Examples: Confirmatory Factor Analysis And
Structural Equation Modeling
55
CHAPTER 5
EXAMPLES: CONFIRMATORY
FACTOR ANALYSIS AND
STRUCTURAL EQUATION
MODELING
Confirmatory factor analysis (CFA) is used to study the relationships
between a set of observed variables and a set of continuous latent
variables. When the observed variables are categorical, CFA is also
referred to as item response theory (IRT) analysis (Fox, 2010; van der
Linden, 2016). CFA with covariates (MIMIC) includes models where
the relationship between factors and a set of covariates are studied to
understand measurement invariance and population heterogeneity.
These models can include direct effects, that is, the regression of a factor
indicator on a covariate in order to study measurement non-invariance.
Structural equation modeling (SEM) includes models in which
regressions among the continuous latent variables are estimated (Bollen,
1989; Browne & Arminger, 1995; Joreskog & Sorbom, 1979). In all of
these models, the latent variables are continuous. Observed dependent
variable variables can be continuous, censored, binary, ordered
categorical (ordinal), unordered categorical (nominal), counts, or
combinations of these variable types.
CFA is a measurement model. SEM has two parts: a measurement
model and a structural model. The measurement model for both CFA
and SEM is a multivariate regression model that describes the
relationships between a set of observed dependent variables and a set of
continuous latent variables. The observed dependent variables are
referred to as factor indicators and the continuous latent variables are
referred to as factors. The relationships are described by a set of linear
regression equations for continuous factor indicators, a set of censored
normal or censored-inflated normal regression equations for censored
factor indicators, a set of probit or logistic regression equations for
binary or ordered categorical factor indicators, a set of multinomial
logistic regression equations for unordered categorical factor indicators,
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