Modeling Heterogeneity in Temporal Dynamics: Extending Latent State-Trait Autoregressive and Cross-lagged Panel Models to Mixture Distribution Models

References

• American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorders (5th ed.).
   Google Scholar
• Asparouhov, T., Hamaker, E. L., & Muthén, B. (2018). Dynamic structural equation models. Structural Equation Modeling: A Multidisciplinary Journal, 25(3), 359–388. https://doi.org/10.1080/10705511.2017.1406803
   Web of Science ®Google Scholar
• Asparouhov, T., & Muthén, B. (2016). Structural equation models and mixture models with continuous nonnormal skewed distributions. Structural Equation Modeling: A Multidisciplinary Journal, 23(1), 1–19. https://doi.org/10.1080/10705511.2014.947375
   Web of Science ®Google Scholar
• Bauer, D. J., & Curran, P. J. (2003). Distributional assumptions of growth mixture models: Implications for overextraction of latent trajectory classes. Psychological Methods, 8(3), 338–363. https://doi.org/10.1037/1082-989X.8.3.338
   PubMed Web of Science ®Google Scholar
• Beltz, A. M., Wright, A. G. C., Sprague, B. N., & Molenaar, P. C. (2016). Bridging the nomothetic and idiographic approaches to the analysis of clinical data. Assessment, 23(4), 447–458. https://doi.org/10.1177/1073191116648209
   PubMed Web of Science ®Google Scholar
• Brose, A., Voelkle, M. C., Lövdén, M., Lindenberger, U., & Schmiedek, F. (2015). Differences in the between-person and within-person structures of affect are a matter of degree. European Journal of Personality, 29(1), 55–71. https://doi.org/10.1002/per.1961
   Web of Science ®Google Scholar
• Bulteel, K., Tuerlinckx, F., Brose, A., & Ceulemans, E. (2016). Clustering vector autoregressive models: Capturing qualitative differences in within-person dynamics. Frontiers in Psychology, 7, 1540. https://doi.org/10.3389/fpsyg.2016.01540
   PubMed Web of Science ®Google Scholar
• Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.) Erlbaum.
   Google Scholar
• Cole, D. A., Martin, N. C., & Steiger, J. H. (2005). Empirical and conceptual problems with longitudinal trait-state models: Introducing a trait-state-occasion model. Psychological Methods, 10(1), 3–20. https://doi.org/10.1037/1082-989X.10.1.3
   PubMed Web of Science ®Google Scholar
• Courvoisier, D. S., Eid, M., & Nussbeck, F. W. (2007). Mixture distribution latent state-trait analysis: Basic ideas and applications. Psychological Methods, 12(1), 80–104. https://doi.org/10.1037/1082-989X.12.1.80
   PubMed Web of Science ®Google Scholar
• Curran, P. J., Howard, A. L., Bainter, S. A., Lane, S. T., & McGinley, J. S. (2014). The separation of between-person and within-person components of individual change over time: a latent curve model with structured residuals. Journal of Consulting and Clinical Psychology, 82(5), 879–894. https://doi.org/10.1037/a0035297
   PubMed Web of Science ®Google Scholar
• Dolan, C. V., & van der Maas, H. L. J. (1998). Fitting multivariate normal finite mixtures subject to structural equation modeling. Psychometrika, 63(3), 227–253. https://doi.org/10.1007/BF02294853
   Web of Science ®Google Scholar
• Driver, C. C., & Voelkle, M. C. (2018). Hierarchical Bayesian continuous time dynamic modeling. Psychological Methods, 23(4), 774–799. https://doi.org/10.1037/met0000168
   PubMed Web of Science ®Google Scholar
• Eid, M., Courvoisier, D. S., & Lischetzke, T. (2012). Structural equation modeling of ambulatory assessment data. In M. R. Mehl & T. S. Conner (Eds.), Handbook of research methods for studying daily life (pp. 384–406). Guilford Press.
   Google Scholar
• Eid, M., Holtmann, J., Santangelo, P., & Ebner-Priemer, U. (2017). On the definition of latent-state-trait models with autoregressive effects: Insights from LST-R theory. European Journal of Psychological Assessment, 33(4), 285–295. https://doi.org/10.1027/1015-5759/a000435
   Web of Science ®Google Scholar
• Ernst, A. F., Albers, C. J., Jeronimus, B. F., & Timmerman, M. E. (2020). Inter-individual differences in multivariate time-series. Latent class vector-autoregressive modeling. European Journal of Psychological Assessment, 36(3), 482–491. https://doi.org/10.1027/1015-5759/a000578
   Web of Science ®Google Scholar
• Ernst, A. F., Timmerman, M. E., Jeronimus, B. F., & Albers, C. J. (2021). Insight into individual differences in emotion dynamics with clustering. Assessment, 28(4), 1186–1206. https://doi.org/10.1177/1073191119873714
   PubMed Web of Science ®Google Scholar
• Faul, F., Erdfelder, E., Lang, A.-G., & Buchner, A. (2007). G* power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behavior Research Methods, 39(2), 175–191. https://doi.org/10.3758/bf03193146
   PubMed Web of Science ®Google Scholar
• Fisher, A. J., Reeves, J. W., Lawyer, G., Medaglia, J. D., & Rubel, J. A. (2017). Exploring the idiographic dynamics of mood and anxiety via network analysis. Journal of Abnormal Psychology, 126(8), 1044–1056. https://doi.org/10.1037/abn0000311
   PubMed Web of Science ®Google Scholar
• Gates, K. M., Lane, S. T., Varangis, E., Giovanello, K., & Guskiewicz, K. (2017). Unsupervised classification during time-series model building. Multivariate Behavioral Research, 52(2), 129–148. https://doi.org/10.1080/00273171.2016.1256187
   PubMed Web of Science ®Google Scholar
• Geiser, C., Keller, B. T., Lockhart, G., Eid, M., Cole, D. A., & Koch, T. (2015). Distinguishing state variability from trait change in longitudinal data: The role of measurement (non)invariance in latent state-trait analyses. Behavior Research Methods, 47(1), 172–203. https://doi.org/10.3758/s13428-014-0457-z
   PubMed Web of Science ®Google Scholar
• Hamaker, E. L. (2012). Why researchers should think “within-person”: A paradigmatic rationale. In M. R. Mehl & T. S. Conner (Eds.), Handbook of research methods for studying daily life (p. 43–61). Guilford Press.
   Google Scholar
• Hamaker, E. L., Kuiper, R. M., & Grasman, R. P. (2015). A critique of the cross-lagged panel model. Psychological Methods, 20(1), 102–116. https://doi.org/10.1037/a0038889
   PubMed Web of Science ®Google Scholar
• Henson, J. M., Reise, S. P., & Kim, K. H. (2007). Detecting mixtures from structural model differences using latent variable mixture modeling: A comparison of relative model fit statistics. Structural Equation Modeling: A Multidisciplinary Journal, 14(2), 202–226. https://doi.org/10.1080/10705510709336744
   Web of Science ®Google Scholar
• Hohmann, L., Holtmann, J., & Eid, M. (2018). Skew t mixture latent state-trait analysis: A Monte Carlo simulation study on statistical performance. Frontiers in Psychology, 9, 1323. https://doi.org/10.3389/fpsyg.2018.01323
   PubMed Web of Science ®Google Scholar
• Kockler, T. D., Santangelo, P. S., Eid, M., Kuehner, C., Bohus, M., Schmaedeke, S., & Ebner-Priemer, U. W. (2022). Self-esteem instability might be more characteristic of borderline personality disorder than affective instability: Findings from an e-diary study with clinical and healthy controls. Journal of Psychopathology and Clinical Science, 131(3), 301–313. https://doi.org/10.1037/abn0000731
   PubMedGoogle Scholar
• Kuppens, P., Allen, N. B., & Sheeber, L. B. (2010). Emotional inertia and psychological maladjustment. Psychological Science, 21(7), 984–991. https://doi.org/10.1177/0956797610372634
   PubMed Web of Science ®Google Scholar
• Lane, S. T., Gates, K. M., Pike, H. K., Beltz, A. M., & Wright, A. G. C. (2019). Uncovering general, shared, and unique temporal patterns in ambulatory assessment data. Psychological Methods, 24(1), 54–69. https://doi.org/10.1037/met0000192
   PubMed Web of Science ®Google Scholar
• Lo, Y., Mendell, N., & Rubin, D. B. (2001). Testing the number of components in a normal mixture. Biometrika, 88(3), 767–778. https://doi.org/10.1093/biomet/88.3.767
   Web of Science ®Google Scholar
• Masyn, K. E. (2013). Latent class analysis and finite mixture modeling. In T. D. Little (Ed.), The oxford handbook of quantitative methods (vol. 2: Statistical analysis) (p. 551–611). Oxford University Press.
   Google Scholar
• Maydeu-Olivares, A., & Coffman, D. L. (2006). Random intercept item factor analysis. Psychological Methods, 11(4), 344–362. https://doi.org/10.1037/1082-989X.11.4.344
   PubMed Web of Science ®Google Scholar
• McLachlan, G., & Peel, D. (2000). Finite mixture models. Wiley.
   Google Scholar
• McNeish, D., & Harring, J. R. (2017). The effect of model misspecification on growth mixture model class enumeration. Journal of Classification, 34(2), 223–248. https://doi.org/10.1007/s00357-017-9233-y
   Web of Science ®Google Scholar
• Meredith, W. (1993). Measurement invariance, factor analysis and factorial invariance. Psychometrika, 58(4), 525–543. https://doi.org/10.1007/BF02294825
   Web of Science ®Google Scholar
• Meredith, W., & Horn, J. (2001). The role of factorial invariance in modeling growth and change. In L. M. Collins & A. G. Sayer (Eds.), New methods for the analysis of change (pp. 203–240). American Psychological Association.
   Google Scholar
• Millsap, R. E. (2011). Statistical approaches to measurement invariance (1st ed.). Routledge.
   Google Scholar
• Molenaar, P. C. M. (2004). A manifesto on psychology as idiographic science: Bringing the person back into scientific psychology, this time forever. Measurement: Interdisciplinary Research and Perspesctive, 2(4), 201–218. https://doi.org/10.1207/s15366359mea0204_1
   Google Scholar
• Molenaar, P. C. M., & Campbell, C. G. (2009). The new person-specific paradigm in psychology. Current Directions in Psychological Science, 18(2), 112–117. https://doi.org/10.1111/j.1467-8721.2009.01619.x
   Web of Science ®Google Scholar
• Mulder, J. D., & Hamaker, E. L. (2021). Three extensions of the random intercept cross-lagged panel model. Structural Equation Modeling: A Multidisciplinary Journal, 28(4), 638–648. https://doi.org/10.1080/10705511.2020.1784738
   Web of Science ®Google Scholar
• Muthén, B. (2001). Latent variable mixture modeling. In G. Marcoulides & R. Schumacker (Eds.), New developments and techniques in structural equation modeling (pp. 1–33). Erlbaum.
   Google Scholar
• Muthén, B. (2003). Statistical and substantive checking in growth mixture modeling: Comment on Bauer and Curran (2003). Psychological Methods, 8(3), 369–377. https://doi.org/10.1037/1082-989X.8.3.369
   PubMed Web of Science ®Google Scholar
• Muthén, L. K., & Muthén, B. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling: A Multidisciplinary Journal, 9(4), 599–620. https://doi.org/10.1207/S15328007SEM0904_8
   Web of Science ®Google Scholar
• Muthén, L. K., & Muthén, B. O. (1998-2017). Mplus user’s guide (8th ed.).
   Google Scholar
• Myin-Germeys, I., & Kuppens, P. (2021). The open handbook of experience sampling methodology: A step-by-step guide to designing, conducting, and analyzing ESM studies. Center for Research on Experience Sampling and Ambulatory Methods Leuven.
   Google Scholar
• Nylund, K. L., Asparouhov, T., & Muthén, B. O. (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo simulation study. Structural Equation Modeling: A Multidisciplinary Journal, 14(4), 535–569. https://doi.org/10.1080/10705510701575396
   Web of Science ®Google Scholar
• Nylund-Gibson, K., & Choi, A. Y. (2018). Ten frequently asked questions about latent class analysis. Translational Issues in Psychological Science, 4(4), 440–461. https://doi.org/10.1037/tps0000176
   Google Scholar
• Oeltjen, L., Koch, T., Holtmann, J., Münch, F. F., Eid, M., & Nussbeck, F. W. (2020). A general framework for the inclusion of time-varying and time-invariant covariates in latent state trait models. Psychological Methods.
   Google Scholar
• Oravecz, Z., Tuerlinckx, F., & Vandekerckhove, J. (2009). A hierarchical Ornstein–Uhlenbeck model for continuous repeated measurement data. Psychometrika, 74(3), 395–418. https://doi.org/10.1007/s11336-008-9106-8
   Web of Science ®Google Scholar
• Oravecz, Z., Tuerlinckx, F., & Vandekerckhove, J. (2016). Bayesian data analysis with the bivariate hierarchical ornstein-uhlenbeck process model. Multivariate Behavioral Research, 51(1), 106–119. https://doi.org/10.1080/00273171.2015.1110512
   PubMed Web of Science ®Google Scholar
• Piccirillo, M. L., & Rodebaugh, T. L. (2019). Foundations of idiographic methods in psychology and applications for psychotherapy. Clinical Psychology Review, 71, 90–100. https://doi.org/10.1016/j.cpr.2019.01.002
   PubMed Web of Science ®Google Scholar
• R Core Team (2019). R: A language and environment for statistical computing [Computer software manual]. Vienna, Austria. Retrieved from https://www.R-project.org
   Google Scholar
• Ram, N., & Grimm, K. J. (2009). Methods and measures: Growth mixture modeling: A method for identifying differences in longitudinal change among unobserved groups. International Journal of Behavioral Development, 33(6), 565–576. https://doi.org/10.1177/0165025409343765
   PubMed Web of Science ®Google Scholar
• Rosenberg, M. (1965). Society and the adolescent self-image. University Press.
   Google Scholar
• Santangelo, P. S., Holtmann, J., Hosoya, G., Bohus, M., Kockler, T. D., Koudela-Hamila, S., Eid, M., & Ebner-Priemer, U. W. (2020). Within- and between-persons effects of self-esteem and affective state as antecedents and consequences of dysfunctional behaviors in the everyday lives of patients with borderline personality disorder. Clinical Psychological Science, 8(3), 428–449. https://doi.org/10.1177/2167702620901724
   Web of Science ®Google Scholar
• Santangelo, P. S., Reinhard, I., Koudela-Hamila, S., Bohus, M., Holtmann, J., Eid, M., & Ebner-Priemer, U. W. (2017). The temporal interplay of self-esteem instability and affective instability in borderline personality disorder patients’ everyday lives. Journal of Abnormal Psychology, 126(8), 1057–1065. https://doi.org/10.1037/abn0000288
   PubMed Web of Science ®Google Scholar
• Santangelo, P., Reinhard, I., Mussgay, L., Steil, R., Sawitzki, G., Klein, C., Trull, T. J., Bohus, M., & Ebner-Priemer, U. W. (2014). Specificity of affective instability in patients with borderline personality disorder compared to posttraumatic stress disorder, bulimia nervosa, and healthy controls. Journal of Abnormal Psychology, 123(1), 258–272. https://doi.org/10.1037/a0035619
   PubMed Web of Science ®Google Scholar
• Schultzberg, M., & Muthén, B. (2018). Number of subjects and time points needed for multilevel time-series analysis: A simulation study of dynamic structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 25(4), 495–515. https://doi.org/10.1080/10705511.2017.1392862
   Web of Science ®Google Scholar
• Schuurman, N. K., & Hamaker, E. L. (2019). Measurement error and person-specific reliability in multilevel autoregressive modeling. Psychological Methods, 24(1), 70–91. https://doi.org/10.1037/met0000188
   PubMed Web of Science ®Google Scholar
• Schuurman, N. K., Houtveen, J., & Hamaker, E. (2015). Incorporating measurement error in n = 1 psychological autoregressive modeling. Frontiers in Psychology, 6, 1038. https://doi.org/10.3389/fpsyg.2015.01038
   PubMed Web of Science ®Google Scholar
• Song, H., & Zhang, Z. (2014). Analyzing multiple multivariate time series data using multilevel dynamic factor models. Multivariate Behavioral Research, 49(1), 67–77. https://doi.org/10.1080/00273171.2013.851018
   PubMed Web of Science ®Google Scholar
• Steyer, R., Mayer, A., Geiser, C., & Cole, D. A. (2015). A theory of states and traits - revised. Annual Review of Clinical Psychology, 11, 71–98. https://doi.org/10.1146/annurev-clinpsy-032813-153719
   PubMed Web of Science ®Google Scholar
• Suls, J., Green, P., & Hillis, S. (1998). Emotional reactivity to everyday problems, affective inertia, and neuroticism. Personality and Social Psychology Bulletin, 24(2), 127–136. https://doi.org/10.1177/0146167298242002
   Web of Science ®Google Scholar
• Tofighi, D., & Enders, C. K. (2007). Identifying the correct number of classes in a growth mixture model. In G. R. Hancock (Ed.), Mixture models in latent variable research. (p. 317–341) Information Age.
   Google Scholar
• Voelkle, M. C., Brose, A., Schmiedek, F., & Lindenberger, U. (2014). Toward a unified framework for the study of between-person and within-person structures: Building a bridge between two research paradigms. Multivariate Behavioral Research, 49(3), 193–213. https://doi.org/10.1080/00273171.2014.889593
   PubMed Web of Science ®Google Scholar
• Wang, L. P., & Maxwell, S. E. (2015). On disaggregating between-person and within-person effects with longitudinal data using multilevel models. Psychological Methods, 20(1), 63–83. https://doi.org/10.1037/met0000030
   PubMed Web of Science ®Google Scholar
• Wilhelm, P., & Schoebi, D. (2007). Assessing mood in daily life: Structural validity, sensitivity to change, and reliability of a short-scale to measure three basic dimensions of mood. European Journal of Psychological Assessment, 23(4), 258–267. https://doi.org/10.1027/1015-5759.23.4.258
   Web of Science ®Google Scholar
• Wright, A. G. C., Gates, K. M., Arizmendi, C., Lane, S. T., Woods, W. C., & Edershile, E. A. (2019). Focusing personality assessment on the person: Modeling general, shared, and person specific processes in personality and psychopathology. Psychological Assessment, 31(4), 502–515. https://doi.org/10.1037/pas0000617
   PubMed Web of Science ®Google Scholar
• Wright, A. G. C., Hallquist, M. N., Stepp, S. D., Scott, L. N., Beeney, J. E., Lazarus, S. A., & Pilkonis, P. A. (2016). Modeling heterogeneity in momentary interpersonal and affective dynamic processes in borderline personality disorder. Assessment, 23(4), 484–495. https://doi.org/10.1177/1073191116653829
   PubMed Web of Science ®Google Scholar
• Wright, A. G. C., & Woods, W. C. (2020). Personalized models of psychopathology. Annual Review of Clinical Psychology, 16, 49–74. https://doi.org/10.1146/annurev-clinpsy-102419-125032
   PubMed Web of Science ®Google Scholar
• Wright, A. G. C., & Zimmermann, J. (2019). Applied ambulatory assessment: Integrating idiographic and nomothetic principles of measurement. Psychological Assessment, 31(12), 1467–1480. https://doi.org/10.1037/pas0000685
   PubMed Web of Science ®Google Scholar