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A random effects model is proposed for the analysis of binary dyadic data that represent a social network or directed graph, using nodal and/or dyadic attributes as covariates. The network structure is reflected by modeling the dependence between the relations to and from the same actor or node. Parameter estimates are proposed that are based on an iterated generalized least‐squares procedure. An application is presented to a data set on friendship relations between American lawyers.

Survival models allowing for random effects (e.g., frailty models) have been widely used for analyzing clustered time‐to‐event data. Accelerated failure time (AFT) models with random effects are useful alternatives to frailty models. Because survival times are directly modeled, interpretation of the fixed and random effects is straightforward. Moreover, the fixed effect estimates are robust against various violations of the assumed model. In this paper, we propose a penalized h‐likelihood (HL) procedure for variable selection of fixed effects in the AFT random‐effect models. For the purpose of variable selection, we consider three penalty functions, namely, least absolute shrinkage and selection operator (LASSO), smoothly clipped absolute deviation (SCAD), and HL. We demonstrate via simulation studies that the proposed variable selection procedure is robust against the misspecification of the assumed model. The proposed method is illustrated using data from a bladder cancer clinical trial.

AbstractRandom walks, intrinsic autoregression, state‐space models, smoothing splines, and so on have been widely used in various areas of statistics. However, practitioners wanting to fit these models using existing packages for random‐effects models are often faced with the difficulty that their covariance matrices are not uniquely determined. Unfortunately, different specifications of the model lead to different covariance structures, giving different analyses. Even if we make a decision on specification it is not immediately obvious how to make inferences from these models. There have been various suggestions on how to overcome such difficulties. However, they differ, implying that there is as yet no agreed remedy. In this article we provide a unified view on these alternatives and show how the analysis can be made invariant with respect to the choice of covariance by inclusion of a suitable set of covariates. Several examples are used to illustrate the approach.

With the development of an MCMC algorithm, Bayesian model selection for the p2 model for directed graphs has become possible. This paper presents an empirical exploration in using approximate Bayes factors for model selection. For a social network of Dutch secondary school pupils from different ethnic backgrounds it is investigated whether pupils report that they receive more emotional support from within their own ethnic group. Approximated Bayes factors seem to work, but considerable margins of error have to be reckoned with.

Linear mixed effects models have been widely used in different disciplines and have become a large research field of Statistics. With the development of science and technology, a large amount of variables are always available to choose for a model and it is necessary to control the numbers of variables to avoid the overfitting problem and use the most efficient way to explain data. Most methods published pay more attention to the selection and estimation of fixed effects but it is meaningful to get a deep insight into variable selection for random effects. Some adjustments have been made in this thesis to obtain the specific methods for variable selection on random effects model based on reviews of some classic or latest methods for variable selection on mixed effects model. These methods and algorithms have been applied on some simulation data and compared through changes on number of subjects and observations. Additionally, these methods have been applied into a real world dataset to study how some effects will influence the democracy index among different countries.

When evaluating the effects of public health interventions, larger units, or clusters, of individuals are often the unit of randomization and implementation. Ignoring dependency in the data due to clustering can misrepresent intervention effects. Random-effects models (REMs) may be a useful way to analyze such data. The present study compares results of analyses of data from a nutrition intervention program using four different methods: (a) usual multiple regression analysis using indivtdual subject data, (b) usual multiple regression analysis using the classroom cluster as the unit of analysis, (c) two-level REM model with subjects clustered within class rooms, and (d) two-level REM model with subjects clustered within sites.