scholarly journals VC: a method for estimating time-varying coefficients in linear models

2021 ◽  
Author(s):  
Ekkehart Schlicht
Keyword(s):  
Linear Models ◽  
State Space Model ◽  
Maximum Likelihood Estimates ◽  
Initial State ◽  
Varying Coefficients ◽  
Conditional Expectations ◽  
Time Varying Coefficients ◽  
Moments Estimates ◽  
Available Information ◽  
Time Invariant

AbstractThis paper describes a moments estimator for a standard state-space model with coefficients generated by a random walk. The method calculates the conditional expectations of the coefficients, given the observations. A penalized least squares estimation is linked to the GLS (Aitken) estimates of the corresponding linear model with time-invariant parameters. The estimates are moments estimates. They do not require the disturbances to be Gaussian, but if they are, the estimates are asymptotically equivalent to maximum likelihood estimates. In contrast to Kalman filtering, no specification of an initial state or an initial covariance matrix is required. While the Kalman filter is one sided, the filter proposed here is two sided and therefore uses more of the available information for estimating intermediate states. Further, the proposed filter has a clear descriptive interpretation.

Variable selection for joint models with time-varying coefficients

2019 ◽  
Vol 29 (1) ◽  
pp. 309-322
Author(s):  
Yujing Xie ◽  
Zangdong He ◽  
Wanzhu Tu ◽  
Zhangsheng Yu
Keyword(s):  
Variable Selection ◽  
Survival Data ◽  
Biliary Cirrhosis ◽  
Time Varying ◽  
Joint Models ◽  
Closed Form Solutions ◽  
Varying Coefficients ◽  
Shared Random Effects ◽  
Time Varying Coefficients ◽  
Time Invariant

Many clinical studies collect longitudinal and survival data concurrently. Joint models combining these two types of outcomes through shared random effects are frequently used in practical data analysis. The standard joint models assume that the coefficients for the longitudinal and survival components are time-invariant. In many applications, the assumption is overly restrictive. In this research, we extend the standard joint model to include time-varying coefficients, in both longitudinal and survival components, and we present a data-driven method for variable selection. Specifically, we use a B-spline decomposition and penalized likelihood with adaptive group LASSO to select the relevant independent variables and to distinguish the time-varying and time-invariant effects for the two model components. We use Gaussian-Legendre and Gaussian-Hermite quadratures to approximate the integrals in the absence of closed-form solutions. Simulation studies show good selection and estimation performance. Finally, we use the proposed procedure to analyze data generated by a study of primary biliary cirrhosis.

Hierarchical Linear Models for Multivariate Outcomes

1997 ◽  
Vol 22 (1) ◽  
pp. 77-108 ◽  
Author(s):  
Yeow Meng Thum
Keyword(s):  
Linear Models ◽  
Hierarchical Linear Model ◽  
Hierarchical Linear Models ◽  
Maximum Likelihood Estimates ◽  
Outcome Variable ◽  
Redundant Information ◽  
Full Spectrum ◽  
Available Information ◽  
Univariate Analyses ◽  
Blind Spots

In this article, we develop a class of two-stage models to accommodate three common characteristics of behavioral data. First, behavior is invariably multivariate in its conceptualization and communication. Separate univariate analyses of related outcome variables are fraught with potential interpretive blind spots for the researcher. This practice also suffers, from an inferential standpoint, because it fails to take advantage of any redundant information in the outcomes. Second, studies of behavior, especially in experimental research, employ smaller samples. This situation raises issues of robustness of inference with respect to outlying individuals. Third, the outcome variable may have observations missing because of accidents or by design. The model permits the estimation of the full spectrum of plausible measurement error structures while using all the available information. Maximum likelihood estimates are obtained for various members of a multivariate hierarchical linear model (MHLM), and, in the context of several illustrative examples, these estimates match closely the results from a Bayesian approach to the normal-normal MHLM and to the normal- t MHLM.

A Direct Analysis of Nonlinear Systems With External Periodic Excitations Via Normal Forms

2007 ◽  
Author(s):  
Amit P. Gabale ◽  
S. C. Sinha
Keyword(s):  
Normal Forms ◽  
Numerical Solutions ◽  
Direct Analysis ◽  
Periodic Case ◽  
Time Varying ◽  
Simple Modification ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
Time Invariant ◽  
Time Periodic

This study presents a direct methodology for the analysis of nonlinear dynamic systems with external periodic forcing via an application of the theory of normal forms. Rather than introducing a new state variable to reduce the problem to a homogenous one, we apply a set of time-dependant near-identity transformations to construct the normal forms. The proposed method can be applied to time-invariant as well as time varying systems. After discussing the time-invariant case, the methodology is extended to systems with time-periodic coefficients. The time periodic case is handled through an application of the Lyapunov-Floquet (L-F) transformation. It has been shown that all resonance conditions can be obtained in a closed form. Further, for time invariant case, if the superharmonic response is dominant, a simple modification can be made to yield accurate results. An example for each type of system, viz., constant coefficients and time-varying coefficients is included to demonstrate effectiveness of the method. It is observed that the linear parametric excitation term need not be small as generally assumed in perturbation and averaging techniques. The results obtained by proposed method are compared with numerical solutions.

scholarly journals The impact of the output gap on the unemployment rate: evidence from Mexico, 1987q1-2018q4

2019 ◽  
Vol 23 (48) ◽  
pp. 4-15
Author(s):  
Manuel García-Ramos
Keyword(s):  
Unemployment Rate ◽  
State Space Model ◽  
Point Of View ◽  
Output Gap ◽  
Econometric Modeling ◽  
Potential Output ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
The Impact

Using quarterly data for Mexico from 1987Q1 to 2018Q4, we measure the impact of output gap on the unemployment rate based on a State-Space model with time-varying coefficients. From an econometric modeling point of view, this model allows asymmetrical interactions between the output gap and unemployment rate. Our principal conclusions are: 1) The long-term equilibrium unemployment rate is equal to 3.06; 2) the unemployment rate does not exhibit hysteresis; 3) when GDP is lower than potential output, the impact of its growth on the unemployment rate is -0.43 percent points; and 4) when GDP is higher than potential output, the impact of its growth on the unemployment rate is close to zero. It implies that the reaction of the unemployment rate to output gap is different when the output gap is increasing from that when the output gap is decreasing; i.e., the output gap does not have the same effect on the unemployment rate over time.

Multivariable modeling and control of an activated sludge process

1998 ◽  
Vol 37 (12) ◽  
pp. 149-156 ◽  
Author(s):  
Carl-Fredrik Lindberg
Keyword(s):  
Activated Sludge ◽  
Nitrate Concentration ◽  
State Space Model ◽  
Activated Sludge Process ◽  
Invariant State ◽  
Linear Quadratic ◽  
Modeling And Control ◽  
Space Model ◽  
And Control ◽  
Time Invariant

This paper contains two contributions. First it is shown, in a simulation study using the IAWQ model, that a linear multivariable time-invariant state-space model can be used to predict the ammonium and nitrate concentration in the last aerated zone in a pre-denitrifying activated sludge process. Secondly, using the estimated linear model, a multivariable linear quadratic (LQ) controller is designed and used to control the ammonium and nitrate concentration.

A binary choice model with partial observability for panel data

2020 ◽  
Vol 15 (4) ◽  
pp. 315-322
Author(s):  
Ekaterina Batalova ◽  
Kirill Furmanov ◽  
Ekaterina Shelkova
Keyword(s):  
Job Search ◽  
Latent Class ◽  
Choice Model ◽  
Maximum Likelihood Estimates ◽  
Binary Choice ◽  
Panel Model ◽  
Binary Response Variable ◽  
Monitoring Survey ◽  
Binary Choice Model ◽  
Time Invariant

We consider a panel model with a binary response variable that is a product of two unobservable factors, each determined by a separate binary choice equation. One of these factors is assumed to be time-invariant and may be interpreted as a latent class indicator. A simulation study shows that maximum likelihood estimates from even the shortest panel are much more reliable than those obtained from a cross-section. As an illustrative example, the model is applied to Russian Longitudinal Monitoring Survey data to estimate a proportion of the non-employed population who are participating in job search.

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