Statistical methods with varying coefficient models

What is a varying coefficient model?
Varying coefficient models are a useful extension of classical linear models.
They arise naturally when one wishes to examine how regression coefficients change over different groups characterized by certain covariates such as age.
The appeal of these models is that the coef ..
What is the time varying coefficient model?
Time-varying coefficient models have been widely used to characterize changing relationships among economic and financial variables.
The existing literature usually specifies the time-varying coefficient vector as a stationary stochastic process, a deterministic function of time, and a unit root process, respectively..
One of the most interesting forms of nonlinear regression models is the varying coefficient model (VCM).
Unlike the linear regression model, VCMs were introduced by Hastie and Tibshirani (1993) to allow the regression coefficients to vary systematically and smoothly in more than one dimension.

The varying coefficient models are not stimulated by the desire of purely mathematical extension, rather they come from the need in practice. In many scientific areas where statistics is needed, there are some commonly used traditional parametric models found by the people in the area in the light of their experience.

Varying coefficient models are basically locally parametric models. The computation involved in the estimation is cheap and simple: Any existing software for Why varying coefficient models?Varying coefficient modelsSurvival analysis

Can varying coefficient models be used in covariate adjusted correlation analysis?

For example, Sent ̈ urk and M ̈ uller (2005) applied the varying coefficient models in covariate adjusted correlation analysis.
We only focus on the major developments on the stan- dard varying coefficient models and their extensions in time series, longitudinal data analysis and survival anal- ysis.

Can varying coefficients be used in a logistic regression model?

Cheng and Zhang (2007) studied the infant mortality data in China, and found the impacts were indeed varying with time.
So, it is more sensible to change the constant coefficients in the logistic regression to functional coefficients, which leads to generalized varying coefficient models.

How do you estimate a varying-coefficient model?

really a varying-coefficient model and the functional coeffi- cients can be estimated by using the method in Section 2.1.1, resulting in the estimates g( ˆ , β) .
Now, substituting this E(Y X) = gj(βT ˆ X, β)) xj.
The least-squares method can then be applied to estimate β.

What are varying coefficient models?

They are natural extensions of classical parametric models with good interpretability and are becoming more and more popular in data analysis.
Thanks to their flexibility and interpretability, in the past ten years, the varying coefficient models have experienced deep and exciting developments on methodological, theoretical and applied sides.

Estimates from regression analysis on data with unit variance

In statistics, standardized (regression) coefficients, also called beta coefficients or beta weights, are the estimates resulting from a regression analysis where the underlying data have been standardized so that the variances of dependent and independent variables are equal to 1.
Therefore, standardized coefficients are unitless and refer to how many standard deviations a dependent variable will change, per standard deviation increase in the predictor variable.

Statistical methods with varying coefficient models

What is a varying coefficient model?

What is the time varying coefficient model?

Can varying coefficient models be used in covariate adjusted correlation analysis?

Can varying coefficients be used in a logistic regression model?

How do you estimate a varying-coefficient model?

What are varying coefficient models?