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.

Testing the fit of a regression model via score tests in random effects models.

Abstract: This paper considers testing the goodness-of-fit of regression models. Emphasis is on a goodness-of-fit test for generalized linear models with canonical link function and known dispersion parameter. The test is based on the score test for extra variation in a random effects model. By choosing a suitable form for the dispersion matrix, a goodness-of-fit test statistic is obtained which is quite similar to test statistics based on non-parametric kernel methods. We consider the distribution of the test statistic and discuss the choice of the dispersion matrix. The testing method can handle models with continuous and discrete covariates. Corrections for bias when parameters are estimated are available and extensions to models with unknown dispersion parameters, and more general nonlinear models are discussed. The proposed goodness-of-fit method is demonstrated in a simulation study and on real data of bone marrow transplant patients. The individual contributions of observations to the test statistic are used to perform residual analyses.

Spatial Dynamic Panel Data Models with Random Effects

Abstract: We develop a general space-time filter applied to panel data models in order to control for heterogeneity as well as both time and spatial dependence. Treatment of initial period observations is analyzed when the number of time periods is small. A second issue relates to an implied restriction on the space-time cross-product term that can greatly simplify the estimation procedures. An applied illustration of the method is provided using a Solow growth model. The application shows that the theoretical restriction implied for the cross-product term in our space-time filter specification is consistent with this particular dynamic space-time panel data set.

Hierarchical bayes for structured, variable populations: from recapture data to life‐history prediction

Abstract: Understanding population dynamics requires models that admit the complexity of natural populations and the data ecologists obtain from them. Populations possess structure, which may be defined as “fixed” stages through which individuals pass, with superimposed variability among individuals and groups. Data contain missing values and inaccurate censuses. From limited data ecologists attempt to predict life history schedules and population growth. We extend the “missing value” framework for Bayesian analysis of structured populations to admit the heterogeneity in demography and the limitations of data that are typical of ecological populations. Our hierarchical treatment of capture–recapture data allows inference on demographic rates contained in matrix transition models for populations that may be stratified by location and by other variables. Simulations with artificial data sets demonstrate the ability of the Bayesian model to successfully estimate underlying parameters, even with incomplete census data. In contrast, traditional nonhierarchical models may lead to biased parameter estimates because of variation in recapture rates of individuals. Analyses of published demographic data on Common Terns and Taitu Hills rats illustrate the utility of the model. Predictive distributions of maturation age, survivorship, and population growth demonstrate profound impacts of population and data complexity.

The Hospital Compare mortality model and the volume-outcome relationship.

Abstract: Objective. We ask whether Medicare's Hospital Compare random effects model correctly assesses acute myocardial infarction (AMI) hospital mortality rates when there is a volume–outcome relationship. Data Sources/Study Setting. Medicare claims on 208,157 AMI patients admitted in 3,629 acute care hospitals throughout the United States. Study Design. We compared average-adjusted mortality using logistic regression with average adjusted mortality based on the Hospital Compare random effects model. We then fit random effects models with the same patient variables as in Medicare's Hospital Compare mortality model but also included terms for hospital Medicare AMI volume and another model that additionally included other hospital characteristics. Principal Findings. Hospital Compare's average adjusted mortality significantly underestimates average observed death rates in small volume hospitals. Placing hospital volume in the Hospital Compare model significantly improved predictions. Conclusions. The Hospital Compare random effects model underestimates the typically poorer performance of low-volume hospitals. Placing hospital volume in the Hospital Compare model, and possibly other important hospital characteristics, appears indicated when using a random effects model to predict outcomes. Care must be taken to insure the proper method of reporting such models, especially if hospital characteristics are included in the random effects model.

Proportional hazards models with frailties and random effects.

Abstract: We discuss some of the fundamental concepts underlying the development of frailty and random effects models in survival. One of these fundamental concepts was the idea of a frailty model where each subject has his or her own disposition to failure, their so-called frailty, additional to any effects we wish to quantify via regression. Although the concept of individual frailty can be of value when thinking about how data arise or when interpreting parameter estimates in the context of a fitted model, we argue that the concept is of limited practical value. Individual random effects (frailties), whenever detected, can be made to disappear by elementary model transformation. In consequence, unless we are to take some model form as unassailable, beyond challenge and carved in stone, and if we are to understand the term 'frailty' as referring to individual random effects, then frailty models have no value. Random effects models on the other hand, in which groups of individuals share some common effect, can be used to advantage. Even in this case however, if we are prepared to sacrifice some efficiency, we can avoid complex modelling by using the considerable power already provided by the stratified proportional hazards model. Stratified models and random effects models can both be seen to be particular cases of partially proportional hazards models, a view that gives further insight. The added structure of a random effects model, viewed as a stratified proportional hazards model with some added distributional constraints, will, for group sizes of five or more, provide no more than modest efficiency gains, even when the additional assumptions are exactly true. On the other hand, for moderate to large numbers of very small groups, of sizes two or three, the study of twins being a well known example, the efficiency gains of the random effects model can be far from negligible. For such applications, the case for using random effects models rather than the stratified model is strong. This is especially so in view of the good robustness properties of random effects models. Nonetheless, the simpler analysis, based upon the stratified model, remains valid, albeit making a less efficient use of resources.