Exploratory factor analysis (EFA) is a frequently used multivariate analysis technique in statistics.
Jennrich and Sampson (1966) solved a significant EFA factor loading matrix rotation problem
by deriving the direct Quartimin rotation. Jennrich was also the first to develop standard errors
for rotated solutions, although these have still not made their way into most statistical software
programs. This is perhaps because Jennrich’s achievements were partly overshadowed by the
subsequent development of confirmatory factor analysis (CFA) by Jöreskog (1969). The strict
requirement of zero cross-loadings in CFA, however, often does not fit the data well and has
led to a tendency to rely on extensive model modification to find a well-fitting model. In such
cases, searching for a well-fitting measurement model may be better carried out by EFA (Browne,
2001). Furthermore, misspecification of zero loadings usually leads to distorted factors with overestimated
factor correlations and subsequent distorted structural relations. This article describes an
EFA-SEM (ESEM) approach, where in addition to or instead of a CFA measurement model, an
EFA measurement model with rotations can be used in a structural equation model. The ESEM
approach has recently been implemented in the Mplus program. ESEM gives access to all the
usual SEM parameters and the loading rotation gives a transformation of structural coefficients
as well. Standard errors and overall tests of model fit are obtained. Geomin and Target rotations
are discussed. Examples of ESEM models include multiple-group EFA with measurement and
structural invariance testing, test–retest (longitudinal) EFA, EFA with covariates and direct effects,
and EFA with correlated residuals. Testing strategies with sequences
Exploratory factor analysis (EFA) is a frequently used multivariate analysis technique in statistics.
Jennrich and Sampson (1966) solved a significant EFA factor loading matrix rotation problem
by deriving the direct Quartimin rotation. Jennrich was also the first to develop standard errors
for rotated solutions, although these have still not made their way into most statistical software
programs. This is perhaps because Jennrich’s achievements were partly overshadowed by the
subsequent development of confirmatory factor analysis (CFA) by Jöreskog (1969). The strict
requirement of zero cross-loadings in CFA, however, often does not fit the data well and has
led to a tendency to rely on extensive model modification to find a well-fitting model. In such
cases, searching for a well-fitting measurement model may be better carried out by EFA (Browne,
2001). Furthermore, misspecification of zero loadings usually leads to distorted factors with overestimated
factor correlations and subsequent distorted structural relations. This article describes an
EFA-SEM (ESEM) approach, where in addition to or instead of a CFA measurement model, an
EFA measurement model with rotations can be used in a structural equation model. The ESEM
approach has recently been implemented in the Mplus program. ESEM gives access to all the
usual SEM parameters and the loading rotation gives a transformation of structural coefficients
as well. Standard errors and overall tests of model fit are obtained. Geomin and Target rotations
are discussed. Examples of ESEM models include multiple-group EFA with measurement and
structural invariance testing, test–retest (longitudinal) EFA, EFA with covariates and direct effects,
and EFA with correlated residuals. Testing strategies with sequences
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