A Systematic Study into the Factors that Affect the Predictive Accuracy of Multilevel VAR(1) Models.

cross-validation intensive longitudinal data linear mixed effect models multicollinearity principal components

Journal

Psychometrika
ISSN: 1860-0980
Titre abrégé: Psychometrika
Pays: United States
ID NLM: 0376503

Informations de publication

Date de publication:
06 2022
Historique:
received: 13 07 2020
accepted: 02 08 2021
revised: 13 07 2021
pubmed: 2 11 2021
medline: 9 6 2022
entrez: 1 11 2021
Statut: ppublish

Résumé

The use of multilevel VAR(1) models to unravel within-individual process dynamics is gaining momentum in psychological research. These models accommodate the structure of intensive longitudinal datasets in which repeated measurements are nested within individuals. They estimate within-individual auto- and cross-regressive relationships while incorporating and using information about the distributions of these effects across individuals. An important quality feature of the obtained estimates pertains to how well they generalize to unseen data. Bulteel and colleagues (Psychol Methods 23(4):740-756, 2018a) showed that this feature can be assessed through a cross-validation approach, yielding a predictive accuracy measure. In this article, we follow up on their results, by performing three simulation studies that allow to systematically study five factors that likely affect the predictive accuracy of multilevel VAR(1) models: (i) the number of measurement occasions per person, (ii) the number of persons, (iii) the number of variables, (iv) the contemporaneous collinearity between the variables, and (v) the distributional shape of the individual differences in the VAR(1) parameters (i.e., normal versus multimodal distributions). Simulation results show that pooling information across individuals and using multilevel techniques prevent overfitting. Also, we show that when variables are expected to show strong contemporaneous correlations, performing multilevel VAR(1) in a reduced variable space can be useful. Furthermore, results reveal that multilevel VAR(1) models with random effects have a better predictive performance than person-specific VAR(1) models when the sample includes groups of individuals that share similar dynamics.

Identifiants

pubmed: 34724142
doi: 10.1007/s11336-021-09803-z
pii: 10.1007/s11336-021-09803-z
doi:

Types de publication

Journal Article Research Support, Non-U.S. Gov't

Langues

eng

Sous-ensembles de citation

IM

Pagination

432-476

Informations de copyright

© 2021. The Psychometric Society.

Références

Asparouhov, T., Hamaker, E. L., & Muthén, B. (2018). Dynamic structural equation models. Structural Equation Modeling: A Multidisciplinary Journal, 25(3), 359–388.
Babyak, M. A. (2004). What you see may not be what you get: A brief, nontechnical introduction to overfitting in regression-type models. Psychosomatic Medicine, 66(3), 411–421.
pubmed: 15184705
Barr, D. J., Levy, R., Scheepers, C., & Tily, H. J. (2013). Random effects structure for confirmatory hypothesis testing: Keep it maximal. Journal of Memory and Language, 68(3), 255–278.
Bates, D., Kelman, T., Simon, A. B., Noack, A., Hatherly, M., & Bouchet-Valat, M. (2016). Dmbates/Mixedmodels.Jl: Drop Julia V0.4.X and earlier support. Zenodo.
Bates, D., Kliegl, R., Vasishth, S., & Baayen, H. (2015a). Parsimonious mixed models. arXiv preprint arXiv:1506.04967 .
Bates, D., Mächler, M., Bolker, B., & Walker, S. (2015b). Fitting linear mixed-effects models using lme4. Journal of Statistical Software, 67(1), 1–48.
Bezanson, J., Edelman, A., Karpinski, S., & Shah, V. B. (2017). Julia: A fresh approach to numerical computing. SIAM Review, 59(1), 68–98.
Borsboom, D., & Cramer, A. O. (2013). Network analysis: An integrative approach to the structure of psychopathology. Annual Review of Clinical Psychology, 9, 91–121.
pubmed: 23537483
Bringmann, L. F., Pe, M. L., Vissers, N., Ceulemans, E., Borsboom, D., Vanpaemel, W., & Kuppens, P. (2016). Assessing temporal emotion dynamics using networks. Assessment, 23(4), 425–435.
pubmed: 27141038
Bringmann, L. F., Vissers, N., Wichers, M., Geschwind, N., Kuppens, P., Peeters, F., & Tuerlinckx, F. (2013). A network approach to psychopathology: New insights into clinical longitudinal data. PLoS ONE, 8(4), e60188.
pubmed: 23593171 pmcid: 3617177
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.
Browne, M. W., & Nesselroade, J. R. (2005). Representing psychological processes with dynamic factor models: Some promising uses and extensions of autoregressive moving average time series models. In A. Maydeu-Olivares & J. J. McArdle (Eds.), Contemporary psychometrics: A festschrift for Roderick P. McDonald (pp. 415–452). Mahwah, NJ: Lawrence Erlbaum Associates.
Bulteel, K., Mestdagh, M., Tuerlinckx, F., & Ceulemans, E. (2018a). VAR (1) based models do not always outpredict AR (1) models in typical psychological applications. Psychological Methods, 23(4), 740–756.
pubmed: 29745683
Bulteel, K., Tuerlinckx, F., Brose, A., & Ceulemans, E. (2016a). Clustering vector autoregressive models: Capturing qualitative differences in within-person dynamics. Frontiers in Psychology, 7, 1540.
pubmed: 27774077 pmcid: 5054011
Bulteel, K., Tuerlinckx, F., Brose, A., & Ceulemans, E. (2016b). Using raw VAR regression coefficients to build networks can be misleading. Multivariate Behavioral Research, 51(2–3), 330–344.
pubmed: 27028486
Bulteel, K., Tuerlinckx, F., Brose, A., & Ceulemans, E. (2018b). Improved insight into and prediction of network dynamics by combining VAR and dimension reduction. Multivariate Behavioral Research, 53(6), 853–875.
pubmed: 30453783
Campbell, J. Y., & Thompson, S. B. (2008). Predicting excess stock returns out of sample: Can anything beat the historical average? The Review of Financial Studies, 21(4), 1509–1531.
Cattell, R. B. (1966). The scree test for the number of factors. Multivariate Behavioral Research, 1(2), 245–276.
pubmed: 26828106
Ceulemans, E., & Kiers, H. A. (2009). Discriminating between strong and weak structures in three-mode principal component analysis. British Journal of Mathematical and Statistical Psychology, 62(3), 601–620.
pubmed: 19055869
Ceulemans, E., & Kiers, H. A. L. (2006). Selecting among three-mode principal component models of different types and complexities: A numerical convex hull based method. British Journal of Mathematical and Statistical Psychology, 59(1), 133–150.
pubmed: 16709283
Ceulemans, E., Timmerman, M. E., & Kiers, H. A. (2011). The CHull procedure for selecting among multilevel component solutions. Chemometrics and Intelligent Laboratory Systems, 106(1), 12–20.
Ceulemans, E., & Van Mechelen, I. (2005). Hierarchical classes models for three-way three-mode binary data: Interrelations and model selection. Psychometrika, 70(3), 461–480.
Ceulemans, E., Wilderjans, T. F., Kiers, H. A. L., & Timmerman, M. E. (2016). MultiLevel simultaneous component analysis: A computational shortcut and software package. Behavior Research Methods, 48, 1008–1020.
pubmed: 26170054
Clark, T. S., & Linzer, D. A. (2015). Should I use fixed or random effects. Political Science Research and Methods, 3(2), 399–408.
Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2013). Applied multiple regression/correlation analysis for the behavioral sciences. Milton Park: Routledge.
Crawford, A. V., Green, S. B., Levy, R., Lo, W. J., Scott, L., Svetina, D., & Thompson, M. S. (2010). Evaluation of parallel analysis methods for determining the number of factors. Educational and Psychological Measurement, 70(6), 885–901.
Eisele, G., Lafit, G., Vachon, H., Kuppens, P., Houben, M., Myin-Germeys, I., & Viechtbauer, W. (2020). Affective structure, measurement invariance, and reliability across different experience sampling protocols.
Ernst, A. F., Timmerman, M. E., Jeronimus, B. F., & Albers, C. J. (2019). Insight into individual differences in emotion dynamics with clustering. Assessment, first online.
Friedman, J., Hastie, T., & Tibshirani, R. (2001). The elements of statistical learning. Springer series in statistics (Vol. 1(10)). New York: Springer.
Friedman, J. H. (1997). On bias, variance, 0/1-loss, and the curse-of-dimensionality. Data Mining and Knowledge Discovery, 1(1), 55–77.
Gates, K. M., & Molenaar, P. C. (2012). Group search algorithm recovers effective connectivity maps for individuals in homogeneous and heterogeneous samples. NeuroImage, 63(1), 310–319.
pubmed: 22732562
Gelman, A. (2005). Analysis of variance-why it is more important than ever. Annals of Statistics, 33(1), 1–53.
Goldstein, H. (2011). Multilevel statistical models (Vol. 922). Hoboken: Wiley.
Hamaker, E., Ceulemans, E., Grasman, R., & Tuerlinckx, F. (2015). Modeling affect dynamics: State of the art and future challenges. Emotion Review, 7(4), 316–322.
Hamilton, J. (1994). Time series analysis (Vol. 2). Princeton: Princeton University Press.
Horn, J. L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 30(2), 179–185.
pubmed: 14306381
Hox, J. J. (2010). Multilevel analysis: Techniques and applications. New York, NY: Routledge.
Jongerling, J., Laurenceau, J. P., & Hamaker, E. L. (2015). A multilevel AR (1) model: Allowing for inter-individual differences in trait-scores, inertia, and innovation variance. Multivariate Behavioral Research, 50(3), 334–349.
pubmed: 26610033
Kiers, H. A., & Smilde, A. K. (2007). A comparison of various methods for multivariate regression with highly collinear variables. Statistical Methods and Applications, 16(2), 193–228.
Kiers, H. A. L., & ten Berge, J. M. F. (1994a). Hierarchical relations between methods for simultaneous component analysis and a technique for rotation to a simple simultaneous structure. British Journal of Mathematical and Statistical Psychology, 47, 109–126.
Kiers, H. A. L., & ten Berge, J. M. F. (1994b). The Harris-Kaiser independent cluster rotation as a method for rotation to simple component weights. Psychometrika, 59, 81–90.
Krone, T., Albers, C. J., Kuppens, P., & Timmerman, M. E. (2018). A multivariate statistical model for emotion dynamics. Emotion, 18(5), 739–754.
pubmed: 29265839
Krone, T., Albers, C. J., & Timmerman, M. E. (2016). Comparison of estimation procedures for multilevel AR (1) models. Frontiers in Psychology, 7, 486.
pubmed: 27242559 pmcid: 4876370
Krone, T., Albers, C. J., & Timmerman, M. E. (2017). A comparative simulation study of AR(1) estimators in short time series. Quality & Quantity, 51(1), 1–21.
Kuppens, P., Allen, N. B., & Sheeber, L. B. (2010). Emotional inertia and psychological maladjustment. Psychological Science, 21(7), 984–991.
pubmed: 20501521
Kuppens, P., Champagne, D., & Tuerlinckx, F. (2012). The dynamic interplay between appraisal and core affect in daily life. Frontiers in Psychology, 3, 380.
pubmed: 23060842 pmcid: 3466066
Lafit, G., Adolf, J., Dejonckheere, E., Myin-Germeys, I., Viechtbauer, W., & Ceulemans, E. (2021). Selection of the number of participants in intensive longitudinal studies: A user-friendly shiny app and tutorial for performing power analysis in multilevel regression models that account for temporal dependencies. In Advances in methods and practices in psychological science.
Larson, R., & Csikszentmihalyi, M. (1983). The experience sampling method. In H. T. Reis (Ed.), New directions for methodology of social and behavioral science (pp. 41–56). San Francisco: Jossey-Bass.
Liu, S. (2017). Person-specific versus multilevel autoregressive models: Accuracy in parameter estimates at the population and individual levels. British Journal of Mathematical and Statistical Psychology, 70(3), 480–498.
pubmed: 28225554
Lorenzo-Seva, U., Timmerman, M. E., & Kiers, H. A. (2011). The Hull method for selecting the number of common factors. Multivariate Behavioral Research, 46(2), 340–364.
pubmed: 26741331
Lütkepohl, H. (2005). New introduction to multiple time series analysis. Berlin: Springer.
Mansueto, A. C., Wiers, R., van Weert, J. C., Schouten, B. C., & Epskamp, S. (2020). Investigating the feasibility of idiographic network models.
McNeish, D., & Hamaker, E. L. (2020). A primer on two-level dynamic structural equation models for intensive longitudinal data in Mplus. Psychological Methods, 25(5), 610.
pubmed: 31855015
Merz, E. L., & Roesch, S. C. (2011). Modeling trait and state variation using multilevel factor analysis with PANAS daily diary data. Journal of Research in Personality, 45(1), 2–9.
pubmed: 21516166 pmcid: 3079913
Molenaar, P. (2004). A manifesto on psychology as idiographic science: Bringing the person back into scientific psychology, this time forever. Measurement, 2(4), 201–218.
Morren, M., Van Dulmen, S., Ouwerkerk, J., & Bensing, J. (2009). Compliance with momentary pain measurement using electronic diaries: a systematic review. European Journal of Pain, 13(4), 354–365.
pubmed: 18603458
Müller, S., Scealy, J. L., & Welsh, A. H. (2013). Model selection in linear mixed models. Statistical Science, 28(2), 135–167.
Muthén, B., & Muthén, B. O. (2009). Statistical analysis with latent variables. New York, NY: Wiley.
Myin-Germeys, I., Kasanova, Z., Vaessen, T., Vachon, H., Kirtley, O., Viechtbauer, W., & Reininghaus, U. (2018). Experience sampling methodology in mental health research: New insights and technical developments. World Psychiatry, 17(2), 123–132.
pubmed: 29856567 pmcid: 5980621
Ono, M., Schneider, S., Junghaenel, D. U., & Stone, A. A. (2019). What affects the completion of ecological momentary assessments in chronic pain research? An individual patient data meta-analysis. Journal of Medical Internet Research, 21(2), e11398.
pubmed: 30720437 pmcid: 6379815
Pe, M. L., Kircanski, K., Thompson, R. J., Bringmann, L. F., Tuerlinckx, F., Mestdagh, M., & Kuppens, P. (2015). Emotion-network density in major depressive disorder. Clinical Psychological Science, 3(2), 292–300.
R Core Team. (2020). R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing.
Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods (2nd ed.). Thousand Oaks, CA: Sage.
Schepers, J., Ceulemans, E., & Van Mechelen, I. (2008). Selecting among multi-mode partitioning models of different complexities: A comparison of four model selection criteria. Journal of Classification, 25(1), 67.
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.
Schuurman, N. K., & Hamaker, E. L. (2019). Measurement error and person-specific reliability in multilevel autoregressive modeling. Psychological Methods, 24(1), 70.
pubmed: 30188157
Sels, L., Ceulemans, E., Bulteel, K., & Kuppens, P. (2016). Emotional interdependence and well-being in close relationships. Frontiers in Psychology, 7, 283.
pubmed: 27014114 pmcid: 4786571
Song, H., & Zhang, Z. (2014). Analyzing multiple multivariate time series data using multilevel dynamic factor models. Multivariate Behavioral Research, 49(1), 67–77.
pubmed: 26745674
Timmerman, M. E., & Kiers, H. A. L. (2003). Four simultaneous component models of multivariate time series for more than one subject to model intraindividual and interindividual differences. Psychometrika, 86, 105–122.
Trull, T. J., & Ebner-Priemer, U. (2013). Ambulatory assessment. Annual Review of Clinical Psychology, 9, 151–176.
pubmed: 23157450
Vachon, H., Viechtbauer, W., Rintala, A., & Myin-Germeys, I. (2019). Compliance and retention with the experience sampling method over the continuum of severe mental disorders: Meta-analysis and recommendations. Journal of Medical Internet Research, 21(12), e14475.
pubmed: 31808748 pmcid: 6925392
Wainer, H. (1976). Estimating coefficients in linear models: It dont make no nevermind. Psychological Bulletin, 83(2), 213.
Watson, D., Clark, L. A., & Tellegen, A. (1988). Development and validation of brief measures of positive and negative affect: The PANAS scales. Journal of Personality and Social Psychology, 54(6), 1063.
pubmed: 3397865
Wichers, M. (2014). The dynamic nature of depression: A new micro-level perspective of mental disorder that meets current challenges. Psychological Medicine, 44(7), 1349–1360.
pubmed: 23942140
Wigman, J. T. W., Van Os, J., Borsboom, D., Wardenaar, K. J., Epskamp, S., Klippel, A., & Wichers, M. (2015). Exploring the underlying structure of mental disorders: Cross-diagnostic differences and similarities from a network perspective using both a top-down and a bottom-up approach. Psychological Medicine, 45(11), 2375–2387.
pubmed: 25804221
Wilderjans, T. F., Ceulemans, E., & Meers, K. (2013). CHull: A generic convex hull based model selection method. Behavior Research Methods, 45(1), 1–15.
pubmed: 23055156
Yarkoni, T., & Westfall, J. (2017). Choosing prediction over explanation in psychology: Lessons from machine learning. Perspectives on Psychological Science, 12(6), 1100–1122.
pubmed: 28841086 pmcid: 6603289
Zautra, A. J., Affleck, G. G., Tennen, H., Reich, J. W., & Davis, M. C. (2005). Dynamic approaches to emotions and stress in everyday life: Bolger and Zuckerman reloaded with positive as well as negative affects. Journal of Personality, 73(6), 1511–1538.
pubmed: 16274444 pmcid: 2577560

Auteurs

Ginette Lafit (G)

Research Group of Quantitative Psychology and Individual Differences, KU Leuven - University of Leuven, Leuven, Belgium. ginette.lafit@kuleuven.be.

Kristof Meers (K)

Research Group of Quantitative Psychology and Individual Differences, KU Leuven - University of Leuven, Leuven, Belgium.

Eva Ceulemans (E)

Research Group of Quantitative Psychology and Individual Differences, KU Leuven - University of Leuven, Leuven, Belgium.

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