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Dear Colleagues,

I have a client that would like to use principal components analysis to create a score for patient responses to a set of 4 self-report adherence questions and then use this score as a dependent variable in a regression model.  I have seen this done where PCA is applied and then the resulting first component is used as an independent variable in a regression model (e.g., Reynolds et al optimizing Measurement of Self-Reported Adherence with the ACTG Adherence Questionnaire, Clinical Science 2007).  However, I could not find any examples in which PCA is used to create a variable for the dependent variable.  Any input/suggestions and/or references would be greatly appreciated.

Thank you,
Kara

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Kara Bennett
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Yes, I've used say, the variables derived from principal components (PC) as dependent variables in exploratory analyses of Patient reported outcomes" (a.k.a "PRO's" for work submitted to FDA)  .  Presumably the PC uses variables that are reasonably understood to be dependent variables.

I've read some  very  interesting applications of PC in meteorology, ecology etc.

on a quick google search - some links that may be helpful:

http://www.muskokawatershed.org/wp-content/uploads/UofG-Phosphorus.pdf

http://bio.classes.ucsc.edu/bio286/MIcksBookPDFs/QK17.PDF

http://www.cc.gatech.edu/~isbell/classes/reading/papers/sparsepc.pdf

https://entuk.org/docs/prof/clinical_outcomes/voiss_patient_derived_symptom_scale

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2834659/

http://www.biomedcentral.com/content/pdf/1477-7525-8-22.pdf

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Chris Barker, Ph.D.
Consultant and
Adjunct Associate Professor of Biostatistics
www,barkerstats.com

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"In composition you have all the time you want to decide what to say in 15 seconds, in improvisation you have 15 seconds."
-Steve Lacy
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I have seen this done, although I don't recall where.  I think it is fine; perhaps better than using PCA to reduce the space of the independent variables (where partial least squares might be better). However, perhaps your client wants factor analysis rather than PCA?

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Peter Flom
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Kara, I agree with earlier comments that this sounds reasonable. I seem to recall PCA for independent variable reduction being advocated in Harrell's book on Regression Modeling Strategies. But it actually may work out really well in the dependent variable scenario depending on the type of data you have. Someone once told me to think of the first PCA component as the 'best' weighted sum of the input variables. If the measures all point to the same general latent or unmeasured construct, then separate regressions may work out poorly if those separate outcomes have low variability or have small ranges. Suppose you were trying to regress on three or five Likert score outcomes, a weighted composite would likely fall on a morespread out contiuum than the separate indices. Also, if you are only pulling off the first component then the PCA versus FA is moot. But if you are doing more than 1 then I agree with Peter. But if you only have 4 items to begin with then 1 PCA seems a more likely goal. Good Luck! ------------------------------------------- Jason Brinkley East Carolina University -------------------------------------------
Original Message: Sent: 04-09-2014 05:44 From: Peter Flom Subject: principal components analysis applied to dependent variable in regression I have seen this done, although I don't recall where. I think it is fine; perhaps better than using PCA to reduce the space of the independent variables (where partial least squares might be better). However, perhaps your client wants factor analysis rather than PCA? ------------------------------------------- Peter Flom -------------------------------------------
Original Message: Sent: 04-08-2014 22:25 From: Kara Bennett Subject: principal components analysis applied to dependent variable in regression Dear Colleagues, I have a client that would like to use principal components analysis to create a score for patient responses to a set of 4 self-report adherence questions and then use this score as a dependent variable in a regression model. I have seen this done where PCA is applied and then the resulting first component is used as an independent variable in a regression model (e.g., Reynolds et al optimizing Measurement of Self-Reported Adherence with the ACTG Adherence Questionnaire, Clinical Science 2007). However, I could not find any examples in which PCA is used to create a variable for the dependent variable. Any input/suggestions and/or references would be greatly appreciated. Thank you, Kara ------------------------------------------- Kara Bennett -------------------------------------------

Another option is to select the combination that is best predicted by the independent variables. This could be obtained using canonical correlation analysis and the first canonical.  This would essentially find the linear correlation most related to the predictor variables,

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Pedro Saavedra
Technical Director
ICF International
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You may wish to consider canonical correlation analysis so that you do not restrict the dependence to a single variable

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Keith Ord
Professor
Georgetown Univ
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Dear All,

Thank you so much for all of your helpful responses.  I greatly appreciate your time in responding to my question and you have given me some good ideas for further reading and investigation.  (Arthur, I have had a chance to discuss your questions with my client and will respond to your questions in a separate email).

Sincerely,
Kara

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Kara Bennett
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Original Message:
Sent: 04-09-2014 09:51
From: J. Ord
Subject: principal components analysis applied to dependent variable in regression

You may wish to consider canonical correlation analysis so that you do not restrict the dependence to a single variable

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Keith Ord
Professor
Georgetown Univ
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Also, how many respondents do you have?


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Arthur Kendall
Social Research Consultants
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What is the response scale on the 4 items?
Had the instrument been developed using some form of factor analysis? (PCA, PFA, etc.)
Was internal consistency reliability reported when the scale was developed?

Scale scores are frequently used as DVs when the DVs are values, attitudes, achievement, etc.



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Arthur Kendall
Social Research Consultants
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