed only while a change is under way.
3Where the mathematics comes from
The method has no mathematics of its own. Mathematics enters on the side that measures the cohort difference.
The apparent-time method is less a statistical technique than a reinterpretation built into the survey design. Positing that a cohort difference may be read as a difference in time involves no formula at all. Mathematics becomes necessary only at the next stage: how that cohort difference is to be measured and tested.
In this research, the difference in usage rates between cohorts is defined as loss and gain, and those proportions are modelled by beta regression. The beta distribution, which handles proportions, belongs to the exponential family and is tied to a linear predictor within the generalised linear model framework. The mathematical roots therefore lie not on the side of the apparent-time method but on the side of the exponential family and the generalised linear model.
\(g_{sj}\) … the proportion of the older cohort (aged 60 and over) in settlement \(s\) who use item \(j\)
\(m_{sj}\) … the proportion of lower-secondary school pupils who use the same item
\(J\) … the number of items for which both cohorts have data
\(\max(\cdot,0)\) … counts only the decrease as loss and only the increase as gain
Why only the positive part is taken
Averaging the raw differences would let items that decreased and items that increased cancel out. Loss and gain can occur independently of one another, so the positive part of each is extracted separately. This definition reproduces the original aggregate values, with a Pearson correlation of \(r=0.999\).
4Definitions and assumptions
What has to be posited for the proxy to hold.
What is observed is a cohort difference; what is to be claimed is change over time. Linking the two requires the following assumptions.
- Stability of the individual grammar An individual's language is more or less fixed after a certain age and does not change greatly thereafter. It is this assumption that allows the language of the older cohort to be read as preserving an earlier state.
- No age-related alternation That the cohort difference reflects change rather than a norm of the form "that is how one speaks at that age". The phenomenon that breaks this assumption is called age-grading, and it is the subject of Section 6.
- Continuity of the population That the older and younger cohorts represent different moments of the same speech community. Where there has been large-scale in- or out-migration, a cohort difference reflects turnover of the population rather than change.
How the sample was constructed in this research
From a dialect survey conducted between 21 November and 20 December 2015 across three school districts in Maibara (Shiga Prefecture) and two in Sekigahara (Gifu Prefecture), 544 lower-secondary school pupils and 142 respondents aged 60 and over were used. The cohort aged 40 to 50 was excluded so that the contrast lay between the youngest and the oldest cohorts. "Older cohort" is defined by age (60 and over) and does not necessarily mean the grandparents of the participating pupils.
Non-independence within households cannot be ruled out
The survey was administered by area, and carries no information about which respondents belong to the same household. A grandparent and a grandchild living together may both have responded, in which case their languages are not two independent observations. This is stated explicitly as a limitation.
5How the method is used in this research
Loss, measured as a cohort difference, is regressed on the demographic conditions of each settlement.
- Designing the items Forty question concepts elicit 106 dialect variants, classified in advance into 45 Kansai/Ōmi forms, 31 Tokyo/standard forms, 26 Mino/Owari forms and 4 youth or neo-dialect items.
- Computing loss and gain These are computed per settlement by the definition in Section 3. The 25 settlements with data for both cohorts enter the analysis.
- Modelling Loss and gain are modelled with a beta distribution and a logit link, with standardised population growth rate, log pupil sample size and log older-cohort sample size as predictors. The five school districts enter as a random intercept.
- Estimation Estimation proceeds under weakly informative priors in brms and Stan: Normal(0,1) on the slopes, Normal(0,2) on the intercept, Gamma(0.1,0.1) on the precision \(\phi\).
- Defining the population growth rate The 2010 population of a settlement divided by its 2005 population. This is not a direct measurement of migration or of turnover among residents, but a proxy for recent population change.
Keeping what is observed separate from what is inferred
The population growth rate is an observation; the turnover of residents it is taken to signify is an inference. The research keeps the two explicitly apart in its wording, and uses the observed population growth as material for examining the assumption of population continuity as well.
6Limits — how age-grading is separated out
The possibility that a cohort difference is not change but an alternation tied to age.
The greatest weakness of the method is age-grading. Speakers use youthful forms when young and shift to more formal ones with age. In that case the same cohort is merely changing how it speaks as it ages, and the language of the community is not changing at all. A cross-sectional survey nonetheless records this as a cohort difference.
From the observations alone there is no way to tell whether a cohort difference is a change in progress or an alternation tied to age, because the two interpretations generate the same data. That is also why this method belongs under the perspective of causality.
Adding a middle cohort makes the two interpretations predict different shapes. If a change is advancing across generations, the effect moves monotonically in cohort order. Under an age-related alternation, the middle cohort may fall outside the two ends — an inverted-U shape, for instance.
How the separation was done in this research
A middle cohort of 211 respondents aged 30 to 59 was added, and an interaction between cohort and population growth was modelled across the 21 settlements for which all three cohorts were available (lme4, a binomial model with an observation-level random effect). The cohort-specific slopes on population growth are as follows.
| Cohort | Slope on growth | Standard error |
|---|---|---|
| Older (60 and over) | +0.049 | 0.170 |
| Middle (30–59) | −0.053 | 0.170 |
| Pupils | −0.184 | 0.168 |
Figures quoted from three_gen_summary.txt, the output of 23_three_gen_model.R. None of the slopes is individually significant.
How to read this — the ordering, not the individual significance
The slope falls monotonically from the older cohort through the middle cohort to the pupils: the higher the growth of a settlement, the lower the use of the vocabulary in question among younger speakers. This shape is consistent with a reading in which a change is advancing across generations, and is not easily explained by age-grading alone. The standard error of each estimate is about 0.17, however, and no individual slope is significant. The grounds for the claim lie in the ordering of the three points rather than in individual significance.
This is not a proof that age-grading has been ruled out
Monotonicity is consistent with a change in progress; it does not show that age-grading is absent. Both may be operating at once. Settling the question would require a real-time study, and it is precisely because that cannot be done that the apparent-time method is used — a circularity that sits at the centre of the method.
The research does not conceal this. The introduction states the adoption of apparent time alongside the reservation about age-grading, and the limitations section says so again. To acknowledge that the measure is a proxy, and then to test with other data the direction in which the proxy would break, is the most honest stance available towards this method.
7Sources and data
The language data come from a dialect survey conducted in 2015 in Maibara and Sekigahara by the citizens' group Habiro Net, in whose design Onohara took part. It collected 873 respondents, 4.27% of the population of the area. Land use is taken from the National Land Numerical Information of the Ministry of Land, Infrastructure, Transport and Tourism; population from the small-area tabulations of the 2010 Population Census (Statistics Bureau, Ministry of Internal Affairs and Communications); elevation from the Fundamental Geospatial Data of the Geospatial Information Authority of Japan. The analysis is laid out as a sequence of R scripts, arranged so that the original data files are never modified and are read only through working copies.
- Analysis scripts:
01_prep_data.R(data preparation),12_brms_loss.R(loss model),23_three_gen_model.R(three-cohort model), among others. - Position in the research lineage: a 2016 poster at the Geographic Information Systems Association of Japan on extralinguistic factors and vocabulary loss and gain, then the 2017–2018 analyses of population size and lexical diversity, leading to the present analysis.
References on the method
- Labov, W. (1963) The social motivation of a sound change. Word, 19(3), 273–309. doi:10.1080/00437956.1963.11659799
- Labov, W. (1966) The Social Stratification of English in New York City.
- Labov, W. (1994, 2001, 2010) Principles of Linguistic Change, Vols. 1–3.
- Ferrari, S. & Cribari-Neto, F. (2004) Beta regression for modelling rates and proportions. Journal of Applied Statistics, 31(7), 799–815.
Which perspective this method belongs to
The apparent-time method lays a second interpretation — change over time — on an observed cohort difference. Since the same observation could arise from age-grading, which of the two holds is not settled by the data, and assumptions about the stability of the individual grammar and the continuity of the population are required. A structure in which change can be spoken of only once assumptions have been made is Perspective 7 (causality) of the seven perspectives in equations itself. The sentence written there — that the independence of treatment assignment from the outcome is, in observational data, an assumption and not something that can be verified — applies to this method unchanged.
This page sets out a method Onohara uses in her own research, written for readers in the same field. Every figure is quoted from the output of the analysis scripts; no estimates or approximations have been supplied.
For how the methods sit relative to one another see the seven perspectives in equations; for which course session falls under which perspective see Methods & Mathematics.