estimation in generalized mixed models regression models containing fixed and random effects may have a response variable which is not normally distributed the generalized mixed model includes both discrete and continuous response variables and is developed here for problems in which the regression variables enter linearly into the model best linear unbiased predictor methods are extended to maximum likelihood and residual maximum likelihood estimation procedures applications in modelling discrete response variables and in survival analysis are discussed

robust estimation in generalized partial linear models for clustered data in this article we consider robust generalized estimating equations for the analysis of semiparametric generalized partial linear models gplms for longitudinal data or clustered data in general we approximate the nonparametric function in the gplm by a regression spline and use bounded scores and leverage based weights in the estimating equation to achieve robustness against outliers we show that the regression spline approach avoids some of the intricacies associated with the profile kernel method and that robust estimation and inference can be carried out operationally as if a generalized linear model were used

broadband muller mlfma for electromagnetic scattering by dielectric objects the multilevel fast multipole algorithm mlfma is very efficient for solving large scale electromagnetic scattering problems however at low frequencies or when the discretization is small compared with the wavelength both the mlfma and the underlying integral equation formulation typically suffer from a subwavelength breakdown for the electromagnetic scattering from a homogeneous dielectric object we obtain a stable and well conditioned surface integral formulation using a variant of the classical muumlller formulation and linear basis functions to overcome the subwavelength breakdown of the mlfma we use both propagating and evanescent plane waves to represent the fields the implementation is based on a combination of the spectral representation of the green s function and rokhlin s translation formula we also present a new interpolation scheme for the evanescent part which significantly improves the error controllability of the mlfma implementation several numerical results verify both the error controllability and scalability of the proposed algorithm

reml estimation for survival models with frailty a method of estimation for generalised mixed models is applied to the estimation of regression parameters in proportional hazards models for failure times when there are repeated observations of failure on each subject the subject effect is incorporated into the model as a random frailty term best linear unbiased predictors are used as an initial step in the computation of maximum likelihood and residual maximum likelihood estimates

robust restricted maximum likelihood in mixed linear models summary definitions of robust maximum likelihood robust ml and robust restricted maximum likelihood robust reml are introduced and the definitions are applied to data from biological and chemical experiments a simulation study is undertaken to investigate the asymptotic properties of robust ml and robust reml in small samples and to examine the advantages of using robust methods 1 introduction and definitions linear models with multiple sources of error are widely used in designed experiments across many scientific fields an example of such an experiment is described by patterson and nabugoomu 1992 from patterson and silvey 1980 six varieties of wheat were grown at ten centres that formed a sample of the main types of growing area for wheat in scotland and the yields in tonnes hectare were recorded the experiment is unbalanced because of 60 possible variety centre combinations only 46 were used at seven centres four varieties were grown and at the remaining three centres all six varieties were grown in this paper we fit the simplest mixed linear model proposed for this data by patterson and nabugoomu namely

robust estimation in generalized linear mixed models generalized linear mixed models glmms are widely used to analyse non normal response data with extra variation but non robust estimators are still routinely used we propose robust methods for maximum quasi likelihood and residual maximum quasi likelihood estimation to limit the influence of outlying observations in glmms the estimation procedure parallels the development of robust estimation methods in linear mixed models but with adjustments in the dependent variable and the variance component the methods proposed are applied to three data sets and a comparison is made with the nonparametric maximum likelihood approach when applied to a set of epileptic seizure data the methods proposed have the desired effect of limiting the influence of outlying observations on the parameter estimates simulation shows that one of the residual maximum quasi likelihood proposals has a smaller bias than those of the other estimation methods we further discuss the equivalence of two glmm formulations when the response variable follows an exponential family their extensions to robust glmms and their comparative advantages in modelling are described some possible modifications of the robust glmm estimation methods are given to provide further flexibility for applying the method

bounded influence estimation in the mixed linear model abstract bounded influence estimation also known as generalized m or gm estimation in the regression model is reviewed the definitions of bounded influence estimation proposed by mallows and schweppe are then extended to the mixed linear model this is achieved by applying appropriate weight functions to maximum likelihood and restricted maximum likelihood estimating equations the asymptotic properties of the new estimators are obtained and the estimators are applied to an artificial dataset the article concludes with an extension of the example into a small simulation study designed to test some properties of the estimators in samples of moderate size

estimation in generalized linear models with random effects summary a conceptually very simple but general algorithm for the estimation of the fixed effects random effects and components of dispersion in generalized linear models with random effects is proposed conditions are described under which the algorithm yields approximate maximum likelihood or quasi maximum likelihood estimates of the fixed effects and dispersion components and approximate empirical bayes estimates of the random effects the algorithm is applied to two data sets to illustrate the estimation of components of dispersion and the modelling of overdispersion

theory of morphological evolution in ostwald ripening abstract the multiple expansion theory for ostwald ripening in a three dimensional system is presented analogously to the case in two dimensional coarsening t imaeda and k kawasaki physica a 164 1990 335 the migration and the shape deformation of droplets caused by the diffusional interaction are taken into account in our kinetic equations of motion the derived equations can be solved numerically within a fairly resonable computation time the role of the mullins sekerka instability in the coarsening kinetics is examined

asymptotic properties and information criteria for misspecified generalized linear mixed models summary the problem of misspecification poses challenges in model selection the paper studies the asymptotic properties of estimators for generalized linear mixed models with misspecification under the framework of conditional kullback leibler divergence a conditional generalized information criterion is introduced and a model selection procedure is proposed by minimizing the criterion we prove that the model selection procedure proposed is asymptotically loss efficient when all the candidate models are misspecified the model selection consistency of the model selection procedure is also established when the true data generating procedure lies within the set of candidate models simulation experiments confirm the effectiveness of the method proposed the use of the criterion for model selection is illustrated through an analysis of the european currency opinion survey data

spectral method study of domain coarsening the self organization of particles in a two phase system in the coexistence region through a diffusive mechanism is known as ostwald ripening the late stage of ostwald ripening is studied here through the use of a mesoscopic model in conjunction with a special configuration that allows for the direct measurement of system characteristics such as domain size the mesoscopic model is a stochastic partial integrodifferential equation and is studied through the use of recently developed and benchmarked spectral schemes the size of the growing region is not observed to increase as a power law in this model during the late stages of self organization in contrast to the power law growth observed in simulations of the earlier stages of self organization the results included here also demonstrate the effect of adjusting the interparticle interaction on the morphological evolution of the system

a general maximum likelihood analysis of variance components in generalized linear models this paper describes an em algorithm for nonparametric maximum likelihood ml estimation in generalized linear models with variance component structure the algorithm provides an alternative analysis to approximate mql and pql analyses mcgilchrist and aisbett 1991 biometrical journal 33 131 141 breslow and clayton 1993 journal of the american statistical association 88 9 25 mcgilchrist 1994 journal of the royal statistical society series b 56 61 69 goldstein 1995 multilevel statistical models and to gee analyses liang and zeger 1986 biometrika 73 13 22 the algorithm first given by hinde and wood 1987 in longitudinal data analysis 110 126 is a generalization of that for random effect models for overdispersion in generalized linear models described in aitkin 1996 statistics and computing 6 251 262 the algorithm is initially derived as a form of gaussian quadrature assuming a normal mixing distribution but with only slight variation it can be used for a completely unknown mixing distribution giving a straightforward method for the fully nonparametric ml estimation of this distribution this is of value because the ml estimates of the glm parameters can be sensitive to the specification of a parametric form for the mixing distribution the nonparametric analysis can be extended straightforwardly to general random parameter models with full npml estimation of the joint distribution of the random parameters this can produce substantial computational saving compared with full numerical integration over a specified parametric distribution for the random parameters a simple method is described for obtaining correct standard errors for parameter estimates when using the em algorithm several examples are discussed involving simple variance component and longitudinal models and small area estimation

bias correction in generalised linear mixed models with a single component of dispersion summary general expressions are derived for the asymptotic biases in three approximate estimators of regression coefficients and variance component for small values of the variance component in generalised linear mixed models with canonical link function and a single source of extraneous variation the estimators involve first and second order laplace expansions of the integrated likelihood and a related procedure known as penalised quasilikelihood numerical studies of a series of matched pairs of binary outcomes show that the first order estimators of the variance component are seriously biased easily computed correction factors produce satisfactory estimators of small variance components comparable to those obtained with a second order laplace expansion and markedly improve the asymptotic performance for larger values for a series of matched pairs of binomial observations the variance correction factors rapidly approach one as the binomial denominators increase these results greatly extend the range of parameter values for which the approximate estimation procedures have satisfactory asymptotic properties

a global interpolator with low sample rate for multilevel fast multipole algorithm a new improved version of a global interpolator utilizing trigonometric polynomials is presented for the high frequency multilevel fast multipole algorithm the number of required points to sample the outgoing and incoming field patterns is low almost half in some levels compared with the earlier published versions compared with local interpolators based on lagrange interpolating polynomials the proposed technique performs even more favorably and reduces the number of sample points by a factor of eight the numerical examples demonstrate that the interpolator allows full numerical accuracy control during the aggregation and disaggregation phases regardless of the number of the levels in the octree

variance components models for dependent cell populations cells grown in culture can be tracked for several generations and measurements taken on size or age at division and other cell characteristics the observations for the offspring of each cell form a family tree of dependent data such cell lineage data are here modeled as repeated measurements on different family trees arising from individual ancestor cells selected at random from a population of cultured cells the bifurcating autoregression model is embedded in a process that allows for measurement error and variation from tree to tree robust methods are presented that accommodate outliers in this time dependent and branching environment while allowing the statistician to interactively build a variance components model for the process the methodology is illustrated on a substantial data set of 41 trees of emt6 cells with the surprising conclusion that after removing measurement error sister cell lifetimes are nearly identical

robust modeling for inference from generalized linear model classes generalized linear models glms are widely used for data analysis however their maximum likelihood estimators can be sensitive to outliers we propose new statistical models that allow robust inferences from the glm class of models including poisson and binomial glms and their extension to generalized linear mixed models the likelihood score equations from the new models give estimators with bounded influence so that the resulting estimators are robust against outliers while maintaining high efficiency in the absence of outliers

optimal interpolation of translation operator in multilevel fast multipole algorithm lagrange interpolation of the translation operator in the three dimensional multilevel fast multipole algorithm mlfma is revisited parameters of the interpolation namely the number of interpolation points and the oversampling factor are optimized for controllable error via optimization it becomes possible to obtain the desired level of accuracy with the minimum processing time

robust reml estimation for k component poisson mixture with random effects application to the epilepsy seizure count data and urinary tract infections data a robust version of residual maximum likelihood estimation for poisson log linear mixed model is developed and the method is extended to k component poisson mixture with random effects the method not only provides the robust estimators for the fixed effects and variance component parameters but also gives the robust prediction of random effects simulation results show that the proposed method is effective in limiting the impact of outliers under different data contamination schemes the method is adopted to analyze the epilepsy seizure count data and the urinary tract infections data which are deemed to contain several potential outliers the results show that the proposed method provides better goodness of fit to the data and demonstrate the effect of the robust tuning mechanism copyright 2012 john wiley sons ltd

high breakdown inference for mixed linear models mixed linear models are used to analyze data in many settings these models have a multivariate normal formulation in most cases the maximum likelihood estimator mle or the residual mle reml is usually chosen to estimate the parameters however the latter are based on the strong assumption of exact multivariate normality welsh and richardson have shown that these estimators are not robust to small deviations from multivariate normality this means that in practice a small proportion of data even only one can drive the value of the estimates on their own because the model is multivariate we propose a high breakdown robust estimator for very general mixed linear models that include for example covariates this robust estimator belongs to the class of s estimators from which we can derive asymptotic properties for inference we also use it as a diagnostic tool to detect outlying subjects we discuss the advantages of this estimator compared with other robust estimators proposed previously and i

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

some covariance models for longitudinal count data with overdispersion a family of covariance models for longitudinal counts with predictive covariates is presented these models account for overdispersion heteroscedasticity and dependence among repeated observations the approach is a quasi likelihood regression similar to the formulation given by liang and zeger 1986 biometrika 73 13 22 generalized estimating equations for both the covariate parameters and the variance covariance parameters are presented large sample properties of the parameter estimates are derived the proposed methods are illustrated by an analysis of epileptic seizure count data arising from a study of progabide as an adjuvant therapy for partial seizures

hierarchical monte carlo methods for fractal random fields two hierarchical monte carlo methods for the generation of self similar fractal random fields are compared and contrasted the first technique successive random addition sra is currently popular in the physics community despite the intuitive appeal of sra rigorous mathematical reasoning reveals that sra cannot be consistent with any stationary power law gaussian random field for any hurst exponent furthermore there is an inherent ratio of largest to smallest putative scaling constant necessarily exceeding a factor of 2 for a wide range of hurst exponentsh with 0 30 h 0 85 thus sra is inconsistent with a stationary power law fractal random field and would not be useful for problems that do not utilize additional spatial averaging of the velocity field the second hierarchical method for fractal random fields has recently been introduced by two of the authors and relies on a suitable explicit multiwavelet expansion mwe with high moment cancellation this method is described briefly including a demonstration that unlike sra mwe is consistent with a stationary power law random field over many decades of scaling and has low variance

asymptotically unbiased estimation in generalized linear models with random effects 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

robustified maximum likelihood estimation in generalized partial linear mixed model for longitudinal data summary in this article we study the robust estimation of both mean and variance components in generalized partial linear mixed models based on the construction of robustified likelihood function under some regularity conditions the asymptotic properties of the proposed robust estimators are shown some simulations are carried out to investigate the performance of the proposed robust estimators just as expected the proposed robust estimators perform better than those resulting from robust estimating equations involving conditional expectation like sinha 2004 journal of the american statistical association99 451 460 and qin and zhu 2007 journal of multivariate analysis98 1658 1683 in the end the proposed robust method is illustrated by the analysis of a real data set

multipole expansion in the ostwald ripening theory abstract a multipole expansion theory for ostwald ripening is presented the theory takes into account morphological deformation as well as migration of coarsening droplets numerical computation are performed for the two dimensional ripening process even in a few mode truncation our results reproduce well the direct numerical solution of the laplace equation at a small spatial separation between droplets the importance of these degrees of freedom in the coarsening kinetics is discussed

broadband mlfma with plane wave expansions and optimal memory demand a broadband multilevel fast multipole algorithm mlfma in 3d is presented based on plane wave expansions and diagonal translations on all division levels the radiation and incoming wave patterns on all levels are presented by trigonometric polynomials and optimal sampling rates and translator degrees are found and tabulated on the super wavelength levels the memory need and the computational cost are lowered more than by half compared to the traditional approach on the sub wavelength levels also a novel saving method for the field patterns is presented which is as efficient as saving the multipole series coefficients while all translations with the proposed method can still be carried out in the fast diagonal form also the direction dependence of the radiation and incoming wave patterns is lowered by half the proposed broadband mlfma has a very good error control on all division levels which we demonstrate by numerical testing

numerical study of the cahn hilliard equation in one two and three dimensions abstract the cahn hilliard ch equation is related with a number of interesting physical phenomena like the spinodal decomposition phase separation and phase ordering dynamics on the other hand this equation is very stiff and the difficulty to solve it numerically increases with the dimensionality and therefore there are several published numerical studies in one dimension 1d dealing with different approaches and much fewer in two dimensions 2d in three dimensions 3d there are very few publications usually concentrate in some specific result without the details of the used numerical scheme we present here a stable and fast conservative finite difference scheme to solve the ch with two improvements a splitting potential into an implicit and explicit in time part and the use of free boundary conditions we show that gradient stability is achieved in one two and three dimensions with large time marching steps than normal methods

multilevel models for survival analysis with random effects a method for modeling survival data with multilevel clustering is described the cox partial likelihood is incorporated into the generalized linear mixed model glmm methodology parameter estimation is achieved by maximizing a log likelihood analogous to the likelihood associated with the best linear unbiased prediction blup at the initial step of estimation and is extended to obtain residual maximum likelihood reml estimators of the variance component estimating equations for a three level hierarchical survival model are developed in detail and such a model is applied to analyze a set of chronic granulomatous disease cgd data on recurrent infections as an illustration with both hospital and patient effects being considered as random only the latter gives a significant contribution a simulation study is carried out to evaluate the performance of the reml estimators further extension of the estimation procedure to models with an arbitrary number of levels is also discussed

a particle model for spinodal decomposition we study a one dimensional lattice gas where particles jump stochastically obeying an exclusion rule and having a small drift toward regions of higher concentration we prove convergence in the continuum limit to a nonlinear parabolic equation whenever the initial density profile satisfies suitable conditions which depend on the strengtha of the drift there is a critical valuea c ofa fora a c the density values are unrestricted while fora a c they should all be to the right or to the left of a given interval a the diffusion coefficient of the limiting equation can be continued analytically to a and in the interior of a it has negative values which should correspond to particle aggregation phenomena we also show that the dynamics can be obtained as a limit of a kawasaki evolution associated to a kac potential the coefficienta plays the role of the inverse temperature the critical value ofa coincides with the critical inverse temperature in the van der waals limit and a with the spinodal region it is finally seen that in a scaling intermediate between the microscopic and the hydrodynamic the system evolves according to an integrodifferential equation the instanton solutions of this equation as studied by dal passo and de mottoni are then related to the phase transition region in the thermodynamic phase diagram analogies with the cahn hilliard equations are also discussed

monte carlo em estimation for time series models involving counts abstract the observations in parameter driven models for time series of counts are generated from latent unobservable processes that characterize the correlation structure these models result in very complex likelihoods and even the em algorithm which is usually well suited for problems of this type involves high dimensional integration in this article we discuss a monte carlo em mcem algorithm that uses a markov chain sampling technique in the calculation of the expectation in the e step of the em algorithm we propose a stopping criterion for the algorithm and provide rules for selecting the appropriate monte carlo sample size we show that under suitable regularity conditions an mcem algorithm will with high probability get close to a maximizer of the likelihood of the observed data we also discuss the asymptotic efficiency of the procedure we illustrate our monte carlo estimation method on a time series involving small counts the polio incidence time series previously analyzed by zeger

robust estimation of variance components outliers may occur with respect to any of the random components in the mixed linear model a procedure for limiting the influence of these outliers on the estimates of the model parameters is described given the variances or estimates of them the model effects are estimated by augmenting the original observations with auxiliary observations that contain the prior information represented by the variances large residuals among either the original or the auxiliary observations are interpreted as outlying random errors or outlying random effects as appropriate and winsorized the robust estimation of the variances is obtained by modifying the defining equations for the restricted maximum likelihood estimates under normality along the lines of huber s proposal 2 a numerical example illustrates the use of the methodology both as a diagnostic and as an estimation tool

performing interpolation and anterpolation entirely by fast fourier transform in the 3 d multilevel fast multipole algorithm the fast multipole methods are used for solving a scalar acoustic or vector electromagnetic wave equation by integral equation methods with a large number of unknowns in this paper a new method is presented for performing interpolation and anterpolation in both spherical coordinates theta and phi by fft in the three dimensional 3 d multilevel fast multipole algorithm mlfma the key idea is to approximate functions on the unit sphere by truncated fourier series in two variables rather than by the usual spherical harmonics the proposed method is exact in interpolating and anterpolating and has the high numerical efficiency of fft the method is numerically compared to the method of performing interpolation and anterpolation using lagrangian interpolation which presently is probably the fastest method for those operations and the results suggest that the proposed new method is equally or more efficient depending on the desired accuracy

a kernel independent adaptive fast multipole algorithm in two and three dimensions we present a new fast multipole method for particle simulations the main feature of our algorithm is that it does not require the implementation of multipole expansions of the underlying kernel and it is based only on kernel evaluations instead of using analytic expansions to represent the potential generated by sources inside a box of the hierarchical fmm tree we use a continuous distribution of an equivalent density on a surface enclosing the box to find this equivalent density we match its potential to the potential of the original sources at a surface in the far field by solving local dirichlet type boundary value problems the far field evaluations are sparsified with singular value decomposition in 2d or fast fourier transforms in 3d we have tested the new method on the single and double layer operators for the laplacian the modified laplacian the stokes the modified stokes the navier and the modified navier operators in two and three dimensions our numerical results indicate that our method compares very well with the best known implementations of the analytic fmm method for both the laplacian and modified laplacian kernels its advantage is the relative simplicity of the implementation and its immediate extension to more general kernels

residuals for the linear model with general covariance structure a general theory is presented for residuals from the general linear model with correlated errors it is demonstrated that there are two fundamental types of residual associated with this model referred to here as the marginal and the conditional residual these measure respectively the distance to the global aspects of the model as represented by the expected value and the local aspects as represented by the conditional expected value these residuals may be multivariate some important dualities are developed which have simple implications for diagnostics the results are illustrated by reference to model diagnostics in time series and in classical multivariate analysis with independent cases

a mixed form fast multipole algorithm the fast multipole algorithm manifests in two very different forms at low frequencies and at mid frequencies each can operate in their respective regimes but are not tenable in the other regimes the paper reports on a way to factorize the green s function for fast algorithm using a mixed form the low frequency fast multipole algorithm lf fma will be used at low frequencies or the long wavelength regime and the multilevel fast multipole algorithm mlfma will be used for the mid frequencies or the shorter wavelength regime for object modeling where both long wavelength and wave physics are important we propose a mixed form fast multipole algorithm mf fma this algorithm has no low frequency break down and it can work seamlessly from static where circuit physics is important to dynamic where wave physics is important

phase separation kinetics in a model with order parameter dependent mobility we present extensive results from two dimensional simulations of phase separation kinetics in a model with order parameter dependent mobility we find that the time dependent structure factor exhibits dynamical scaling and the scaling function is numerically indistinguishable from that for the cahn hilliard ch equation even in the limit where surface diffusion is the mechanism for domain growth this supports the view that the scaling form of the structure factor is universal and leads us to question the conventional wisdom that an accurate representation of the scaled structure factor for the ch equation can only be obtained from a theory which correctly models bulk diffusion

on the splitting up method and stochastic partial differential equations we consider two stochastic partial differential equations du varepsilon t l ru varepsilon t f r t dv varepsilon t r m k u varepsilon t g k t circ dy t k qquad hspace 5pt varepsilon 0 1 driven by the same multidimensional martingale y yk and by different increasing processes vr0 vr1 r 1 2 d1 where lr and mk are second and first order partial differential operators and stands for the stratonovich differential we estimate the moments of the supremum in t of the sobolev norms of u1 t u0 t in terms of the supremum of the differences break vr0t vr1t hence we obtain moment estimates for the error of a multistage splitting up method for stochastic pdes in particular for the equation of the unnormalized conditional density in nonlinear filtering

a fourier wavelet monte carlo method for fractal random fields a new hierarchical method for the monte carlo simulation of random fields called the fourier wavelet method is developed and applied to isotropic gaussian random fields with power law spectral density functions this technique is based upon the orthogonal decomposition of the fourier stochastic integral representation of the field using wavelets the meyer wavelet is used here because its rapid decay properties allow for a very compact representation of the field the fourier wavelet method is shown to be straightforward to implement given the nature of the necessary precomputations and the run time calculations and yields comparable results with scaling behavior over as many decades as the physical space multiwavelet methods developed recently by two of the authors however the fourier wavelet method developed here is more flexible and in particular applies to anisotropic spectra generated through solutions of differential equations simulation results using this new technique and the well known nonhierarchical simulation technique the randomization method are given and compared for both a simple shear layer model problem as well as a two dimensional isotropic gaussian random field the fourier wavelet method results are more accurate for statistical quantities depending on moments higher than order 2 in addition to showing a quite smooth decay to zero on the scales smaller than the scaling regime when compared with the randomization method results the only situation in which the nonhierarchical randomization method is more computationally efficient occurs when no more than four decades of scaling behavior are needed and the statistical quantities of interest depend only on second moments

fence methods for mixed model selection many model search strategies involve trading off model fit with model complexity in a penalized goodness of fit measure asymptotic properties for these types of procedures in settings like linear regression and arma time series have been studied but these do not naturally extend to nonstandard situations such as mixed effects models where simple definition of the sample size is not meaningful this paper introduces a new class of strategies known as fence methods for mixed model selection which includes linear and generalized linear mixed models the idea involves a procedure to isolate a subgroup of what are known as correct models of which the optimal model is a member this is accomplished by constructing a statistical fence or barrier to carefully eliminate incorrect models once the fence is constructed the optimal model is selected from among those within the fence according to a criterion which can be made flexible in addition we propose two variations of the fence the first is a stepwise procedure to handle situations of many predictors the second is an adaptive approach for choosing a tuning constant we give sufficient conditions for consistency of fence and its variations a desirable property for a good model selection procedure the methods are illustrated through simulation studies and real data analysis

bias correction in generalized linear mixed models with multiple components of dispersion abstract general formulas are derived for the asymptotic bias in regression coefficients and variance components estimated by penalized quasi likelihood pql in generalized linear mixed models with canonical link function and multiple sets of independent random effects easily computed correction matrices result in variance component estimates that have satisfactory asymptotic behavior for small values of the variance components and significantly reduce bias for larger values both first order and second order correction procedures are developed for regression coefficients estimated by pql the methods are illustrated through an analysis of an experiment on salamander matings involving crossed male and female random effects and their properties are evaluated in a simulation study

a regression model for time series of counts summary this paper discusses a model for regression analysis with a time series of counts correlation is assumed to arise from an unobservable process added to the linear predictor in a log linear model an estimating equation approach used for parameter estimation leads to an iterative weighted and filtered least squares algorithm asymptotic properties for the regression coefficients are presented we illustrate the technique with an analysis of trends in u s polio incidence since 1970