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RE: st: Composite measures

From   Nick Cox <>
To   "''" <>
Subject   RE: st: Composite measures
Date   Wed, 15 Feb 2012 12:38:05 +0000

If you consider that exploratory factor analysis is the way to go, then you use values of (often called scores of) your first factor as the best summary of the two variables. It will in effect be, or be related to, a weighted mean of your two variables. 

However, you do have categorical variables, but exploratory factor analysis, unless you use some special flavour specifically designed for your problem, would treat those as measurements on continuous scales. Any jury of statistical people would divide into factions on whether that is still a good idea, dubious at best, or totally inappropriate. 

Cameron's suggestions may contain more positive advice, but something that is quick and easy is a cross-tabulation or appropriate graph of your two categorical variables, which will suggest how strongly they are related. If the relationship is weak, no composite variable is going to work well as a substitute for both. 


Alessandro Freire

Maarten, thank you for your reply. I believe exploratory factor
analysis is more appropriate for my case. Nevertheless, I still don´t
know how to extract the mean from two variables with different scales.
Any ideas on that?

On Wed, Feb 15, 2012 at 12:43 AM, Cameron McIntosh <> wrote:

> Thanks Maarten for the link to your paper, very interesting. I might also suggest some more general conceptual and methodological treatments of this topic, which is pretty hot these days in marketing and social psych research:

> Hardin, A.M., & Marcoulides, G.A. (2011). A Commentary on the Use of Formative Measurement. Educational and Psychological Measurement, Online First.
> Hardin, A.M., Chang, J.C.-J., Fuller, M.A., & Torkzadeh, G. (2011). Formative Measurement and Academic Research: In Search of Measurement Theory. Educational and Psychological Measurement, 71(2), 281-305.
> Grace, J.B., & Bollen, K.A. (2008). Representing general theoretical concepts in structural equation models: the role of composite variables. Environmental and Ecological Statistics, 15(2), 191-213.
> Cadogan, J.W., & Lee, N. Improper Use of Endogenous Formative Variables. Journal of Business Research, forthcoming.
> Kim, G., Shin, B., & Grover, V. (2010). Investigating Two Contradictory Views of Formative Measurement in Information Systems Research. MIS Quarterly, 34(2), 345-365.
> Edwards, J.R. (2011). The fallacy of formative measurement. Organizational Research Methods, 14(2), 370-388.
> Treiblmaier, H., Bentler, P.M., & Mair, P. (2011). Formative constructs implemented via common factors. Structural Equation Modeling, 18(1), 1-17.
> Baxter, R. (2009). Reflective and formative metrics of relationship value: A commentary essay. Journal of Business Research, 62(12), 1370-1377.
> Bollen, K.A., & Davis, W.R. (2009). Causal Indicator Models: Identification, Estimation, and Testing. Structural Equation Modeling, 16(3), 498-522.
> Howell, R. D., Breivik, E., & Wilcox, J.B. (2007). Reconsidering Formative Measurement. Psychological Methods, 12(2), 205-218.
> Bagozzi, R. P. (2007). On the Meaning of Formative Measurement and How It Differs From Reflective Measurement: Comment on Howell, Breivik and Wilcox. Psychological Methods, 12(2), 229-237.
> Bollen, K. A. (2007). Interpretational Confounding IS Due to Misspecification, Not to Type of Indicator:  Comment on Howell, Breivik, and Wilcox. Psychological Methods, 12(2), 219-228.
> Howell, R. D., Breivik, E., & Wilcox, J. B. (2007). Is Formative Measurement Really Measurement? Psychological Methods, 12(2), 238-245.
> Franke, G. R., Preacher, K. J., & Rigdon, E. E. (2008). The Proportional Structural Effects of Formative Indicators. Journal of Business Research, 61(12), 1229-1237.
> Wilcox, J. B., Howell, R. D., & Breivik, E. (2008). Questions About Formative Measurement. Journal of Business Research, 61(12), 1219-1228.
> Diamantopoulos, A., Riefler, P., & Roth, K. P. (2008). Advancing Formative Measurement Models. Journal of Business Research, 61(12), 1203-1218.
> Coltman, T., Devinney, T.M., Midgley, D.F. & Veniak, S. (2008). Formative versus reflective measurement models: Two applications of formative measurement. Journal of Business Research, 61(12), 1250-1262.
> Bollen, K.A., Lennox, R.D., & Dahly, D.L. (2009). Practical application of the vanishing tetrad test for causal indicator measurement models: An example from health-related quality of life. Statistics in Medicine, 28(10), 1524-1536.
> Roberts, N., & Thatcher, J. (2009). Conceptualizing and testing formative constructs: tutorial and annotated example. ACM SIGMIS Database archive, 40(3), 9-39. ACM New York, NY.

>> From:

>> The key question is whether you believe that there is some latent
>> concept (interest in politics) that influences the answers on those
>> two questions or whether you believe that the things asked in those
>> two questions add up / influence the latent concept. In the former
>> case you can use techniques like factor analysis (see: -help factor-)
>> to create the composite and in the latter case you use sheaf
>> coefficients to create the composite (see -ssc desc sheafcoef- and
>> <>.

>> On Tue, Feb 14, 2012 at 7:25 PM, Alessandro Freire wrote:

>> > I want to create a composite measure by using the mean of two
>> > variables regarding interest in politics, but their scales are
>> > different. One of them is scaled from 0 to 10, the other goes from 1
>> > to 5. What should I do so that their weights are equally distributed
>> > in the new variable?

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