Transcript CFA-SEM - National Chung Cheng University

Chapter 11
SEM: An Introduction
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-1
Chapter 11
SEM: An Introduction
LEARNING OBJECTIVES
Upon completing this chapter, you should be able to do
the following:
 Understand the distinguishing characteristics of SEM.
 Distinguish between variables and constructs.
 Understand structural equation modeling and how it
can be thought of as a combination of familiar
multivariate techniques.
 Know the basic conditions for causality and how SEM
can help establish a cause-and-effect relationship.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-2
Chapter 11
SEM: An Introduction
LEARNING OBJECTIVES continued . . .
Upon completing this chapter, you should be able to do
the following:
 Explain the types of relationships involved in SEM.
 Understand that the objective of SEM is to explain
covariance and how this translates into the “fit” of a
model.
 Know how to represent a SEM visually with a path
diagram.
 List the six stages of structural equations modeling
and understand the role of theory in the process.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-3
Structural Equations Modeling
• What is it?
• Why use it?
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-4
Structural Equations Modeling Defined
Structural Equations Modeling . . . is a family of
statistical models that seek to explain the
relationships among multiple variables. To do so, it
examines the “structure” of interrelationships
expressed in a series of equations, similar to a series
of multiple regression equations. These equations
depict all of the relationships among constructs (the
dependent and independent variables) involved in the
analysis. Constructs are unobservable or latent
factors that are represented by multiple variables.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-5
Distinguishing Features of SEM
 Estimation of Multiple and Interrelated


Relationships.
Represents unobserved (latent) concepts
and corrects for measurement error.
Defines a model to explain an entire set of
relationships.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-6
Latent Constructs and Abbreviations
 Exogenous constructs are the latent, multi-item
equivalent of independent variables. They use a
variate (linear combination) of measures to
represent the construct, which acts as an
independent variable in the model.
•
Multiple measured variables (x) represent the exogenous
constructs.
 Endogenous constructs are the latent, multi-item
equivalent to dependent variables. These
constructs are theoretically determined by factors
within the model.
•
Multiple measured variables (y) represent the
endogenous constructs.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-7
Two Latent Constructs and the Measured
Variables that Represent Them
Endogenous
Construct
Exogenous
Construct
X1


X2
X3
X4
Y1
Y2
Y3
Y4
Loadings represent the relationships from constructs to
variables as in factor analysis.
Path estimates represent the relationships between
constructs as does B in regression analysis.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-8
Distinguishing the Types of
Relationships Involved in SEM
Exogenous
•
•
A. Relationship Between
a Construct and a
Measured Variable
A Measurement Model
can be represented with
Type A, B and D
relationships.
The Structural Model
includes all types of
relationships.
B. Relationship Between a
Construct and Multiple
Measured Variables
X
or
Endogenous
Y
X1
Exogenous
X2
X3
C. Dependence Relationship
Between Two Constructs
(Structural Relationship)
D. Correlational
Relationship
Between Constructs
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
Construct 1
Construct 2
Construct 1
Construct 2
12-9
Establishing Causation – “Causal Modeling”
•
Causal Inference –
Hypothesizes a “cause-andeffect” relationship.
1.
2.
3.
4.
Covariation
Sequence
Nonspurious Covariance
Theoretical Support
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-10
Basics of SEM Estimation
 SEM explains the observed covariance among a set
of measured variables:
•
It does so by estimating the observed covariance matrix
with an estimated covariance matrix constructed based on
the estimated relationships among variables.
Observed
Covariance
Matrix
S
Estimated
Covariance
Matrix
• The closer these are, the
better the fit. When they
are equal, the fit is perfect.
Σk
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-11
Structural Equations Modeling Stages
Stage 1: Defining Individual Constructs
Stage 2: Developing the Overall Measurement Model
Stage 3: Designing a Study to Produce Empirical
Results
Stage 4: Assessing the Measurement Model Validity
Stage 5: Specifying the Structural Model
Stage 6: Assessing Structural Model Validity
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-12
Rules of Thumb 11–1
•
•
Structural Equation Modeling Introduction
No model should be developed for use with SEM
without some underlying theory. Theory is needed
to develop both the . . .
o Measurement model specification.
o Structural model specification.
Models can be represented visually with a path
diagram.
o Dependence relationships are represented with
single headed directional arrows.
o Correlational (covariance) relationships are
represented with two-headed arrows.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-13
•
•
Rules of Thumb 11–1 Continued . . .
Dependence relationships are sometimes, but not
always, hypothesized to be causal in nature. Causal
relationships are the strongest type of inference
made in applying multivariate statistics. Therefore,
they can be supported only when precise conditions
for causality exist.
o Covariance between the cause and effect.
o The cause must occur before the effect.
o Nonspurious association must exist between the cause and
effect.
o Theoretical support exists for the relationship between the
cause and effect.
Models developed with a model development
strategy should be cross-validated with an
independent sample.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-14
Stage 1: Defining Individual Constructs
•
•
•
•
Operationalizing the Constructs
Scales from Prior Research
New Scale Development
Pretesting
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-15
Stage 2: Developing the
Overall Measurement Model
•
•
•
Can the validity and unidimensionality
of the constructs be supported?
How many indicators for each
construct?
Is the measurement model reflective or
formative?
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-16
Stage 2: Developing the Overall
Measurement Model
•
•
Make constructs from measured
variables.
Draw a path diagram for the
measurement model.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-17
Stage 3: Designing a Study to
Produce Empirical Results
Missing Data
Options:
• Complete Case
or List-Wise
Deletion.
•
All-Available or
Pair-Wise
Deletion.
•
•
Assess the adequacy of the
sample size.
Select the estimation method
and missing data approach.
• Model-Based
Deletion.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-18
Stage 3: Designing a Study to
Produce Empirical Results
Six Issues . . .
Research Design
1. Type of data analyzes: covariances or
correlations.
2. Missing data.
3. Sample size.
Model Estimation
4. Model structure.
5. Estimation techniques.
6. Computer software used.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-19
SEM Sample Size Issues
Five considerations affecting the required
sample size for SEM include . . .
1. multivariate distribution of the data
2. estimation technique
3. model complexity
4. amount of missing data, and
5. amount of average error variance among
the reflective indicators.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-20
Rules of Thumb 11–2
•
•
SEM STAGES 1-3
When a model has scales borrowed from various
sources reporting other research, a pretest using
respondents similar to those from the population to be
studied is recommended to screen items for
appropriateness.
Pair-wise deletion of missing cases (all available
approach) is a good alternative for handling missing
data when the amount of missing data is less than 10
percent and the sample size is around 250 or more.
o As sample sizes become small or when missing data exceeds
10 percent, one of the imputation methods for missing data
becomes a good alternative for handling missing data.
o When the amount of missing data becomes very high (15
percent or more), SEM may not be appropriate.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-21
Rules of Thumb 11–2 continued . . .
•
•
•
Covariance matrices provide the researcher with far more flexibility
due to the relatively greater information content they contain and
are the recommended form of input to SEM models.
The minimum sample size for a particular SEM model depends on
several factors including the model complexity and the
communalities (average variance extracted among items) in each
factor. The following guidelines are offered:
o SEM models containing five or fewer constructs, each with
more than three items (observed variables), and with high Item
communalities (.6 or higher), can be adequately estimated with
samples as small as 100-150.
o When the number of factors is larger than six, some of which
have fewer than three measured items as indicators, and
multiple low communalities are present, sample size
requirements may exceed 500.
The sample size must be sufficient to allow the model to run, but
more important, it must adequately represent the population.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-22
Stage 4: Assessing Measurement
Model Validity
•
What is Goodness of Fit (GOF)?
   ( N 1)(S  k )
df 
•
•
1
[( p )( p  1)]  k
2
Types of GOF:
o Absolute Fit Measures.
o Incremental Fit Measures.
o Parsimonious Fit Measures.
Evaluate construct validity of the
measurement model.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-23
Guidelines for Establishing
Acceptable and Unacceptable Fit
•
•
•
•
Use multiple indices of differing types.
Adjust the index cutoff values based on model
characteristics.
Use indices to compare models.
The pursuit of better fit at the expense of testing
a true model is not a good trade-off.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-24
Is the Measurement Model Valid?
•
•
No – refine measures and design a
new study.
Yes – proceed to test the structural
model with stages 5 and 6.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-25
Stage 5: Specifying the Structural Model
•
•
Stage five involves specifying the structural
model by assigning relationships from one
construct to another based on the proposed
theoretical model. That is, the dependence
relationships that exist among the constructs
representing each of the hypotheses are
specified.
The end result is to convert the measurement
model to a structural model.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-26
Stage 5: Specifying the Structural Model
E
E
E
E
X1
X2
X3
X4
Price
E
X5
E
X6
E
X7
E
X8
(ξ1)
H1
Service (ξ2)
H2
Customer Share
Customer
Commitment (η2)
H4
(η1)
H3
Atmosphere (ξ3)
X9
E
X10
E
X11
E
Y1
Y2
Y3
Y4
Y5
Y6
Y7
Y8
E
E
E
E
E
E
E
E
X12
E
note: Measurement model specifications are shown in gray. Structural model specifications are shown in black.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-27
Stage 6: Assessing the
Structural Model Validity
•
•
Assess the goodness of fit (GOF) of the
structural model.
Evaluate the significance, direction, and
size of the structural parameter estimates.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-28
Rules of Thumb 11–3
•
•
Assessing Predictive Accuracy
As models become more complex, the likelihood of
alternative models with equivalent fit increases.
Multiple fit indices should be used to assess a model’s
goodness of fit. They should include:
o The X2 value and the associated df
o One absolute fit index (like the GFI, RMSEA or
SRMR)
o One incremental fit index (like the CFI or TLI)
o One goodness of fit index (GFI, CFI, TLI, . . . )
o One badness of fit index (RMSEA, SRMR, . . . )
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-29
Rules of Thumb 11–3 continued . . .
•
•
Assessing Predictive Accuracy
No single “magic” value for the fit indices that separates good
from poor models. It is not practical to apply a single set of cut-off
rules that apply for all measurement models and for that matter to
all SEM models of any type. The quality of fit depends heavily on
model characteristics including sample size and model complexity.
The quality of fit depends heavily on model characteristics,
including sample size and complexity . . .
 Simple models with small samples should be held to very
strict fit standards. Even an insignificant p-value for a very
simple model may not be very meaningful.
 More complex models with larger samples should not be held
to the same strict standards. Thus, when samples are large
and the model contains a large number of measured variables
and parameter estimates, cut-off values of .95 on key GOF
measures are unrealistic.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-30
Types of SEM GOF Measures
SEM has no single statistical test that best describes the “strength” of
the model’s predictions. Instead, researchers have developed three
different types of measures that in combination assess the results from three
perspectives: overall fit, comparative fit, and model parsimony.
1.
Absolute (overall) = measures overall goodness-of-fit for both the structural
and measurement models collectively. This type of measure does not make
any comparison to a specified null model (incremental fit measure) or adjust
for the number of parameters in the estimated model (parsimonious fit
measure).
2.
Incremental (comparative) = measures goodness-of-fit that compares the
current model to a specified “null” (independence) model to determine the
degree of improvement over the null model.
3.
Parsimonious = measures goodness-of-fit representing the degree of
model fit per estimated coefficient. This measure attempts to correct for
any “overfitting” of the model and evaluates the parsimony of the model
compared to the goodness-of-fit.
Selecting a rigid cutoff for the fit indices is like selecting a minimum R2
for a regression equation. Almost any value can be challenged.
Awareness of the factors affecting the values and good judgment are the
best guides to evaluating the size of the GOF indices.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-31
Is the Structural Model Valid?
• No
•
– refine model and test with
new data.
Yes – draw substantive
conclusions and
recommendations.
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-32
HBAT CFA/SEM Constructs and Indicator Variables
Organizational Commitment
OC1 = My work at HBAT gives me a sense of accomplishment.
OC2 = I am willing to put in a great deal of effort beyond that normally expected to help HBAT
be successful.
OC3 = I have a sense of loyalty to HBAT.
OC4 = I am proud to tell others that I work for HBAT.
Staying Intentions
SI1 = I am not actively searching for another job.
SI2 = I seldom look at the job listings on monster.com.
SI3 = I have no interest in searching for a job in the next year.
SI4 = How likely is it that you will be working at HBAT one year from today?
Attitudes Towards Co-Workers
AC1 = How happy are you with the work of your coworkers?
AC2 = How do you feel about your coworkers?
AC3 = How often do you do things with your coworkers on your days off?
AC4 = Generally, how similar are your coworkers to you?
Environmental Perceptions
EP1 = I am very comfortable with my physical work environment at HBAT.
EP2 = The place I work in is designed to help me do my job better.
EP3 = There are few obstacles to make me less productive in my workplace.
EP4 = What term best describes your work environment at HBAT?
Job Satisfaction
JS1 = All things considered, I feel very satisfied when I think about my job.
JS2 = When you think of your job, how satisfied do you feel?
JS3 = How satisfied are you with your current job at HBAT?
JS4 = How satisfied are you with HBAT as an employer?
JS5 = Please indicate your satisfaction with your current job with HBAT by placing a percentage in
the blank, with 0% = not satisfied at all and 100% = highly satisfied.
33
Description of HBAT CFA-SEM Database Variables
JS1
OC1
OC2
EP1
OC3
OC4
EP2
EP3
AC1
EP4
JS2
JS3
AC2
SI1
JS4
SI2
JS5
AC3
SI3
AC4
SI4
X22
X23
X24
X25
X26
X27
Variable Description
Variable Type
I feel satisfied when I think about my job. (0-10, Agree-Disagree)
Metric
My work at HBAT give me a sense of accomplishment (0-10, Agree-Disagree).
Metric
I am willing to put in a great deal of effort . . to help HBAT (0-10, Agree-Disagree).
Metric
I am . . . comfortable with my . . . work environment at HBAT (0-10, Agree-Disagree).
Metric
I have a sense of loyalty to HBAT (0-10, Agree-Disagree).
Metric
I am proud to tell others that I work for HBAT (0-10, Agree-Disagree).
Metric
The place I work in is designed to help me do my job better (0-10, Agree-Disagree).
Metric
There are few obstacles to make me less productive in my workplace (0-10, Ag-Disa). Metric
How happy are you with the work of your coworkers? (5-pt. Happy-Unhappy)
Metric
What term best describes your work environment? (7-pt. Hectic-Soothing?)
Metric
When you think of your job, how satisfied do you feel? (7-pt)
Metric
How satisfied are you with your current job with HBAT? (7-pt)
Metric
How do you feel about your coworkers? (7-pt. Unfavorable-Favorable)
Metric
I am not actively searching for another. (5-pt. Agree/Disagree)
Metric
How satisfied are you with HBAT as an employer? (5-pt. Not vs. Very Much)
Metric
I seldom look at the job listings on Monster.com. (5-pt. Agree-Disagree)
Metric
Please indicate your satisfaction with your current job. (0-100% Satisfied)
Metric
How often do you do things with your coworkers on your days off? (5-pt. Never-Often) Metric
I have no interest in searching for a job in the next year. (5-pt. Agree-Disagree)
Metric
Generally, how similar are your coworkers to you? (6-pt. Different-Similar)
Metric
How likely is it that you will be working at HBAT one year from today? (5-pt)
Metric
Your work type – full time or part time?
(0 = Full Time/1 = Part Time)
Nonmetric
Your gender – male or female?
(0 = Female/1 = Male)
Nonmetric
Your geographic location – in USA or outside USA? (0 = Outside/1 = USA)
Nonmetric
Your age in years ___?
Metric
34
How long have you worked for HBAT – years and months?
Metric
Performance – as measured by their supervisor.
Metric
Structural Equations Modeling
Learning Checkpoint
1.
2.
3.
4.
What is SEM?
What is confirmatory factor analysis (CFA)?
How does CFA differ from SEM?
What are the important issues to resolve in
designing a CFA/SEM study?
5. What is “fit” and how do you evaluate it?
Comment on “fit” for both CFA and SEM.
6. How do you know if you have a valid SEM
model?
Copyright © 2010 Pearson Education, Inc., publishing as Prentice-Hall.
12-35