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.

scholarly journals Group MCP for Cox Models with Time-Varying Coefficients

2016 ◽  
Vol 4 (5) ◽  
pp. 476-488
Author(s):  
Xiaodong Xie ◽  
Shaozhi Zheng
Keyword(s):  
Variable Selection ◽  
Group Lasso ◽  
Partial Likelihood ◽  
Time Varying ◽  
Proportional Hazard ◽  
Cox Models ◽  
Varying Coefficients ◽  
Spline Basis ◽  
Time Varying Coefficients ◽  
Lasso Method

AbstractCox’s proportional hazard models with time-varying coefficients have much flexibility for modeling the dynamic of covariate effects. Although many variable selection procedures have been developed for Coxs proportional hazard model, the study of such models with time-varying coefficients appears to be limited. The variable selection methods involving nonconvex penalty function, such as the minimax concave penalty (MCP), introduces numerical challenge, but they still have attractive theoretical properties and were indicated that they are worth to be alternatives of other competitive methods. We propose a group MCP method that uses B-spline basis to expand coefficients and maximizes the log partial likelihood with nonconvex penalties on regression coefficients in groups. A fast, iterative group shooting algorithm is carried out for model selection and estimation. Under some appropriate conditions, the simulated example shows that our method performs competitively with the group lasso method. By comparison, the group MCP method and group lasso select the same amount of important covariates, but group MCP method tends to outperform the group lasso method in selection of unimportant covariates.

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 VIT Transform Approach to Discrete-Time Signals and Linear Time-Varying Systems

Eng ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 99-125
Author(s):  
Edward W. Kamen
Keyword(s):  
Discrete Time ◽  
Initial Conditions ◽  
Linear Time ◽  
Order Term ◽  
Initial Time ◽  
Time Varying ◽  
Varying Coefficients ◽  
Time Signals ◽  
Time Varying Systems ◽  
Time Varying Coefficients

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z−1, which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z−i by time functions, which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of zi at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

scholarly journals Estimating latent group structure in time-varying coefficient panel data models

2019 ◽  
Author(s):  
Jia Chen
Keyword(s):  
Panel Data ◽  
Data Models ◽  
Panel Data Models ◽  
Time Varying ◽  
Clustering Method ◽  
Varying Coefficient ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
Latent Group ◽  
Group Structures

Summary This paper studies the estimation of latent group structures in heterogeneous time-varying coefficient panel data models. While allowing the coefficient functions to vary over cross-sections provides a good way to model cross-sectional heterogeneity, it reduces the degree of freedom and leads to poor estimation accuracy when the time-series length is short. On the other hand, in a lot of empirical studies, it is not uncommon to find that heterogeneous coefficients exhibit group structures where coefficients belonging to the same group are similar or identical. This paper aims to provide an easy and straightforward approach for estimating the underlying latent groups. This approach is based on the hierarchical agglomerative clustering (HAC) of kernel estimates of the heterogeneous time-varying coefficients when the number of groups is known. We establish the consistency of this clustering method and also propose a generalised information criterion for estimating the number of groups when it is unknown. Simulation studies are carried out to examine the finite-sample properties of the proposed clustering method as well as the post-clustering estimation of the group-specific time-varying coefficients. The simulation results show that our methods give comparable performance to the penalised-sieve-estimation-based classifier-LASSO approach by Su et al. (2018), but are computationally easier. An application to a panel study of economic growth is also provided.

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