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Published in: BMC Medical Research Methodology 1/2012

Open Access 01-12-2012 | Debate

Should researchers use single indicators, best indicators, or multiple indicators in structural equation models?

Authors: Leslie A Hayduk, Levente Littvay

Published in: BMC Medical Research Methodology | Issue 1/2012

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Abstract

Background

Structural equation modeling developed as a statistical melding of path analysis and factor analysis that obscured a fundamental tension between a factor preference for multiple indicators and path modeling’s openness to fewer indicators.

Discussion

Multiple indicators hamper theory by unnecessarily restricting the number of modeled latents. Using the few best indicators – possibly even the single best indicator of each latent – encourages development of theoretically sophisticated models. Additional latent variables permit stronger statistical control of potential confounders, and encourage detailed investigation of mediating causal mechanisms.

Summary

We recommend the use of the few best indicators. One or two indicators are often sufficient, but three indicators may occasionally be helpful. More than three indicators are rarely warranted because additional redundant indicators provide less research benefit than single indicators of additional latent variables. Scales created from multiple indicators can introduce additional problems, and are prone to being less desirable than either single or multiple indicators.
Appendix
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Literature
1.
go back to reference Thurstone LL: Multiple Factor Analysis. 1947, Chicago: University of Chicago Press Thurstone LL: Multiple Factor Analysis. 1947, Chicago: University of Chicago Press
2.
go back to reference Harman HH: Modern Factor Analysis. 1967, Chicago: University of Chicago Press, 2 Harman HH: Modern Factor Analysis. 1967, Chicago: University of Chicago Press, 2
3.
go back to reference Lawley DN, Maxwell AE: Factor Analysis as a Statistical Method. 1971, London: Butterworth & Co, 2 Lawley DN, Maxwell AE: Factor Analysis as a Statistical Method. 1971, London: Butterworth & Co, 2
4.
go back to reference Mulaik SA: The Foundations of Factor Analysis. 1972, New York: McGraw-Hill Mulaik SA: The Foundations of Factor Analysis. 1972, New York: McGraw-Hill
5.
go back to reference Wright S: Correlation and causation. J Agric Res. 1921, 20: 557-585. Wright S: Correlation and causation. J Agric Res. 1921, 20: 557-585.
6.
go back to reference Wright S: The method of path coefficients. Ann Math Stat. 1934, 5: 161-215. 10.1214/aoms/1177732676.CrossRef Wright S: The method of path coefficients. Ann Math Stat. 1934, 5: 161-215. 10.1214/aoms/1177732676.CrossRef
7.
go back to reference Blalock HM: Causal Inferences in Nonexperimental Research. 1964, Chapel Hill: University of North Carolina Press Blalock HM: Causal Inferences in Nonexperimental Research. 1964, Chapel Hill: University of North Carolina Press
8.
go back to reference Duncan OD: Introduction to Structural Equation Models. 1975, New York: Academic Press Duncan OD: Introduction to Structural Equation Models. 1975, New York: Academic Press
9.
go back to reference Heise DR: Causal Analysis. 1975, New York: John Wiley and Sons Heise DR: Causal Analysis. 1975, New York: John Wiley and Sons
10.
go back to reference Byrne BM: A Primer of LISREL: Basic Applications and Programming for Confirmatory Factor Analytic Models. 1989, New York: Springer-VerlagCrossRef Byrne BM: A Primer of LISREL: Basic Applications and Programming for Confirmatory Factor Analytic Models. 1989, New York: Springer-VerlagCrossRef
11.
go back to reference Kline RB: Principles and Practice of Structural Equation Modeling. 2005, New York: Guilford Press Kline RB: Principles and Practice of Structural Equation Modeling. 2005, New York: Guilford Press
12.
go back to reference Byrne BM: Structural Equation Modeling with LISREL, PRELIS, and SIMPLIS. 1998, Lawrence Erlbaum Associate: Mahwah NJ Byrne BM: Structural Equation Modeling with LISREL, PRELIS, and SIMPLIS. 1998, Lawrence Erlbaum Associate: Mahwah NJ
13.
go back to reference Byrne BM: Structural Equation Modeling with EQS: Basic Concepts, Applications, and Programming. 2006, Lawrence Erlbaum Associates: Mahwah NJ, 2 Byrne BM: Structural Equation Modeling with EQS: Basic Concepts, Applications, and Programming. 2006, Lawrence Erlbaum Associates: Mahwah NJ, 2
14.
go back to reference Bollen KA: Structural Equations with Latent Variables. 1989, New York: WileyCrossRef Bollen KA: Structural Equations with Latent Variables. 1989, New York: WileyCrossRef
15.
go back to reference Hayduk LA: Structural Equation Modeling with LISREL: Essentials and Advances. 1987, Baltimore: Johns Hopkins University Press Hayduk LA: Structural Equation Modeling with LISREL: Essentials and Advances. 1987, Baltimore: Johns Hopkins University Press
16.
go back to reference Hayduk LA: LISREL Issues, Debates and Strategies. 1996, Baltimore: Johns Hopkins University Press Hayduk LA: LISREL Issues, Debates and Strategies. 1996, Baltimore: Johns Hopkins University Press
17.
go back to reference Anderson JC, Gerbing DW: Structural equation modeling in practice: a review and recommended two-step approach. Psychol Bull. 1988, 103: 411-423.CrossRef Anderson JC, Gerbing DW: Structural equation modeling in practice: a review and recommended two-step approach. Psychol Bull. 1988, 103: 411-423.CrossRef
18.
go back to reference Anderson JC, Gerbing DW: Assumptions and comparative strengths of the two-step approach: comment on Fornell and Yi. Sociol Method Res. 1992, 20: 321-33. 10.1177/0049124192020003002.CrossRef Anderson JC, Gerbing DW: Assumptions and comparative strengths of the two-step approach: comment on Fornell and Yi. Sociol Method Res. 1992, 20: 321-33. 10.1177/0049124192020003002.CrossRef
19.
go back to reference Fornell C, Yi Y: Assumptions of the two-step approach to latent variable modeling. Sociol Method Res. 1992, 20: 291-320. 10.1177/0049124192020003001.CrossRef Fornell C, Yi Y: Assumptions of the two-step approach to latent variable modeling. Sociol Method Res. 1992, 20: 291-320. 10.1177/0049124192020003001.CrossRef
20.
go back to reference Fornell C, Yi Y: Assumptions of the two-step approach to latent modeling. Sociol Method Res. 1992, 20: 334-339. 10.1177/0049124192020003003.CrossRef Fornell C, Yi Y: Assumptions of the two-step approach to latent modeling. Sociol Method Res. 1992, 20: 334-339. 10.1177/0049124192020003003.CrossRef
22.
go back to reference Hayduk LA, Glaser DN: Jiving the four-step, waltzing around factor analysis, and other serious fun. Struct Equ Model. 2000, 7: 1-35. 10.1207/S15328007SEM0701_01.CrossRef Hayduk LA, Glaser DN: Jiving the four-step, waltzing around factor analysis, and other serious fun. Struct Equ Model. 2000, 7: 1-35. 10.1207/S15328007SEM0701_01.CrossRef
23.
go back to reference Mulaik SA, Millsap RE: Doing the four-step right. Struct Equ Model. 2000, 7: 36-73. 10.1207/S15328007SEM0701_02.CrossRef Mulaik SA, Millsap RE: Doing the four-step right. Struct Equ Model. 2000, 7: 36-73. 10.1207/S15328007SEM0701_02.CrossRef
24.
go back to reference Bollen KA: Modeling strategies: in search of the holy grail. Struct Equ Model. 2000, 7: 74-81. 10.1207/S15328007SEM0701_03.CrossRef Bollen KA: Modeling strategies: in search of the holy grail. Struct Equ Model. 2000, 7: 74-81. 10.1207/S15328007SEM0701_03.CrossRef
25.
go back to reference Bentler PM: Rites, wrongs, and gold in model testing. Struct Equ Model. 2000, 7: 82-91. 10.1207/S15328007SEM0701_04.CrossRef Bentler PM: Rites, wrongs, and gold in model testing. Struct Equ Model. 2000, 7: 82-91. 10.1207/S15328007SEM0701_04.CrossRef
26.
go back to reference Herting JR, Costner HL: Another perspective on the “proper number of factors” and the appropriate number of steps. Struct Equ Model. 2000, 7: 92-110. 10.1207/S15328007SEM0701_05.CrossRef Herting JR, Costner HL: Another perspective on the “proper number of factors” and the appropriate number of steps. Struct Equ Model. 2000, 7: 92-110. 10.1207/S15328007SEM0701_05.CrossRef
27.
go back to reference Hayduk LA, Glaser DN: Doing the four-step, right-2-3, wrong-2-3: A brief reply to Mulaik and Millsap; Bollen; Bentler; and Herting and Costner. Struct Equ Model. 2000, 7: 111-123. 10.1207/S15328007SEM0701_06.CrossRef Hayduk LA, Glaser DN: Doing the four-step, right-2-3, wrong-2-3: A brief reply to Mulaik and Millsap; Bollen; Bentler; and Herting and Costner. Struct Equ Model. 2000, 7: 111-123. 10.1207/S15328007SEM0701_06.CrossRef
28.
go back to reference Barrett P: Structural equation modelling: Adjudging model fit. Personal Individ Differ. 2007, 42: 815-824. 10.1016/j.paid.2006.09.018.CrossRef Barrett P: Structural equation modelling: Adjudging model fit. Personal Individ Differ. 2007, 42: 815-824. 10.1016/j.paid.2006.09.018.CrossRef
29.
go back to reference Hayduk LA, Cummings GG, Boadu K, Pazderka-Robinson H, Boulianne S: Testing! Testing! One, two, three – Testing the theory in structural equation models!. Personal Individ Differ. 2007, 42: 841-850. 10.1016/j.paid.2006.10.001.CrossRef Hayduk LA, Cummings GG, Boadu K, Pazderka-Robinson H, Boulianne S: Testing! Testing! One, two, three – Testing the theory in structural equation models!. Personal Individ Differ. 2007, 42: 841-850. 10.1016/j.paid.2006.10.001.CrossRef
30.
go back to reference McIntosh CN: Rethinking fit assessment in structural equation modelling: A commentary and elaboration on Barrett (2007). Personal Individ Differ. 2007, 42: 859-867. 10.1016/j.paid.2006.09.020.CrossRef McIntosh CN: Rethinking fit assessment in structural equation modelling: A commentary and elaboration on Barrett (2007). Personal Individ Differ. 2007, 42: 859-867. 10.1016/j.paid.2006.09.020.CrossRef
31.
go back to reference Millsap RE: Structural equation modeling made difficult. Personal Individ Differ. 2007, 42: 875-881. 10.1016/j.paid.2006.09.021.CrossRef Millsap RE: Structural equation modeling made difficult. Personal Individ Differ. 2007, 42: 875-881. 10.1016/j.paid.2006.09.021.CrossRef
32.
go back to reference Mulaik SA: There is a place for approximate fit in structural equation modelling. Personal Individ Differ. 2007, 42: 883-891. 10.1016/j.paid.2006.10.024.CrossRef Mulaik SA: There is a place for approximate fit in structural equation modelling. Personal Individ Differ. 2007, 42: 883-891. 10.1016/j.paid.2006.10.024.CrossRef
33.
go back to reference Steiger JH: Understanding the limitations of global fit assessment in structural equation modeling. Personal Individ Differ. 2007, 42: 893-898. 10.1016/j.paid.2006.09.017.CrossRef Steiger JH: Understanding the limitations of global fit assessment in structural equation modeling. Personal Individ Differ. 2007, 42: 893-898. 10.1016/j.paid.2006.09.017.CrossRef
34.
go back to reference Hayduk LA, Pazderka-Robinson H: Fighting to understand the world causally: Three battles connected to the causal implications of structural equation models. Pp 147-171 in Outhwaite W, Turner S (eds.), Sage Handbook of Social Science Methodology. 2007, London: Sage Publications Hayduk LA, Pazderka-Robinson H: Fighting to understand the world causally: Three battles connected to the causal implications of structural equation models. Pp 147-171 in Outhwaite W, Turner S (eds.), Sage Handbook of Social Science Methodology. 2007, London: Sage Publications
35.
go back to reference Jöreskog K, Sörbom D: LISREL 8: Users Reference Guide. 1996, Chicago: Scientific Software International Jöreskog K, Sörbom D: LISREL 8: Users Reference Guide. 1996, Chicago: Scientific Software International
36.
go back to reference Entwisle DR, Hayduk LA, Reilly TW: Early Schooling: Cognitive and Affective Outcomes. 1982, Baltimore: Johns Hopkins University Press Entwisle DR, Hayduk LA, Reilly TW: Early Schooling: Cognitive and Affective Outcomes. 1982, Baltimore: Johns Hopkins University Press
37.
go back to reference Hayduk LA: Personal space: understanding the simplex model. J Nonverbal Behav. 1994, 18: 245-260. 10.1007/BF02170028.CrossRef Hayduk LA: Personal space: understanding the simplex model. J Nonverbal Behav. 1994, 18: 245-260. 10.1007/BF02170028.CrossRef
38.
go back to reference Hayduk LA: Personal space: the conceptual and measurement implications of structural equation models. Can J Behav Sci. 1985, 17: 140-149.CrossRef Hayduk LA: Personal space: the conceptual and measurement implications of structural equation models. Can J Behav Sci. 1985, 17: 140-149.CrossRef
39.
go back to reference Hayduk LA, Stratkotter RF, Rovers MW: Sexual orientation and the willingness of Catholic seminary students to conform to church teachings. J Sci Stud Relig. 1997, 36: 455-467. 10.2307/1387861.CrossRef Hayduk LA, Stratkotter RF, Rovers MW: Sexual orientation and the willingness of Catholic seminary students to conform to church teachings. J Sci Stud Relig. 1997, 36: 455-467. 10.2307/1387861.CrossRef
40.
go back to reference Hayduk LA, Pazderka-Robinson H, Cummings GG, Boadu K, Verbeek EL, Perks TA: The weird world, and equally weird measurement models: Reactive indicators and the validity revolution. Struct Equ Model. 2007, 14: 280-310. 10.1080/10705510709336747.CrossRef Hayduk LA, Pazderka-Robinson H, Cummings GG, Boadu K, Verbeek EL, Perks TA: The weird world, and equally weird measurement models: Reactive indicators and the validity revolution. Struct Equ Model. 2007, 14: 280-310. 10.1080/10705510709336747.CrossRef
41.
go back to reference Borsboom D, Mellenbergh GJ, van Heerden J: The concept of validity. Psychol Rev. 2004, 111: 1061-1071.CrossRefPubMed Borsboom D, Mellenbergh GJ, van Heerden J: The concept of validity. Psychol Rev. 2004, 111: 1061-1071.CrossRefPubMed
Metadata
Title
Should researchers use single indicators, best indicators, or multiple indicators in structural equation models?
Authors
Leslie A Hayduk
Levente Littvay
Publication date
01-12-2012
Publisher
BioMed Central
Published in
BMC Medical Research Methodology / Issue 1/2012
Electronic ISSN: 1471-2288
DOI
https://doi.org/10.1186/1471-2288-12-159

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