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.

Asymptotically Unbiased Estimation in Generalized Linear Models with Random Effects

Abstract: SUMMARY Obtaining estimates that are nearly unbiased has proven to be difficult when random effects are incorporated into a generalized linear model. In this paper, we propose a general method of adjusting any conveniently defined initial estimates to result in estimates which are asymptotically unbiased and consistent. The method is motivated by iterative bias correction and can be applied in principle to any parametric model. A simulation-based approach of implementing the method is described and the relationship of the method proposed with other sampling-based methods is discussed. Results from a small scale simulation study show that the method proposed can lead to estimates which are nearly unbiased even for the variance components while the standard errors are only slightly inflated. A new analysis of the famous salamander mating data is described which reveals previously undetected between-animal variation among the male salamanders and results in better prediction of mating outcomes.

Estimating the Multilevel Rasch Model: With the lme4 Package

Abstract: Traditional Rasch estimation of the item and student parameters via marginal maximum likelihood, joint maximum likelihood or conditional maximum likelihood, assume individuals in clustered settings are uncorrelated and items within a test that share a grouping structure are also uncorrelated. These assumptions are often violated, particularly in educational testing situations, in which students are grouped into classrooms and many test items share a common grouping structure, such as a content strand or a reading passage. Consequently, one possible approach is to explicitly recognize the clustered nature of the data and directly incorporate random effects to account for the various dependencies. This article demonstrates how the multilevel Rasch model can be estimated using the functions in R for mixed-effects models with crossed or partially crossed random effects. We demonstrate how to model the following hierarchical data structures: a) individuals clustered in similar settings (e.g., classrooms, schools), b) items nested within a particular group (such as a content strand or a reading passage), and c) how to estimate a teacher x content strand interaction.

Functional mixed effects models

Abstract: Functional mixed effects model (FMM) is a mixed effects modeling framework that both the fixed effects and the random effects are modeled by nonparametric curves. The combination of mixed effects model and nonparametric smoothing enables FMMs to handle outcomes with complex profiles and at the same time to incorporate complex experimental designs and include covariates. Estimation and inference can be performed either using techniques from linear mixed effects models or using fully Bayesian approaches. As in functional data analysis, inference in FMMs is preliminary and needs to be further investigated. Several software packages have been developed to implement FMMs, although computational challenges do exist no matter which smoothing method is used. WIREs Comput Stat 2012, 4:527–534. doi: 10.1002/wics.1226 For further resources related to this article, please visit the WIREs website

Value-Added Models and the Measurement of Teacher Quality

Abstract: The recent availability of administrative databases that track individual students and their teachers over time has lead to both a surge in research measuring teacher quality and interest in developing accountability systems for teachers. Existing studies employ a variety of empirical models, yet few studies explicitly state or test the assumptions underlying their models. Using an extensive database from the State of Florida, we test many of the central assumptions of existing models and determine the impact of alternative methods on measures of teacher quality. We find that the commonly used “restricted valueadded” or “achievement-gain” model is a good approximation of the more cumbersome cumulative achievement model. Within the context of the restricted value-added model, we find it is important to control for unmeasured student, teacher and school heterogeneity. Relying on measurable characteristics of students, teachers and schools alone likely produces inconsistent estimates of the effects of teacher characteristics on student achievement. Moreover, individual-specific heterogeneity is more appropriately captured by fixed effects than by random effects; the random effects estimator yields inconsistent parameter estimates and estimates of time-invariant teacher quality that diverge significantly from the fixed effects estimator. In contrast, the exclusion of peer characteristics and class size each have relatively little effect on the estimates of teacher quality. Using aggregated grade-within-school measures of teacher characteristics produces somewhat less precise estimates of the impact of teacher professional development than do measures of the characteristics of specific teachers. Otherwise, aggregation to the grade level doesn’t have a substantial effect. These findings suggest that many models currently employed to measure the impact of teachers on student achievement are mis-specified.