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An anonymous reader posted the following question on my blog.

Context:

The reader wanted to run a factor analysis on scales from a questionnaire - but the data was from paired husbands and wives.

Question:

  • Can factor analysis be run on dyadic data? If so, how?
  • Would the independence assumption hold for factor analysis?
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Structural equation models are better suited for this kind of data, e.g. by introducing an extra factor for couple which allows to account for the dependence structure (paired responses). David A. Kenny reviewed the main points for analysis dyadic data; although it doesn't focus on questionnaire analysis, it may help.

A couple of references :

  1. Olsen, JA and Kenny, DA (2006). Structural Equation Modeling With Interchangeable Dyads. Psychological Methods, 11(2), 127–141.
  2. McMahon,, JM, Pouget, ER, and Tortu, S (2006). A guide for multilevel modeling of dyadic data with binary outcomes using SAS PROC NLMIXED. Comput Stat Data Anal., 50(12), 3663–3680.
  3. Thompson, L and Walker, AJ (1982). The Dyad as the Unit of Analysis: Conceptual and Methodological Issues. Journal of Marriage and the Family, 889-900.
  4. Newsom, JT (2002). A multilevel structural equation model for dyadic data. Structural Equation Modeling, 9(3), 441-447.
  5. González, J, Tuerlinckx, F, and De Boeck, P (2009). Analyzing structural relations in multivariate dyadic binary data. Applied Multivariate Research, 13, 77-92.
  6. Gill, PS (2005). Bayesian Analysis of Dyadic Data.

For more thorough description of the models for dyadic data (although not restrained to item analysis), I would suggest

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  • $\begingroup$ Wow. That's a great set of references. I'm assuming that husbands and wives would not be interchangeable. I wonder if that matters. $\endgroup$ – Jeromy Anglim Sep 23 '10 at 9:51
  • $\begingroup$ It depends on the questions asked in the questionnaire. I came across a clinical study dealing with erectile function and sexual life (wife + husband), in this case the role of the respondents are not symmetric. $\endgroup$ – chl Sep 23 '10 at 9:55
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Yes, s/he can run a factor analysis on dyadic data. I would start with Kenny et al.'s (2006) "Dyadic Data Analysis". It is a great and extremly helpful book!

Another option is "Modeling Dyadic and Interdependent Data in the Developmental and Behavioral Sciences" (Card et al. 2008).

(If your anonymous read is able to read German, s/he might be interested in this presentation "Dyadische Datenanalyse: Lineare Strukturgleichungsmodelle").

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  • $\begingroup$ I pointed to similar books in my own response, sorry didn't see your response while I was writing... Card's book is very great! $\endgroup$ – chl Sep 23 '10 at 9:36
  • $\begingroup$ @chl Great, that you mentioned the Thompson/Walker-paper about "The Dyad as the Unit of Analysis". $\endgroup$ – Bernd Weiss Sep 23 '10 at 10:00

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