Changes to the Mixed Effects Models chapters in ELM
نویسنده
چکیده
The book “Extending the Linear Model with R” (ELM) [5] first appeared in 2005 and was based on R version 2.2.0. R is updated regularly and so it is natural that some incompatibilities with the current version have been introduced. For most of the chapters, these changes have been minor and have been addressed in the errata and/or subsequent reprintings of the text. However, for chapter 8 and 9, the changes have been much more substantial. These chapters are based on the lme4 package [2]. The package author, Doug Bates of the University of Wisconsin has made some significant changes to this software, most particularly in the way that inference is handled for mixed models. Fitting mixed effects models is a complex subject because of the large range of possible models and because the statistical theory still needs some development. lme4 is perhaps the best software generally available for fitting such models, but given the state of the field, there will be scope for significant improvements for some time. It is important to understand the reason behind these changes. For standard linear models (such as those considered in “Linear Models with R” [4]), the recommended way to compare an alternative hypothesis of a larger model compared to a null hypothesis of a smaller model nested within this larger model, is to use an F-test. Under the standard assumptions and when the errors are normally distributed, the F-statistic has an exact F-distribution with degrees of freedom that can be readily computed given the sample size and the number of parameters used by each model. For linear mixed effects models, that is models having some random effects, we might also wish to test fixed effect terms using an F-test. One way of approaching this is to assume that the estimates of the parameters characterizing the random effects of the model are in fact the true values. This reduces the mixed models to fixed effect models where the error has a particular covariance structure. Such models can be fit using generalized least squares and F-tests can be conducted using standard linear models theory. Several statistics software packages take this approach including the nlme package developed earlier and still available within R. Earlier versions of lme4 also took this approach and hence the output seen in the current version of ELM. However, there are two serious problems with this test. Firstly, the random effects are not actually known, but estimated. This means that the F-statistic does not follow an F-distribution exactly. In some cases, it may be a good approximation, but not in general. Secondly, even if
منابع مشابه
عیبیابی سازهها با استفاده از شاخص تابع پاسخ فرکانسی و مدل جایگزین مبتنی بر الگوریتم ماشین یادگیری حداکثر بهینه شده
Utilizing surrogate models based on artificial intelligence methods for detecting structural damages has attracted the attention of many researchers in recent decades. In this study, a new kernel based on Littlewood-Paley Wavelet (LPW) is proposed for Extreme Learning Machine (ELM) algorithm to improve the accuracy of detecting multiple damages in structural systems. ELM is used as metamo...
متن کاملTransition Models for Analyzing Longitudinal Data with Bivariate Mixed Ordinal and Nominal Responses
In many longitudinal studies, nominal and ordinal mixed bivariate responses are measured. In these studies, the aim is to investigate the effects of explanatory variables on these time-related responses. A regression analysis for these types of data must allow for the correlation among responses during the time. To analyze such ordinal-nominal responses, using a proposed weighting approach, an ...
متن کاملPotentials of Evolving Linear Models in Tracking Control Design for Nonlinear Variable Structure Systems
Evolving models have found applications in many real world systems. In this paper, potentials of the Evolving Linear Models (ELMs) in tracking control design for nonlinear variable structure systems are introduced. At first, an ELM is introduced as a dynamic single input, single output (SISO) linear model whose parameters as well as dynamic orders of input and output signals can change through ...
متن کاملParameter Estimation in Spatial Generalized Linear Mixed Models with Skew Gaussian Random Effects using Laplace Approximation
Spatial generalized linear mixed models are used commonly for modelling non-Gaussian discrete spatial responses. We present an algorithm for parameter estimation of the models using Laplace approximation of likelihood function. In these models, the spatial correlation structure of data is carried out by random effects or latent variables. In most spatial analysis, it is assumed that rando...
متن کاملA laboratory investigation on the potential of computational intelligence approaches to estimate the discharge coefficient of piano key weir
The piano key weir (PKW) is a type of nonlinear control structure that can be used to increase unit discharge over linear overflow weir geometries, particularly when the weir footprint area is restricted To predict the outflow passing over a piano key weir, the discharge coefficient in the general equation of weir needs to be known. This paper presents the results of laboratory model testing of...
متن کامل