scholarly journals Subgraph Network Random Effects Error Components Models: Specification and Testing

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Gabriel Montes-Rojas
Keyword(s):  
Random Effects ◽  
Quadratic Forms ◽  
Variance Components ◽  
Network Effects ◽  
Interbank Market ◽  
Error Components ◽  
Finite Samples ◽  
Random Components ◽  
Error Components Models ◽  
Lagrange Multiplier Tests

Abstract This paper develops a subgraph random effects error components model for network data linear regression where the unit of observation is the node. In particular, it allows for link and triangle specific components, which serve as a basal model for modeling network effects. It then evaluates the potential effects of ignoring network effects in the estimation of the coefficients’ variance-covariance matrix. It also proposes consistent estimators of the variance components using quadratic forms and Lagrange Multiplier tests for evaluating the appropriate model of random components in networks. Monte Carlo simulations show that the tests have good performance in finite samples. It applies the proposed tests to the Call interbank market in Argentina.

scholarly journals On the Estimated Variances of Regression Coefficients in Misspecified Error Components Models

1991 ◽  
Vol 7 (3) ◽  
pp. 369-384 ◽  
Author(s):  
Philippe J. Deschamps
Keyword(s):  
Variance Components ◽  
Asymptotic Variance ◽  
Matrix Multiplication ◽  
Regression Coefficients ◽  
Linear Combinations ◽  
Error Components ◽  
Restricted Model ◽  
Time Component ◽  
Error Components Models ◽  
The Difference

In a regression model with an arbitrary number of error components, the covariance matrix of the disturbances has three equivalent representations as linear combinations of matrices. Furthermore, this property is invariant with respect to powers, matrix addition, and matrix multiplication. This result is applied to the derivation and interpretation of the inconsistency of the estimated coefficient variances when the error components structure is improperly restricted. This inconsistency is defined as the difference between the asymptotic variance obtained when the restricted model is correctly specified, and the asymptotic variance obtained when the restricted model is incorrectly specified; when some error components are improperly omitted, and the remaining variance components are consistently estimated, it is always negative. In the case where the time component is improperly omitted from the two-way model, we show that the difference between the true and estimated coefficient variances is of order greater than N–1 in probability.

A note on autoregressive error components models

1985 ◽  
Vol 28 (2) ◽  
pp. 231-245 ◽  
Author(s):  
P. Sevestre ◽  
A. Trognon
Keyword(s):  
Error Components ◽  
Error Components Models

scholarly journals Genetic evaluation of growth traits in Nellore cattle through multi-trait and random regression models

2018 ◽  
Vol 63 (No. 6) ◽  
pp. 212-221 ◽  
Author(s):  
B.B. Teixeira ◽  
R.R. Mota ◽  
R.B. Lôbo ◽  
L.P. Silva ◽  
A.P. Souza Carneiro ◽  
...  
Keyword(s):  
Random Effects ◽  
Variance Components ◽  
Regression Models ◽  
Growth Traits ◽  
Growth Curves ◽  
Genetic Evaluation ◽  
Information Criteria ◽  
Random Regression ◽  
Nellore Cattle ◽  
Heritability Estimates

We aimed to evaluate different orders of fixed and random effects in random regression models (RRM) based on Legendre orthogonal polynomials as well as to verify the feasibility of these models to describe growth curves in Nellore cattle. The proposed RRM were also compared to multi-trait models (MTM). Variance components and genetic parameters estimates were performed via REML for all models. Twelve RRM were compared through Akaike (AIC) and Bayesian (BIC) information criteria. The model of order three for the fixed curve and four for all random effects (direct genetic, maternal genetic, permanent environment, and maternal permanent environment) fits best. Estimates of direct genetic, maternal genetic, maternal permanent environment, permanent environment, phenotypic and residual variances were similar between MTM and RRM. Heritability estimates were higher via RRM. We presented perspectives for the use of RRM for genetic evaluation of growth traits in Brazilian Nellore cattle. In general, moderate heritability estimates were obtained for the majority of studied traits when using RRM. Additionally, the precision of these estimates was higher when using RRM instead of MTM. However, concerns about the variance components estimates in advanced ages via Legendre polynomial must be taken into account in future studies.

Estimators of Random Effects Variance Components in Meta-Analysis

2000 ◽  
Vol 25 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Lynn Friedman
Keyword(s):  
Closed Form ◽  
Random Effects ◽  
Quadratic Forms ◽  
Relative Efficiency ◽  
Variance Component ◽  
Linear Models ◽  
Random Effect ◽  
Linear Functions ◽  
Effect Sizes ◽  
Random Effects Model

In meta-analyses, groups of study effect sizes often do not fit the model of a single population with only sampling, or estimation, variance differentiating the estimates. If the effect sizes in a group of studies are not homogeneous, a random effects model should be calculated, and a variance component for the random effect estimated. This estimate can be made in several ways, but two closed form estimators are in common use. The comparative efficiency of the two is the focus of this report. We show here that these estimators vary in relative efficiency with the actual size of the random effects model variance component. The latter depends on the study effect sizes. The closed form estimators are linear functions of quadratic forms whose moments can be calculated according to a well-known theorem in linear models. We use this theorem to derive the variances of the estimators, and show that one of them is smaller when the random effects model variance is near zero; however, the variance of the other is smaller when the model variance is larger. This leads to conclusions about their relative efficiency.

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