1 A Multiple Logistic Curve Model for a Change in Language in Okazaki City YOKOYAMA Shoichi*, ASAHI Yoshiyuki* and SANADA Haruko** *The National Institute for Japanese Language **Saitama Gakuen University

2 1. Overview The purpose of this paper is (1) to propose a model to explain and estimate language changes, (2) to discuss a theoretical explanation for the mechanism behind language changes over time.

3 1. Overview The proposed model is a multiple logistic regression model to describe and predict language changes, with time in various forms, such as participants' ages and the time of data collection.

4 1. Overview The theoretical discussion explains the mechanism behind the observed language change phenomena from a psychological perspective, focusing on memory, an intra-personal variable.

5 2. S-shaped curve model applied to the longitudinal survey data The model proposed in this paper is as follows: log [ p / (1 − p) ] = a1 ∙ x1 + a2 ∙ x2 + b,(1) where p stands for the observed rate of selection of two competing language forms, x1 stands for the birth years of the participants, and x2 for the year of data collection. The values for a1, a2, and b were computed based on the data obtained from observation in 1953 and 1972.

6 2. S-shaped curve model applied to the longitudinal survey data Equation(1) is called a logistic regression model, log is the logarithm of base e. log [ p / (1 − p) ] = a1 ∙ x1 + a2 ∙ x2 + b(1) This paper refers to p / ( 1 － p ) as odds and log [ p / (1 − p) ] as logit. Logistic regression models, in other words, are expressed with logits on the left side and multiple regression models on the right side in the equations.

7 2. S-shaped curve model applied to the longitudinal survey data Equation (1) can be transformed to p = 1 / { 1 + exp [− ( a1 ∙ x1 + a2 ∙ x2 + b ) ] }(2) The model was applied to the longitudinal survey data on honorifics in Japanese, and computation with Equation (2) yielded p values, which were compared to the data obtained in 1953 and 1972.

8 2. S-shaped curve model applied to the longitudinal survey data NIJLA chose Okazaki city in Aichi Prefecture, and conducted large-scale surveys in 1953, 1972 and Every surveys carried out by random sampling about N=400. We analyzed the data of attitudes on whether or not one should use honorifics towards the oldest or senior family members.

9 2. S-shaped curve model applied to the longitudinal survey data The same question was asked in both the 1953, 1972 and 2006 surveys. The result shows the probability which respondents said that honorifics should be used. This result indicates that non-use of the honorifics at home has become widespread; this tendency can be only verified through a real-time study framework.

10 Figure 1. The probability which respondents said that honorifics should be used towards the oldest or senior family members at home.

11 2. S-shaped curve model applied to the longitudinal survey data S-shaped curves on which the model is based conceptually are known to depict language changes over time. Aitchison(1991) said that language changes are often represented by S-shaped curves, which starts with little and slow changes at the beginning, fast and vast changes in the middle, and little and slow changes again at the end.

12 2. S-shaped curve model applied to the longitudinal survey data Application of logistic regression analyses are, indeed, found in sociolinguistic studies as well. Labov (1972), for example, employed a logistic regression model to analyze empirical data. However, few specific models have been available with multiple variables, such as ages of the participants as well as the time of data collection.

13 2. S-shaped curve model applied to the longitudinal survey data In addition, linear regression models were not adequate for prediction, because they yield less than zero values for probabilities, which is mathematically invalid. In contrast, logistic regression models produce probability values between zero and one, supporting their validity for the purpose of prediction.

14 3. Psychological discussion of the mechanism of the language change The discussion emphasizes the role of memory, a psychological variable. This psychological variable is dependent on the relative frequencies of the language forms to which language users are exposed.

15 3. Psychological discussion of the mechanism of the language change The birth years decide the language acquisition term.  Acquisition term memory The year of data collection is related to social situation and ageing effect.  Life span memory

16 3. Psychological discussion of the mechanism of the language change The model proposed in this paper can be interpreted in as follows: log [ p / (1 − p) ] = a1 ∙ x1 + a2 ∙ x2 + b,(1) where x1 stands for strength of acquisition term memory, and x2 for strength of life span memory.

17 3. Psychological discussion of the mechanism of the language change It is well-known that age, gender, occupation, and educational background, i.e. socio-cultural variables, affect language variations and changes. In contrast, this paper asserts that the mechanisms behind the S-shaped curves of language changes produced by the model are dependent on an intra-personal psychological variable.

18 3. Psychological discussion of the mechanism of the language change To be precise, the discussion in the paper argues that the most critical variable is the relative strengths of competing language forms in memory. The paper argues that memory of the more frequent variation of two competing forms, leaves a stronger memory trace in the human brain, consequently guiding language users to choose the stronger item.

19 3. Psychological discussion of the mechanism of the language change In other words, it argues that changes of memory, i.e. intra-personal psychological phenomena, reflect frequencies of the given forms used in spoken and written communication, an inter-personal factor, in the given community.

20 3. Psychological discussion of the mechanism of the language change Thus the framework proposes a reciprocal relationship among frequencies of language forms, time-related variables, and memory, connecting the linguistic, socio-cultural, and human psychological factors.

21 Circular model The role and predictive power of frequency in language use can be explained by a circular model as illustrated in this Figure.

22 Language policies and social frequency represent the social phenomena observable in the given community. The two-way arrow represents mutual contribution between language policy and social frequency.

23 Social frequency contributes to exposure frequency in a one-way manner, as represented by the one-way arrow. Exposure frequency is the degree of exposure, at which individual language users are exposed to the given language forms in the given community.

24 Exposure frequency mediates the contribution of the social frequency to individuals’ mental lexicon. In other words, it is the gateway for social phenomena to get integrated into the individuals’ psychology.

25 Individual’s psychology is typically represented by mental lexicon in the figure, which includes familiarity, preference, and utility.

26 Positive behavior of mental lexicon, increased familiarity for example, leads to increased reproduction of the given language forms in the series of chain reaction as illustrated in this Figure, consequently promoting the social frequency even more.

27 Such a circular relationship provides social frequency with increasingly stronger impacts in the chained and circular phenomena.

28 The increasingly stronger impacts of social frequency allow a heavier and increasingly more reliable role of frequency data, which is amplified in a non-linear fashion due to the circular flow of the phenomena involving multiple variables.

29 4. Conclusion The model proposed in this paper can be expressed in as follows: Acquisition term memory + Life span memory → Language change The birth years + The year of data collection → Prediction for Language change

30 Thank you for your attention.