Guttman error graphs: a visual approach to scalability analysis
DOI:
https://doi.org/10.11606/s1518-8787.2026060007015Keywords:
Psychometrics, Bias, Measures in EpidemiologyAbstract
OBJECTIVE: To develop an innovative graphical tool to represent Guttman errors and facilitate scalability analysis of measurement instruments in epidemiology. METHODS: Implemented in R (RStudio), the guttemap function was developed to fill this gap. It provides an intuitive visual representation of Guttman errors, with color gradients that facilitate the assessment of measurement instruments, revealing internal patterns of inconsistency. The rationale underlying the proposed Guttman error map is presented, along with an annotated summary of the routine for its implementation. RESULTS: Seven synthetic examples show the potential of graphical representation in identifying problem areas and how this helps to inform adjustments and develop more robust instruments. CONCLUSIONS: With guttemap, Guttman error analysis becomes more accessible and interpretable, contributing to the improvement of measurement instruments and the advancement of epidemiological research.
References
1. Streiner DL, Norman GR, Cairney J. Health measurement scales. A practical guide to their development and use. 5th ed. Oxford: Oxford University Press; 2015.
2. Reichenheim M, Bastos JL. What, what for and how? Developing measurement instruments in epidemiology. Rev Saúde Pública. 2021 Aug;55(40):1-17. https://doi.org/10.11606/s1518-8787.2021055002813
3. Bastos JL, Reichenheim ME, Moraes CL. Measurement instruments for use in oral epidemiology. In: Peres MA, Antunes JL, Watt RG, editors. Oral Epidemiology: A Textbook on Oral Health Conditions, Research Topics and Method. New York: Springer; 2021. p. 465-77.
4. Sijtsma K, Molenaar IW. Introduction to nonparametric item response theory. Thousand Oaks: Sage Publications; 2002.
5. Wilson M. Constructing measures. An item response modeling approach. London: Routledge:Taylor & Francis; 2023.
6. Guttman L. The basis for scalogram analysis. In: Stouffer SA, Guttman L, Suchman EA, Lazarsfeld PF, Star SA, Clausen JA, editors. Measurement and predictio. Princeton: Princeton University Press; 1950. p. 60-90.
7. Sijtsma K, Molenaar IW. Mokken Models (chapter 18). In: Van der Linden, WJ, editor. Handbook of Item Response Theory, Volume One: Models. Boca Raton: Chapman and Hall/ CRC; 2018. p. 303-21.
8. Mokken RJ. A theory and procedure of scale analysis. Berlin: De Gruyter; 1971.
9. Hardouin JB, Bonnaud-Antignac A, Sebille V. Nonparametric item response theory using Stata. Stata Journal. 2011 Mar;11(1):30-51. https://doi.org/ 10.1177/1536867X1101100102
10. van der Ark LA, Koopman L, Straat JH, van den Bergh D. mokken: R Package for Nonparametric Item Response Theory and Mokken Scale Analysis (Version 3.1.2) [Internet]. 2022 [citado 2025 out 8]. Disponível em: https://cran.r-project.org/package=mokken2022
11. Molenaar IW, Sijtsma K, Boer P. MSP5 for Windows. User’s Manual for MSP5 for Windows: A Program for Mokken Scale Analysis for Polytomous Items (Version 5.0). Groningen: iec ProGAMMA; 2000.
12. Bastos JL, Bernardo FR, Reichenheim ME. One step further in mistreatment research: Assessing the scalability of the Explicit Discrimination Scale among Brazilian working-age adult respondents. J Community Psychol. 2025 Jan;53(1):e23146. https://doi.org/10.1002/jcop.23146
13. R Core Team. R: A language and environment for statistical computing [Internet]. Viena: R Foundation for Statistical Computing; 2023 [citado 2025 out 8]. Disponível em: http://www.R-project.org/
14. RStudio Team. RStudio: Integrated Development for R. RStudio [Internet]. Boston: PBC; 2024 [citado 2025 out 8]. Disponível em: http://www.rstudio.com/
15. StataCorp. Stata Statistical Software: Release 16. College Station: StataCorp LLC; 2019-2002.
16. OpenAI. ChatGPT [Large language model] [Internet]. São Francisco: OpenAI; 2024 [citado 2025 out 8]. Disponível em: https://chat.openai.com2024
17. Muthén B. A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika. 1984;49(1):115-32.
18. Muthén BO, Muthén LK, Asparouhov A. Regression and Mediation Analysis using Mplus. Los Angeles: Muthén & Muthén; 2016.
19. Dima AL. Scale validation in applied health research: tutorial for a 6-step R-based psychometrics protocol. Health Psychol Behav Med. 2018 May;6(1):136-61. https://doi.org/10.1080/21642850.2018.1472602
20. Epstein J, Osborne RH, Elsworth GR, Beaton DE, Guillemin F. Cross-cultural adaptation of the Health Education Impact Questionnaire: experimental study showed expert committee, not back-translation, added value. J Clin Epidemiol. 2015 Apr;68(4):360-9. https://doi.org/10.1016/j.jclinepi.2013.07.013
Published
Issue
Section
License
Copyright (c) 2026 Michael Eduardo Reichenheim, Claudia Leite de Moraes, João Luiz Bastos
This work is licensed under a Creative Commons Attribution 4.0 International License.
