Structural Equation Modeling with AMOS

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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
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Agenda

• Introduction
• What is SEM?
• Why SEM?
• What is AMOS?
• Brief Statistical Background
• Correlation and Regression Analysis
• Path Analysis
• Factor Analysis
• Structural Equation Modeling

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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)

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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)

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Agenda

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

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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)

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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.

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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.

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Brief Statistical Background

• The relationship between regression analysis,
  path analysis, and factor analysis

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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)

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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
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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.

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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

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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

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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.

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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

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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

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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

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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.

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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.

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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.

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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.

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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

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Errors in Prediction

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

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Latent or Unobserved variable

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

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Sample Researches that used SEM
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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
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Objectives

• To determine if the STAR-SDEAS instrument is
  valid and reliable.
• To determine if the STAR-SDEAS instrument is
  Learner-Centered.

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• 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

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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.
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Participants

• 218 SDEAS students from 15 subjects handled by 15
  faculty members.
• Per class consisted of 9 to 28 students.

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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.

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STAR-PE Instrument is significantly correlated to
the LC Instrument
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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
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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
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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.
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Results
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Emerging Model
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Demonstration/Hands-on with Amos 17
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1. Data Input
Raw Data
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Correlation Matrix
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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.

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SEM Assumptions (contd)

• Continuously and Normally Distributed Endogenous
  Variables

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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

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Missing data in SEM

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

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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
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• Thank you!