Continuous-Time Dynamic Models

2012 ◽  
pp. 136-167
Keyword(s):  
Continuous Time ◽  
Dynamic Models ◽  
Time Dynamic

Selecting optimal weighting factors in iPDA for parameter estimation in continuous-time dynamic models

2008 ◽  
Vol 32 (12) ◽  
pp. 3011-3022 ◽  
Author(s):  
M.S. Varziri ◽  
A.A. Poyton ◽  
K.B. McAuley ◽  
P.J. McLellan ◽  
J.O. Ramsay
Keyword(s):  
Parameter Estimation ◽  
Continuous Time ◽  
Dynamic Models ◽  
Time Dynamic ◽  
Weighting Factors ◽  
Optimal Weighting

scholarly journals Parameter estimation in continuous-time dynamic models using principal differential analysis

2006 ◽  
Vol 30 (4) ◽  
pp. 698-708 ◽  
Author(s):  
A.A. Poyton ◽  
M.S. Varziri ◽  
K.B. McAuley ◽  
P.J. McLellan ◽  
J.O. Ramsay
Keyword(s):  
Parameter Estimation ◽  
Continuous Time ◽  
Dynamic Models ◽  
Differential Analysis ◽  
Time Dynamic

The Estimation of Open Higher-Order Continuous Time Dynamic Models with Mixed Stock and Flow Data

1986 ◽  
Vol 2 (3) ◽  
pp. 350-373 ◽  
Author(s):  
A. R. Bergstrom
Keyword(s):  
Maximum Likelihood ◽  
Continuous Time ◽  
Dynamic Models ◽  
Higher Order ◽  
Maximum Likelihood Estimates ◽  
Order System ◽  
Exogenous Variables ◽  
Time Dynamic ◽  
Mixed Stock ◽  
Order Continuous

This article extends recent work on the Gaussian or quasi-maximum likelihood estimation of the parameters of a closed higher-order continuous time dynamic model by introducing exogenous variables into the model The method presented yields exact maximum likelihood estimates when the innovations are Gaussian and the exogenous variables are polynomials in time of degree not exceeding two, and it can be expected to yield very good estimates under more general conditions. It is applicable, in principle, to a system of any order with mixed stock and iow data. The precise formulas for its implementation are derived, in this article, for a second-order system in which both the endog-enous and exogenous variables are a mixture of stock and flow variables.

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.

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