Person-specific versus multilevel autoregressive models: Accuracy in parameter estimates at the population and individual levels

British Journal of Mathematical and Statistical Psychology

Volumn 70, Issue 3, 2017, Pages 480-498

  Liu, Siwei ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

autoregressive models; intensive longitudinal data; multilevel modelling; person specific; time series

Indexed keywords

COMPUTER SIMULATION; HUMAN; MULTILEVEL ANALYSIS; PROCEDURES; REGRESSION ANALYSIS; SAMPLE SIZE; STATISTICAL MODEL; TIME FACTOR;

COMPUTER SIMULATION; HUMANS; MODELS, STATISTICAL; MULTILEVEL ANALYSIS; REGRESSION ANALYSIS; SAMPLE SIZE; TIME FACTORS;

EID: 85013468566     PISSN: 00071102     EISSN: 20448317     Source Type: Journal    
DOI: 10.1111/bmsp.12096     Document Type: Article

References (39)

1. Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716–723. doi:10.1109/TAC.1974.1100705
2. Bell, B. A., Schoeneberger, J. A., Morgan, G. B., Kromrey, J. D., & Ferron, J. M. (2010). Fundamental diagnostics for two-level mixed models: The SAS macro MIXED_DX. Proceedings of the Annual SAS Global Forum. Seattle, WA.
3. Beltz, A. M., Wright, A. G. C., Sprague, B. N., & Molenaar, P. C. M. (2016). Bridging the nomothetic and idiographic approaches to the analysis of clinical data. Assessment, 23, 447–458. doi:10.1177/1073191116648209
4. Bollen, K. A., & Curran, P. J. (2006). Unconditional latent curve model. In K. A. Bollen & P. J. Curran (Eds.), Latent curve models: A structural equation perspective (pp. 16–57). Hoboken, NJ: John Wiley & Sons.
5. 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. doi:10.1371/journal.pone.0060188
6. Cattell, R. B. (1952). The three basic factor-analytic research designs – Their interrelations and derivatives. Psychological Bulletin, 49, 499–520. doi:10.1037/h0054245
7. Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Hillsdale, NJ: Erlbaum.
8. Ding, M., Chen, Y., & Bressler, S. L. (2006). Granger causality: Basic theory and application to neuroscience. In B. Schelter, M. Winterhalder & J. Timmer (Eds.), Handbook of time series analysis: Recent theoretical developments and applications (pp. 437–460). Weinheim, Germany: Wiley-VCH.
9. Dziak, J. J., Li, R., Tan, X., Shiffman, S., & Shiyko, M. P. (2015). Modeling intensive longitudinal data with mixtures of nonparametric trajectories and time-varying effects. Psychological Methods, 20, 444–469. doi:10.1037/met0000048
10. Gates, K. M., & Molenaar, P. C. M. (2012). Group search algorithm recovers effective connectivity maps for individuals in homogeneous and heterogeneous samples. NeuroImage, 63(1), 310–319. doi:10.1016/j.neuroimage.2012.06.026
11. Gates, K. M., Molenaar, P. C. M., Hillary, F. G., Ram, N., & Rovine, M. J. (2010). Automatic search for fMRI connectivity mapping: An alternative to Granger causality testing using formal equivalences among SEM path modeling, VAR, and unified SEM. NeuroImage, 50, 1118–1125. doi:10.1016/j.neuroimage.2009.12.117
12. Gates, K. M., Molenaar, P. C. M., Hillary, F. G., & Slobounov, S. (2011). Extended unified SEM approach for modeling event-related fMRI data. NeuroImage, 54, 1151–1158. doi:10.1016/j.neuroimage.2010.08.051
13. Greven, S., & Kneib, T. (2010). On the behaviour of marginal and conditional AIC in linear mixed models. Biometrika, 97, 773–789. doi:10.1093/biomet/asq042
14. Hamaker, E. L., & Grasman, R. P. P. P. (2015). To center or not to center? Investigating inertia with a multilevel autoregressive model. Frontiers in Psychology, 5, 1–15. doi:10.3389/fpsyg.2014.01492
15. Hamaker, E. L., van Hattum, P., Kuiper, R. M., & Hoijtink, H. (2011). Model selection based on information criteria in multilevel modeling. In J. Hox & K. Roberts (Eds.), Handbook of advanced multilevel analysis (pp. 231–255). New York, NY: Routledge.
16. Hannan, E. J. (1970). Multiple time series. New York, NY: John Wiley & Sons.
17. Hox, J. (2002). Estimation and hypothesis testing in multilevel regression. In J. Hox (Ed.), Multilevel analysis: Techniques and applications (pp. 37–48). Mahwah, NJ: Lawrence Erlbaum Associates.
18. Jiang, J., Rao, J. S., Gu, Z., & Nguyen, T. (2008). Fence methods for mixed model selection. Annals of Statistics, 36, 1669–1692.
19. 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, 334–349. doi:10.1080/00273171.2014.1003772
20. Liu, S., & Molenaar, P. C. M. (2016). Testing for Granger causality in the frequency domain: A phase resampling method. Multivariate Behavioral Research, 51(1), 53–66. doi:10.1080/00273171.2015.1100528
21. Liu, S., Rovine, M. J., Klein, L. C., & Almeida, D. M. (2013). Synchrony of diurnal cortisol pattern in couples. Journal of Family Psychology, 27, 579–588. doi:10.1037/a0033735
22. Lodewyckx, T., Tuerlinckx, F., Kuppens, P., Allen, N. B., & Sheeber, L. (2011). A hierarchical state space approach to affective dynamics. Journal of Mathematical Psychology, 55(1), 68–83. doi:10.1016/j.jmp.2010.08.004
23. Maas, C. J. M., & Hox, J. J. (2004). The influence of violations of assumptions on multilevel parameter estimates and their standard errors. Computational Statistics & Data Analysis, 46, 427–440. doi:10.1016/j.csda.2003.08.006
24. 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 & Perspective, 2, 201–218. doi:10.1207/s15366359mea0204_1
25. Molenaar, P. C. M., & Campbell, C. G. (2009). The new person-specific paradigm in psychology. Current Directions in Psychological Science, 18(2), 112–117. doi:10.1111/j.1467-8721.2009.01619.x
26. Muller, S., Scealy, J. L., & Welsh, A. H. (2013). Model selection in linear mixed models. Statistical Science, 28(2), 135–167. doi:10.1214/12-STS410
27. Myers, J. L. (1979). Fundamentals of research design. New York, NY: Allyn & Bacon.
28. Pinheiro, J., Bates, D., DebRoy, S., Sarkar, D., & R Core Team. (2016). nlme: Linear and nonlinear mixed effects models (Version 3.1-126). Retrieved from http://CRAN.R-project.org/package=nlme
29. R Core Team. (2015). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Retrieved from http://www.R-project.org/
30. Robinson, G. K. (1991). That BLUP is a good thing: The estimation of random effects. Statistical Science, 6(1), 15–51. doi:10.1214/ss/1177011926
31. Rovine, M. J., & Walls, T. A. (2006). Multilevel autoregressive modeling of interindividual differences in the stability of a process. In T. A. Walls & J. L. Schafer (Eds.), Models for intensive longitudinal data (pp. 124–147). Oxford, UK: Oxford University Press.
32. Schuurman, N. K., Grasman, R. P. P. P., & Hamaker, E. L. (2016). A comparison of inverse-Wishart prior specifications for covariance matrices in multilevel autoregressive models. Multivariate Behavioral Research, 51(2–3), 185–206. doi:10.1080/00273171.2015.1065398
33. Shumway, R. H., & Stoffer, D. S. (2006). Time series analysis and its applications with R examples. New York, NY: Springer.
34. Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. New York, NY: Oxford University Press.
35. Song, H., & Zhang, Z. (2014). Analyzing multiple multivariate time series data using multilevel dynamic factor models. Multivariate Behavioral Research, 49(1), 67–77. doi:10.1080/00273171.2013.851018
36. Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & van der Linde, A. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64, 583–639. doi:10.1111/1467-9868.00353
37. Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & van der Linde, A. (2014). The deviance information criterion: 12 years on. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 76, 485–493. doi:10.1111/rssb.12062
38. Verbeke, G., & Molenberghs, G. (2000). Estimation of the marginal model. In G. Verbeke & G. Molenberghs (Eds.), Linear mixed models for longitudinal data (pp. 41–54). New York, NY: Springer.
39. Zheng, Y., Wiebe, R. P., Cleveland, H. H., Molenaar, P. C. M., & Harris, K. S. (2013). An idiographic examination of day-to-day patterns of substance use craving, negative affect, and tobacco use among young adults in recovery. Multivariate Behavioral Research, 48, 241–266. doi:10.1080/00273171.2013.763012