Random effects model

About: Random effects model is a research topic. Over the lifetime, 8388 publications have been published within this topic receiving 438823 citations. The topic is also known as: random effects & random effect.

On spatial prediction of soil properties in the presence of a spatial trend: the empirical best linear unbiased predictor (E‐BLUP) with REML

Abstract: Geostatistical estimates of a soil property by kriging are equivalent to the best linear unbiased predictions (BLUPs). Universal kriging is BLUP with a fixed-effect model that is some linear function of spatial coordinates, or more generally a linear function of some other secondary predictor variable when it is called kriging with external drift. A problem in universal kriging is to find a spatial variance model for the random variation, since empirical variograms estimated from the data by method-of-moments will be affected by both the random variation and that variation represented by the fixed effects. The geostatistical model of spatial variation is a special case of the linear mixed model where our data are modelled as the additive combination of fixed effects (e.g. the unknown mean, coefficients of a trend model), random effects (the spatially dependent random variation in the geostatistical context) and independent random error (nugget variation in geostatistics). Statisticians use residual maximum likelihood (REML) to estimate variance parameters, i.e. to obtain the variogram in a geostatistical context. REML estimates are consistent (they converge in probability to the parameters that are estimated) with less bias than both maximum likelihood estimates and method-of-moment estimates obtained from residuals of a fitted trend. If the estimate of the random effects variance model is inserted into the BLUP we have the empirical BLUP or E-BLUP. Despite representing the state of the art for prediction from a linear mixed model in statistics, the REML-E-BLUP has not been widely used in soil science, and in most studies reported in the soils literature the variogram is estimated with methods that are seriously biased if the fixed-effect structure is more complex than just an unknown constant mean (ordinary kriging). In this paper we describe the REML-E-BLUP and illustrate the method with some data on soil water content that exhibit a pronounced spatial trend.

Linear mixed-effects models and the analysis of nonindependent data: A unified framework to analyze categorical and continuous independent variables that vary within-subjects and/or within-items.

Abstract: In this article we address a number of important issues that arise in the analysis of nonindependent data. Such data are common in studies in which predictors vary within "units" (e.g., within-subjects, within-classrooms). Most researchers analyze categorical within-unit predictors with repeated-measures ANOVAs, but continuous within-unit predictors with linear mixed-effects models (LMEMs). We show that both types of predictor variables can be analyzed within the LMEM framework. We discuss designs with multiple sources of nonindependence, for example, studies in which the same subjects rate the same set of items or in which students nested in classrooms provide multiple answers. We provide clear guidelines about the types of random effects that should be included in the analysis of such designs. We also present a number of corrective steps that researchers can take when convergence fails in LMEM models with too many parameters. We end with a brief discussion on the trade-off between power and generalizability in designs with "within-unit" predictors. (PsycINFO Database Record

P2: A random effects model with covariates for directed graphs

Abstract: 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.

The nonlinear mixed effects model with a smooth random effects density

Abstract: SUMMARY The fixed parameters of the nonlinear mixed effects model and the density of the random effects are estimated jointly by maximum likelihood. The density of the random effects is assumed to be smooth but is otherwise unrestricted. The method uses a series expansion that follows from the smoothness assumption to represent the density and quadrature to compute the likelihood. Standard algorithms are used for optimization. Empirical Bayes estimates of random coefficients are obtained by computing posterior modes. The method is applied to data from pharmacokinetics, and properties of the method are investigated by application to simulated data.

Zero-inflated models with application to spatial count data

Abstract: Count data arises in many contexts. Here our concern is with spatial count data which exhibit an excessive number of zeros. Using the class of zero-inflated count models provides a flexible way to address this problem. Available covariate information suggests formulation of such modeling within a regression framework. We employ zero-inflated Poisson regression models. Spatial association is introduced through suitable random effects yielding a hierarchical model. We propose fitting this model within a Bayesian framework considering issues of posterior propriety, informative prior specification and well-behaved simulation based model fitting. Finally, we illustrate the model fitting with a data set involving counts of isopod nest burrows for 1649 pixels over a portion of the Negev desert in Israel.