A mixed model for variance of successive difference of stationary time series : modeling temporal instability in intensive longitudinal data

Title from PDF of title page (University of Missouri--Columbia, viewed on Feb. 18, 2010).The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file.Dr. Stanislav Kolenikov, Thesis SupervisorM.S. University of Missouri--Columbia 2008.Temporal instability of a stochastic process has been of interest in many areas of behavioral and social science. Recent development in data collection techniques in behavioral and health sciences, such as Ecological Momentary Assessment (EMA) enables researchers in these areas to get direct assessment on temporal fluctuations over time for many individuals. Although many researchers have used variance and autocorrelation as a temporal instability measure, their utility and interpretation are limited to index temporal instability. I propose variance of successive difference (VSD) of stationary time series as an overall index of temporal instability such that it is a function of variance and first order autocorrelation of time series. A version of variance of successive difference of unequally spaced time series is also presented as well as distinction of within-day and between-day instability measures. Given that VSD is an individual difference measure, it is proposed that group differences on these indices be explored using a mixed variance model proposed by Hedeker et al. (2008). To illustrate, we present EMA data from a study of negative mood in borderline personality disorder (BPD) and major depressive disorder (MDD) patients, resulting that BPD patients showed more negative affective instability than MDD patients.Includes bibliographical reference

Analysis of affective instability on ecological momentary assessments data: successive difference, variance decomposition, and mean comparison via multilevel modeling

The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file.Title from title screen of research.pdf file (viewed on May 11, 2009)Includes bibliographical references.Thesis (M.A.) University of Missouri-Columbia 2007.Dissertations, Academic -- University of Missouri--Columbia -- Psychology.Temporal instability of affect is a defining characteristic of some psychological disorders such as Borderline Personality Disorder and mood cycling disorders. Use of Ecological Momentary Assessments (EMA) enables researchers to directly assess such frequent and extreme fluctuations over time. Two specific operationalizations of such temporal instability are proposed: Mean squared successive differences (MSSD) and probability of acute change (PAC). Additionally, resiudalizing scores by controlling time effects, such as long-term trend or diurnal effect, at the individual level is useful for identifying artifactual sources of temporal variability due to those time factors. Given that MSSD and PAC are individual differences measures, it is proposed that these measures be analyzed within generalized multilevel models. An illustrative example using EMA data on negative mood for borderline personality disorder (BPD) and major depressive disorder (MDD) groups is presented which shows that MSSD and PAC capture affective instability better than within-person variance, and that negative affect reports of the BPD group demonstrate more temporal instability than the MDD group. Versions of MSSD and PAC which adjust for the differently elapsed time between assessments are also discussed

Multilevel models for intensive longitudinal data with heterogeneous error structure : covariance transformation and variance function models

Title from PDF of title page (University of Missouri--Columbia, viewed on November 18, 2010).The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file.Dissertation advisor: Dr. Phillip K. Wood.Vita.Ph. D. University of Missouri--Columbia 2008.Recent developments in data collection methods in the behavioral and social sciences, such as Ecological Momentary Assessment (EMA) enables researchers to gather intensive longitudinal data (ILD) and to examine more detailed features of intraindividual variation of a variable(s) over time. Due to its high intensity of assessments within individuals, ILD often has different characteristics from traditional longitudinal data with a few measurement occasions and requires different assumptions of statistical models in use. In the present thesis, issues in the analysis of ILD and problems of current use of statistical models for the analysis of ILD are discussed and investigated. Specifically, the issue of heterogeneity of autocorrelation and variance across individuals in ILD is extensively studied for multilevel models (MLMs). In chapter 2, a brief introduction to multilevel models and issues in modeling residual covariance structure in MLMs are provided and discussed. In chapter 3, it is shown that bias in estimation of parameters in MLMs under homogeneity assumption is not ignorable when autocorrelation differs across individuals and its average is high. It is also shown that a transformation method, which multiplies variables in the model by the inverse of Cholesky factor of individual-specific error covariance, attenuates the bias for ILD. Chapter 4 reviews variance function models for heterogeneous variance and introduces a two-step MLM approach for modeling heterogeneous variance using squared residuals. A simulation study showed that the two-step MLM does not suffer from non-convergence and is applicable to ILD.Includes bibliographical references (p. 70-79)

(2023) Incorporating Measurement Error in the Dynamic Structural Equation Modeling Using a Single Indicator or Multiple Indicators

Data files and mplus input and output files for Table 1 and Table 2 in the articl