Transcript Introduction to Supply Chain Management

第4章 管理研究的统计分析方法
Part 2: 结构方程模型方法
Outline

Introduction to SEM

Objectives of SEM

SEM Software

Graphical Representation of SEM

Stages of Applying SEM

Examples
©2006, Fang Weiguo
School of Economics and Management, BUAA
Introduction to SEM

Structural Equation Modeling (SEM) is a very general
linear statistical modeling technique used for specifying and
estimating models of linear relationships among variables.

Variables in a model may include both measured variables
and latent variables.
– Many important marketing, psychological or cultural concepts are
latent variables.
©2006, Fang Weiguo
School of Economics and Management, BUAA
Introduction to SEM

Latent variables are such theoretical constructs as attitudes,
customer satisfaction, perception, evaluation, and behavior
measures, which can only be determined to exist as a
combination of other measured variables.

In SEM each such construct is typically represented by
mutual measured variables that serve as indicators of the
construct.
©2006, Fang Weiguo
School of Economics and Management, BUAA
Introduction to SEM

An SEM analysis comprises two basic contents:
– First is the measurement model definition, i.e. the development of
the latent constructs through measuring their hypothesized observed
indicators.
– This is implemented by proposing a set of theoretical relationships
first, and then testing them against the empirical data to confirm the
existence of the proposed structure.
– The second part of an SEM analysis is the development of structural
model, which involves investigating the relationships, or paths,
between the latent constructs in a proposed model.
©2006, Fang Weiguo
School of Economics and Management, BUAA
Introduction to SEM

SEM represents a generalization of both regression and
factor analysis, and subsumes most linear modeling
methods as special cases.

Structural equation models, provide researchers with a
comprehensive method for the quantification and testing of
theories.
©2006, Fang Weiguo
School of Economics and Management, BUAA
Objectives of SEM

The primary aim of SEM
– explain the pattern of a series of inter-related dependence
relationships simultaneously between a set of latent (unobserved)
constructs, each measured by one or more manifest (observed)
variables.

The measured (observed) variables in SEM have a finite
number of values.
– Examples of measured variables are distance, cost, size, weight or
height.
©2006, Fang Weiguo
School of Economics and Management, BUAA
Objectives of SEM

The measured (manifest) variables are gathered from
respondents through data collection methods, or collected as
secondary data from a published source.
– They are represented by the numeric responses to a rating scale item
on a questionnaire. Measured variables in SEM are usually
continuous.

Latent (unobserved) variables are not directly observed, have
an infinite number of values, and are usually continuous.
– Examples of latent constructs are attitudes, customer satisfaction,
perception of value or quality.
©2006, Fang Weiguo
School of Economics and Management, BUAA
Objectives of SEM

In the primary form of analysis, SEM is similar to combining
multiple regression and factor analysis.
– As such the SEM expresses the linear causal relationship between two
separate sets of latent constructs (which may have been derived by
two separate factor analyses).

When using SEM these latent constructs are termed
"exogenous" (independent) constructs and "endogenous"
(dependent) constructs.
©2006, Fang Weiguo
School of Economics and Management, BUAA
Objectives of SEM
©2006, Fang Weiguo
School of Economics and Management, BUAA
Objectives of SEM

Endogenous latent constructs such as repeat visitation and
satisfaction depend on independent exogenous latent
constructs such as culture and perception.

The SEMs include one or more linear regression equations
that describe how the endogenous constructs depend upon
the exogenous constructs.
– Their coefficients are called path coefficients, or sometimes regression
weights.
©2006, Fang Weiguo
School of Economics and Management, BUAA
Objectives of SEM

Although the primary purpose of SEM is the analysis of latent
constructs and in particular the analysis of causal links
between latent constructs, SEM is also capable of other forms
of analysis.
– SEM can be used to estimate variance and covariance, test hypotheses,
conventional linear regression, and factor analysis.

SEM is a powerful method for effectively dealing with
multicollinearity (when two or more variables are highly
correlated) which is one of the benefit of SEM over multiple
regression and factor analysis.
©2006, Fang Weiguo
School of Economics and Management, BUAA
SEM Software

The available products — Amos, Proc CALIS, Cosan, EQS,
Lincs, Liscomp, LISREL, Mecosa, Mx, Ramona, SEPath,
and others.

Lisrel stands for LInear Structural RELationships and is a
computer program for covariance structure analysis.
– LISREL is a multivariate technique which combines (confirmatory)
factor analysis modeling from psychometric theory and structural
equations modeling associated with econometrics.
©2006, Fang Weiguo
School of Economics and Management, BUAA
Graphical Representation of SEM

Geometric symbols and mathematical notations
x - measured independent variable
y - measured dependent variable
- latent exogenous construct explained by x-variables
 - latent endogenous construct explained by y-variables
 - error for x-variable
ε - error for y-variable
λ - correlation between measured variables and all latent
constructs
 - correlation between latent constructs  (exogenous)
and  (endogenous)
 - correlation between exogenous latent constructs 
 - correlations between endogenous latent constructs  .
©2006, Fang Weiguo
School of Economics and Management, BUAA
Graphical Representation of SEM
©2006, Fang Weiguo
School of Economics and Management, BUAA
Graphical Representation of SEM
©2006, Fang Weiguo
School of Economics and Management, BUAA
Stages of Applying SEM
©2006, Fang Weiguo
School of Economics and Management, BUAA
Stages of Applying SEM
©2006, Fang Weiguo
School of Economics and Management, BUAA
Stage 1 Development of a theoretical
model

The first part focuses on the development of a theoretical
model with the linkages (defined causal relationships)
between latent constructs and their measurable variables,
reflecting proposed hypotheses.
– This part represents the development of a structural model.

The second part involves the operationalization of the latent
constructs via the measured variables and describing the
way in which they are represented by empirical indicators
(manifest variables).
– This part represents the development of a measurement model.
©2006, Fang Weiguo
School of Economics and Management, BUAA
Stage 2 Construction of a path diagram

In a path diagram all causal relationships between
constructs and their indicators are graphically presented
with arrows.
– They form a visual presentation of the hypotheses and the
measurement scheme.

All constructs fall into two categories: exogenous and
endogenous.
– Exogenous constructs are independent variables and are not
caused/predicted by any other variable in a model.
– Endogenous constructs are predicted by other constructs and
relationships contained in the model. They can also predict other
endogenous constructs.
©2006, Fang Weiguo
School of Economics and Management, BUAA
Stage 2 Construction of a path diagram

A path diagram should show all causal relationships.
– The number of causal paths should be theoretically justified.
– All relationships are to be linear.
©2006, Fang Weiguo
School of Economics and Management, BUAA
Stage 3 Conversion of path diagram into a
set of structural and measurement equations

This stage involves the formal mathematical specification of
the model by
– describing the nature and number of parameters to be estimated
(which variables measure which constructs)
– translating the path diagram into a series of linear equations which
link constructs
– translating the specified model into software language in the form of
matrices
– indicating hypothesized correlations among constructs or variables.
©2006, Fang Weiguo
School of Economics and Management, BUAA
Stage 4 Choosing the input matrix type

This stage considers whether the variance/covariance or
correlation matrix is to be used as the input data, and this
involves an assessment of the sample size.

After the structural and measurement models are specified
and the input data type is selected, the computer program
for model estimation should be chosen.
– The Lisrel computing program has been the most widely used
program.
©2006, Fang Weiguo
School of Economics and Management, BUAA
Stage 5 Model identification

The extent to which the information provided by the data
is sufficient to enable parameter estimation.
– If a model is not identified, then it is not possible to determine the
model parameters.

A necessary condition for the identification
– The number of independent parameters is less than or equal to the
number of elements of the sample matrix of covariances among the
observed variables.
– If t parameters are to be estimated, the minimum condition for
identification is t s, where s=1/2(p + q)(p + q +1), p is the number
of y-variables and q the number of x-variables.
©2006, Fang Weiguo
School of Economics and Management, BUAA
Stage 5 Model identification

There are several different kinds of parameter estimation
methods
– instrumental variables (IV)
– two-stage least squares (TSLS)
– unweighted-least squares (ULS)
– generalized least squares (GLS)
– maximum likelihood (ML)
– generally weighted least squares (WLS)
– diagonally weighted least squares (DWLS)

The most widely used are the TSLS and ML methods.
©2006, Fang Weiguo
School of Economics and Management, BUAA
Step 6 Evaluation of model fit

This stage involves the assessment of the model fit using a
variety of fit measures for the measurement and structural
model (and supporting/rejecting the proposed hypotheses).

The literature of SEM offers a stunning number of
alternative fit indices. Three that deserve special attention
are
– the chi-square statistic (2)
– the root mean square error of approximation (RMSEA)
– the comparative fit index (CFI)
©2006, Fang Weiguo
School of Economics and Management, BUAA
Step 6 Evaluation of model fit

A "good" value for the chi-square, is one that is not much
larger than the statistic's degrees of freedom, and one that is
associated with a "large" p-value.
– Typical rules of thumb look for p-values larger than .05 or .10.

RMSEA values between 0 and .05 imply good approximate
overall fit, whereas values above .10 indicate significant fit
problems.

CFI always ranges between 0 and 1.
– Values near 1 imply that the model is doing a reasonable job of
explaining covariance among the measures.
– CFI values of .90 or above indicate adequate fit.
©2006, Fang Weiguo
School of Economics and Management, BUAA
Stage 7 Model modification

This stage considers whether modifications to the model
have to be made in the light of the results obtained at the
previous stage.
– At this stage the analysis becomes exploratory in nature and results
from previous analysis are used to develop a better fitting model.

The aim is to identify specification errors and produce a new
model which fits the data better.
– This new model has to be verified on a second independent sample.
©2006, Fang Weiguo
School of Economics and Management, BUAA
Stage 8 Model cross-validation

This stage involves the cross-validation of the model with a
new data set.
– This is done by dividing the sample into two parts to
conduct a validation test.

Cross-validation test is important when modification indices
are used and the model didn’t provide an acceptable fit.
©2006, Fang Weiguo
School of Economics and Management, BUAA
Stage 8 Model cross-validation

Cross-validation can also be used to
– compare competing models in terms of predictive validity and
facilitate the selection of a model;
– compare the difference between samples belonging to different
populations;
– assess the impact of moderating variables.
©2006, Fang Weiguo
School of Economics and Management, BUAA
EXAMPLES

Example 1 Commercial research
©2006, Fang Weiguo
School of Economics and Management, BUAA
EXAMPLES
– Loyalty is directly dependent on Value and Satisfaction
– Value is dependent on Price and Satisfaction
– Satisfaction is dependent on Value and Quality
– The model proposes a reciprocal relationship between Value and
Satisfaction.
©2006, Fang Weiguo
School of Economics and Management, BUAA
EXAMPLES

A data set of 275 observations is used to compute a
correlation matrix, which is then used to test the model.
©2006, Fang Weiguo
School of Economics and Management, BUAA
EXAMPLES

The parameter estimates for the structural model lead to
these structural equations:
Value = 0.15 * Satisfaction - 0.47 * Price + 1
Satisfaction = 0.29 * Value + 0.54 * Quality +  2
Loyalty = 0.00 * Value + 0.83 * Satisfaction +  3

Fit indices
2(DF)
p-value
RMSEA
CFI
©2006, Fang Weiguo
97.11(48)
<0.001
0.061
0.96
School of Economics and Management, BUAA
EXAMPLES

Example 2 Insurance research
– Insuring intentions can be grouped into two kinds: transferring risk
vs. investing.
– Our objective is to investigate the effects of customer characteristics
on customers’ insuring intention.
– In particular, we are interested in identifying the difference in effects
of customer characteristics on intention of transferring risk and on
intention of investing.
©2006, Fang Weiguo
School of Economics and Management, BUAA
EXAMPLES

Based on the relevant results in consumer behavior research,
eight customer characteristics are hypothesized as
influencing customers’ insuring intention
– cultural sense
– social class
– economic ability
– Age
– Gender
– marital status
– family structure
– insurance consciousness
©2006, Fang Weiguo
School of Economics and Management, BUAA
EXAMPLES
©2006, Fang Weiguo
School of Economics and Management, BUAA
EXAMPLES

Four constructs, i.e., age, marital status, gender and family
structure, are not truly latent variables because they can be
measured directly.
– They are identical to their individual measurement items.

Cultural sense and social position, are measured by single
indicator.
– adopt educational level to measure the cultural sense construct
– adopt occupation position to measure the social class construct
©2006, Fang Weiguo
School of Economics and Management, BUAA
EXAMPLES

The measurement for economic ability involves
– income level
– income stability
– asset amount
– their influencing extension on insuring

The measurement for insurance consciousness includes
– risk perception
– insurance cognition

Insuring intention is measured by
– acceptance extension to insurance
– insuring inclination
©2006, Fang Weiguo
School of Economics and Management, BUAA
EXAMPLES

We adopted questionnaire survey to gather data from
people who live in Beijing.

A total of 350 questionnaires were distributed in various
sectors including finance service, IT, manufacturing,
education and so on.

278 were returned and finally 195 screened from the
responses were used in our empirical study.
©2006, Fang Weiguo
School of Economics and Management, BUAA
EXAMPLES

Cronbach’s alpha was used to evaluate the reliability of the
measurement scales of the various constructs.
– Results shows that the scales used in our empirical study are reliable.

Lisrel program was used to estimate and test the
hypothesized research model.

The variance/covariance matrix of the sample is as the input
of Lisrel to estimate the model parameters.
©2006, Fang Weiguo
School of Economics and Management, BUAA
EXAMPLES
©2006, Fang Weiguo
School of Economics and Management, BUAA
EXAMPLES

The customer characteristics that affecting the insuring
intention of transferring risk includes
– cultural sense
– social class
– insurance consciousness
– economic ability
– marital status

Other customer characteristics, including age, family
structure and gender, have no significant effect on the
insuring intention of transferring risk.
©2006, Fang Weiguo
School of Economics and Management, BUAA
EXAMPLES



Insurance consciousness (=0.65) is positively related to and
constitutes the most important determinant of the insuring
intention of transferring risk.
Social class (=0.14) and economic ability (=0.20) are
positively related to insuring intention of transferring risk.
Cultural sense (=-0.11) and marital status (=-0.22) are
negatively related to insuring intention of transferring risk.
– This means that the stronger insurance consciousness and economic
ability, the more likely a customer is to purchase insurance products
featured with transferring risk.
©2006, Fang Weiguo
School of Economics and Management, BUAA
EXAMPLES

One with higher educational level but with lower occupation
position has stronger intention to transferring risk through
purchasing insurance products.

The unmarried unfolds stronger insuring intention of
transferring risk than the married.
©2006, Fang Weiguo
School of Economics and Management, BUAA
EXAMPLES

The determinants of the insuring intention of investing are
different from that of the insuring intention of transferring
risk.
– Social class (=0.18), insurance consciousness (=0.12), and
economic ability (=0.37) are positively related to the insuring
intention of investing but with different strengths to that in Model 1.
– Cultural sense (=-0.14) and gender (=-0.27) are negatively related
to the insuring intention of investing.
– Age, martial status, and family structure have no significant effect
on the insuring intention of investing.
©2006, Fang Weiguo
School of Economics and Management, BUAA
EXAMPLES

The result reveals that
– the stronger is insurance consciousness and economic ability, the
stronger the intention to purchasing insurance products featured
with investing.
– those with higher educational level but with lower occupation
position more intended to obtain investment revenue through
purchasing insurance products.
– man pays more interest in obtaining revenue from insuring than
woman.
– Economic ability and gender constitute the most and second
important determinants of the insuring intention of investing
respectively.
©2006, Fang Weiguo
School of Economics and Management, BUAA