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Applying Latent Variable Models to Estimate Cumulative Exposure Burden to Chemical Mixtures and Identify Latent Exposure Subgroups: A Critical Review and Future Directions

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Abstract

Environmental mixtures, which reflect joint exposure to multiple environmental agents, are a major focus of environmental health and risk assessment research. Advancements in latent variable modeling and psychometrics can be used to address contemporary questions in environmental mixtures research. In particular, latent variable models can quantify an individual’s cumulative exposure burden to mixtures and identify hidden subpopulations with distinct exposure patterns. Here, we first provide a review of measurement approaches from the psychometrics field, including structural equation modeling and latent class/profile analysis, and discuss their prior environmental epidemiologic applications. Then, we discuss additional, underutilized opportunities to leverage the strengths of psychometric approaches. This includes using item response theory to create a common scale for comparing exposure burden scores across studies; facilitating data harmonization through the use of anchors. We also discuss studying fairness or appropriateness of measurement models to quantify exposure burden across diverse populations, through the use of mixture item response theory and through evaluation of measurement invariance and differential item functioning. Multi-dimensional models to quantify correlated exposure burden sub-scores, and methods to adjust for imprecision of chemical exposure data, are also discussed. We show that there is great potential to address pressing environmental epidemiology and exposure science questions using latent variable methods.

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References

  1. Taylor KW, Joubert BR, Braun JM, Dilworth C, Gennings C, Hauser R, Heindel JJ, Rider CV, Webster TF, Carlin DJ (2016) Statistical approaches for assessing health effects of environmental chemical mixtures in epidemiology: lessons from an innovative workshop. Environ Health Perspect 124:A227–A229

    Article  Google Scholar 

  2. Joubert BR, Kioumourtzoglou MA, Chamberlain T, Chen HY, Gennings C, Turyk ME, Miranda ML, Webster TF, Ensor KB, Dunson DB, Coull BA (2022) Powering research through innovative methods for mixtures in epidemiology (PRIME) program: novel and expanded statistical methods. Int J Environ Res Public Health 19:1378

    Article  Google Scholar 

  3. Bobb JF, Valeri L, Claus Henn B, Christiani DC, Wright RO, Mazumdar M, Godleski JJ, Coull BA (2015) Bayesian kernel machine regression for estimating the health effects of multi-pollutant mixtures. Biostatistics 16:493–508

    Article  MathSciNet  Google Scholar 

  4. Carrico G, Gennings C, Wheeler DC, Factor-Litvak P (2015) Characterization of weighted quantile sum regression for highly correlated data in a risk analysis setting. J Agric Biol Environ Stat 20:100–120

    Article  MathSciNet  Google Scholar 

  5. Liu SH, Bobb J, Claus Henn B, Schnaas L, Tellez-Rojo MM, Bellinger DC, Arora M, Wright RJ, Coull BA (2018) Bayesian varying coefficient kernel machine regression to assess neurodevelopmental trajectories associated with exposure to complex mixtures. Stat Med 37:4680–4694

    Article  MathSciNet  Google Scholar 

  6. Liu SH, Bobb JF, Lee KH, Gennings C, Claus Henn B, Bellinger D, Austin C, Schnaas L, Tellez-Rojo MM, Hu H, Wright RO, Arora M, Coull BA (2017) Lagged kernel machine regression for identifying time windows of susceptibility to exposures of complex mixtures. Biostatistics 19:325–341

    Article  MathSciNet  Google Scholar 

  7. Liu SH, Bobb J, Schnaas L, Tellez-Rojo MM, Claus Henn B, Gennings C, Arora M, Wright RJ, Coull BA, Wand MP (2018) Modeling the health effects of time-varying complex environmental mixtures: mean field variational Bayes for lagged kernel machine regression. Environmetrics 29:e2504

    Article  MathSciNet  Google Scholar 

  8. Gibson EA, Nunez Y, Abuawad A, Zota AR, Renzetti S, Devick KL, Gennings C, Goldsmith J, Coull BA, Kioumourtzoglou MA (2019) An overview of methods to address distinct research questions on environmental mixtures: an application to persistent organic pollutants and leukocyte telomere length. Environ Health 18:76

    Article  Google Scholar 

  9. Hamra GB, Buckley JP (2018) Environmental exposure mixtures: questions and methods to address them. Curr Epidemiol Rep 5:160–165

    Article  Google Scholar 

  10. Liu SH, Feuerstahler L, Chen Y, Braun JM, Buckley JP (2023) Toward advancing precision environmental health: developing a customized exposure burden score to PFAS mixtures to enable equitable comparisons across population subgroups, using mixture item response theory. Environ Sci Technol 57:18104–18115

    Article  Google Scholar 

  11. Daniel MH (1997) Intelligence testing: status and trends57. Am Psychol 52:1038–1045

    Article  Google Scholar 

  12. Choi SW, Schalet B, Cook KF, Cella D (2014) Establishing a common metric for depressive symptoms: linking the BDI-II, CES-D, and PHQ-9 to PROMIS depression. Psychol Assess 26:513–527

    Article  Google Scholar 

  13. Cella D, Choi SW, Condon DM, Schalet B, Hays RD, Rothrock NE, Yount S, Cook KF, Gershon RC, Amtmann D, DeWalt DA, Pilkonis PA, Stone AA, Weinfurt K, Reeve BB (2019) PROMIS® Adult health profiles: efficient short-form measures of seven health domains. Value Health 22:537–544

    Article  Google Scholar 

  14. Budtz-Jorgensen E, Keiding N, Grandjean P, Weihe P (2002) Estimation of health effects of prenatal methylmercury exposure using structural equation models. Environ Health 1:2

    Article  Google Scholar 

  15. Budtz-Jørgensen E, Debes F, Weihe P, Grandjean P (2010) Structural equation models for meta-analysis in environmental risk assessment. Environmetrics 21:510–527

    Article  MathSciNet  Google Scholar 

  16. Mogensen UB, Grandjean P, Heilmann C, Nielsen F, Weihe P, Budtz-Jorgensen E (2015) Structural equation modeling of immunotoxicity associated with exposure to perfluorinated alkylates. Environ Health 14:47

    Article  Google Scholar 

  17. Przybyla J, Geldhof GJ, Smit E, Kile ML (2018) A cross sectional study of urinary phthalates, phenols and perchlorate on thyroid hormones in US adults using structural equation models (NHANES 2007–2008). Environ Res 163:26–35

    Article  Google Scholar 

  18. Spearman C (1904) General intelligence, objectively determined and measured. Am J Psychol 15:201–293

    Article  Google Scholar 

  19. Grandjean P, Andersen EW, Budtz-Jorgensen E, Nielsen F, Molbak K, Weihe P, Heilmann C (2012) Serum vaccine antibody concentrations in children exposed to perfluorinated compounds. JAMA 307:391–397

    Article  Google Scholar 

  20. Aune SE, Abal FJP, Attorresi HF (2019) Application of the graded response model to a scale of empathic behavior. Int J Psychol Res (Medellin) 12:49–56

    Article  Google Scholar 

  21. Chang CH, Reeve BB (2005) Item response theory and its applications to patient-reported outcomes measurement. Eval Health Prof 28:264–282

    Article  Google Scholar 

  22. Chen Y, Feuerstahler L, Martinez-Steele E, Buckley JP, Liu SH (2023) Phthalate mixtures and insulin resistance: an item response theory approach to quantify exposure burden to phthalate mixtures. J Expo Sci Environ Epidemiol. https://doi.org/10.1038/s41370-023-00535-z

    Article  Google Scholar 

  23. Curran PJ, Hussong AM, Cai L, Huang W, Chassin L, Sher KJ, Zucker RA (2008) Pooling data from multiple longitudinal studies: the role of item response theory in integrative data analysis. Dev Psychol 44:365–380

    Article  Google Scholar 

  24. Dorans NJ, Kulick E (2006) Differential item functioning on the Mini-Mental State Examination. An application of the Mantel-Haenszel and standardization procedures. Med Care 44:S107–S114

    Article  Google Scholar 

  25. Houseman EA, Marsit C, Karagas M, Ryan LM (2007) Penalized item response theory models: application to epigenetic alterations in bladder cancer. Biometrics 63:1269–1277

    Article  MathSciNet  Google Scholar 

  26. Lee W, Lee G (2018) IRT linking and equating. In: Irwing P, Booth T, Hughes DJ (eds) The Wiley handbook of psychometric testing: a multidisciplinary reference on survey scale and test development. Wiley, New York

    Google Scholar 

  27. Liu SH, Chen Y, Bellinger D, de Water E, Horton M, Tellez-Rojo MM, Wright RO (In Press) Pre-natal and early life lead exposure and childhood inhibitory control: an item response theory approach to improve measurement precision of inhibitory control. Environ Health

  28. Liu SH, Juster RP, Dams-O’Connor K, Spicer J (2021) Allostatic load scoring using item response theory. Compr Psychoneuroendocrinol 5:100025

    Article  Google Scholar 

  29. Liu SH, Kiuper J, Chen Y, Feuerstahler L, Teresi JA, Buckley JP (2022) Developing an exposure burden score for chemical mixtures using item response theory, with applications to PFAS mixtures. Environ Health Perspect. https://doi.org/10.1289/EHP10125

    Article  Google Scholar 

  30. McHorney CA, Cohen AS (2000) Equating health status measures with item response theory: illustrations with functional status items. Med Care 38(2):43–59

    Google Scholar 

  31. Orlando Edelen MO, Thissen D, Teresi JA, Kleinman M, Ocepek-Welikson K (2006) ’Identification of differential item functioning using item response theory and the likelihood-based model comparison approach. Application to the Mini-mental state examination. Med Care 44:S134–S142

    Article  Google Scholar 

  32. Perkins AJ, Stump TE, Monahan PO, McHorney CA (2006) Assessment of differential item functioning for demographic comparisons in the MOS SF-36 health survey. Qual Life Res 15:331–348

    Article  Google Scholar 

  33. Teresi JA, Kleinman M, Ocepek-Welikson K (2000) Modern psychometric methods for detection of differential item functioning: application to cognitive assessment measures. Stat Med 19:1651–1683

    Article  Google Scholar 

  34. Teresi JA, Ocepek-Welikson K, Kleinman M, Cook KF, Crane PK, Gibbons LE, Morales LS, Orlando-Edelen M, Cella D (2007) Evaluating measurement equivalence using the item response theory log-likelihood ratio (IRTLR) method to assess differential item functioning (DIF): applications (with illustrations) to measures of physical functioning ability and general distress. Qual Life Res 16(Suppl 1):43–68

    Article  Google Scholar 

  35. Thomas ML (2019) Advances in applications of item response theory to clinical assessment. Psychol Assess 31:1442–1455

    Article  Google Scholar 

  36. Hastie T, Tibshirani R, Friedman J (2009) Unsupervised learning. In: The elements of statistical learning. Springer, New York

  37. Borsboom D, Mellenbergh GJ, van Heerden J (2003) The theoretical status of latent variables. Psychol Rev 110:203–219

    Article  Google Scholar 

  38. Pearl J (2010) The foundations of causal inference. Sociol Methodol 40:75–149

    Article  Google Scholar 

  39. Hotelling H (1933) Analysis of a complex of statistical variables into principal components. J Educ Psychol 24:417–441

    Article  Google Scholar 

  40. Magidson J, Vermunt JK (2002) Latent class models for clustering: a comparison with K-means. Can J Mark Res 20:37–44

    Google Scholar 

  41. Skrondal A, Rabe-Hesketh S (2007) Latent variable modelling: a survey. Scand J Stat 34:712–745

    Article  MathSciNet  Google Scholar 

  42. Collins LM, Lanza ST (2009) Latent class and latent transition analysis: with applications in the social, behavioral, and health sciences. Hoboken, Wiley

    Book  Google Scholar 

  43. Nylund-Gibson K, Choi AY (2018) Ten frequently asked questions about latent class analysis. Transl Issues Psychol Sci 4:440–461

    Article  Google Scholar 

  44. Nylund KL, Asparouhov T, Muthén BO (2007) Deciding on the number of classes in latent class analysis and growth mixture modeling: a Monte Carlo simulation study. Struct Equ Model 14:535–569

    Article  MathSciNet  Google Scholar 

  45. Vermunt JK, Magidson J (2003) Latent class models for classification. Comput Stat Data Anal 41:531–537

    Article  MathSciNet  Google Scholar 

  46. Yang C-C (2006) Evaluating latent class analysis models in qualitative phenotype identification. Comput Stat Data Anal 50:1090–1104

    Article  MathSciNet  Google Scholar 

  47. Tein J-Y, Coxe S, Cham H (2013) Statistical power to detect the correct number of classes in latent profile analysis. Struct Equ Model 20:640–657

    Article  MathSciNet  Google Scholar 

  48. Lee YH, von Davier AA (2013) Monitoring scale scores over time via quality control charts, model-based approaches, and time series techniques. Psychometrika 78:557–575

    Article  MathSciNet  Google Scholar 

  49. Sinharay S (2017) Some remarks on applications of tests for detecting a change point to psychometric problems. Psychometrika 82:1149–1161

    Article  MathSciNet  Google Scholar 

  50. Grandjean P, Budtz-Jorgensen E (2007) Total imprecision of exposure biomarkers: implications for calculating exposure limits. Am J Ind Med 50:712–719

    Article  Google Scholar 

  51. Grandjean P, Heilmann C, Weihe P, Nielsen F, Mogensen UB, Budtz-Jorgensen E (2017) Serum vaccine antibody concentrations in adolescents exposed to perfluorinated compounds. Environ Health Perspect 125:077018

    Article  Google Scholar 

  52. Heilmann C, Grandjean P, Weihe P, Nielsen F, Budtz-Jorgensen E (2006) Reduced antibody responses to vaccinations in children exposed to polychlorinated biphenyls. PLoS Med 3:e311

    Article  Google Scholar 

  53. Jaafari S, Shabani AA, Moeinaddini M, Danehkar A, Sakieh Y (2020) Applying landscape metrics and structural equation modeling to predict the effect of urban green space on air pollution and respiratory mortality in Tehran. Environ Monit Assess 192:412

    Article  Google Scholar 

  54. Shook-Sa BE, Chen DG, Zhou H (2017) Using structural equation modeling to assess the links between tobacco smoke exposure, volatile organic compounds, and respiratory function for adolescents aged 6 to 18 in the United States. Int J Environ Res Public Health 14:1112

    Article  Google Scholar 

  55. Trzeciakowski JP, Gardiner L, Parrish AR (2014) Effects of environmental levels of cadmium, lead and mercury on human renal function evaluated by structural equation modeling. Toxicol Lett 228:34–41

    Article  Google Scholar 

  56. Tu R, Hou J, Liu X, Li R, Dong X, Pan M, Yin S, Hu K, Mao Z, Huo W, Chen G, Guo Y, Wang X, Li S, Wang C (2021) Low socioeconomic status aggravated associations of exposure to mixture of air pollutants with obesity in rural Chinese adults: a cross-sectional study. Environ Res 194:110632

    Article  Google Scholar 

  57. Wang L, Hou J, Hu C, Zhou Y, Sun H, Zhang J, Li T, Gao E, Wang G, Chen W, Yuan J (2019) Mediating factors explaining the associations between polycyclic aromatic hydrocarbons exposure, low socioeconomic status and diabetes: a structural equation modeling approach. Sci Total Environ 648:1476–1483

    Article  Google Scholar 

  58. Welch BM, Branscum A, Geldhof GJ, Ahmed SM, Hystad P, Smit E, Afroz S, Megowan M, Golam M, Sharif O, Rahman M, Quamruzzaman Q, Christiani DC, Kile ML (2020) Evaluating the effects between metal mixtures and serum vaccine antibody concentrations in children: a prospective birth cohort study. Environ Health 19:41

    Article  Google Scholar 

  59. Buncher CR, Succop PA, Dietrich KN (1991) Structural equation modeling in environmental risk assessment. Environ Health Perspect 90:209–213

    Google Scholar 

  60. Baja ES, Schwartz JD, Coull BA, Wellenius GA, Vokonas PS, Suh HH (2013) Structural equation modeling of parasympathetic and sympathetic response to traffic air pollution in a repeated measures study. Environ Health 12:81

    Article  Google Scholar 

  61. Baja ES, Schwartz JD, Coull BA, Wellenius GA, Vokonas PS, Suh HH (2013) Structural equation modeling of the inflammatory response to traffic air pollution. J Expo Sci Environ Epidemiol 23:268–274

    Article  Google Scholar 

  62. Carbone JT (2021) Allostatic load and mental health: a latent class analysis of physiological dysregulation. Stress 24:394–403

    Article  Google Scholar 

  63. Conley S (2017) Symptom cluster research with biomarkers and genetics using latent class analysis. West J Nurs Res 39:1639–1653

    Article  Google Scholar 

  64. Kuiper JR, Hirsch AG, Bandeen-Roche K, Sundaresan AS, Tan BK, Kern RC, Schleimer RP, Schwartz BS (2020) A new approach to categorization of radiologic inflammation in chronic rhinosinusitis. PLoS ONE 15:e0235432

    Article  Google Scholar 

  65. Lee JY, Walton DM (2021) Latent profile analysis of blood marker phenotypes and their relationships with clinical pain and interference reports in people with acute musculoskeletal trauma. Can J Pain 5:30–42

    Article  Google Scholar 

  66. Berg CJ, Duan X, Romm K, Pulvers K, Le D, Ma Y, Krishnan N, Abroms LC, Getachew B, Henriksen L (2021) Young adults’ vaping, readiness to quit, and recent quit attempts: the role of co-use with cigarettes and marijuana. Nicotine Tob Res 23:1019–1029

    Article  Google Scholar 

  67. Clawson AH, Ruppe NM, Nwankwo CN, Blair AL (2022) Profiles of nicotine and cannabis exposure among young adults with asthma. Behav Med 48:18–30

    Article  Google Scholar 

  68. Gohari MR, Cook RJ, Dubin JA, Leatherdale ST (2020) Identifying patterns of alcohol use among secondary school students in Canada: a multilevel latent class analysis. Addict Behav 100:106120

    Article  Google Scholar 

  69. Johnson AL, Collins LK, Villanti AC, Pearson JL, Niaura RS (2018) Patterns of nicotine and tobacco product use in youth and young adults in the United States, 2011–2015. Nicotine Tob Res 20:S48-s54

    Article  Google Scholar 

  70. Lanza HI, Leventhal AM, Cho J, Braymiller JL, Krueger EA, McConnell R, Barrington-Trimis JL (2020) Young adult e-cigarette use: a latent class analysis of device and flavor use, 2018–2019. Drug Alcohol Depend 216:108258

    Article  Google Scholar 

  71. Lanza HI, Motlagh G, Orozco M (2020) E-cigarette use among young adults: a latent class analysis examining co-use and correlates of nicotine vaping. Addict Behav 110:106528

    Article  Google Scholar 

  72. Carroll R, White AJ, Keil AP, Meeker JD, McElrath TF, Zhao S, Ferguson KK (2020) Latent classes for chemical mixtures analyses in epidemiology: an example using phthalate and phenol exposure biomarkers in pregnant women. J Expo Sci Environ Epidemiol 30:149–159

    Article  Google Scholar 

  73. Hendryx M, Luo J (2018) Latent class analysis of the association between polycyclic aromatic hydrocarbon exposures and body mass index. Environ Int 121:227–231

    Article  Google Scholar 

  74. Hendryx M, Luo J (2018) Latent class analysis to model multiple chemical exposures among children. Environ Res 160:115–120

    Article  Google Scholar 

  75. Oberski D (2016) Mixture models: latent profile and latent class analysis. In: Robertson J, Kaptein M (eds) Modern statistical methods for HCI. Springer, Cham

    Google Scholar 

  76. Bolck A, Croon M, Hagenaars J (2004) Estimating latent structure models with categorical variables: one-step versus three-step estimators. Polit Anal 12:3–27

    Article  Google Scholar 

  77. McCarthy DE, Ebssa L, Witkiewitz K, Shiffman S (2016) Repeated measures latent class analysis of daily smoking in three smoking cessation studies. Drug Alcohol Depend 165:132–142

    Article  Google Scholar 

  78. Kiuper J, Liu SH, Lanphear BP, Calafat AM, Cecil KM, Xu Y, Yolton K, Kalkwarf HJ, Chen A, Braun JM, Buckley JP (2023) Estimating effects of longitudinal and cumulative exposure to PFAS mixtures on early adolescent body composition. Am J Epidemiol (In press)

  79. Zhang B, Chen Z, Albert PS (2012) Latent class models for joint analysis of disease prevalence and high-dimensional semicontinuous biomarker data. Biostatistics 13:74–88

    Article  Google Scholar 

  80. Hwang BS, Chen Z, Buck Louis GM, Albert PS (2019) A Bayesian multi-dimensional couple-based latent risk model with an application to infertility. Biometrics 75:315–325

    Article  MathSciNet  Google Scholar 

  81. Peng C, Wang J, Asante I, Louie S, Jin R, Chatzi L, Casey G, Thomas DC, Conti DV (2020) A latent unknown clustering integrating multi-omics data (LUCID) with phenotypic traits. Bioinformatics (Oxford, England) 36:842–850

    Google Scholar 

  82. Alderete TL, Jin R, Walker DI, Valvi D, Chen Z, Jones DP, Peng C, Gilliland FD, Berhane K, Conti DV, Goran MI, Chatzi L (2019) Perfluoroalkyl substances, metabolomic profiling, and alterations in glucose homeostasis among overweight and obese Hispanic children: a proof-of-concept analysis. Environ Int 126:445–453

    Article  Google Scholar 

  83. Jin R, McConnell R, Catherine C, Shujing Xu, Walker DI, Stratakis N, Jones DP, Miller GW, Peng C, Conti DV, Vos MB, Chatzi L (2020) Perfluoroalkyl substances and severity of nonalcoholic fatty liver in Children: an untargeted metabolomics approach. Environ Int 134:105220–105320

    Article  Google Scholar 

  84. Stratakis N, Conti DV, Borras E, Sabido E, Roumeliotaki T, Papadopoulou E, Agier L, Basagana X, Bustamante M, Casas M, Farzan SF, Fossati S, Gonzalez JR, Grazuleviciene R, Heude B, Maitre L, McEachan RRC, Theologidis I, Urquiza J, Vafeiadi M, West J, Wright J, McConnell R, Brantsaeter A-L, Meltzer H-M, Vrijheid M, Chatzi L (2020) Association of fish consumption and mercury exposure during pregnancy with metabolic health and inflammatory biomarkers in children. JAMA Netw Open 3:e201007–e201107

    Article  Google Scholar 

  85. Stratakis N, Conti DV, Jin R, Margetaki K, Valvi D, Siskos AP, Maitre L, Garcia E, Varo N, Zhao Y, Roumeliotaki T, Vafeiadi M, Urquiza J, Fernández-Barrés S, Heude B, Basagana X, Casas M, Fossati S, Gražulevičienė R, Andrušaitytė S, Uppal K, McEachan RRC, Papadopoulou E, Robinson O, Haug LS, Wright J, Vos MB, Keun HC, Vrijheid M, Berhane KT, McConnell R, Chatzi L (2020) Prenatal exposure to perfluoroalkyl substances associated with increased susceptibility to liver injury in children. Hepatology (Baltimore, MD) 72:1758–1770

    Article  Google Scholar 

  86. Holland PW, Wainer H (2012) Differential item functioning. Routledge, New York

    Book  Google Scholar 

  87. Millsap RE (2012) Statistical approaches to measurement invariance. Routledge, New York

    Book  Google Scholar 

  88. Pichon LC, Corral I, Landrine H, Mayer JA, Norman GJ (2010) Sun protection behaviors among African Americans. Am J Prev Med 38:288–295

    Article  Google Scholar 

  89. Holland PW, Thayer DT (1986) Differential item performance and the Mantel-Haenszel procedure. In: American Educational Research Association Annual Meeting. San Francisco, CA

  90. Thissen D, Steinberg L, Wainer H (1993) Detection of differential item functioning using the parameters of item response models. In: Holland PW, Wainer H (eds) Differential item functioning. Lawrence Erlbaum, Hillsdale

    Google Scholar 

  91. Kopf J, Zeileis A, Strobl C (2015) Anchor selection strategies for DIF analysis: review, assessment, and new approaches. Educ Psychol Measur 75:22–56

    Article  Google Scholar 

  92. Lopez-Rivas GE, Stark S, Chernyshenko OS (2009) The effects of referent item parameters on differential item functioning detection using the free baseline likelihood ratio test. Appl Psychol Meas 33:251–265

    Article  MathSciNet  Google Scholar 

  93. Wang W-C, Yeh Y-L (2003) Effects of anchor item methods on differential item functioning detection with the likelihood ratio test. Appl Psychol Meas 27:479–498

    Article  MathSciNet  Google Scholar 

  94. Woods CM (2009) Empirical selection of anchor item methods on differential item functioning detection with the likelihood ratio test. Appl Psychol Meas 33:42–57

    Article  MathSciNet  Google Scholar 

  95. Meredith W (1993) Measurement invariance, factor analysis and factorial invariance. Psychometrika 58:525–543

    Article  MathSciNet  Google Scholar 

  96. Putnick DL, Bornstein MH (2016) Measurement invariance conventions and reporting: the state of the art and future directions for psychological research. Dev Rev 41:71–90

    Article  Google Scholar 

  97. Vandenberg RJ, Lance CE (2000) A review and synthesis of the measurement invariance literature: suggestions, practices, and recommendations for organizational research. Organ Res Methods 2:4–69

    Article  Google Scholar 

  98. Kenny D (2020) Measuring model fit. https://davidakenny.net/cm/fit.htm. Accessed 4 June

  99. Maydeu-Olivares A (2015) Evaluating fit in IRT models. In: Reise SP, Reviicki DA (eds) Handbook of item response theory modeling: applications to typical performance assessment. New York, Routledge

    Google Scholar 

  100. Maydeu-Olivares A, Cai L (2006) A cautionary note on using G2(dif) to assess relative model fit in categorical data analysis. Multivar Behav Res 41:55–64

    Article  Google Scholar 

  101. Jung E, Yoon M (2016) Comparisons of three empirical methods for partial factorial invariance: forward backward, and factor-ratio tests. Struct Equ Model 23:567–584

    Article  MathSciNet  Google Scholar 

  102. Liu X, Rogers HJ (2022) Treatments of differential item functioning: a comparison of four methods. Educ Psychol Measur 82:225–253

    Article  Google Scholar 

  103. Cho S-J, Suh Y, Lee W-Y (2016) After differential item functioning is detected: IRT item calibration and scoring in the presence of DIF. Appl Psychol Meas 40:573–591

    Article  Google Scholar 

  104. Carroll RJ, Ruppert D, Stefanski LA, Crainiceanu CM (2006) Measurement error in nonlinear models: a modern perspective. Chapman & Hall/CRC Press, Boca Raton

    Book  Google Scholar 

  105. Budtz-Jørgensen E, Keiding N, Grandjean P, Weihe P (2002) Estimation of health efefcts of prenatal and methylmercury exposure using structural equation models. Environ Health 1:1–22

    Article  Google Scholar 

  106. Przybyla J, John Geldhof G, Smit E, Kile ML (2018) A cross sectional study of urinary phthalates, phenols and perchlorate on thyroid hormones in US adults using structural equation models. Environ Res 163:26–35

    Article  Google Scholar 

  107. Marsman M, Maris G, Bechger T, Glas C (2016) What can we learn from plausible values? Psychometrika 81:274–289

    Article  MathSciNet  Google Scholar 

  108. Fischer HF, Wahl I, Nolte S, Liegl G, Brähler E, Löwe B, Rose M (2016) Language-related differential item functioning between English and German PROMIS Depression items is negligible. Int J Methods Psychiatr Res 26:e1530

    Article  Google Scholar 

  109. Reckase MD (2009) Multidimensional item response theory. Springer, New York

    Book  Google Scholar 

  110. Reise SP (2012) The rediscovery of bifactor measurement models. Multivar Behav Res 47:667–696

    Article  Google Scholar 

  111. Yung YF, Thissen D, McLeod LD (1999) On the relationship between the higher-order factor model and the hierarchical factor model. Psychometrika 64:113–128

    Article  MathSciNet  Google Scholar 

  112. Auerswald M, Moshagen M (2019) How to determine the number of factors to retain in exploratory factor analysis: a comparison of extraction methods under realistic conditions. Psychol Methods 24:468–491

    Article  Google Scholar 

  113. Maydeu-Olivares A, Cai L, Hernandez A (2011) Comparing the fit of item response theory and factor analysis models. Struct Equ Model 18:333–356

    Article  MathSciNet  Google Scholar 

  114. Drasgow F, Parson CK (1983) Application of unidimensional item response theory models to multidimensional data. Appl Psychol Meas 7:189–199

    Article  Google Scholar 

  115. Reckase MD (1990) Unidimensional data from multidimensional tests and multidimensional data from unidimensional tests. Americal Educational Research Association, Boston

    Google Scholar 

  116. Matsunaga M (2010) How to factor analyze your data right: do’s don’ts and how-to’s. Int J Psychol Res 3:97–110

    Article  Google Scholar 

  117. Ma W, de la Torre J (2016) A sequential cognitive diagnosis model for polytomous responses. Br J Math Stat Psychol 69:253–275

    Article  Google Scholar 

  118. Templin J, Henson R, Rupp A, Jang E, Ahmed M (2008) Cognitive diagnosis models for nominal response data. In: National Council on Measurement in Education

  119. Chan KS, Gross AL, Pezzin LE, Brandt J, Kasper JD (2015) Harmonizing measures of cognitive performance across international surveys of aging using item response theory. J Aging Health 27:1392–1414

    Article  Google Scholar 

  120. Dorans NJ (2007) Linking scores from multiple health outcome instruments. Qual Life Res 16:85–94

    Article  Google Scholar 

  121. Vale CD (1986) Linking item parameters onto a common scale. Appl Psychol Meas 10:333–344

    Article  Google Scholar 

  122. Kim S-H, Cohen AS (1998) A comparison of linking and concurrent calibration under item response theory. Appl Psychol Meas 22:131–143

    Article  Google Scholar 

  123. Mittelhaeuser M-A, Beguin AA, Sijtsma K (2011) Comparing the effectiveness of different linking designs: the internal anchor versus the external anchor and pre-test data. In: CITO

  124. Robitzsch A (2021) A comparison of linking methods for two groups for the two-parameter logistic item response model in the presence and absence of random differential item functioning. Foundations 1:116–144

    Article  Google Scholar 

  125. Watkins, M. W. (2018). Exploratory factor analysis: a guide to best practice. J Black Psychol 44(3):219–246

    Article  Google Scholar 

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Acknowledgements

S.H.L. was supported by National Institute for Environmental Health Sciences (NIEHS) R03ES033374 and National Institute of Child Health and Human Development (NICHD) K25HD104918. J.R.K. and J.P.B. were supported by NIEHS R01ES030078 and R01ES033252.

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Liu, S.H., Chen, Y., Kuiper, J.R. et al. Applying Latent Variable Models to Estimate Cumulative Exposure Burden to Chemical Mixtures and Identify Latent Exposure Subgroups: A Critical Review and Future Directions. Stat Biosci (2024). https://doi.org/10.1007/s12561-023-09410-9

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