Measurement invariance tests of revisions to archaically worded items in the Mach IV scale

Autoři: Brian K. Miller aff001;  Kay Nicols aff001;  Robert Konopaske aff001
Působiště autorů: Department of Management, Texas State University, San Marcos, Texas, United States of America aff001
Vyšlo v časopise: PLoS ONE 14(10)
Kategorie: Research Article


The Machiavellian IV [1] instrument, developed almost 50 years ago to measure trait Machiavellianism and still in wide use in personality research, uses item wording that is not gender-neutral, makes use of idiomatic expressions, and includes archaic references. In this two-sample study, exploratory factor analysis (EFA) was conducted on one sample to examine the structure of responses to the Mach IV. In an independent second sample the resulting EFA structure was analyzed using confirmatory factor analysis-based measurement equivalence/invariance (ME/I) tests in a control group with the original archaic items and a treatment group with eight items rewritten in a more modern vernacular. Specific model testing steps [2] and statistical tests [3] were applied in a bottom-up approach [4] to ME/I tests on these two versions of the Mach IV. The two versions were found to have equal form, equal factor loadings, but unequal indicator error variances. Subsequent item-by-item tests of error invariance resulted in substantial decrements to fit for three revised items suggesting that the error associated with these items was not equal across the two versions.

Klíčová slova:

Covariance – Employment – Factor analysis – Language – Personality – principal component analysis – Psychometrics – Skewness


1. Christie R, Geis FL. Studies in Machiavellianism. New York: Academic Press; 1970.

2. Cheung GW, Rensvold RB. Testing factorial invariance across groups: A reconceptualization and proposed new method. J Mgmt. 1999; 25: 1–27.

3. Cheung GW, Rensvold RB. Evaluating goodness-of-fit indexes for testing measurement invariance. Struct Eq Model. 2002; 9: 233–255.

4. Brown TA. Confirmatory factor analysis for applied research. New York: The Guilford Press; 2006.

5. Paulhus DL, Williams KM. The dark triad of personality: Narcissism, Machiavellianism, and psychopathy. J Res Pers. 2002; 36: 556–563.

6. Jones D. The nature of Machiavellianism: Distinct patterns of misbehavior. In Zeigler-Hill V, Marcus DK, editors. The dark side of personality: Science and practice in social, personality, and clinical psychology. Washington, DC: American Psychological Association; 2016.

7. Panitz E. Psychometric investigation of the Mach IV scale measuring Machiavellianism. Psych Rep. 1989; 64(3): 963–968.

8. Hunter JE, Gerbing DW, Boster FJ. Machiavellian beliefs and personality: Construct invalidity of the Machiavellian dimension. J Pers Soc Psych. 1982; 43(6): 1293–1305.

9. Monaghan C., Bizumic B, Sellbom M. The role of Machiavellian views and tactics in psychopathology. Pers Indiv Diff. 2016; 94: 72–81.

10. Hanel HP, Vione KC. Do student samples provide an accurate estimate of the general public? Plos One; 2016: 11(12).

11. Henry PJ. College sophomores in the laboratory redux: Influences of a narrow data base on social psychology’s view of the nature of prejudice. Psycho Inq: Inter J Adv Psych Theory; 2008: 19: 49–71.

12. National Center for Education Statistics, Table 187: College enrollment rates of high school graduates, by sex from 1960 to 1998. See, accessed December 6, 2018.

13. National Center for Education Statistics, What are the new back to school statistics for 2017? See, accessed December 6, 2018.

14. Ruiz NG. New foreign student enrollment at U.S. colleges and universities doubled since Great Recession. Pew Research Center, November 20, 2017, .

15. Tara J. International students in U.S. colleges and universities Top 1 million. Time, November 14, 2017.

16. Abel B. (2003). English idioms in the first language and second language lexicon: A dual representation approach. Sec Lang Res. 2003; 19(4): 329–358.

17. Bortfield H. What native and non-native speakers' images for idioms tell us about figurative language. In Heredia RR, Altarriba J, editors. Advances in Psychology: Vol. 134; 2002.

18. Reise SP, Widaman KF, Pugh R.H. Confirmatory factor analysis and item response theory: Two approaches for exploring measurement invariance. Psych Bull. 1993; 114: 552–566.

19. Williams ML, Hazleton V, Renshaw S. The measurement of Machiavellianism: A factor analytic and correlational study of Mach IV and Mach V. Speech Mon. 1975; 42(2):151–159.

20. Ahmed S, Stewart R. Factor analysis of the Machiavellian Scale. Soc Behav Pers: Int J. 1981; 9: 113–116.

21. Andreou E. Bully/victim problems and their association with Machiavellianism and self-efficacy in Greek primary school children. Brit J Ed Psych. 2004; 74(2): 297–309.

22. Kuo HK, Marsella AJ. The meaning and measurement of Machiavellianism in Chinese and America College Students. J Soc Psych. 1977; 101(2): 165–173.

23. O'Hair D, Cody MJ. Machiavellian beliefs and social influence. West J Speech Comm. 1987; 51(3): 279–303.

24. Dahling JJ, Whitaker BG, Levy PE. The development and validation of a new Machiavellian scale. J Mgmt. 2009; 35: 219–257.

25. Miller BK, Konopaske R. Dispositional correlates of perceived work entitlement. J Mgmt Psych. 2014; 29: 808–828.

26. Miller BK, Smart DL, Rechner PL. Confirmatory factor analysis of the Machiavellian Personality Scale. Pers Indiv Diff. 2015; 82: 120–124.

27. Niemi L, Young L. Caring across boundaries versus keeping boundaries intact: Links between moral values and interpersonal orientations. PLoS One. 2013; 8: e81605. doi: 10.1371/journal.pone.0081605 24349095

28. Rauthmann JF, Will T. Proposing a multidimensional Machiavellianism conceptualization. Soc Behav Pers. 2011; 39: 391–404.

29. Rauthmann JF. Towards multifaceted Machiavellianism: Content, factorial, and construct validity of a German Machiavellianism Scale. Pers Indiv Diff. 2012; 52: 345–351.

30. Hair JE, Anderson RE, Tatham RL, Black WC. Multivariate data analysis, 5th ed. Upper Saddle River, NJ: Prentice Hall; 1998.

31. Cummings G. Understanding the new statistics: Effect sizes, confidence intervals, and meta-analysis. New York: Routledge; 2012.

32. Trafimow D, Marks M. Editorial. Basic App Soc Psych. 2015; 37: 1–2.

33. Comrey AL. A first course in factor analysis. New York, NY: Academic Press; 1973.

34. Gorsuch RL. Factor analysis, 2nd ed. Hillsdale, NJ: Erlbaum.; 1983.

35. Tabachnik BG, Fidell LS. Using Multivariate Statistics, 5th ed. Boston: Pearson; 2007.

36. Thompson B, Daniel L. Factor analytic evidence for the construct validity of scores: An historical overview and some guidelines. Ed Psych Meas. 1996; 5: 197–208

37. West SG, Finch JD, Curran PJ. (1995). Structural equation models with non-normal data. In Hoyle RH, editor. Structural equation modeling. Thousand Oaks, CA: Sage; 1995.

38. Cortina J. What is coefficient alpha? An examination of theory and applications. J App Psych 1993; 78(1): 98–104.

39. Campbell DT, Stanley JC. Experimental and quasi-experimental designs for research. Boston: Houghton Mifflin Company; 1963.

40. Cook TD, Campbell DT. Quasi-experimentation: Design and analysis issues for field settings. Boston: Houghton Mifflin Company; 1979.

41. Bollen KA. Structural equation modeling with latent variables. New York: Wiley; 1989.

42. Byrne BM. Structural equation modeling with LISREL, PRELIS, and SIMPLIS: Basic concepts, applications, and programming. Mahwah, NJ: Lawrence Erlbaum Associates; 1998.

43. Byrne BM, Shavelson RJ, Muthèn B. Testing for the equivalence of factor covariance and mean structures: The issue of partial measurement invariance. Psych Bull. 1989; 105: 456–466.

44. Kline RB. Principles and Practice of Structural Equation Modeling, 3rd ed. New York: Guilford Press; 2011.

45. Steenkamp JB, Baumgartner H. Assessing measurement invariance in cross-national consumer research. J Consum Res. 1998; 25: 78–90.

46. Bentler PM. Comparative fit indexes in structural equation models. Psych Bull. 1990; 107: 238–246.

47. Browne MW, Cudeck R. Alternative ways of assessing model fit. In Bollen KA, Long JS, editors. Testing structural equation models. California: Sage Publications; 1993.

48. Hu LT, Bentler PM. Cutoff criteria for fit indexes in covariance structure analysis: conventional criteria versus new alternatives. Struct Eq Mod. 1999; 6: 1, 1–55.

49. Hopwood CJ, Donnellan MB. How should the internal structure of personality inventories be evaluated? Pers Soc Psych Rev. 2010; 14: 332–346.

50. Marsh HW, Hau K, Wen Z. In search of golden rules: Comment on hypothesis-testing approaches to setting cutoff values for fit indexes and dangers in overgeneralizing Hu and Bentler’s (1999) findings. Struct Eq Mod. 2004; 11: 320–341.

51. Henson RK. Multivariate normality: What is it and how is it assessed? In Thompson B, editor. Advances in social science methodology. Stamford, CT: JAI Press; 1999.

52. DeCarlo LT. On the meaning and use of kurtosis. Psychological Methods. 1997; 2: 292–307.

53. Bentler PM. Re: Kurtosis, residuals, fit indices. [Message posted to SEMNET listserv]. Msg 011264. Archived at March 10, 1998.

54. Bentler PM, Wu EJ. EQS for Windows User's Guide. Encino, CA: Multivariate Software; 2002.

55. Jöreskog K. Sörbom D. LISREL 8.80 [Computer Software]. Chicago: Scientific Software International; 2006.

56. Satorra A. Scaled and adjusted restricted tests in multi-sample analysis of moment structures. In Heijmans RDH, Pollock DSG, Satorra A, editors. Innovations in Multivariate Statistical Analysis. A Festschrift for Heinz Neudecker. London: Kluwer Academic Publishers; 2000.

57. Andrew J, Cooke M, Muncer SJ. The relationship between empathy and Machiavellianism: An alternative to empathizing–Systemizing theory. Pers Indiv Diff. 2008; 44: 1203–1211.

58. Corral S, Calvete E. Machiavellianism: Dimensionality of the Mach IV and its relation to self-monitoring in a Spanish sample. Span J Psych. 2000; 3(1): 3–13.

59. Schmitt N, Kuljanin G. Measurement invariance: Review of practice and implications. Hum Res Mgmt. 2008; 18:210–222.

60. Vandenberg RJ, Lance CE. A review and synthesis of the measurement invariance literature: Suggestions, practices, and recommendations for organizational research. Org Res Meth. 2000; 3: 4–70.

61. Mirels HL, Garrett JB. The Protestant ethic as a personality variable. J Consult Clin Psych. 1971; 36: 40–44.

62. Goldberg LR. (1999). A broad-bandwidth, public domain, personality inventory measuring the lower-level facets of several five-factor models. In Mervielde I, Deary I, De Fruyt F, Ostendorf F, editors. Personality Psychology in Europe, Vol. 7. Tilburg, Netherlands: Tilburg University Press; 1999.

63. Google Ngram Viewer. Retrieved January 02, 2019, from

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