Page 68 - Contributed Paper Session (CPS) - Volume 8

CPS2187 Lukasz Widla-Domaradzki

Anchored SEM – merging structural equation
models
Lukasz Widla-Domaradzki
Polish Agency for Enterprise Development
Abstract
When performing Classical Structural Equation Model a researcher quickly
discovers one main limitation: preparing SEM is very data-consuming
process . In most cases that means either find another statistical tool which
1
allows produce desired estimates or try to simplify proposed model, for
example cutting number of variables. Anchored SEM is the analytical tool that
allows to analytically create a connection between independent SEM models
drawn from the same sample. This allows to build smaller SEMs independently
and merge them on the latter stage. Anchored SEM may be a solution when
complex model is not computable. At this approach one SEM is embedded in
another not fully, but by the anchor: as part of other SEM model. An anchor in
this case is this part that allows to estimate to what extent both SEMs are
connected and – therefore – what estimates of the hypothetical larger SEM
(built from SEM1 and SEM2) should look like.

Keywords
Structural Equation Model; SEM

1. Introduction
Structural Equation Models (SEM) are still one of the most recognized tools
2
for preparing complex and composite indicators . They are often used when
the relation between latent variables is known and a researcher can assign
specific observed variables to the latent constructs. However, SEMs have
several limitations: 1) they require large sample to obtain satisfactory results ;
3
2) the variables cannot be multicollinear; 3) Structure of the model should be
known and well described in the theory. As a result very complex indicators
may not be computable because of that constraints. In this paper I propose
how to overcome the first problem. It usually occurs when sample is too small
but may also be useful to simplify very complex Structural Equation Models.

1 "The sample size, as a rule of thumb, is recommended to be more than 25 times the number
of parameters to be estimated, the minimum being a subject-parameter-ratio of 10:1",
Nachtigall C., Kroehne U., Funke F., Steyer S. “(Why) Should We Use SEM? Pros and Cons of
Structural Equation Modeling” in Methods of Psychological Research Online, 2003
2 E.g. Composite Learning Index: http://www.niagaraknowledgeexchange.com/wp-
content/uploads/sites/2/2014/10/2010CLI-Booklet_EN.pdf
3 Barbara M. Byrne, Structural Equation Modeling with AMOS, Routledge, 2009
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