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Structural Equation Modeling with AMOS

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Title: Structural Equation Modeling with AMOS


1
Structural Equation Modeling with AMOS
Johnny Amora De la Salle-College of Saint
Benilde Taft Avenue, Manila
SPSS Directions Philippines December 4,
2008 Sofitel Philippines Plaza Manila
2
Agenda
  • Introduction
  • What is SEM?
  • Why SEM?
  • What is AMOS?
  • Brief Statistical Background
  • Correlation and Regression Analysis
  • Path Analysis
  • Factor Analysis
  • Structural Equation Modeling

3
Agenda
  • 3. Sample Researches that used SEM
  • Construction and Validation of STAR-SDEAS
    Instrument
  • Effects of Language Dominance on the Attitudes of
    College HRM Students in Learning English
  • Effects of the Students Attitudes and
    Motivational Behavior in Learning English as a
    Second Language to their English Achievement
  • - Predicting Decisions of International Hotel
    Chains(IHCs) to invest Out of Country
    Training(OCT)

4
Agenda
  • 4. Demonstration/Hands-on with Amos 17
  • Data Input to the analysis with Amos
  • Predicting Decisions of International Hotel
    Chains(IHCs) to invest Out of Country
    Training(OCT)

5
Agenda
  • 5. SEM Assumptions
  • 6. Missing Data in SEM

6
What is SEM?
  • General approach of multivariate analysis used to
    study complex dependencies among variables
  • Extends standard techniques such as regression
    and factor analysis
  • Variables may be observed or unobserved (latent)

7
Why SEM?
  • Confirm relationships and test hypothesis-verify
    how variables affect each other and by how much.
  • Test complex relationships-any variable, observed
    or latent, can be used to predict any numeric
    variable.
  • Compare multiple groups or perform longitudinal
    studies.
  • Constrain parameters for more precise models.

8
What is AMOS?(Analysis of MOment Structures)
  • Amos is an easy to use SEM program that tests
    relationships among observed and latent variables
    and uses those models to test the hypotheses and
    confirm relationships.
  • Graphical language - no need to write equations
    or type commands
  • Easy to learn-user-friendly features such as
    drawing tools, configurable toolbars, and drag
    and drop capabilities.
  • Fast- models that once took days to create are
    now completed in minutes.

9
Brief Statistical Background
  • The relationship between regression analysis,
    path analysis, and factor analysis

10
Correlation Simple Regression
  • Correlation measures the strength and the
    direction of the relationship between two or more
    variables.
  • Simple Regression analysis extends to measure the
    extent to which a predictor variable (X) can be
    used to make a prediction about a criterion
    measure (Y)

11
Multiple Linear Regression Analysis
  • An extension of simple regression analysis in
    which several predictor variables are used to
    predict one criterion measure (Y).

Y b0 b1x1 b2x2 b3x3
12
Path Analysis
  • Path analysis is an extension of regression
  • In path analysis the researcher is examining the
    ability of more than one predictor variable to
    explain or predict multiple dependent variables.

13
Factor Analysis
  • FA is a fundamental component of SEM.
  • FA explores the inter-relationships among
    variables to discover if those variables can be
    grouped into a smaller set of underlying factors.
  • Three primary applications of FA
  • Explore data for patterns
  • Data reduction
  • Confirm hypothesis of factor structure

14
Exploratory FA EFA reveals pattern among the
inter-relationships of the variables
  • Data Reduction
  • Reduce a number of variables into a smaller and
    more manageable number of factors
  • FA can create scores for each subject that
    represents these higher order variables

15
Confirmatory Factor Analysis
  • CFA confirms an existing or hypothesized factor
    structure
  • CFA meets the third application of FA
  • To confirm a hypothesize factor structure
  • Use as a validity procedure in measurement
    research.

16
CFA versus EFA
  • CFA differs from EFA in that CFA, a specific
    relationship between the variables and the
    factors is confirmed.
  • Certain variables are hypothesized to go to given
    factors
  • Not all variables go to all factors

17
EFA CFA
  • In CFA, only certain items are proposed to be
    indicators of each factor.
  • The curved line indicates the relationship that
    could exist between the factors

18
Definition of Terms
  • As we enter into the first of our modeling
    procedures we must clarify some key terms
  • Measured variables
  • Exogenous variables
  • Endogenous variables
  • Direct effects
  • Indirect effects
  • Errors in prediction
  • Latent variable

19
Measured variables
  • Variables that the researcher has observed or
    measured
  • In all diagrams, measured variables are depicted
    by squares or rectangles
  • In path analysis, all variables are measured.

20
Exogenous Variables
  • A variable in a model that is not affected by
    another variable in the model.
  • In this path analysis, there are two exogenous
    variables X1 and X2.

21
Endogenous Variables
  • A variable in a model that is affected by another
    variable in the model.
  • In this path analysis, there are two endogenous
    variables Y1 and Y2.

22
Direct Effects
  • Those parameters that estimate the direct effect
    one variable has on another
  • These are indicated by the arrows that are drawn
    from one variable to another.
  • In this model, four direct effects are measured.

23
Indirect Effects
  • Indirect effects are those influences that one
    variable may have on another that is mediated
    through a third variable.
  • In this model, X1 and X2 have a direct effect on
    Y1 and indirect effect on Y2 through Y1

24
Errors in Prediction
  • As in any prediction model, errors in prediction
    always exist
  • Thus, Y1 and Y2 will have errors in prediction.

25
Latent or Unobserved variable
  • A variable not directly measured, but is inferred
    by the relationships or correlations among
    measured variables in the analysis.

26
Sample Researches that used SEM
27
Example 1 Construction and Validation of the
STAR-SDEAS Instrument
(Note This is a project of De La Salle-College
of Saint Benilde. Only the SEM part of the
project is presented)
STAR Students Teachers Assessment Results SDEAS
School of Deaf Education Applied Sciences
28
Objectives
  • To determine if the STAR-SDEAS instrument is
    valid and reliable.
  • To determine if the STAR-SDEAS instrument is
    Learner-Centered.

29
  • The 50-item STAR-SDEAS Instrument
  • The STAR-SDEAS instrument was developed based on
    the framework of Danielson with four domains
  • Planning Preparation - 7 items
  • Classroom Environment 20 items
  • Instruction 20 items
  • Professional Responsibilities 3 items

30
To determine if the STAR-SDEAS instrument is LC,
the correlation of the instrument with the
19-item Learner Centered Practices
Questionnaire(LCPQ) by McCombs(1997) was tested
using SEM approach.
31
Participants
  • 218 SDEAS students from 15 subjects handled by 15
    faculty members.
  • Per class consisted of 9 to 28 students.

32
Four-factor Hierarchical Model
  • The data fits the 4-factor Hierarchical model.
  • All variables within each domain are confirmed
    indicators of the domain.
  • The Planning Preparation, Classroom
    Environment, Instruction, Professional
    Responsibilities are confirmed significant
    domains of STAR-SDEAS.
  • The findings support the structural validity of
    the STAR-SDEAS instrument.

33
STAR-PE Instrument is significantly correlated to
the LC Instrument
34
Example 2 Effects of Language Dominance on the
Attitudes of College HRM Students in Learning
English
Part of the Masters thesis of Tess Castro, Univ
of Regina Carmeli-Malolos City
35
Effects of the Students Attitudes and
Motivational Behavior in Learning English as a
Second Language to the English Achievement
Part of the Masters thesis of Tess Castro, Univ
of Regina Carmeli-Malolos City
36
Example3 Predicting Decisions of International
Hotel Chains(IHCs) to invest Out of Country
Training(OCT)
The study postulated that the decision of the
international hotel chain (IHC) to invest
out-of-country training for their managers
depends on the three major factors benefits and
usefulness of the out-of-country training,
barriers encountered, and attitudes about the
out-of-country training. Moreover, the attitude
of the IHC is affected by the barriers
encountered and benefits and usefulness of the
out-of country training.
37
Results
38
Emerging Model
39
Demonstration/Hands-on with Amos 17
40
1. Data Input
Raw Data
41
Correlation Matrix
42
SEM Assumptions
  • A Reasonable Sample Size
  • a good rule of thumb is 15 cases per predictor in
    a standard ordinary least squares multiple
    regression analysis.
  • Applied Multivariate Statistics
    for the Social Sciences,
  • by James Stevens
  • researchers may go as low as five cases per
    parameter estimate in SEM analyses, but only if
    the data are perfectly well-behaved

  • Bentler and Chou (1987)
  • Usually 5 cases per parameter is equivalent to 15
    measured variables.

43
SEM Assumptions (contd)
  • Continuously and Normally Distributed Endogenous
    Variables

44
SEM Assumptions (contd)
  • Model Identification
  • P is of measured variables
  • P(P1)/2
  • DfP(P1)/2-( of estimated parameters)
  • If DFgt0 model is over identified
  • If DF0 model is just identified
  • If DFlt0 model is under identified

45
Missing data in SEM
  • Types of missing data
  • MCAR
  • Missing Completely at Random
  • MAR
  • Missing at Random
  • MNAR
  • Missing Not at Random

46
Handling Missing data in SEM
  • Listwise
  • Pairwise
  • Mean substitution
  • Regression methods
  • Expectation Maximization (EM) approach
  • Full Information Maximum Likelihood (FIML)
  • Multiple imputation(MI)

The two best methods FIML and MI
47
  • Thank you!
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