MICOM and reflective measurement models

[Green]

Hi

i have a question regarding the applicability of MICOM. Henseler et al. (2015) says, that MICOM is applicable to composite, reflective and formative models:

"All variance-based SEM techniques model latent variables as composites; that is, they create proxies as
linear combinations of indicator variables. In particular, no matter which outer weighting scheme is used
in PLS (Mode A, Mode B, or Mode C), the resulting latent variable is always modeled as a composite
(Henseler, 2010)."

It is not clear to me why its applicable to reflective models as the arrows are directed in the formative way in composite models. Additionally it needs the weights to calculate the "C", but reflective models only offer loadings.

[jmbecker]

In PLS path modeling all latent variables are represented as composites. In contrast to factor-based SEM (CBSEM/LISREL), where all latent variables are represented as common factors.
If you have a reflective measurement model, you still have outer weights (see also the report output) that are calculated. You usually only interpret the outer loadings for reflective measurement models, but the proxy for your conceptual latent variable in PLS is still a composite, regardless of measurement type (formative, reflective).

[AAljabr]

Hi all,

I have read the paper "Testing Measurement Invariance of Composites Using Partial Least Squares". Also, I have consulted other related papers (Henseler et al. 2016) and (Rigdon, 2012).

Regarding the issue related to the composites and factors, what I understood from the paper "Testing measurement invariance of composites using partial least squares", is that all constructs in PLS are composites, and these composites can be built on either formative or reflective measurement models. Also, in the empirical example section, the authors used the MICOM model invaraince test with formative and reflective constructs.

On page 20 and 21:
" We use the corporate reputation model (Schwaiger, 2004), as shown with its latent variables in
Figure 5, to provide a MICOM example with empirical data......... While the exogenous latent variables
(i.e., QUAL, PERF, CSOR, ATTR) represent composites that build on a formative measurement model
(Mode A), the endogenous latent variables (i.e., LIKE, COMP, CUSL) are composites with a reflective
measurement model (Mode A);"

However, what I understood from Henseler et al 2016 paper "PLS path modeling in new technology research: updated guidelins", is that PLS can contain two types of constructs, namely, factors and composites.

On page 4:
"PLS path models can contain two different forms of construct measurement: factor
models or composite models (see Rigdon, 2012, for a nice comparison of both types
of measurement models). The factor model hypothesizes that the variance of a set of
indicators can be perfectly explained by the existence of one unobserved variable (the
common factor) and individual random error. It is the standard model of behavioral
research. In Figure 1, the exogenous construct ξ and the endogenous construct η are
modeled as factors. In contrast, composites are formed as linear combinations of their
respective indicators. The composite model does not impose any restrictions on the
covariances between indicators of the same construct, i.e. it relaxes the assumption that
all the covariation between a block of indicators is explained by a common factor.
The composites serve as proxies for the scientific concept under investigation
(Ketterlinus et al., 1989; Rigdon, 2012; Maraun and Halpin, 2008; Tenenhaus, 2008)[1].
The fact that composite models are less restrictive than factor models makes it likely
that they have a higher overall model fit (Landis et al., 2000).".

On page 6:
"In some PLS path modeling software (e.g. SmartPLS and PLS-Graph), the depicted
direction of arrows in the measurement model does not indicate whether a factor or
composite model is estimated, but whether correlation weights (Mode A, represented by
arrows pointing from a construct to its indicators) or regression weights (Mode B,
represented by arrows pointing from indicators to their construct) shall be used to create
the proxy. In both cases PLS will estimate a composite model. Indicator weights estimated
by Mode B are consistent (Dijkstra, 2010) whereas indicators weights estimated by
Mode A are not, but the latter excel in out-of-sample prediction (Rigdon, 2012)."

In addition, what I understood is that MICOM is suitable for composites, and there are other model invariance tests for factor models.
On page 13:
"There is a plethora of papers discussing how to assess the measurement invariance of factor
models (see e.g. French and Finch, 2006), there is only one approach for assessing the
measurement invariance of composite models (Henseler et al., forthcoming).


From the above, the distinction between reflective constructs and factor models is not clear to me.

1. What is the real difference between reflective constructs and factor models? What would be a reflective composite and what would be a factor? And how the difference is transferred to the PLS context in terms of model specification?


2. Can I use the MICOM for both reflective and formative constructs? if not, how can I test for measurement model invariance test for reflective constructs. I could not find a suitable model invariance test for reflective constructs that is available in SmartPLS 3. The program provides the permutation p values for the difference between the two groups in terms of, for example, AVE and composite reliability. Should I use these for reflective constructs? Isn't similar to Ringle et al. (2011) approach when they tested for measurement invariance for their model's reflective constructs.

Thanks,

Henseler, J., Hubona, G., & Ray, P. A. (2016). Using PLS path modeling in new technology research: updated guidelines. Industrial Management & Data Systems, 116(1), 2-20

Henseler, J., Ringle, C.M. and Sarstedt, M. (forthcoming), “Testing measurement invariance of
composites using partial least squares”, International Marketing Review (in print).

Rigdon, E.E. (2012), "Rethinking partial least squares path modeling: in praise of simple
methods", Long Range Planning, Vol. 45 Nos 5/6, pp. 341-358.

Ringle, C. M., Sarstedt, M. and Zimmermann, L. (2011), "Customer Satisfaction with Commercial
Airlines: The Role of Perceived Safety and Purpose of Travel", Journal of Marketing Theory and
Practice, Vol. 19 No. 4, pp. 459-472.