A Statistical Analysis of OSH III
by a Psychological Model
YOKOYAMA Shoichi
National Institute for
Japanese Language and Linguistics
(NINJAL)
1
Introduction
The first purpose of this study is to discuss a
psychological model for the mechanism
behind language behavior changes over
time.
The second purpose of this study is to
propose a statistical analysis to estimate
language behavior changes.
2
The proposed statistical analysis is a logistic
regression analysis.
A logistic regression analysis is able to
describe and predict language behavior
change, based on various temporal
parameters, such as the birth year of
participants and the year of survey for data
collection.
3
Applications of logistic regression analyses
are, indeed, found in sociolinguistic studies.
For example, Labov(1972) employed a
logistic regression analysis to analyze
empirical data in sociolinguistic studies.
However, few specific models have been
available for multiple variables, such as the
birth year and year of survey.
4
A psychological model of
language behavior change
The psychological model explains the
mechanism behind the observed language
behavior changes.
We are focusing on the mental lexicon
assuming a life long development of mental
abilities from a psychological perspective.
5
The birth year is related to the period of
language acquisition. The critical period for
language acquisition starts around 10 years
after birth year.
 Critical Period Acquisition: CPA
The year of survey is related to aging and
historical social trends.
 Life Long Acquisition: LLA
6
We propose a new model as follows:
CPA + LLA  Mental Lexicon  Change,
where CPA stands for effect of critical period
acquisition, and LLA for effect of life long
acquisition.
Then, we assume as follows:
CPA = a1×the birth year
LLA = a2×the year of survey
7
A statistical model of
longitudinal survey data
The statistical model in this study is
p = 1 / {1+exp [ − (a1 ∙ x1+a2 ∙ x2+b) ] },
where p stands for probability of choice of
two competing language behaviors, x1
stands for the birth year of the participants,
and x2 for the year of survey for data
collection.
8
We apply a logistic regression model to the
longitudinal survey data in Japan, OSH1, 2
and 3.
p = 1 / {1+exp [−(CPA＋LLA) ] }
= 1 / [1+exp (− CPA − LLA) ]
= 1 / [1+exp (−a1×the birth year
−a2×the year of survey
−b)]
9
p = 1 / [ 1+exp (−a1×the birth year
−a2×the year of survey
−b)]
The parameters for a1, a2, and b are
computed based on the data obtained from
the longitudinal survey.
For example;
p = 1 / [1+exp ( 0.0105×the birth year
+0.0467×the year of survey
−111.0888 ) ]
10
An analysis of a longitudinal survey data
in OSH1, 2 and 3
NIJLA chose Okazaki city in Aichi prefecture,
and conducted large-scale surveys in 1953,
1972 and 2008.
Each survey was carried out by random
sampling about N=400.
The same question was asked in each
survey.
11
We analyzed the data of attitudes on
whether or not one should use honorifics
towards the oldest or senior family members.
The result shows the probability with which
respondents said that honorifics should be
used.
12
0.5
Observed
Probability
0.4
1953
0.3
1972
0.2
0.1
0
1880
1900
1920
1940
1960
1980
2000
Year of the birth
Fig.1. The observed probability with which respondents
said that honorifics should be used towards the oldest or
senior family members at home in 1953 and 1972.
13
This data indicates that use of honorifics at
home has been decreasing.
This tendency can only be verified through a
real-time study framework.
14
Now, we apply a logistic regression model to
the longitudinal survey data in OSH1 and 2.
The prediction model is as follows:
p = 1 / [1+exp ( 0.0105×the birth year
+0.0467×the year of survey
−111.0888 ) ]
15
0.5
Observed
Probability
0.4
1953
0.3
1972
0.2
0.1
Predicted
0
1880
1900
1920
1940
2008
1960
1980
2000
Year of the birth
Fig.2. The predicted probability with which respondents
said that honorifics should be used towards the oldest or
senior family members at home.
16
Next, we show the data of OSH3 in 2008.
17
0.5
Probability
0.4
1953
0.3
1972
0.2
Observed
0.1
2008
Predicted
0
1880
1900
1920
1940
1960
1980
2000
Year of the birth
Fig.3. The observed probability with which respondents
said that honorifics should be used towards the oldest or
senior family members at home in 2008.
18
The predicted probabilities fit the 2008 data
for respondents in their 20’s and 30’s very
well.
These results confirm that use of the
honorifics at home has decreased over all.
However, many people use the honorifics at
home in the senior groups, i.e. more than 40
years old.
19
General Discussion
This discussion emphasizes the role of
memory, a psychological factor.
The psychological factor is dependent on
the relative frequencies of the language
usage to which language users are exposed.
20
We propose a new model as follows:
CPA + LLA  Mental Lexicon  Change,
where CPA stands for effect of critical period
acquisition, and LLA for effect of life long
acquisition.
Then, we assume as follows:
CPA = a1×the birth year
LLA = a2×the year of survey
21
It is well-known that age, gender, occupation,
and educational background affect language
variations and changes.
In contrast, this study proposes that the
mechanisms behind the language behavior
changes depend on life long cognitive and
psychological developments.
22
To be precise, the discussion in this study
argues that the most critical factor is the
relative strengths of competing language
knowledge in mental lexicon.
We think that memory of the more frequent
variant of two competing forms leaves a
stronger memory trace in the mental lexicon,
consequently guiding language users to
choose the stronger item.
23
The social frequency used in spoken and written
language in the given community makes changes
of CPA and LLA in the mental lexicon.
Exposure
frequency
Language
policy
CPA ＋ LLA
Social frequency
Preference
Familiarity
Mental lexicon
24
The mental lexicon is part of intra-personal
environment.
The mental lexicon is shaped by the usage
frequencies of linguistic features in society,
which in turn reflect the inter-personal
environment.
This tendency can only be verified through a
real-time study framework.
25
Conclusion
The model proposed in this study can be expressed
as follows:
Critical Period Acquisition + Life Long Acquisition
 Mental lexicon change
 Use of the honorifics at home has decreased
Equation of Use of the honorifics at home in OSH
p = 1 / [1+exp ( 0.0105×the birth year
+0.0467×the year of survey
−111.0888 ) ]
26
Thank you for your attention.
27
以下は参考資料
28
Equation(1) is a logistic regression analysis.
log [ p / (1 − p) ] = a1 ∙ x1 + a2 ∙ x2 + b
(1)
This equation can be transformed to
p = 1 / {1+exp [− (a1 ∙ x1+a2 ∙ x2+b)]}.
(2)
log is the logarithm of base e.
p / ( 1－p ) is called “odds”.
log [ p / (1 − p) ] is “logit”.
29
p = 1 / {1+exp [− (a1 ∙ x1+a2 ∙ x2+b)]}
(2)
Equation (2) yields p values, that is the
probability of occurrence of some event.
These p values may be compared to the data
obtained in OSH1, 2 and 3.
30
This study emphasizes the role of the
mental lexicon as a psychological factor.
This psychological factor is dependent on
the frequencies of the language usage to
which language users are exposed.
31
In addition, linear regression analyses are
not adequate for prediction, because they
can yield probabilities of less than zero,
which is mathematically invalid.
In contrast, logistic regression analyses
produce probabilities between zero and one.
This supports their validity for our purpose of
prediction.
32
log [ p / (1 − p) ] =
a1 ( the birth year )
+ a2 ( the year of survey )
+b
Logistic regression analysis is expressed
with logits on the left side, and multiple
regression models on the right side in the
equation.
33
Aitchison(1991) said that language changes
are often represented by S-shaped curves.
S-shaped curves of language change starts
with little and slow changes at the beginning,
fast and large changes in the middle, and
little and slow changes again at the end.
34
S-shaped curves are very similar to the
curves of Equation(2), which is a logistic
regression analysis.
p = 1 / {1+exp [− (a1 ∙ x1+a2 ∙ x2+b)]}
(2)
35