scholarly journals Controlling for cohort effects in accelerated longitudinal designs using continuous- and discrete-time dynamic models.

2021 ◽  
Author(s):  
Eduardo Estrada ◽  
Silvia A. Bunge ◽  
Emilio Ferrer
Keyword(s):  
Discrete Time ◽  
Dynamic Models ◽  
Cohort Effects ◽  
Time Dynamic

The Art of Model Development

1999 ◽  
Author(s):  
Ronald K. Pearson
Keyword(s):  
Discrete Time ◽  
Dynamic Models ◽  
Empirical Modeling ◽  
Model Structure ◽  
Time Dynamic ◽  
Structure Selection ◽  
Modeling Process ◽  
Class C ◽  
Model Structure Selection

The primary objective of this book has been to present a reasonably broad overview of the different classes of discrete-time dynamic models that have been proposed for empirical modeling, particularly in the process control literature. In its simplest form, the empirical modeling process consists of the following four steps: 1. Select a class C of model structures 2. Generate input/output data from the physical process P 3. Determine the model M ∊ C that best fits this dataset 4. Assess the general validity of the model M. The objective of this final chapter is to briefly examine these four modeling steps, with particular emphasis on the first since the choice of the model class C ultimately determines the utility of the empirical model, both with respect to the application (e.g., the difficulty of solving the resulting model-based control problem) and with respect to fidelity of approximation. Some of the basic issues of model structure selection are introduced in Sec. 8.1 and a more detailed treatment is given in Sec. 8.3, emphasizing connections with results presented in earlier chapters; in addition, the problem of model structure selection is an important component of the case studies presented in Secs. 8.2 and 8.5. The second step in this procedure—input sequence design—is discussed in some detail in Sec. 8.4 and is an important component of the second case study (Sec. 8.5). The literature associated with the parameter estimation problem—the third step in the empirical modeling process—is much too large to attempt to survey here, but a brief summary of some representative results is given in Sec. 8.1.1. Finally, the task of model validation often depends strongly on the details of the physical system being modelled and the ultimate application intended for the model. Consequently, detailed treatment of this topic also lies beyond the scope of this book but again, some representative results are discussed briefly in Sec. 8.1.3 and illustrated in the first case study (Sec. 8.2). Finally, Sec. 8.6 concludes both the chapter and the book with some philosophical observations on the problem of developing moderate-complexity, discrete-time dynamic models to approximate the behavior of high-complexity, continuous-time physical systems.

scholarly journals Controlling for cohort effects in accelerated longitudinal designs using continuous- and discrete-time dynamic models

2021 ◽  
Author(s):  
Eduardo Estrada ◽  
Silvia A. Bunge
Keyword(s):  
Continuous Time ◽  
Dynamic Models ◽  
Monte Carlo Study ◽  
Time Frame ◽  
Change Score ◽  
Cohort Effects ◽  
Time Dynamic ◽  
Cohort Differences ◽  
Study Designs ◽  
And Control

Accelerated longitudinal designs (ALDs) allow examining developmental changes over a period of time longer than the duration of the study. In ALDs, participants enter the study at different ages (i.e., different cohorts), and provide measures during a time frame shorter than the total study. They key assumption is that participants from the different cohorts come from the same population and, therefore, can be assumed to share the same general trajectory. The consequences of not meeting that assumption have not been examined systematically. In this paper, we propose an approach to detect and control for cohort differences in ALDs using Latent Change Score models in both discrete and continuous time. We evaluated the effectiveness of such a method through a Monte Carlo study. Our results indicate that, in a broad set of empirically relevant conditions, both LCS specifications can adequately estimate cohort effects ranging from very small to very large, with slightly better performance of the continuous-time version. Across all conditions, cohort effects on the asymptotic level (dAs) caused much larger bias than on the latent initial level (d0). When cohort differences were present, including them in the model led to unbiased estimates. In contrast, not including them led to tenable results only when such differences were not large (d0 ≤ 1 and dAs ≤ 0.2). Among the sampling schedules evaluated, those including at least three measurements per participant over 4 years or more led to the best performance. Based on our findings, we offer recommendations regarding study designs and data analysis.

Discrete-Time Dynamic Models

Technometrics ◽  
2001 ◽  
Vol 43 (1) ◽  
pp. 110-111
Author(s):  
Stergios B Fotopoulos
Keyword(s):  
Discrete Time ◽  
Dynamic Models ◽  
Time Dynamic

NARMAX Models

1999 ◽  
Author(s):  
Ronald K. Pearson
Keyword(s):  
Discrete Time ◽  
General Class ◽  
Dynamic Models ◽  
Linear Models ◽  
Moving Average ◽  
Qualitative Behavior ◽  
Time Model ◽  
Time Dynamic ◽  
Linear And Nonlinear ◽  
Output Behavior

As noted In Chapter 1, the general class of NARMAX models is extremely broad and includes almost all of the other discrete-time model classes discussed in this book, linear and nonlinear. Because of its enormity, little can be said about the qualitative behavior of the NARMAX family in general, but it is surprising how much can be said about the behavior of some important subclasses. In particular, there are sharp qualitative distinctions between nonlinear moving average models (NMAX models) and nonlinear autoregressive models (NARX models). Since these representations are equivalent for linear models (c.f. Chapter 2), this observation highlights one important difference between linear and nonlinear discrete-time dynamic models. Consequently, this chapter focuses primarily on the structure and qualitative behavior of various subclasses of the NARMAX family, particularly the NMAX and NARX classes. More specifically, Sec. 4.1 presents a brief discussion of the general NARMAX class, defining five important subclasses that are discussed in subsequent sections: the NMAX class (Sec. 4.2), the NARX class (Sec. 4.3), the class of (structurally) additive NARMAX models (Sec. 4.4), the class of polynomial NARMAX models (Sec. 4.5), and the class of rational NARMAX models (Sec. 4.6). More complex NARMAX models are then discussed briefly in Sec. 4.7 and Sec. 4.8 concludes the chapter with a brief summary of the NARMAX class. The general class of NARMAX models was defined and discussed in a series of papers by Billings and various co-authors (Billings and Voon, 1983, 1986a; Leontartis and Billings, 1985; Zhu and Billings, 1993) and is defined by the equation . . . y(k) = F(y(k – 1), . . . , y(k – p), u(k), . . . , u(k – q), e(k – 1), . . . , e(k – r)) + e(k). (4.1) . . . Because this book is primarily concerned with the qualitative input/output behavior of these models, it will be assumed that e(k) = 0 identically as in the class of linear ARMAX models discussed in Chapter 2.

Sign in / Sign up

Export Citation Format

Share Document