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So with reduced rank regression we identify response variables associated with our outcome of interest (Y) and model proc pls relationships between the independent variables say dietary data vs. the selected responses. If there is an association between the selected factor from this initial modelling and the outcome variable (Y), could I conclude that the association is due to mediating effects of the response variables or to the independent effect of the selected factor?

Thanks

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A comment from Wikipedia on Factor Analysis:

Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. For example, it is possible that variations in six observed variables mainly reflect the variations in two unobserved (underlying) variables. Factor analysis searches for such joint variations in response to unobserved latent variables. The observed variables are modelled as linear combinations of the potential factors, plus "error" terms. Factor analysis aims to find independent latent variables.

And also:

The theory behind factor analytic methods is that the information gained about the interdependencies between observed variables can be used later to reduce the set of variables in a dataset. Factor analysis is commonly used in biology, psychometrics, personality theories, marketing, product management, operations research, and finance. It may help to deal with data sets where there are large numbers of observed variables that are thought to reflect a smaller number of underlying/latent variables. It is one of the most commonly used inter-dependency techniques and is used when the relevant set of variables shows a systematic inter-dependence and the objective is to find out the latent factors that create a commonality.

So, to answer your question, "If there is an association between the selected factor from this initial modelling and the outcome variable (Y), could I conclude that the association is due to mediating effects of the response variables or to the independent effect of the selected factor?", per above, it is the latter, in my assessment,"the independent effect of the selected factor".

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  • $\begingroup$ Nice interpretation @AJKOER! However, factor analysis and RRR have different methodologies as explained. $\endgroup$
    – Patsy
    Commented Jul 2, 2020 at 16:55

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