Abstract
The Posttraumatic Stress Disorder Checklist (PCL) is widely used in research and clinical settings to assess posttraumatic stress disorder (PTSD) symptomatology, including to examine PTSD symptoms/severity across diverse groups. However, the validity of these studies depends on the degree to which the PCL captures a conceptually equivalent construct of PTSD across the compared groups. This study examined the factor structure and invariance of PTSD as assessed by the PCL for DSM-5 (PCL-5) across a sample of trauma-exposed students (n = 412) and trauma-exposed participants recruited online through Amazon’s Mechanical Turk (MTurk; n = 346) platform. Participants from both samples completed the Stressful Life Events Screening Questionnaire (exposure to traumatic events) and the PCL-5. Using confirmatory factor analysis (CFA), we examined the factor structure of the DSM-5 and five alterative models of PTSD separately in both samples. We then tested measurement invariance of the DSM-5 and the optimal model of PTSD across these samples. All PTSD models fit the data well; however, the Hybrid model provided a significantly better fit for both samples. Both the Hybrid and DSM-5 models of PTSD demonstrated invariance for item mappings on factors (configural), factor loadings (metric), intercepts (scalar), and error variances (residual). Our findings support the stability, applicability, and meaningful comparisons of the PCL-5 assessed DSM-5 and Hybrid model factors across samples of trauma-exposed students and MTurk participants.
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References
American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorders (5th ed.). Washington, DC: American Psychiatric Association. https://doi.org/10.1176/appi.books.9780890425596.
Armour, C., Elhai, J. D., Layne, C. M., Shevlin, M., Duraković-Belko, E., Djapo, N., & Pynoos, R. S. (2011). Gender differences in the factor structure of posttraumatic stress disorder symptoms in war-exposed adolescents. Journal of Anxiety Disorders, 25(4), 604–611. https://doi.org/10.1016/j.janxdis.2011.01.010.
Armour, C., Tsai, J., Durham, T. A., Charak, R., Biehn, T. L., Elhai, J. D., & Pietrzak, R. H. (2015). Dimensional structure of DSM-5 posttraumatic stress symptoms: Support for a hybrid Anhedonia and externalizing behaviors model. Journal of Psychiatric Research, 61, 106–113. https://doi.org/10.1016/j.jpsychires.2014.10.012.
Armour, C., Contractor, A. A., Shea, M. T., Elhai, J. D., & Pietrzak, R. H. (2016). Factor structure of the PCL-5: Relationships among symptom clusters, anger, and impulsivity. Journal of Nervous & Mental Disease, 204, 108–115.
Ashbaugh, A. R., Houle-Johnson, S., Herbert, C., El-Hage, W., & Brunet, A. (2016). Psychometric validation of the English and French versions of the posttraumatic stress disorder checklist for DSM-5 (PCL-5). PLoS One, 11(10), e0161645. https://doi.org/10.1371/journal.pone.0161645.
Asparouhov, T., Muthén, B., & Muthén, B. (2006). Robust chi square difference testing with mean and variance adjusted test statistics. Matrix, 1(5), 1–6.
Baschnagel, J. S., O’Connor, R. M., Colder, C. R., & Hawk, L. W. (2005). Factor structure of posttraumatic stress among Western New York undergraduates following the September 11th terrorist attack on the World Trade Center. Journal of Traumatic Stress, 18(6), 677–684.
Bearden, W. O., Sharma, S., & Teel, J. E. (1982). Sample size effects on chi square and other statistics used in evaluating causal models. Journal of Marketing Research, 19(4), 425–430. https://doi.org/10.2307/3151716.
Blevins, C. A., Weathers, F. W., Davis, M. T., Witte, T. K., & Domino, J. L. (2015). The posttraumatic stress disorder checklist for DSM-5 (PCL-5): Development and initial psychometric evaluation. Journal of Traumatic Stress, 28(6), 489–498. https://doi.org/10.1002/jts.22059.
Borsboom, D., & Cramer, A. O. J. (2013). Network analysis: An integrative approach to the structure of psychopathology. Annual Review of Clinical Psychology, 9(1), 91–121. https://doi.org/10.1146/annurev-clinpsy-050212-185608.
Bovin, M. J., Marx, B. P., Gallagher, M. W., Schnurr, P. P., Weathers, F. W., Rodriguez, P., & Keane, T. M. (2016). Psychometric properties of the PTSD checklist for diagnostic and statistical manual of mental disorders-fifth edition (PCL-5) in veterans. Psychological Assessment, 28(11), 1379–1391. https://doi.org/10.1037/pas0000254.
Bowler, R. M., Han, H., Gocheva, V., Nakagawa, S., Alper, H., DiGrande, L., & Cone, J. E. (2010). Gender differences in probable posttraumatic stress disorder among police responders to the 2001 world trade center terrorist attack. American Journal of Industrial Medicine, 53(12), 1186–1196. https://doi.org/10.1002/ajim.20876.
Brown, M., & Cudeck, R. (1993). EQS structural equations program manual. Los Angeles: Multivariate Software Inc..
Bryant, R. A., McFarlane, A. C., Silove, D., O’Donnell, M. L., Forbes, D., & Creamer, M. (2015). The lingering impact of resolved PTSD on subsequent functioning. Clinical Psychological Science, 4(3), 493–498. https://doi.org/10.1177/2167702615598756.
Byrne, B. M., Shavelson, R. J., & Muthen, B. (1989). Testing for the equivalence of factor covariance and mean structures: The issue of partial measurement invariance. Psychological Bulletin, 105. https://doi.org/10.1037/0033-2909.105.3.456.
Cao, X., Wang, L., Cao, C., Zhang, J., & Elhai, J. D. (2017). DSM-5 posttraumatic stress disorder symptom structure in disaster-exposed adolescents: Stability across gender and relation to behavioral problems. Journal of Abnormal Child Psychology, 45(4), 803–814. https://doi.org/10.1007/s10802-016-0193-1.
Chandler, J., & Shapiro, D. (2016). Conducting clinical research using crowdsourced convenience samples. Annual Review of Clinical Psychology, 12(1), 53–81.
U.S. Census Bureau (2019). American Community Survey (ACS). Retrieved from https://www.census.gov/programs-surveys/acs/
Chandler, D., & Kapelner, A. (2013). Breaking monotony with meaning: Motivation in crowdsourcing markets. Journal of Economic Behavior & Organization, 90, 123–133.
Chen, F., Bollen, K. A., Paxton, P., Curran, P. J., & Kirby, J. B. (2001). Improper solutions in structural equation models: Causes, consequences, and strategies. Sociological Methods & Research, 29(4), 468–508. https://doi.org/10.1177/0049124101029004003.
Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464–504. https://doi.org/10.1080/10705510701301834.
Contractor, A. A., Layne, C. M., Steinberg, A. M., Ostrowski, S. A., Ford, J. D., & Elhai, J. D. (2013). Do gender and age moderate the symptom structure of PTSD? Findings from a national clinical sample of children and adolescents. Psychiatry Research, 210, 1056–1064. https://doi.org/10.1016/j.psychres.2013.09.012.
Contractor, A. A., Caldas, S. V., Dolan, M., Lagdon, S., & Armour, C. (2018a). PTSD's factor structure and measurement invariance across subgroups with differing count of trauma types. Psychiatry Research, 264, 76–84. https://doi.org/10.1016/j.psychres.2018.03.065.
Contractor, A. A., Green, T., Dolan, M., & Elhai, J. D. (2018b). Relations between PTSD and depression symptom clusters in samples differentiated by PTSD diagnostic status. Journal of Anxiety Disorders, 59, 17–26. https://doi.org/10.1016/j.janxdis.2018.08.004.
Contractor, A. A., Caldas, S. V., Dolan, M., Nateson, P., & Weiss, N. H. (2019). Invariance of the construct of posttraumatic stress. Disorder: A Systematic Review. Journal of Traumatic Stress. https://doi.org/10.1002/jts.22389.
Elhai, J. D., Biehn, T. L., Armour, C., Klopper, J. L., Frueh, B. C., & Palmieri, P. A. (2011). Evidence for a unique PTSD construct represented by PTSD’s D1–D3 symptoms. Journal of Anxiety Disorders, 25, 340–345. https://doi.org/10.1016/j.janxdis.2010.10.007.
Elhai, J. D., Miller, M. E., Ford, J. D., Biehn, T. L., Palmieri, P. A., & Frueh, B. C. (2012). Posttraumatic stress disorder in DSM-5: Estimates of prevalence and symptom structure in a nonclinical sample of college students. Journal of Anxiety Disorders, 26, 58–64. https://doi.org/10.1016/j.janxdis.2011.08.013.
Frankfurt, S., Armour, C., Contractor, A. A., & Elhai, J. D. (2016). Do gender and directness of trauma exposure moderate PTSD's latent structure? Psychiatry Research, 245, 365–370. https://doi.org/10.1016/j.psychres.2016.08.049.
Frazier, P., Anders, S., Perera, S., Tomich, P., Tennen, H., Park, C., & Tashiro, T. (2009). Traumatic events among undergraduate students: Prevalence and associated symptoms. Journal of Counseling Psychology, 56(3), 450. https://doi.org/10.1037/a0016412.
Friedman, M. J. (2013). Finalizing PTSD in DSM-5: Getting here from there and where to go next. Journal of Traumatic Stress, 26(5), 548–556. https://doi.org/10.1002/jts.21840.
Goodman, L. A., Corcoran, C., Turner, K., Yuan, N., & Green, B. L. (1998). Assessing traumatic event exposure: General issues and preliminary findings for the stressful life events screening questionnaire. Journal of Traumatic Stress, 11, 521–542. https://doi.org/10.1023/A:1024456713321.
Gosling, S. D., & Mason, W. (2015). Internet research in psychology. Annual Review of Psychology, 66(1), 877–902.
Gregorich, S. E. (2006). Do self-report instruments allow meaningful comparisons across diverse population groups? Testing measurement invariance using the confirmatory factor analysis framework. Medical Care, 44(Suppl. 3), S78–S94. https://doi.org/10.1097/01.mlr.0000245454.12228.8f.
Hamby, T., & Taylor, W. (2016). Survey satisficing inflates reliability and validity measures: An experimental comparison of college and Amazon mechanical Turk samples. Educational and Psychological Measurement, 76(6), 912–932. https://doi.org/10.1177/0013164415627349.
Hancock, G. R., & Mueller, R. O. (2013). Structural equation modeling: A second course. Charlotte, NC: Information Age Pub.
Hayduk, L. A. (2016). Improving measurement-invariance assessments: Correcting entrenched testing deficiencies. BMC Medical Research Methodology, 16(1), 130. https://doi.org/10.1186/s12874-016-0230-3.
Hayduk, L. A., & Glaser, D. N. (2000). Jiving the four-step, waltzing around factor analysis, and other serious fun. Structural Equation Modeling, 7(1), 1–35. https://doi.org/10.1207/S15328007SEM0701_01.
U.S. Department of Health and Human Services, National Institutes of Health, National Institute of Mental Health (2016). Mental Health Information Statistics: Post-Traumatic Stress Disorder (PTSD). Retrieved from https://www.nimh.nih.gov/health/statistics/post-traumatic-stress-disorder-ptsd.shtml
Henrich, J., Heine, S. J., & Norenzayan, A. (2010). The weirdest people in the world? Behavioral and Brain Sciences, 33(2–3), 61–83. https://doi.org/10.1017/S0140525X0999152X.
Henry, P. J. (2008). College sophomores in the laboratory redux: Influences of a narrow data base on social Psychology's view of the nature of prejudice. Psychological Inquiry, 19(2), 49–71. https://doi.org/10.1080/10478400802049936.
Hoge, C. W., Riviere, L. A., Wilk, J. E., Herrell, R. K., & Weathers, F. W. (2014). The prevalence of post-traumatic stress disorder (PTSD) in US combat soldiers: A head-to-head comparison of DSM-5 versus DSM-IV-TR symptom criteria with the PTSD checklist. The Lancet Psychiatry, 1(4), 269–277.
Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6(1), 1–55. https://doi.org/10.1080/10705519909540118.
Idemudia, E. S., William, J. K., Boehnke, K., & Wyatt, G. (2013). Gender differences in trauma and posttraumatic stress symptoms among displaced Zimbabweans in South Africa. Journal of Traumatic Stress Disorders & Treatment, 2(3), 1340. https://doi.org/10.4172/2324-8947.1000110.
Jamison-Eddinger, J. R., & McDevitt-Murphy, M. E. (2017). A confirmatory factor analysis of the PTSD checklist 5 in veteran and college student samples. Psychiatry Research, 255, 219–224. https://doi.org/10.1016/j.psychres.2017.05.035.
Jamshidian, M., Jalal, S. J., & Jansen, C. (2014). MissMech: An R package for testing homoscedasticity, multivariate normality, and missing completely at random (MCAR). Journal Statistical Software. https://doi.org/10.18637/jss.v056.i06.
Keane, T., Rubin, A., Lachowicz, M., Brief, D., Enggasser, J., Roy, M., Hermos, J., Rosenbloom, H. E., & D. (2014). Temporal stability of DSM-5 posttraumatic stress disorder criteria in a problem-drinking sample. Psychological Assessment, 26(4), 1138–1145. https://doi.org/10.1037/a0037133.
Kessler, R. C., Sonnega, A., Bromet, E., Hughes, M., & Nelson, C. B. (1995). Posttraumatic stress disorder in the National Comorbidity Survey. Archives of General Psychiatry, 52(12), 1048–1060.
Kip, K. E., Hernandez, D. F., Shuman, A., Witt, A., Diamond, D. M., Davis, S., Kip, R., Abhayakumar, A., Wittenberg, T., Girling, S. A., Rosenzweig, W. S., & L. (2015). Comparison of accelerated resolution therapy (ART) for treatment of symptoms of PTSD and sexual trauma between civilian and military adults. Military Medicine, 180(9), 964–971. https://doi.org/10.7205/milmed-d-14-00307.
Kline, R. B. (2015). Principles and practice of structural equation modeling. New York, NY: The Gulford Press.
Li, C.-H. (2016). Confirmatory factor analysis with ordinal data: Comparing robust maximum likelihood and diagonally weighted least squares. Behavior Research Methods, 48(3), 936–949. https://doi.org/10.3758/s13428-015-0619-7.
Little, R. J. A. (1988). A test of missing completely at random for multivariate data with missing values. Journal of the American Statistical Association, 83(404), 1198–1202. https://doi.org/10.2307/2290157.
Liu, P., Wang, L., Cao, C., Wang, R., Zhang, J., Zhang, B., Wu, Q., Zhang, H., Zhao, Z., Elhai, F. G., & J. D. (2014). The underlying dimensions of DSM-5 posttraumatic stress disorder symptoms in an epidemiological sample of Chinese earthquake survivours. Journal of Anxiety Disorders, 28, 345–351. https://doi.org/10.1016/j.janxdis.2014.03.008.
Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57, 519–530. https://doi.org/10.2307/2334770.
Meredith, W. (1993). Measurement invariance, factor analysis and factorial invariance. Psychometrika, 58(4), 525–543. https://doi.org/10.1007/BF02294825.
Millsap, R. E., & Kwok, O. (2004). Evaluating the impact of partial factorial invariance on selection in two populations. Psychological Methods, 9, 93–115. https://doi.org/10.1037/1082-989X.9.1.93.
Muthén, B. (1993). Goodness of fit with categorical and other non-normal variables. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 205–243). Newbury Park, CA: Sage Publications.
Newman, D. A., Joseph, D. L., & Feitosa, J. (2015). External validity and multi-organization samples: Levels-of-analysis implications of crowdsourcing and college student samples. Industrial and Organizational Psychology, 8(2), 214–220.
Oppenheimer, D. M., Meyvis, T., & Davidenko, N. (2009). Instructional manipulation checks: Detecting satisficing to increase statistical power. Journal of Experimental Social Psychology, 45, 867–872. https://doi.org/10.1016/j.jesp.2009.03.009.
Paolacci, G., & Chandler, J. (2015). Inside the Turk: Understanding mechanical Turk as a participant pool. Current Directions in Psychological Science, 23(3), 184–188. https://doi.org/10.1177/0963721414531598.
Paolacci, G., Chandler, J., & Ipeirotis, P. G. (2010). Running experiments on amazon mechanical turk. Judgment and Decision making, 5(5), 411–419.
Pietrzak, R. H., Goldstein, R. B., Southwick, S. M., & Grant, B. F. (2011). Prevalence and Axis I comorbidity of full and partial posttraumatic stress disorder in the United States: Results from wave 2 of the National Epidemiologic Survey on alcohol and related conditions. Journal of Anxiety Disorders, 25, 456–465. https://doi.org/10.1016/j.janxdis.2010.11.010.
Raftery, A. E. (1995). Bayesian model selection in social research. Sociological Methodology, 25, 111–164. https://doi.org/10.2307/271063.
Raghavan, S. S., & Sandanapitchai, P. (2019). Cultural predictors of resilience in a multinational sample of trauma survivors. Frontiers in Psychology, 10, 131. https://doi.org/10.3389/fpsyg.2019.00131.
Rasmussen, A., Verkuilen, J., Jayawickreme, N., Wu, Z., McCluskey, T., & S. (2018). When did posttraumatic stress disorder get so many factors? Confirmatory factor models since DSM–5. Clnical Psychological Science, 7(2), 234–248. https://doi.org/10.1177/2167702618809370.
Rogstadius, J., Kostakos, V., Kittur, A., Smus, B., Laredo, J., & Vukovic, M. (2011). An assessment of intrinsic and extrinsic motivation on task performance in crowdsourcing markets. In Paper presented at the 5th international AAAI conference on weblogs and social media. Barcelona: Spain.
Rosseel, Y. (2012). Lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1–36. https://doi.org/10.18637/jss.v048.i02.
Santiago, P. N., Ursano, R. J., Gray, C. L., Pynoos, R. S., Spiegel, D., Lewis-Fernandez, R., et al. (2013). A systematic review of PTSD prevalence and trajectories in DSM-5 defined trauma exposed populations: Intentional and non-intentional traumatic events. PloS One, 8(4), e59236. https://doi.org/10.1371/journal.pone.0059236.
Sareen, J., Cox, B. J., Stein, M. B., Afifi, T. O., Fleet, C., & Asmundson, G. J. G. (2007). Physical and mental comorbidity, disability, and suicidal behavior associated with posttraumatic stress disorder in a large community sample. Psychosomatic Medicine, 69(3), 242–248. https://doi.org/10.1097/PSY.0b013e31803146d8.
Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464. https://doi.org/10.1214/aos/1176344136.
Shapiro, D. N., Chandler, J., & Mueller, P. A. (2013). Using mechanical Turk to study clinical populations. Clinical Psychological Science, 1(2), 213–220. https://doi.org/10.1177/2167702612469015.
Silverstein, M. W., Dieujuste, N., Kramer, L. B., Lee, D. J., & Weathers, F. W. (2017). Construct validation of the hybrid model of posttraumatic stress disorder: Distinctiveness of the new symptom clusters. Journal of Anxiety Disorders. https://doi.org/10.1016/j.janxdis.2017.12.003.
Simms, L., Watson, D., & Doebbeling, B. (2002). Confirmatory factor analyses of posttraumatic stress symptoms in deployed and nondeployed veterans of the gulf war. Journal of Abnormal Psychology, 111(4), 637–647. https://doi.org/10.1037/0021-843X.111.4.637.
Stein, D. J., McLaughlin, K. A., Koenen, K. C., Atwoli, L., Friedman, M. J., Hill, E. D., et al. (2014). DSM-5 and ICD-11 definitions of posttraumatic stress disorder: Investigating "narrow" and "broad" approaches. Depression and Anxiety, 31(6), 494–505. https://doi.org/10.1002/da.22279.
Stolk-Cooke, K., Brown, A., Maheux, A., Parent, J., Forehand, R., & Price, M. (2018). Crowdsourcing trauma: Psychopathology in a trauma-exposed sample recruited via mechanical Turk. Journal of Traumatic Stress. https://doi.org/10.1002/jts.22303.
Trochim, W. M., & Donnelly, J. P. (2006) The research methods knowledge base, 3rd edn. Cincinnati: Atomic Dog.
Tsai, J., Harpaz-Rotem, I., Armour, C., Southwick, S. M., Krystal, J. H., & Pietrzak, R. H. (2015). Dimensional structure of DSM-5 posttraumatic stress symptoms: Results from the National Health and resilience in veterans study. Journal of Clinical Psychiatry, 76, 546–553. https://doi.org/10.4088/JCP.14m09091.
Tucker, L. R., & Lewis, C. (1973). A reliability coefficient for maximum likelihood factor analysis. Psychometrika, 38(1), 1–10. https://doi.org/10.1007/BF02291170.
U.S. Department of Health and Human Services. (2018). A demographic, attitudinal, and behavioral profile of cohabiting adults in the United States, 2011–2015. National Health Statistics Reports, Number, 111, 1–10 Retrieved from: https://www.cdc.gov/nchs/data/nhsr/nhsr111.pdf.
Ullman, S. E., & Long, S. M. (2008). Factor structure of PTSD in a community sample of sexual assault survivors. Journal of trauma & dissociation : the official journal of the International Society for the Study of Dissociation (ISSD), 9(4), 507–524. https://doi.org/10.1080/15299730802223370.
van Buuren, S. (2007). Multiple imputation of discrete and continuous data by fully conditional specification. Statistical Methods in Medical Research, 16(3), 219–242. https://doi.org/10.1177/0962280206074463.
Wang, L., Cao, X., Cao, C., Fang, R., Yang, H., & Elhai, J. D. (2017). Factor structure of DSM-5 PTSD symptoms in trauma-exposed adolescents: Examining stability across time. Journal of Anxiety Disorders, 52, 88–94. https://doi.org/10.1016/j.janxdis.2017.07.001.
Watson, D. (2005). Rethinking the mood and anxiety disorders: A quantitative hierarchical model for DSM-V. Journal of Abnormal Psychology, 114, 522–536. https://doi.org/10.1037/0021-843X.114.4.522.
Watson, P. J., Brymer, M. J., & Bonanno, G. A. (2011). Postdisaster psychological intervention since 9/11. American Psychologist, 66(6), 482–494. https://doi.org/10.1037/a0024806.
Weathers, F., Litz, B., Heman, D., Juska, J., & Keane, T. (1994). PTSD checklist-civilian version. Boston: National Science for PTSD. Behavioral Science Division.
Weathers, F. W., Litz, B. T., Keane, T. M., Palmieri, P. A., Marx, B. P., & Schnurr, P. P. (2013). The PTSD checklist for DSM-5 (PCL-5). Scale available from the National Center for PTSD at www.ptsd.va.gov.
Wortmann, J. H., Jordan, A. H., Resick, P. A., Foa, E. B., Yarvis, J. S., Mintz, J., et al. (2016). Psychometric analysis of the PTSD Checklist-5 (PCL-5) among treatment-seeking military service members. Psychological Assessment, 28(11), 1392–1403. https://doi.org/10.1037/pas0000260.
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Stephanie V. Caldas, Ateka A. Contractor, Sara Koh, and Li Wang declare they have no conflict of interest.
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Caldas, S.V., Contractor, A.A., Koh, S. et al. Factor Structure and Multi-Group Measurement Invariance of Posttraumatic Stress Disorder Symptoms Assessed by the PCL-5. J Psychopathol Behav Assess 42, 364–376 (2020). https://doi.org/10.1007/s10862-020-09800-z
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DOI: https://doi.org/10.1007/s10862-020-09800-z