Title: Structural Equation Modeling with AMOS
1Structural 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
2Agenda
- Introduction
- What is SEM?
- Why SEM?
- What is AMOS?
- Brief Statistical Background
- Correlation and Regression Analysis
- Path Analysis
- Factor Analysis
- Structural Equation Modeling
3Agenda
- 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)
4Agenda
- 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)
5Agenda
- 5. SEM Assumptions
- 6. Missing Data in SEM
6What 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)
7Why 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.
8What 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.
9Brief Statistical Background
- The relationship between regression analysis,
path analysis, and factor analysis
10Correlation 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)
11Multiple 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
12Path 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.
13Factor 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
14Exploratory 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
15Confirmatory 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.
16CFA 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
17EFA 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.
20Exogenous 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.
21Endogenous 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.
22Direct 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.
23Indirect 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
24Errors in Prediction
- As in any prediction model, errors in prediction
always exist - Thus, Y1 and Y2 will have errors in prediction.
25Latent or Unobserved variable
- A variable not directly measured, but is inferred
by the relationships or correlations among
measured variables in the analysis.
26Sample Researches that used SEM
27Example 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
28Objectives
- 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
30To 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.
31Participants
- 218 SDEAS students from 15 subjects handled by 15
faculty members. - Per class consisted of 9 to 28 students.
32Four-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.
33STAR-PE Instrument is significantly correlated to
the LC Instrument
34Example 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
35Effects 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
36Example3 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.
37Results
38Emerging Model
39Demonstration/Hands-on with Amos 17
401. Data Input
Raw Data
41Correlation Matrix
42SEM 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.
43SEM Assumptions (contd)
- Continuously and Normally Distributed Endogenous
Variables
44SEM 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
45Missing data in SEM
- Types of missing data
- MCAR
- Missing Completely at Random
- MAR
- Missing at Random
- MNAR
- Missing Not at Random
46Handling 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