Influencing Factors on the Health of Chinese Elderly

An Analysis using Structural Equation Models

Fan Pan

Supervisor: Fan Yang-Wallentin

Department of Statistics, Uppsala University

June 2012

Abstract

Population aging has been an increasing in many societies during the last century, and

especially in China this issue has become one of the most urgent social phenomenon

in the recent twenty years. Meanwhile, being healthy matters to the senior population

the most. The main purpose of this paper is to investigate how to measure Chinese

elderly health condition, and what the main factors are influencing their health. The

data of this paper is from the China Health and Retirement Longitudinal Study

(CHARLS). A structural equation model(SEM) was established to verify the

relationship between different influencing factors and the elderly health. The latent

variables in this model were pre-studied by both exploratory factor analysis and

confirmatory factor analysis. The conclusion based on this data is elderly health can

be measured in four aspects physical condition, emotional condition, body function

and pain. The significant influencing effects of each aspects of health are time sharing,

exercise, family environment and lifestyle.

Key words: Structural Equation Models, Population Aging, Elderly Health in China

Acknowledgment

The author of this thesis would like to thank the supervisor Fan Yang-Wallentin for

her guidance and support during the process of writing this thesis and thank the fellow

students in the seminar group for their valuable feedback.

The author is also thankful to the China Health and Retirement Longitudinal Study

Program (CHARLS) for their free share of the dataset in this research.

Gratitude to my friends and families for their companionship and encouragement

during this period.

Fan Pan

Department of Statistics

Uppsala University

June 2012

Content

1 Introduction…………………………………...………………........................…1

1.1 Background…………………………………………………………………..1 1.2 Purpose…………….…………………………………………………………1

2 Literature Review………..……………………………………………………..2

2.1 Population Aging.…………………………………………………………..2 2.2 Health of the Elderly.…………………………………………………………3

3 Methodology…………………………………………………………………...4

3.1 Exploratory Factor Analysis Model………………………………………….4 3.2 Confirmatory Factor Analysis Model……………………………………….5 3.3 Structural Equation Model..…………………………………………….........5 3.4 Estimation Methods………………………………………………………….6

3.4.1 Maximum Likelihood……………………………………………....6 3.4.2 Robust Maximum Likelihood………………………………………7

3.5 Goodness of Fit………………………………………………………………7

4 Data……………………………………………………………………………….9

4.1 Data Description..…………………………………………………………….9 4.2 Data Management…………………………………………………………10

4.2.1 Data Cleaning………………………………………………………10 4.2.2 Data Organization……………………………………………………10

4.3 Treatment of Missing Values………………………………………………..12 4.4 Latent Variables Generation………………………………………………...13

5 Model……………………………………………………………………………17

5.1 Model Specification………………………………………………………...17 5.2 Implied Covariance Matrix…………………………………………………19 5.3 Identification………………………………………………………………..20

6 Results………………………………………………………………………...20

6.1 Result of the Initial Model………………………………………………….20 6.2 Model Modification…………………………………………………………21 6.3 Result of the Modified Model………………………………………………23

7 Conclusion…………………………………………………………………….24

Reference…………………………………………………………………………..25

Appendix…………………………………………………………………………..27

A. Variable instructions………………………………………………………...27 B. Output of SPSS for EFA in Section 4.4…………………………………......33 C. List of 44 Observed Variables………..…………………………………......35 D. LISREL Code………………………………………………………………..37

1 Confirmatory Factor Analysis with RML method……………………….37 2 Modified SEM with RML method………………………………………38

E. Estimation of the Modified Measurement Model….………………………..39

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1 Introduction

1.1 Background Population aging is an issue taking place in many societies and countries all over the world. In China, this problem is particularly prominent for several reasons (Ma, 2010). The first one is the family planning controls, which caused birth rate decrease rapidly, and the numbers of children in every family is smaller than preview years. Another main reason is that people nowadays can be alive longer than people before because of the improvement of living standards. Based on the demographic part of China Statistical Yearbook 2011, people in this age group which is older than 65 years old makes up 8.9% of national population in the year 2011, which is 7% in 2000. This situation will cause many economical and social problems. There are many researches about the effects of population aging on many different aspects of the society and the economics. Among all these topics, the elderly health is a issue worth to have public attention, cause as a common knowledge, the old people need more medical care than young people. In addition to the factor economic conditions, psychological health and physical health are another two main factors influencing the quality of the elderly life in China. (Tao, Liu etc, 1997).

1.2 Purpose Based on the background of population aging in China, to figure out what are the sociological influencing factors for the elderly health in China and how to measure their health conditions and what is the relationship between them become a very important and valuable issue, which became the main purpose of this paper. We started with the reviews of previous literature about population aging and researches on people’s health in the related field are reviewed. In the following section, the principles about methods, models, and testing index used in this paper were introduced. Structural Equation Model (SEM) technique is adapted to this analysis, which is a very effective model to study the relationships between latent variables using covariate information from corresponding observed variables. Section 4 describes data management in detail. The data used in this research is from China Health and Retirement Longitudinal Study (CHARLS). In the following section, the main model setup is discussed. The analysis results of both the original and modified models are presented in Section 6. The final conclusions and discussions are given in the last section. A number of theoretical analysis about geriatrics has been done. In this research project, we used the quantitative statistical methods to determine the relationships

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among a set social factors and medical factors and make it believable and reasonable as a theoretical basis for further analysis in this field. Once this research is done, it will give suggestions to other researches in this field, and to make decisions about what improvement and preparation work can be done to the whole society together with the prediction about population aging. And also, based on this, we can use the social resources more effective and efficient to improve the health level of the elderly. As their population proportion is increasing, it is really necessary for the public to do more things to keeping their health, which is good for keeping balance and harmony of the whole society in China.

2 Literature Review

2.1 Population Aging The first definition of aging population was given by United Nation (1956), which is: in a nation 1. The percentage of people who is or older than 65 years old is more than 7%; 2. The percentage of people who is or younger than 14 years old is less than 30%; 3. The ratio of the old and the young is more than 30%; 4. The median of population age is older than 30 years old. After that the population aging became a worldwide trend with a rapid speed. The bound age of the old was changed to 60 years old, during United Nations Vienna International Plan of Action on Ageing (1982). The international standard of a aging society generally used today is: The percentage of people who is or older than 65 years old is more than 7%, or the percentage of people who is or older than 60 years old is more than 10%. According to the standard giving above, China stepped into aging society in 2000. The Oxford Institute of Population Aging has a conclusion that population aging has slowed considerably in Europe and will have the greatest future impact in Asia. As a result of trends in both fertility and longevity, the elderly share of China's population has been increasing, and those aged 60 and over are set to form a rapidly growing share of the population. By 2050, it is forecasted that the population aged 60+ and 80+ will reach 440 million and 101 million, respectively.(Judith Banister, 2010) In order to face this challenging problem, World Health Organization proposed a new concept - Active Aging in Active Ageing: A Policy Framework (2002). Paying more attention to the life quality of old people, prolonging their life, and keeping their healthy and active are becoming a important task for the whole world today.

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Figure 1: The Growing Trend of Percentage of Elderly in Chinese Population

(Judith Banister, 2010)

2.2 Health of the Elderly According to previous research about the life quality of elderly people in China (Tao, Liu, Chen etc., 1997), keeping healthy is a really significant effect of weather the old will satisfied with their life quality. In this research, the main method was Logistic multiple regression, and it was used to determine the effects of life quality of the elderly. Among the 11 assumed effects, Economic condition, Psychological health and Physical health were found to be the three main factors of effecting the old people’s healthy life quality base on the data from Beijing. In Li, Chen and Li’s research (2006) about the life satisfaction of elderly in Beijing, they also concluded that health is a very effective factor influencing the satisfaction of the elderly life by using Path Analysis. Wenger (1984) has presented that a health quality of life containing three aspects, in which function condition means different abilities to normal life, work and emotion, feeling condition means self evaluation about the body functions and symptom means pains or other uncomfortable feeling of one’s body. Zhang (2002) used SEM to study the relationships between Quality of Healthy Life (QHL), Quality of Objective Environment (QOE) and Psychological Well-Being (PWB). In Keller, Ware and their fellow researchers’ paper (1998), the SEM method was used and a second ordered confirmatory factor analysis model was performed to verify their hypothesis about health status indicators with data from ten countries. According to this research, in the first order there are factors Physical Functioning, Role-Physical, Bodily Pain, General Health, Vitality, Social Functioning, Role-Emotional and Mental Health, and based on them, the second order factors are Physical Functioning, General Well-Being and Mental Functioning. The result of Jia’s research (2004) shows that the information about demographic has a close relation to the health quality of life, and diseases, medical care, hobbies and

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bad lifestyle are also factors influencing the quality of life. Another investigation (Xiao, 2009) which is about the health literacy status and its influencing factors of urban and rural residents in China used regression method to show that for urban residents, age, family members, occupation, gender, income and education level are significant influencing factors, and for rural residents, occupation and income are significant influencing factors.

3 Methodology

In this research, exploratory factor analysis and confirmatory factor analysis were used to dealing with the data to generate and test the latent variables together with theoretical information in previous researches, before the hypothesis SEM full model set. In SEM, latent variables are the variables of interest which cannot be observed directly. Therefore in this section, Exploratory Factor Analysis Model, Confirmatory Factor Analysis Model, and Structural Equation Model are introduced here. The estimation methods used in these models and the principles of the important Goodness of fit in SEM are also discussed in this section.

3.1 Exploratory Factor Analysis Model Exploratory Factor Analysis (EFA) Model is a kind of Factor Analysis without restrictions about the relationships between variables, and it is the basis of Confirmatory Factor Analysis. It is often used in the situations that the data with many variables whose dimensions need to be reduced but there is still not any known grouping restrictions and information of these variables. According to Richard A. Johnson (2007), Exploratory Factor Model, in matrix form, can be written as:

x = μ + LF +ε (1)

where, i is the mean of variable i, i is ith specific factor, jF is jth common factor and ijl is the loading of the ith variable on the jth factor. The unobservable random vectors F and ε satisfy the following conditions:

and are independent,( ) 0, ( ) ,( ) 0, ( ) , where is a diagonal matrix.

E CovE Cov

F εF F Iε ε ψ ψ

The factor loading L and the covariance of specific factor ψ can be estimated by equation (2) and (3).

( )Cov X LL'+ ψ (2) ( )Cov X,F L (3)

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3.2 Confirmatory Factor Analysis Model Confirmatory Factor Analysis (CFA) Model is a kind of verification for some structure already exist which shows how large set of observed variables grouped into fewer numbers of factors. It is often used following the exploratory factor analysis model, and it is also a common type of SEM. According to Luo’s summary and study about CFA (2011), a typical CFA model has the form:

xx = Λ ξ +δ. (4)

where x is the vector of observed variables, ξ is the vector of factors which can also be treated as latent variables, δ is the vector of the unique variables assumed uncorrelated, xΛ is the matrix of factor loadings, for in CFA, one observed variable can only put into one factor, thus there is only one non-zero element is every row of the factor loading matrix. The assumptions here are:

E( ) = 0 E( ) = 0, Corr( , ) = 0. ，

Let Φ and δΘ be the covariance matrix of ξ and δ , where δΘ is a diagonal matrix. From equation (4), the relationship can be figured out below:

cov( ) x x x δx = Σ(Λ , Φ) = Λ ΦΛ '+Θ (5)

The factor loadings can be estimated by suitable estimation method using sample covariance to asymptotic population covariance of x . The significant relationships of a latent variable and a set of observed variables will be tested using t-test.

3.3 Structural Equation Model Structural Equation Model (SEM) models the causal relationships between latent variables. The model can be decomposed as two parts. One is Structural Model which shows the causal relationship between latent variables. The other one is Measurement Model which connects the observed variables and the latent variable. Referenced by Yi (2008), the general form of SEM can be written as:

Structural Model: η = Bη Γξ +ζ (6)

Measurement Model: x

y

x = Λ ξ + δy = Λ η + ε

(7)

where

x y1 n 1 ncov( ), cov( ), diag[var( ) , ... , var( )], diag[var( ) , ... , var( )] δ εΦ ξ Ψ ζ Θ Θ

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The free parameters in this model is: x y x yθ' Γ,Φ,Ψ,Λ ,Λ ,Θ ,Θ

The assumptions in this model are: E( ) = 0, E( ) = 0, E( ) = 0, E( ) = 0, E( ) = 0, Corr( ) = 0, Corr( ) = 0,Corr( ) = 0, Corr( ) = 0,Corr( ) = 0, Corr( ) = 0.

ξ η ζ ε δε,ξ ε, ηδ,ξ δ, ηε,δ ξ,ζ

In the general SEM, estimation of parameters is based on the approximation from Σto ( )Σ θ , in which Σ is population covariance matrix of observed variables and we use sample covariance matrix of observed variables S to estimate it, ( )Σ θ is covariance matrix of the model with parameter θ . Population covariance matrix should equals to model covariance if the definition of the model is true. So the distance between S and ( )Σ θ is closer, the fit of model is better. Fit function can be used to measure the proximity of them two, and it can be expressed as F( , ( ))S Σ θ . Fit function is selected according to different estimation method used in the model which will talked about in the next part of this section, and different results will be presented.

3.4 Estimation Methods

3.4.1 Maximum Likelihood Referenced by the paper of Yang-Wallentin etc.(2010), the fit function of maximum likelihood estimation used in SEM is:

log | ( ) | log | | ( )MLF tr p q -1Σ θ SΣ (θ) S (8)

where θ is the free parameters in the model, ( )Σ θ is covariance matrix of the model with parameter θ , S is the sample covariance of variables, p and q are numbers of variables. In cases with large sample size, MLF is smaller, when ( )Σ θ and S are closer or

tr -1SΣ (θ) and p q are closer. The estimated parameter θ̂ which makes MLF

the smallest is called the maximum likelihood estimate of θ . Maximum likelihood estimation have several properties. In ML, θ̂ is an unbiased, valid and consensus estimate of θ . The distribution of data approximate normal distribution which makes it possible to do significant testing of the parameters. The estimates will not change following different scales of variables in ML, so the estimate will be the same no matter if the estimation is based on covariance matrix or correlation matrix. ML method should be used under three assumptions. Matrices of ( )Σ θ and S must be positive definite, and values of their determinants must be positive. In order to get the estimate, 1( )Σ θ must be exist. The observed variables must have a multi-normal

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distribution, otherwise the result of estimation will be biased and the standard error may be wrong. Although ML is a very robust and widely used estimation method, in most reality cases, it is really hard to get a perfect multi-normal distributed data. If the multivariate normal assumption is violated, the standard errors and Chi-square will be wrong estimated. To correct these, the robust maximum likelihood estimation can be applied.

3.4.2 Robust Maximum Likelihood Refer to the paper of Yang-Wallentin etc. (2010), the fit function of RML Method in equation of matrix form:

ˆ ˆRMLF -1 -1(s -σ)'D'(Σ Σ )D(s -σ) (9)

Where s is a 1s vector consisting of the non-duplicated elements of S, σ is the vector of corresponding elements of ( )Σ θ . Here Σ̂ is updated in every iteration by new parameters generated in the last iterated estimation. is the notation of Kronecker product, whose definition is (Magnus and Neudcker, 1999) - Let A be an m n matrix and B a p q matrix. The mp nq matrix defined by

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1

...... ...

...

n

m mn

a a

a a

B B

B B is called the Kronecker product of A and B and written A B . D

is the duplicated matrix used to transform s to vector error correction of S. According to Magnus and Neudecker’s book (1999), let A is a n n symmetric, then vec A means the 2 1n vector with all the elements from matrix A, v(A) means the

( 1) / 2 1n n vector with only the supradiagonal elements of matrix A. Then the duplicated matrix D has the function to change v(A) to vec A, which is to say: D v(A) = vec A, where D is called the duplicated matrix of A. The Robust Maximum Likelihood will valid the assumptions about multi-normal distribution of the data when using normal Maximum Likelihood estimation by using asymptotic covariance matrix.

3.5 Goodness of Fit In this paper, five important indices were used to check the goodness of fit of CFA model, the hypothesis SEM and the modified SEM . They are: Chi-square:

Chi-square value of test used in RML in this research is Satorra and Bentler (1988) SB statistics:

2 ˆ ˆ( / )( 1)df h N -1c c c c(s -σ)'Δ (Δ 'VΔ ) Δ '(s -σ) (10)

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Where df is the degrees of freedom, N is the sample size, s is a 1s vector consisting of the non-duplicated elements of S, σ̂ is the vector of corresponding elements of ˆ( )Σ θ . Here [ ]h tr -1 -1 -1

c c c c(Δ 'V Δ ) (Δ 'W Δ ) , V is the weight matrix, W is the asymptotic covariance matrix, and cΔ is an orthogonal complement to Δ which equals / ρ θ , so that 'cΔ Δ = 0 . (Yang-Wallentin etc., 2010)

RMSEA (Root Mean Square Error of Approximation):

ˆmax ( [ ] ) /( 1),0)RMSEA

F df N

df

S, Σ(θ) (11)

Where N is the sample size, ˆ[ ]F S, Σ(θ) is value of the estimation fit function with estimated parameters, and df is the number of free parameters.

NFI (Normed Fit Index):

NFI 1

i

FF

(12)

Where F is the minimum value of the fit function for the estimated model and Fi is the minimum value of the fit function for the independent model.

CFI (Comparative Fit Index):

CFI 1i

(13)

Where max( ,0)nF df , and max( , ,0)i i inF df nF df

Among these indices, the value of Chi-square is supposed to have a asymptotic Chi-square distribution with (q(q+1)/2-k) degrees of freedom. So if the model fits well, there should be a non-significant p-value of this testing. For RMSEA, <0.05 means the model fits very well, between 0.05 and 0.08 means it fits approximately, and the model cannot be accept if the value larger than 0.1. For NFI and CFI, if the value is larger than 0.90, the model fits well. AIC (Akaike Information Criterion) is used to compare the goodness of fit between different models, and the smaller the better.

ˆAIC ( 1) [ ] 2N F K S,Σ(θ) (14)

Where N is the sample size, ˆ[ ]F S, Σ(θ) is value of the estimation fit function with estimated parameters, and K is the number of free parameters in the model.

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4 Data

In the previous chapter, we have already mentioned that the data used in this study is from China Health and Retirement Longitudinal Study (CHARLS), which is conducted by the National School of Development at Peking University. CHARLS is part of worldwide longitudinal aging surveys. CHARLS aims to set up a high quality, nationally representative and publicly available micro-database that provides a wide range of information about the households of the elderly and also individual information on the elderly respondents and their spouses. (CHARLS, Home, 2009)

4.1 Data Description There are several reasons to choose this data. The most important one is that this program contains different aspects about people’s life and their health. Almost all the information we need here can be found. Other information not used this time may be used in the next time to do related subjects, and the same database will make different researches easily connected with each other. Secondly, this program plan to build this database as a longitudinal data, and continuous standard surveys will be held and data will be put in together, which makes it a potential database for researchers to do further and long-lasting studies in related field. Thirdly, this survey contains data from different various different provinces and even different communities in China. This makes the study of comparative analysis possible based on this data. The last, this program started in 2007, and up to now, only the first round survey data available. So it is in its start-up period, and suggestions can be gathered to improve the whole program, and make it more completely and can be used more effectively and efficiently together with other researchers. The method of sampling is random stratified sampling by probability proportional to size in this survey. Sample used in our research is the pilot sample from Zhejiang and Gansu provinces in 2008 (CHARLS, Sample, 2009). The whole survey includes seven parts: (a) Demographic Background, (b) Family, (c) Health Status and Functioning, (d) Health Care and Insurance, (e) Work, Retirement and Pension, (f, g) Household and Individual Income, Expenditure and Assets, and (h) Interviewer Observation(CHARLS, Home, 2009). Based on the theoretical basis of previous research and the main reason to choose this data is to do study olds’ health and find the factors that affect it. But after first scanning of the whole data, the format of questions from d, e, f, g part is not so suitable for this study and these parts of data are seriously incomplete, almost 70% of the data are missing. In this research, the aim is to test whether there are factors influence the elderly health in China instead of finding all the influencing factors. The author choose to use relative and useable questions from a, b, c parts of the huge questionnaires.

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After the first round wide-selection based on common sense knowledge collected from our daily life and knowledge gathered after literature reviewing, 84 questions were selected and the sample size is 2685, in which 1425 is from Zhejiang Province and 1260 is from Gansu Province.

4.2 Data Management After select the questions that can be used as valid data in our research, we need to change the data into a pattern which is useable in numerical calculation, define variables’ type and reorganize them which is suitable and the distribution fulfills the assumed model. Therefore we need to clean and organize the data by the help of descriptive statistics before numerical statistics.

4.2.1 Data Cleaning In this section, four tasks have been done. Since the selected data were recorded in different types of marks. The first task is to translate all the marks into one standard type. Thus we decided to change all the questions from different categories into numbers. The second task is to combine all the 0-1variables related to the same questions to a categorical variable. Moreover, all the multiple-choice questions were recorded as several 0-1 variables related to each options, which is not convenient to be analyzed. The third task is to filter the data. Because the program recorded all individuals who are older than 45, according to the definition of population aging, the focus group of people are those who are older than 60, therefore there was a need to delete the individuals who are younger than 60 years old. The forth task is individuals deletion. The data from selected questions in which the blank responses were more than 50% were deleted. After this data cleaning step, the data could be put to the software LISREL to data screening.

4.2.2 Data Organization In this part, five tasks have been done. The first task is to put similar questions together and gather their information to generate a new variable.

For example: In the original questionnaire, question CA060 is Have you ever chewed tobacco, smoked a pipe, smoked self-rolled cigarettes or smoked cigarettes/cigars? and question CA062 is if you chose yes in CA060, Do you still have the habit or have you totally quit? The record for both CA060 and CA062 are 0-1 variable. If someone chose 0 in CA060 which means he haven’t ever smoked before, he didn’t need to answer CA062 anymore. It caused many blanks in question CA062. In order to solve this problem, we need to gather two questions together and generate a new variable with 1, 2 and 3 categories. 1 means

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someone hasn’t smoked ever, 2 means someone has smoked but now quit and 3 means someone still smokes.

There are plenty of these kinds of problems in the data, and the details about every variables transformation are shown in Table 10, Appendix A. The second task is to define the variables’ type in LISREL. Among the 73 variables already generated in the previous task, 6 are ages, education years, cigarettes per day, family income, health expenditures and medical expenditures are defined as continuous variables, all the other variables are defined as ordinal variables. The third task is to check and adjust the scale of each variable. The data will be use to fit a SEM which is a model need to gather information from covariance matrix of these variables. The ordinal variables are safe in this task, the scale of one of these 6 continuous variables need to be changed. The measurement unit of income conversed from yuan to thousand yuan. The forth task is to select variables based on the numbers of missing values. The data screening reveals that the numbers of missing values for every variable. In this step, 7 variables are deleted, because there are so many missing values that these variables cannot make sense in the whole research. The fifth task is to make sure that the selected variables are significance in this study based on their distribution. If not, then transfer them, or delete them if they are hard to transfer, and information contained in these variables can also be explained by other significant variables.

For example: Before the transformation, the distributions of 4 different variables which are from the output of data screening in LISREL are:

In these variables, some categories’ frequencies are almost zero, and this kind of distribution will provide little significant contribution to the whole model. After putting the information above together into a

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new variable, the distribution will be changed to:

which is much better than the previous distributions. Part of details about transformation in this task is shown in Table 10, Appendix A. After the second round data processing, which is data cleaning and data organizing, the data contain 48 variables, in which 4 are continuous variables and 44 are ordinal variables. The sample size is 2285, in which 1248 are from Zhejiang Province and 1037 are from Gansu Province.

4.3 Treatment of Missing Values After section 4.2, the data processed can be directly used by the software to do statistical analysis. And before the section of model fitting and modification, we need to use some methods to build a new model which is structured as a SEM. According to the theory, we need to use these observed 48 variables to explain some latent variables, and figure out the relationships between them. Before this, we only know that we need to measure health, so we need to find out what affect people’s health. During this section, we need to figure out how many latent variables can be put in the model based on the 48 observed variables, what are they, how to explain every latent variables, what are used to measure health, what are the effects, and what is the relationship between health and those effects base on the CHARLS data. Actually, in the previous two steps of data management, we have already deleted both cases and variables which have a lot of missing values. In this part, firstly, we put the data in LISREL and do data screening to see the distribution of missing values which is summarized in Table 1. Considering we have a really big sample size 2285 and have 48 variables, it is possible for us to do imputation to fill the missing values in the data. So we do multiple imputation using EM algorithm method in LISREL and all the missing values are retrieved. EM algorithm has been widely used as a kind of iterative computation of maximum likelihood estimation when the data is incomplete. This process has two steps, which are expectation step (E-step) and maximization step (M-step). The E-step performs the conditional expectation of the missing values based on the known parameters and data distributions and then uses them to replace the missing values. The M-step performs the ML estimation of the parameters based on the new data. During the whole process, the two steps repeat until the data converge. (Dempster, 1977).

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Table 1: Distribution of Missing Value

Sample Size is 2285

4.4 Latent Variables Generation As mentioned in the methodology section, before the model is hypothesized, latent variables need to be generated and tested for significance. Firstly, we do exploratory factor analysis to the 48 variables and drop out variables which give little information in factor analysis and are not significant in factor analysis. This time we use program SPSS. The maximum likelihood method is used to generate factors, and the maximum variance method is used to rotate the matrix and make the factors more explainable. During the process of factor analysis, the number of factors is growing from 1, in order to choose the best formation of factors.

Table 2: Test for Factor Analysis with 48 variables

No.M.V. 0 1 2 3 4 5 6 7 8No.Cases 1508 311 58 15 3 16 1 1 5No.M.V. 9 10 11 12 13 14 15 16 17No.Cases 231 73 28 11 10 11 1 1 1

Distribution of Missing Values Total Sample Size = 2285

Variable No.M.V. Variable No.M.V. Variable No.M.V.A002 1 CA074 4 CA032 5A023 1 CA076 1 CA037 0BC001 44 FE009_f 68 CA040 1BD001 50 FE009_g 68 CB000 0BD011 291 CA001 6 CB003 0CA050 11 CA079 2 CB004 11C052A 5 CA003 4 CB007 0C052B 3 CA004 8 CC004 366CA052C 3 CA005 2 CC009 374CA057_1 0 CA006 2 CC010 376CA057_2 0 CA007 0 CC011 380CA057_3 0 CA010_1 0 CC012 375CA059 0 CA010_2 0 CC014 374CA060 1 CA010_3 1 CC015 374CA064 224 CA010_4 1 CC017 377CA072 1 CA031 5 CC018 377

Number of Missing Values per Variable

Enough Sample Kaiser-Meyer-Olkin Measure 0.884Test of Bartlett 27505.457df 1128Sig. 0.000

Test of KMO and Bartlett

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From the output of the test for CFA by SPSS in Table 2, we could see that the measure of Kaiser-Meyer-Olkin (KMO) is 0.884. KMO is value between 0 and 1, it measures the relevance between variables. It means that the relevance is stronger when the KMO value is closer to 1, and the data is more suitable to do factor analysis. According to the standard of KMO, above 0.9 is very suitable to a factor analysis and 0.8 is suitable. At the same time, the test value of Barlett’s is 27505.457, whose significant testing-value is 0.000, which also represents that it is meaningful to do factor analysis. Above all, the Factor Analysis has been done in this data is very effective. According to Table 11 in Appendix B-1, there are another 4 variables which are marked in Table 11 can be deleted, because their absolute values of variance of common variance are less than 0.1 which shows they do little contribution to the whole analysis. They are CA050 – “How would you evaluate your health during childhood, up to and including age 15?”, CA059 – “How many meals do you normally eat every day?”, EF009_f – “What is the proportion of health and fitness expenditures in your family annual cost besides food?”, CA010_3 – “Do you know you have Emotional, nervous, psychiatric problem or Memory-related disease?”. After this work, 44 observed variables are selected, and the sample size does not change during this process. Secondly, we need to do exploratory factor analysis again with these 44 variables repeatedly. Try to explain the formatted factors every time and find a suitable number of factors which can make the model explained reasonable.

Table 3: Test for Factor Analysis with 44 variables

We use the selected 44 variables data to do exploratory factor analysis again in SPSS, the result of the test is shown in Table3. The measure of KMO this time is 0.885 which shows that after deleting 4 variables, the new data will be more valid in factor analysis. From Table 4, we see that a 12-factor model can explain 55.839% information of the original data. Models with factors more than 12 are weak in reducing dimensions here in our research. We did factor analysis in SPSS based on fixed number of factors to see the best factor constitution and find a suitable number of factors with explainable factors. Models with 12, 11, 10, and 9 factors have been done one by one in SPSS, and the 9-factor model has the best classification of the 44 variables and the 9 factors can be easily defined and definite. The details of the estimators of the 9-factor model are attached in Table 12 in Appendix B.

Enough Sample Kaiser-Meyer-Olkin Measure 0.885Test of Bartlett 27011.287df 946Sig. 0.000

Test of KMO and Bartlett

15

Table 4: Sum of Variance Explained in Factor Analysis

The 9 factors of the suggested model by SPSS are shown in table 5. In order to make the readers easy to follow, we use key words to show what these observed variable are in Table 5.

Table 5: Suggested EFA model and Brief Description of Variables

The modification of the 9 factors needs to be done to make them explainable with the

Sum Explain % Accumulation Sum Explain % Accumulation Sum Explain % Accumulation

1 7.862 17.867 17.867 7.862 17.867 17.867 4.305 9.784 9.784

2 2.783 6.325 24.192 2.783 6.325 24.192 2.825 6.420 16.204

3 2.219 5.044 29.236 2.219 5.044 29.236 2.519 5.724 21.928

4 1.715 3.899 33.135 1.715 3.899 33.135 2.378 5.405 27.333

5 1.578 3.587 36.722 1.578 3.587 36.722 2.017 4.584 31.917

6 1.424 3.235 39.957 1.424 3.235 39.957 1.791 4.069 35.986

7 1.356 3.081 43.038 1.356 3.081 43.038 1.636 3.719 39.705

8 1.264 2.872 45.910 1.264 2.872 45.910 1.573 3.575 43.280

9 1.178 2.676 48.587 1.178 2.676 48.587 1.456 3.310 46.590

10 1.128 2.564 51.150 1.128 2.564 51.150 1.390 3.159 49.749

11 1.045 2.374 53.525 1.045 2.374 53.525 1.341 3.047 52.796

12 1.018 2.315 55.839 1.018 2.315 55.839 1.339 3.043 55.839

13 .937 2.130 57.969

14 .905 2.057 60.026

15 .883 2.008 62.034

16 .864 1.964 63.998

17 .832 1.891 65.889

18 .811 1.844 67.733

19 .796 1.809 69.542

20 .789 1.792 71.334

… … … …

44 .229 .519 100.000

Sum of Var iance Exp lained

Factor

initial engenvalue Sum of Variance import Sum of Rotated Variance import

F1 CC011 CC018 CC012 CC009 CC017 CC015 CC014 CC010depressed liking effort bother lonely restless fearful

F2 CB004 CB003 CB000 CB007 CA004 CA006 CA007 CA003 CA010_4climbing extending running carrying wound chest pain disability sleep arthritis

F3 CA031 CA032 CA037 CC004 CA040eyesight eyesight hearing memory chewing

F4 A002 BD001 BD011 BC001 FE009_gage sibling sibling children

F5 CA060 CA064smoking smoking

F6 CA001 CA010_2 CA005 CA079 CA010_1health canser pain health disease

F7 C052A C052B

F8 CA057_2 CA057_1 CA057_3 CA052C A023friends voluntray entertainment walking education

F9 CA076 CA074 CA072drinking drinking drinking

vigorous exercise

medical expenditures

moderate exercise

consentration

16

help of the definitions of every variable in Appendix A. All variables in F1 describe the emotional situation of a person, and this factor can be defined as Emotion F1’. Except CA006 and CA010_4, all the other variables in F2 describe the function of a person’s body, so a new F2’ can be set and defined as Function. CA006 and CA010_4 can be put together with CA005 as F3’, they all measure levels of pains in different part of people’s body which can be named Pain. CA005 has already been used in F3’, and all the other variables in F3 and F6 can be put together in F4’ as Physical, for they all describe the physical features and situations of people’s body. Variables in F4 are all about information of individuals’ families, this factor can be defined as Family F5’. F5 describes individuals’ back ground about smoking and F6 describes their back ground about drinking, they can be put together in F6’ and defined as Life Style. CA052C and F7 are all about people’s exercise activities, so they can be defined as Exercise F7’. Besides CA023, other variables in F8 show how people spend time in their daily life, so we can name it Time Share which is F8’. The last one variable CA023 measures the last factor F9’ Education. The 9 factors of the modified model are: F1’(Emotion): CC011, CC018, CC010, CC012, CC009, CC017, CC015, CC014 F2’(Function): CB004, CB003, CB000, CB007, CA004, CA007, CA003 F3’(Pain): CA005, CA006, CA010D F4’(Physical): CA031, CA032, CA037, CC004, CA040 CA001, CA010B, CA079,

CA010A F5’(Family): A002, BD001, BD011, BC001, FE009g F6’(Life Style): CA060, CA064, CA076, CA074, CA072 F7’(Exercise): C052A, C052B, CA052C F8’(Time Share): CA057B, CA057A, CA057C F9’(Education): A023 Thirdly, we use confirmatory factor analysis to verify the significance of the 9 modified factors and to prove that they can be used as latent variables in the SEM. In LISREL, if the variables are defined as ordinal data, the polychoric correlations and the asymptotic covariance matrix can be estimated. Thus the estimation method is defaulted as Robust Maximum Likelihood when the asymptotic covariance is used (Jöreskog and Sörbom, 1993). Here we also set one observed variable of each group as the reference variable for the corresponding latent variable to scale it.

Table 6: Goodness of fit of CFA

Fit index Fit criteria ValueChi-suqare in a nonsignificant p -value 3002.33

df 867p-value 0.000

RMSEA close fit < 0.05 0.033CFI > or = 0.90 0.98NFI > or = 0.90 0.98

17

From Table 6 we can see that except Chi-square, all the other indices are perfectly shown that this CFA model fit well. And in reality, it is really hard for a model based on a big data base with a big sample size get a non-significant p-value for the test parameter Chi-square. According to this result, the compositions of the latent variables are proved significantly in statistics. This work is the presupposition of the SEM, thus we can use them to the next step of model hypothesizing.

5 Model

5.1 Model Specification With the previous information, we have already matched 44 observed variables to 9 latent variables. Among these 9 factors, we could figure out that F1’-F4’ are descriptive factors which can show conditions about people’s health, and F5’-F9’ are sociological factors which may influence people’s health. Therefore the initial model hypotheses are obtained below. • The structural model part:

1. Emotion, Body Function, Pain and Physical Health are set to be the 4 endogenous latent variables.

2. Family, Lifestyle, Exercise, Time Share and Education are set to be the 5 exogenous latent variables.

3. Every sociological factors affect all of the health status factors. • The measurement model part:

Since the latent variables are generated by EFA and CFA, the hypotheses in the measurement model have already been set.

Therefore according to the above discussion, we can list variables in our hypothetical model. Here we list the 9 latent variables(the list of the 44 observed variables are attached in Appendix C):

1

2

3

4

5

1

2

F5' ξ : Family information [FAM]F6' ξ : Life Style [LIFES]F7' ξ : Exercise [EXE]F8' ξ : Time Share [TIMES]F9' ξ : Education [EDC]F1' η : Emotional Situation [EMOT]F2' η : Body Function [

3

4

FUNC]F3' η : Pain in one's Body [PAIN]F4' η : Physical Problems [PHYS]

18

The initial hypothetical model in this paper the can be presented as following:

Structural Model: η = Γξ +ζ (15)

Measurement Model: x

y

x = Λ ξ + δy = Λ η + ε

(16)

The assumptions are:

E( ) = 0, E( ) = 0, E( ) = 0, E( ) = 0, E( ) = 0, Corr( ) = 0, Corr( ) = 0,Corr( ) = 0, Corr( ) = 0,Corr( ) = 0, Corr( ) = 0.

ξ η ζ ε δε,ξ ε, ηδ,ξ δ, ηε,δ ξ,ζ

where

11 1

2 11 152 2

33 3

4 41 454 4

5

..., , ... ... ... , .

...

η ξ Γ ζ

1111

21 2222

31 32 3333

41 42 43 4444

51 52 53 54 55

0cov( ) , cov( ) .

0 00 0 0

Φ ξ Ψ ζ

1

5

6

1 110

2 211

1217 17

13

14

15

16

17

0 0 0 0... ... ... ... ...

0 0 0 00 0 0 0... ... ... ... ...0 0 0 0

, 0 0 0 0 , ... ...

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

xx

x

xx Λ δ 1 17, diag[var( ) , ... , var( )].

δΘ

19

18

25

26

1 1

2 232

33

3427 27

35

36

44

0 0 0... ... ... ...

0 0 00 0 0... ... ... ...0 0 0

, , , diag[var(0 0 0... ...0 0 00 0 00 0 0... ... ... ...0 0 0

yy

y

y εy Λ ε Θ 1 27) , ... , var( )].

According to the above model the free parameters is: x y x yθ' Γ,Φ,Ψ, Λ ,Λ ,Θ ,Θ

We set one observed variable of each latent variables as the reference variable to scale it the same as it was performed in the CFA model.

5.2 Implied Covariance Matrix As mentioned before, in the general SEM, estimation of parameters is based on the equation ( )Σ Σ θ , in which Σ is the population covariance matrix of the observed variables. We use sample covariance matrix of the observed variables S to estimate it, and ( )Σ θ is the covariance matrix of the model with parameter θ . According to the book (Bollen, 1989),

cov( ) cov( )( ) and =

cov( ) cov( )yy yx

xy xx

Σ Σ y,y y,xΣ θ Σ

Σ Σ x,y x,x (17)

where

( ) (( )( )) ( ) ( )

( )

E E E EE

yy y y y y

y y y y ε

Σ yy' Λ η ε η'Λ ' ε' Λ ηη' Λ ' εε'Λ (Γcov(ξ)Γ + cov(ζ))Λ '+ εε' Λ (ΓΦΓ + Ψ)Λ '+ Θ

(18)

( ) (( )( )) ( ) ( )

( )

E E E EE

yx y x y x

y x y x εδ

Σ yx' Λ η+ ε ξ'Λ '+ δ' Λ ηξ' Λ ' εδ'Λ (Γcov(ξ) + 0)Λ '+ εδ' Λ ΓΦΛ '+ Θ

(19)

( ) (( )( ' ' ')) ( ) ( )

' ' ( ) '

E E E EE

xy x y x y

x y x y δε

Σ xy' Λ ξ + δ η Λ + ε Λ ξη' Λ ' δε'Λ (cov(ξ) Γ + 0)Λ '+ δε' Λ ΦΓ Λ '+ Θ

(20)

20

( ) (( )( )) ( ) ( ) ( )

E E E EE

xx x x x x

x x x x δ

Σ xx' Λ ξ + δ ξ'Λ '+ δ' Λ ξξ' Λ ' δδ'Λ cov(ξ)Λ '+ δδ' Λ ΦΛ '+ Θ

(21)

The implied covariance matrix can be interpreted with the free parameters as below:

( )'

yy yx

xy xx

y y ε y x εδ

x y δε x x δ

Σ Σ Λ (ΓΦΓ + Ψ)Λ '+ Θ Λ ΓΦΛ '+ ΘΣ θ

Σ Σ Λ ΦΓ Λ '+ Θ Λ ΦΛ '+ Θ (22)

Then the information in ( ) and Σ θ Σ can be used together with corresponding fit function to estimate parameters. Therefore what is really important before estimating the model is that we must determine the identification of parameters.

5.3 Identification The precondition of a estimation model is that the parameters in this model can be estimated uniquely by known information and constraints, so testing of identification need to be done before estimation. In this paper, we use T-Rule test, which is a easy, effective and widely used test to identify this model. In T-Rule, the condition 1/ 2( )( 1)t p q p q must be satisfied to say a model is identified, which means the number of non-redundant elements in the covariance matrix of observed variables should be larger than or equal to t (the number of unknown parameters in θ ). In our case, p is 27, and q is 17 which makes (p+q)(p+q+1)/2=990 and t is 116. Thus the model is identified.

6 Results

6.1 Result of the Initial Model We are interested in testing the effects of sociological factors on health status factor of the elderly. RML method is used to deal with non-normality in which the asymptotic covariance matrix is needed.

Table 7: The Goodness of Fit for Initial SEM

Fit index Fit criteria ValueChi-suqare in a nonsignificant p -value 3068.87

df 874p-value 0.000

RMSEA close fit < 0.05 0.033AIC compare, the smaller the better 3300.87CFI > or = 0.90 0.98NFI > or = 0.90 0.98

21

First, the significance of causal relationships between latent factors should be checked, there are 4 paths of the structural model are non-significant. The evaluation of the whole model can be figured out from Table 7. From the table, we see that the Chi-square test indicate that the close fit of model is rejected, RMAEA of 0.033 shows that the model fits approximately. To ensure the model to be more meaningful we made further modification.

6.2 Model Modification In this section, the main goal is to improve the structural of the model. Following the modification indices given by LISREL and the test of parameters’ significance, we re-specified the model to get better fit and easy to interpreted. In the first step, two paths have been added. They are the paths from PAIN to CA010B and from EMOT to CC004. CA010B is a variable about cancer and other visceral diseases and these diseases may cause body pain. CC004 is a variable about someone’s memory condition which might influence someone’s emotional status. Some of the non-significant paths were moved away. These are EDU - PHYS, EDU - PAIN, EDU - EMOT, EDU - FUNC, FAM - FUNC, FAM - PAIN, LIFES - FUNC, and LIFES - PAIN. Because all paths about EDU had been moved away, the latent variable EDU itself was also removed from the structural model. This process has changed the initial model hypotheses directly. The structural model will be further discussed in the next section. Finally, some of the error correlations of observed variables were added. Following the modification indices and variable definition, three correlations were added into the model. The first error correlation is the one between CA032 and CA031. Both of the two variables are about eyesight. The second error correlation is the one between CC011 and CC009, and they are about depressing and bothering. A person may feel depressed when he is bothered by other people or things. The last added error correlation is the one between CA076 and CA060. They are about information about smoking and drinking, and the relevance between them are also reasonable.

Table 8: Goodness of Fit for Initial and Modified Model

Fit index Fit criteria Initial ModifiedChi-suqare in a nonsignificant p -value 3068.87 2675.02

df 874 837p-value 0.000 0.000

RMSEA close fit < 0.05 0.033 0.031AIC compare, the smaller the better 3300.87 2893.02CFI > or = 0.90 0.98 0.99NFI > or = 0.90 0.98 0.98

Indices of Goodness of Fit

22

The goodness of fit of the modified model is shown in Table 8, we could see that the modified model fit better than the initial one. It shows Goodness of Fit indices of both the initial and the modified models. The change of Chi-square value is statistically significant. The values of RMSEA and AIC in the modified model are also smaller and the values of CFI is larger. All of these changes show that the modification makes a positive improvement compare to the initial hypothetical model. The path diagram of the modified model is shown in Figure 2.

Figure 2: The path-diagram of the modified SEM

23

6.3 Result of the Modified Model In the Measurement Model, all of the paths are significant at 5% level and the estimated coefficients are reliable. The estimated parameters are listed in Table 13 in Appendix E. In the Structural Model, two of these paths are not significant at 5% level. They are LIFES – FUNC and PAIN – EXE.

Table 9: RML Estimates of Modified Structural Model

From Table 9, we could get the conclusion below: For PHYS a factor reflecting the general physical condition of someone’s health, FAM, TIMES and EXE are positive sociological factors and LIFES is a negative factor. This result means, if someone spends more time doing exercise and enjoying having fun with other people, and drinking and smoking less, he/she will get a better physical body condition. According to the estimated coefficients , among these four effects, TIMES has the strongest effect. EXE and FAM are the following factors after it. LIFES is the weakest influencing factor. For PAIN a factor measuring the pain occurring in different parts of our body, both of the influencing factors TIMES and EXE have negative effects. It means pain occurs more often and heavier among people who spend less time doing exercise or going out. Also according to the estimated coefficients, TIMES is a stronger influencing factor than EXE. Positive changes in TIMES will provide more contribution to the improvement of pain-related health problems of the elderly. For FUNC a factor measuring various bodily functions, TIMES and EXE have positive effects. The same as the explanation in the paragraph above, it means people who are more willing to do exercise and go out for activities will have a better body function, such as the ability of carrying heavy bags. TIMES also provides stronger effects than EXE to FUNC. For EMOT, which is a factor generally describing a person’s emotional conditions, FAM, TIMES and EXE are positive and LIFES is negative. The relationship in this equation means that, the old individual who has a healthier lifestyle, who has a better family environment or who is more willing to do exercise and go out for activities

FAM TIMES LIFES EXEPHYS 0.21 0.96 -0.18 0.56

(t-value) (2.05) (8.81) (-1.54) (4.21)PAIN - -0.71 - -0.16

(t-value) - (-11.72) - (-1.93)FUNC - 0.88 - 0.54

(t-value) - (7.22) - (4.34)EMOT 0.23 0.95 -0.12 0.38

(t-value) (5.17) (9.65) (-2.04) (2.93)

24

will has a better body function. The order of the importance of factors are TIMES, EXE, FAM and then LIFES. Above all, in this section TIMES and EXE have stronger and higher direct factors which influence people’s health, whereas FAM and LIFES are auxiliary factors.

7 Conclusion

In this paper, we use the elderly data from CHARL to study how to measure their health and what are the significant factors affecting people’s health. The main focus of this work is data management and model specification and estimation. We summarize the research results as the follow: conclusions, some feedback about using the data and the limitations for this research. For SEM, all paths between observed variables and latent variable are significant at 5% level. Based on this data, elderly health can be measured in four aspects. They are physical condition, emotional condition, body function and pain occurs. The hypothesized influencing factors are time sharing, exercise, family environment, education and lifestyle. From the results, the effect of education is verified as a non-significant element, which means people’s health does not depend on their education history. Other four factors are verified that they all have influences on physical conditions and emotional conditions. Time sharing and physical exercise also have effects on pain and body function. In total, the elderly physical health and emotional health are depending on many element of their life and daily activities. Time sharing and exercise are really important to the health of the elderly population. So the public should do more improvement both on public awareness and utilities and encourage the old people to go outside, do physical exercise and other activities or spend more time with friends and relatives. The data collected as the first wave of a longitudinal study. But the pity is that some useful and valuable parts of this whole dataset cannot be used because of the serious missing value problems. Missing values do not provide any information and therefore we have to eliminate some of the variables which with large proportion of missing values. We have to give up the information from those parts and some corresponding research cannot be conducted so far. At last, suggestions for further study on this topic: a second ordered factor analysis can be considered to gather a general factor Health, and then after some modification and standardization of the second factor Health’s score, it can be defined as a single health index. This data contains individuals from two provinces of China, one is from east coast of China, and the other one is from the middle of China. Much information about demographic has been recorded. Therefore, researches about comparison of the elderly health between different provinces can also be conducted as further study.

25

Reference

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Xiao, S., Ma, Y., Li, Y. H., Hu, J. F., Cheng, Y. L., Chen, G. Y., and Tao, M. X. (2009). The Investigation of the Health Literacy Status and its Influencing Factors of Urban and Rural Residents in China. Health Education in China. 25(5): 323-326 Johnson, R. A., and Wichern, D. W. (2007). Applied multivariate statistical analysis, 6th Edition. Upper Saddle River, N.J. : Pearson Prentice Hall Luo, H. (2011). Some Aspects on Confirmatory Factor Analysis of Ordinal Variables and Generating Non-normal Data. Uppsala University, Uppsala Yi, D. H. (2008). Structural Equation Model, Method and Application. Publication of Renmin University of China, Beijing Yang-Wallentin, F., Jöreskog, K. G., and Luo, H. (2010). Confirmatory Factor Analysis of Ordinal Variables with Misspecied Models. Structural Equation Modeling. 17:392-423 Magnus, J. R., and Neudecker, H. (1999). Matrix Differential Calculus with Applications in Statistics and Econometrics (2nd ed.). Hoboken, NJ: Wiley. Satorra, A. and Bentler, P. M. (1988). Scaling corrections for chi-square statistics in covariance structure analysis. In American Statistical Association, Proceedings of the Business and Economic Section CHARLS. (2009). Home. National School of Development at Peking University. http://charls.ccer.edu.cn/charls/index.asp CHARLS. (2009). Sample. National School of Development at Peking University. http://charls.ccer.edu.cn/charls/sample.asp Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society. Series B 39(1):1–38 Jöreskog, K. G. and Sörbom, D. (1993). LISREL 8: structural equation modeling with the SIMPLIS command language. Chicago, IL: Scientific Software International Bollen, K. A. (1989). Structural Equations with Latent Variables. New York: Wiley. Zhao, Y. H., Strauss, J., Park, A., Shen, Y., and Sun, Y. (2009). China Health and Retirement Longitudinal Study, Pilot, User's Guide, National School of Development, Peking University

27

Appendix

A. Variable instructions This table shows that how the variables used in the full SEM converged from the original questions in the questionnaire and what are their categories.

Table 10: Variable Instructions No Variable Question Conversion

1 A022 How old are you?

______Years old 2008(survey year)-A002_a(born year)

2 A023 How many years do you spend in your education?

_____Years Sum of A023 and A026

3 BC001 How many living children do you and your spouse

have?

1,2,3,4,5,6:more than 5

4 BD001 How many of your siblings are still alive?

1,2,3,4,5,6,7:more than 6

5 BD011 How many of your spouse’s siblings are still alive?

1,2,3,4,5,6,7:more than 6

6 C052A How many days do you do at least 10 minutes

vigorous activities during a usual week?

1: No;

2: Yes, but not every day;

3: Almost everyday

if C052_1_ is NO->1; if C052_1_ is Yes

& C053_1_ is 7->2; Else->3

7 C052B How many days do you do at least 10 minutes

moderate physical effort during a usual week?

1: No;

2: Yes, but not every day;

3: Almost everyday

if C052_2_ is NO->1; if C052_2_ is Yes

& C053_2_ is 7->2; Else->3

8 CA052C How many days do you do at least 10 minutes

walking during a usual week?

1: No;

2: Yes, but not every day;

3: Almost everyday

if C052_3_ is NO->1; if C052_3_ is Yes

& C053_3_ is 7->2; Else->3

9 CA057_1 Frequency of voluntary or charity work in the last

month.

3: Almost daily;

2: Almost every week;

1: Not regularly

Conbine

C057:1-3(C057s1-s3&C058_1_-C058_

3_),C058:A->3,L->2,blank->1

10 CA057_2 Frequency of interacting with friends in the last

month.

28

3: Almost daily;

2: Almost every week;

1: Not regularly

Conbine

C057:5(C057s5&C058_5_),C058:A->3,

L->2,blank->1

11 CA057_3 Frequency of going out for entertainment.

3: Almost daily;

2: Almost every week;

1: Not regularly

Combine

C057:6-9(C057s6-s9&C058_6_-C058_

9_),C058:A->3,L->2,blank->1

12 CA060

Have you ever chewed tobacco, smoked a pipe,

smoked self-rolled cigarettes, or smoked

cigarettes/cigars?

1: No;

2: Yes, but now quit;

3: Yes, and still.

Combine CA060&CA062;

if CA060:NO->1;

if CA060:Yes&CA062:St->3;

if CA060:Ye&CA062:Qu->2

13 CA064 In one day about how many cigarettes do/did you

consume now/before totally quitting?

______Cigarettes

14 CA072 How often did you drink liquor, including white

liquor, whisky, and others during the last year?

1: No;

2: At most once a day;

3: At least twice a day

1:No->1; [2-7:On,2-,4-]->2;

[8-9:Tw,Mo]->3

15 CA074 How often did you drink beer in the last year?

1: No;

2: At most once a day;

3: At least twice a day

1:No->1; [2-7:On,2-,4-]->2;

[8-9:Tw,Mo]->3

16 CA076 How often did you drink wine or rice wine per

month in the last year?

1: No;

2: At most once a day;

3: At least twice a day

1:No->1; [2-7:On,2-,4-]->2;

[8-9:Tw,Mo]->3

17 FE009_g What is the proportion of medical expenditures in

your family annual cost besides food? FE009_g/sum of (FE008&FE009)

_______%

18 CA001 Before the survey, how do you feel about your

health?

4: Excellent&Very good;

3: Good;

2:Fair;

1: Poor

Combine CA001&CA079a

Ex&Ve->4;Go->3;Fa->2;Po->1

19 CA079 After the survey, how do you feel about your

health?

29

4: Excellent&Very good;

3: Good;

2:Fair;

1: Poor

Combine CA001a&CA079

Ex&Ve->4;Go->3;Fa->2;Po->1

20 CA003 Do you have to get up often during the night to

urinate?

1: Yes;

2: No

21 CA004 If you have a cut or wound, does it take a long time

to heal?

1: Yes;

2: No

22 CA005 Do you ever feel pain on the left side of your

chest?

1: Yes;

2: No

23 CA006 Do you ever feel chest pains when climbing

stairs/uphill or walking quickly?

1: Yes;

2: No

24 CA007 Do you have these below disabilities?

0: No disabilities;

1: Physical disabilities

2: Mental Problems

3: Vision,Hearing Problem or Speech impediment

4: More than two disabilities listed above

if CA007_1_-CA007_5_are all NO->0

if only CA007_1_ is Ye->1

if only CA007_2_ is Ye->2

if only CA007_3,4,5_ is Ye->3

if more than two->4

25 CA010_1

Do you know you have Hypertension, High

cholesterol, Diabetes, High blood sugar, Stroke

(including transient ischemic attack or TIA), Heart

attack, coronary heart disease, angina, congestive

heart failure, or other heart problems?

if any of CA010_1,2,3,7,8_ is Ye->1

if all of CA010_1,2,3,7,8_ is No->2

1: Yes;

2: No

26 CA010_2

Do you know you have Cancer, malignant tumor,

Chronic lung diseases, such as chronic bronchitis or

emphysema, Liver disease, such as Hepatitis B,

Kidney disease, Stomach or other digestive

disease?

if any of CA010_4,5,6,9,10_ is Ye->1

if all of CA010_4,5,6,9,10_ is No->2

1: Yes;

2: No

27 CA010_4 Do you know you have Arthritis or rheumatism? if CA010_13_ is Ye->1;if CA010_13_ is

No->2

30

1: Yes;

2: No

28 CA031 How good is your eyesight for seeing things at a

distance?

5: Excellent;

4: Very good;

3: Good;

2:Fair;

1: Poor

0: Blind

Ex->5;Ve->4;Go->3;Fa->2;Po->1;Blank

->0

29 CA032 How good is your eyesight for seeing things up

close?

5: Excellent;

4: Very good;

3: Good;

2:Fair;

1: Poor

0: Blind

Ex->5;Ve->4;Go->3;Fa->2;Po->1;Blank

->0

30 CA037 How about your hearing?

5: Excellent;

4: Very good;

3: Good;

2:Fair;

1: Poor

31 CA040 How easily can you chew solid foods?

4: Very well;

3: Pretty well;

2:Fair;

1: Not well

Combine CA040&CA041

32 CB000 Do you have any difficulty with running or walking?

5: No difficulty with running or jogging for 1 km;

4: No difficulty with walking 1 km;

3: No difficulty with walking for 100 m;

2: Have difficulty with walking for 100 m;

1: Can’t walk for 100 m

Combine CB000,CB001&CB002

if CB000:NO->5

if CB001:NO->4

if CB002:NO->3

if CB002:Ye->2

if CB002:I->1

33 CB003

Do you have difficulty Getting uo from a chair after

sitting for a long period, Stooping, kneeling,

crouching, reaching or extending your arms above

shoulders level?

31

3: No, I don’t have any difficulty;

2: Yes, I have difficulty;

1: I cannot do it

Combine CB003,CB005&CB006; In

which, 3: No, I don’t have any

difficulty;2: Yes, I have difficulty; 1: I

cannot do it.

Min(CB003,CB005&CB006)

34 CB004 Do you have difficulty Climbing several flights of

stairs without resting?

3: No, I don’t have any difficulty;

2: Yes, I have difficulty;

1: I cannot do it

35 CB007 Do you have difficulty Lifting or carrying weights

over 5kg, like a heavy bag of groceries?

3: No, I don’t have any difficulty;

2: Yes, I have difficulty;

1: I cannot do it

36 CC004 How would you rate your memory at the present

time?

5: Excellent;

4: Very good;

3: Good;

2:Fair;

1: Poor

37 CC009 In the last week, I was bothered by things that

don't usually bother me.

4: <1 day;

3: 1-2 days;

2: 3-4 days;

1:5-7 days

38 CC010 In the last week, I had trouble keeping my mind on

what I was doing.

4: <1 day;

3: 1-2 days;

2: 3-4 days;

1:5-7 days

39 CC011 In the last week, I felt depressed.

4: <1 day;

3: 1-2 days;

2: 3-4 days;

1:5-7 days

40 CC012 In the last week, I felt everything I did was an

effort.

32

4: <1 day;

3: 1-2 days;

2: 3-4 days;

1:5-7 days

41 CC014 In the last week, I felt fearful.

4: <1 day;

3: 1-2 days;

2: 3-4 days;

1:5-7 days

42 CC015 In the last week, my sleep was restless.

4: <1 day;

3: 1-2 days;

2: 3-4 days;

1:5-7 days

43 CC017 In the last week, I felt lonely.

4: <1 day;

3: 1-2 days;

2: 3-4 days;

1:5-7 days

44 CC018 In the last week, I could not get "going."

4: <1 day;

3: 1-2 days;

2: 3-4 days;

1:5-7 days

33

B. Output of SPSS for EFA in Section 4.4

Table 11: Variance of Common Factorsa

initial Extract initial Extract

A002 .552 .840 CA005 .407 .811

A023 .222 .425 CA006 .405 .462

BC001 .335 .376 CA0070 .151 .193

BD001 .169 .181 CA010_1 .143 .211

BD011 .184 .185 CA010_2 .117 .142

CA050 .067 .068 CA010_3 .044 .028

C052A .268 .399 CA010_40 .110 .109

C052B .214 .373 CA031 .418 .596

CA052C .106 .171 CA032 .338 .520

CA057_10 .121 .200 CA037 .284 .307

CA057_20 .143 .486 CA0400 .269 .304

CA057_3 .147 .212 CB0000 .524 .596

CA059 .075 .078 CB0030 .461 .553

CA060 .601 .887 CB004 .550 .676

CA064 .585 .655 CB007 .371 .429

CA072 .208 .323 CC004 .243 .279

CA074 .202 .371 CC009 .449 .555

CA076 .104 .173 CC010 .441 .492

FE009_f .035 .030 CC011 .529 .638

FE009_g .172 .195 CC012 .478 .552

CA001 .607 .729 CC014 .271 .313

CA079 .643 .795 CC015 .235 .275

CA003 .202 .316 CC017 .324 .441

CA004 .205 .300 CC018 .481 .548

34

Table 12: Rotated Factor Matrix a with 9 Factors

1 2 3 4 5 6 7 8 9

CC011 .757 .125 .144 .008 -.018 -.057 -.048 .025 .133

CC018 .728 .146 .120 .027 -.004 -.108 -.034 .051 .064

CC010 .707 .128 .163 -.005 -.009 -.022 -.036 -.037 .044

CC012 .701 .196 .134 .037 .009 -.102 -.063 .080 .016

CC009 .696 .044 .125 -.031 .009 -.145 -.034 .055 .105

CC017 .604 .175 .064 .069 -.049 .048 .053 .069 .050

CC015 .520 .114 .035 .043 .083 -.172 .057 -.056 -.086

CC014 .515 .283 -.115 .111 .130 -.036 -.040 .039 -.037

CB004 .231 .694 .227 .067 .081 -.085 .208 .091 .064

CB0030 .241 .678 .170 .037 .038 -.042 .150 .073 .070

CB0000 .241 .595 .190 .182 .104 -.082 .280 .202 .053

CB007 .245 .567 .092 .117 .147 .020 .233 .149 -.025

CA004 -.161 -.494 -.110 -.009 .061 .071 .158 .056 -.001

CA006 -.167 -.446 .019 -.069 -.003 .429 .282 -.014 -.167

CA0070 -.130 -.348 -.246 -.163 .146 -.272 -.090 .091 -.088

CA003 -.203 -.317 -.089 -.170 .016 .231 .048 .005 .081

CA010_40 -.086 -.315 -.086 -.033 -.036 .188 .081 -.011 .005

CA031 .142 .159 .744 .075 .016 -.038 -.002 -.032 .069

CA032 .072 .072 .737 -.016 -.020 .016 .007 .055 .012

CA037 .089 .190 .585 .220 -.024 -.075 -.039 -.046 -.027

CC004 .182 .115 .497 .022 .085 -.165 -.180 .106 -.041

CA0400 .148 .184 .395 .303 -.057 -.153 -.096 .112 .115

A002 .030 -.192 -.166 -.770 .016 .021 -.237 -.126 .026

BD001 .052 -.038 .040 .605 -.137 .064 .077 -.035 .107

BD011 .078 .067 -.029 .591 .104 -.025 .094 -.103 .048

BC001 .069 -.245 -.105 -.588 -.058 .085 .010 -.166 -.100

FE009_g -.141 .084 -.144 -.383 -.067 .357 -.028 -.172 .127

CA060 .029 .056 -.008 -.014 .875 -.005 .072 -.002 .151

CA064 .028 .058 -.005 .007 .841 .031 .063 -.016 .206

CA001 .341 .153 .399 -.046 .019 -.540 .152 .093 .144

CA010_2 -.101 -.084 -.065 .006 .106 .533 -.046 .054 -.001

CA005 -.137 -.446 .068 -.052 .010 .501 .294 .042 -.150

CA079 .339 .191 .471 -.038 .020 -.497 .146 .109 .149

CA010_1 -.033 -.093 -.066 -.105 -.118 .430 -.318 .087 .022

C052A -.064 .033 -.009 .175 .264 -.082 .639 -.152 -.001

C052B -.003 .049 -.140 .214 -.085 -.037 .614 .127 .062

CA057_20 .041 .094 -.017 -.039 -.172 .039 .005 .673 .139

CA057_10 -.018 -.068 .096 .157 .079 -.066 .115 .558 -.132

CA057_3 .188 .107 .053 .021 .117 .062 -.222 .476 .165

CA052C -.023 .128 -.047 -.050 -.032 .019 .380 .402 .053

A023 .124 .080 .126 .352 .329 .016 -.258 .365 -.088

CA076 .016 .019 .036 .012 -.016 -.063 .004 .076 .671

CA074 .160 .055 .044 .189 .150 -.004 .062 -.004 .629

CA072 .049 .034 .020 .006 .343 .004 -.003 .034 .604

Factors

Generation Method: Maximum likelihood.

Method of Rotation: Standard orthogonal rotation method with Kaiser.

a. The rotation is converged after 21 times interaction.

35

C. Definition of Observed variables1

2

3

4

: how old are you?[A002]: how many of your siblings are still alive?[BD001]: how many of your spouse's siblings are still alive?[BD011]: how many living children do you and your spouse have?[B

xxxx

5

C001]: proportion of medical expenditures in family annual cost besides food [FE009g]x

6

7

8

9

10

: status about one's smoking history? [CA060]: numbers of cigarettes per day [CA064]: frequency of drinking wine [CA076]: frequency of drinking beer [CA074]: frequency of drinking liquor [C

xxxxx A072]

11

12

13

: days of doing at least 10 minutes vigorous activities per week [C052A]: days of doing at least 10 minutes moderate physical effort per week [C052B]: days of doing at least 10 minutes walkin

xxx g per week [C052C]

14

15

16

: frequency of voluntary or charity work per month [CA057A]: frequency of interacting with friends per month [CA057B]: frequency of going out for entertainments per month [CA057C]

xxx

17: how many years do you spend in your study? [CA023]x

1

2

3

4

: days of feeling depressed during a week [CC011]: days of could not get "going" during a week [CC018]: days of having trouble keeping mind on during a week [CC010]: days of feeling everything

yyyy

5

6

7

did was an effort during a week [CC012]: days of being borthered by very little things during a week [CC009]: days of feeling lonely during a week [CC017]: days of one's sleep was restless duri

yyy

8

ng a week [CC015]: days of feeling fearful during a week [CC014]y

9

10

11

12

: difficulty of climbing stairs without resting [CB004]: difficulty of extending one's body [CB003]: difficulty of running and walking [CB000]: difficulty of lifting or carrying weights [CB

yyyy

13

14

15

007]: time of healing of a cut or wound [CA004]: disabilities [CA007]: getting up during the night to urinate [CA003]

yyy

36

16

17

18

: pain on the left side of one's chest [CA005]: chest pain when climbing or walking quickly [CA006]: arthritis or rheumatism [CA010D]

yyy

19

20

21

22

23

24

: eyesight for seeing things at a distance [CA031]: eyesight for seeing things up close [CA032]: hearing [CA037]: memory [CC004]: chewing solid foods [CA040]: how do you feel your he

yyyyyy

25

26

27

alth before the survey [CA001]: cancer or visceral diseases [CA010B]: how do you feel your health after the survey [CA079]: cardiovascular and cerebrovascular diseases [CA010A]

yyy

37

D. LISREL Code

1 Confirmatory Factor Analysis with RML method Observed variables:

A002 A023 BC001 BD001 BD011 C052A C052B CA052C CA057A CA057B CA057C

CA060 CA064 CA072 CA074 CA076 FE009g CA001 CA079 CA003 CA004 CA005

CA006 CA007 CA010A CA010B CA010D CA031 CA032 CA037 CA040 CB000 CB003

CB004 CB007 CC004 CC009 CC010 CC011 CC012 CC014 CC015 CC017 CC018

Covariance matrix from File C

Asymptotic Covariance Matrix from File ACM

Sample size is 2285

Latent variables: FAM EDC TIMES LIFES EXE PHYS PAIN FUNC EMOT

relationships:

A002 = FAM

BC001 BD001 BD011 FE009g = FAM

A023 = 1.00*EDC

CA057A = TIMES

CA057B CA057C = TIMES

CA060 = LIFES

CA064 CA072 CA074 CA076 = LIFES

C052A = EXE

C052B CA052C = EXE

CA001 = PHYS

CA079 CA010A CA010B CA031 CA032 CA037 CA040 CC004 = PHYS

CA005 = PAIN

CA006 CA010D = PAIN

CA003 = FUNC

CA004 CA007 CB000 CB003 CB004 CB007 = FUNC

CC009 = EMOT

CC010 CC011 CC012 CC014 CC015 CC017 CC018 = EMOT

SET ERROR VARIANCE OF A023 TO ZERO

Options: AD=OFF SS

Method: Robust Maximum Likelihood

Path diagram

end of problem

38

2 Modified SEM with RML method Observed variables:

A002 A023 BC001 BD001 BD011 C052A C052B CA052C CA057A CA057B CA057C

CA060 CA064 CA072 CA074 CA076 FE009g CA001 CA079 CA003 CA004 CA005

CA006 CA007 CA010A CA010B CA010D CA031 CA032 CA037 CA040 CB000 CB003

CB004 CB007 CC004 CC009 CC010 CC011 CC012 CC014 CC015 CC017 CC018

Covariance matrix from File CM

Asymptotic Covariance Matrix from File ACM

Sample size is 2285

Latent variables: FAM TIMES LIFES EXE PHYS PAIN FUNC EMOT

relationships:

A002 = FAM

BC001 BD001 BD011 FE009g = FAM

CA057A = TIMES

CA057B CA057C = TIMES

CA060 = LIFES

CA064 CA072 CA074 CA076 = LIFES

C052A = EXE

C052B CA052C = EXE

CA001 = PHYS

CA079 CA010A CA010B CA031 CA032 CA037 CA040 CC004 = PHYS

CA005 = PAIN

CA006 CA010D CA010B= PAIN

CA003 = FUNC

CA004 CA007 CB000 CB003 CB004 CB007 = FUNC

CC009 = EMOT

CC010 CC011 CC012 CC014 CC015 CC017 CC018 CC004= EMOT

EMOT = FAM TIMES EXE LIFES

PHYS = FAM TIMES EXE LIFES

FUNC = TIMES EXE

PAIN = TIMES EXE

Let the errors of CA032 and CA031 correlated

Let the errors of CC011 and CC009 correlated

Let the errors of CA076 and CA060 correlated

Options: AD=OFF SS

Path diagram

end of problem

39

E. Estimation of the Modified Measurement Model Table 13: RML Estimates of Modified Measurement Model

LatentVariables

ObservedVariables

ParametersΛx

Estimates(T-value)

LatentVariables

ObservedVariables

ParametersΛy

Estimates(T-value)

EMOTCC011 Λ1 1.33

(17.65)FAM

A002 Λ28 9.19(15.87)

CC018 Λ2 1.31(14.24)

BD001 Λ29 -0.75(-9.61)

CC010 Λ3 1.20(14.70)

BD011 Λ30 -0.69(-9.34)

CC012 Λ4 1.17(15.04)

BC001 Λ31 0.48(7.88)

CC009 Λ5 1.26(-)

FE009g Λ32 9.64(12.03)

CC017 Λ6 1.47(9.80)

LIFESCA060 Λ33 3.89

(28.70)CC015 Λ7 1.05

(9.61)CA064 Λ34 8.05

(19.61)CC014 Λ8 1.42

(8.27)CA076 Λ35 1.08

(9.56)CC004 Λbb 0.14

(3.06)CA074 Λ36 0.760

(14.21)

FUNCCB004 Λ9 0.61

(8.80)CA072 Λ37 1.05

(12.76)CB003 Λ10 0.55

(8.36)EXE

C052A Λ38 2.23(17.36)

CB000 Λ11 1.19(7.96)

C052B Λ39 1.54(17.58)

CB007 Λ12 1.07(7.70)

C052C Λ40 0.86(6.41)

CA004 Λ13 0.52(8.12)

TIMESCA057A Λ41 0.25

(3.65)CA007 Λ14 0.46

(3.58)CA057B Λ42 0.63

(7.24)CA003 Λ15 0.47

(-)CA057C Λ43 1.89

(11.17)

PAINCA005 Λ16 0.89

(-)CA006 Λ17 0.94

(22.84)CA010D Λ18 0.35

(8.69)CA010B Λaa -0.17

(-6.10)

PHYSCA031 Λ19 0.25

(6.35)CA032 Λ20 0.18

(4.91)CA037 Λ21 0.45

(9.31)CC004 Λ22 0.28

(10.11)CA040 Λ23 0.60

(13.64)CA001 Λ24 0.88

(-)CA010B Λ25 0.28

(9.88)CA079 Λ26 0.81

(26.28)CA010A Λ27 0.31

(8.68)

The Measurement Equation