Introduction to Structural Equation Modeling with Amos

149 Pages·2014·3.55 MB·English

Introduction to
Structural Equation Modeling
with Amos

Dr. Lluís Coromina (University of Girona, Spain)
Email: [email protected]

nd rd
2 and 3 October 2014
Outline
 Introduction
 Basic concepts. Types of variables. Basic composition
 Intuitive explanation of the basics of SEM
o Path analysis. The regression analysis model
o Indirect effects. Equations. Degrees of freedom. Specification errors
 Measurement errors in regression models
 Full SEM model
 Confirmatory Factor Analysis (CFA)
o Scale Reliability and Validity of a Construct
 SEM and modeling stages.
o Model specification
o Model identification
o Model estimation
o Fit diagnostics and model modification
 Results and interpretation
 Model modification

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Introduction

 To introduce models that relate variables measured with error.
 To introduce Structural Equation Models with latent variables (SEM).
 To learn all stages of fitting these models.
 To become familiar with the Amos software.
 To enable participants to critically read articles in which these models are applied.

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History

 SEM make it possible to:
o Fit linear relationships among a large number of variables. Possibly more than
one is dependent.
o Validate a questionnaire as a measurement instrument.
Quantify measurement error and prevent its biasing effect.
o Freely specify, constrain and test each possible relationship using theoretical
knowledge, testing hypotheses.

 In their most recent and advanced versions, SEM enable researchers to:
o Analyze non-normal data.
o Treat missing values by maximum likelihood.
o Treat complex sample data.

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History of models for the study of causality
 Analysis of variance (1920-1930): decomposition of the variance of a dependent
variable in order to identify the part contributed by an explanatory variable. Control
of third variables (experimental design).

 Macroeconometric models (1940-50): dependence analysis of non-experimental
data. All variables must be included in the model.

 Path analysis (1920-70): analysis of correlations. Otherwise similar to econometric
models.

 Factor analysis (1900-1970): analysis of correlations among multiple indicators of the
same variable. Measurement quality evaluation.

 SEM (1970): Econometric models, path analysis and factor analysis are joined
together. Relationships among variables measured with error, on non-experimental
data from an interdependence analysis perspective.

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History of models for the study of causality
SEM are nowadays very popular because they make it possible to (5 Cs, see Batista &
Coenders 2000):
Work with Constructs/factors/latent variables measured through indicators/observed
variables/manifest variables, and evaluate measurement quality.
Consider the true Complexity of phenomena, thus abandoning uni and bivariate
statistics.
Conjointly consider measurement and prediction, factor and path analysis, and thus
obtain estimates of relationships among variables that are free of measurement error
bias.
Introduce a Confirmatory perspective in statistical modelling. Prior to estimation, the
researcher must specify a model according to theory.
Decompose observed Covariances, and not only variances, from an interdependence
analysis perspective.

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Basic Concepts

 Latent variables (theoretical concepts that cannot be observed directly) =
unobserved = unmeasured

 Observed variables (indicators of the underlying construct which they are
presumed to represent)= manifest = measured

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Basic Concepts

Exogenous (Independent) vs Endogenous (dependent) latent variables.
F1 ‘causes’ F2
Changes in the values of the exogenous variables are not explaine by the model.
Rather, they are considered to be influenced by other factors external to the model
(background variabes such as gender, age, etc.).
Fluctuations in the endogenous variable is said to be explained by the model because
all latent variables that nfluence them are included in the model specification.

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Statistical Modeling

Models explain how the observed and latent variables are related to one another.
Diagram
Equations

Specification: Model based on researcher’s knowledge of the related theory
Testing on sample data
Goodness of fit between the hypothesized model and sample data. Testing how well
the observed data fit the restricted structure.
Observed data – Hypothesized model = Residual
DATA = MODEL + RESIDUAL

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Types of variables

Observed variables

Unobserved latent factors

Measurement error associated with an observed variable
Ei =reflects on their adequacy in measuring the related unobserved
(underlying) factors.

Residual error (disturbance) in the prediction of an unobserved factor

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