multilevel covariance component models summary a straightforward extension to the multilevel linear model with nested covariance components is described this allows the specification and efficient estimation of a very general mixed linear model with both crossed and nested covariance components goldstein 1986 describes the analysis of the multilevel mixed effects linear model with random coefficients where the variance and covariance components have a nested structure across levels the purpose of the present note is to show how a simple extension to the formulae in that paper can accommodate cross classifications of the components within any level of the nesting thus enabling quite general covariance component models to be specified and efficient parameter estimates obtained for simplicity the 3 level model is used with the extension to 4 or more levels being straightforward we write the random part of the 3 level model as

nonlinear multilevel models with an application to discrete response data summary a procedure is proposed for the analysis of multilevel nonlinear models using a linearization the case of log linear models for discrete response data is studied in detail nonlinear models arise in a number of circumstances notably when modelling discrete data in this paper we consider the multilevel nonlinear model as in linear multilevel models we shall consider the general case where any of the model coefficients can be random at any level and where the random parameters may also be specified functions of the fixed parameter estimates discussed by h goldstein r prosser and j rasbash in an as yet unpublished report in the next two sections we set out the model and define notation this is followed by a section on estimation and then some examples

analysis of longitudinal data random coefficient regression modelling we review random coefficient regression rcr models and methods for fitting these models from an applications perspective methods for data with exponential family distributions are presented with the gaussian distribution as a special case attention is given to interpretation of fixed effects and the correlation structures implied by rcr models estimation methods are presented wtih computational approaches problems associated with testing fixed effects include accurate variance estimation and robustness to misspecification of the covariance structure methods for model selection and assessment are presented an example is used to demonstrate recommended approaches

latent variable modeling in heterogeneous populations common applications of latent variable analysis fail to recognize that data may be obtained from several populations with different sets of parameter values this article describes the problem and gives an overview of methodology that can address heterogeneity artificial examples of mixtures are given where if the mixture is not recognized strongly distorted results occur mimic structural modeling is shown to be a useful method for detecting and describing heterogeneity that cannot be handled in regular multiple group analysis other useful methods instead take a random effects approach describing heterogeneity in terms of random parameter variation across groups these random effects models connect with emerging methodology for multilevel structural equation modeling of hierarchical data examples are drawn from educational achievement testing psychopathology and sociology of education estimation is carried out by the liscomp program

multilevel time series models with applications to repeated measures data the analysis of repeated measures data can be conducted efficiently using a two level random coefficients model a standard assumption is that the within individual level 1 residuals are uncorrelated in some cases especially where measurements are made close together in time this may not be reasonable and this additional correlation structure should also be modelled a time series model for such data is proposed which consists of a standard multilevel model for repeated measures data augmented by an autocorrelation model for the level 1 residuals first and second order autoregressive models are considered in detail together with a seasonal component both discrete and continuous time are considered and it is shown how the autocorrelation parameters can themselves be structured in terms of further explanatory variables the models are fitted to a data set consisting of repeated height measurements on children

extending the simple linear regression model to account for correlated responses an introduction to generalized estimating equations and multi level mixed modelling much of the research in epidemiology and clinical science is based upon longitudinal designs which involve repeated measurements of a variable of interest in each of a series of individuals such designs can be very powerful both statistically and scientifically because they enable one to study changes within individual subjects over time or under varied conditions however this power arises because the repeated measurements tend to be correlated with one another and this must be taken into proper account at the time of analysis or misleading conclusions may result recent advances in statistical theory and in software development mean that studies based upon such designs can now be analysed more easily in a valid yet flexible manner using a variety of approaches which include the use of generalized estimating equations and mixed models which incorporate random effects this paper provides a particularly simple illustration of the use of these two approaches taking as a practical example the analysis of a study which examined the response of portable peak expiratory flow meters to changes in true peak expiratory flow in 12 children with asthma the paper takes the reader through the relevant practicalities of model fitting interpretation and criticism and demonstrates that in a simple case such as this analyses based upon these model based approaches produce reassuringly similar inferences to standard analyses based upon more conventional methods

multi level repeated measures growth modelling using extended spline functions this paper explores the fitting of multi level models to growth data over a wide age range using a new class of extended spline models these extend conventional splines based on a function representation by allowing variable order functions and by including fractional polynomial terms the work focuses on modelling human growth in height and head circumference with example data sets the procedures can be used with covariates and for comparing population parameters

general methods for analysing repeated measures we present an overview of issues and methods for analysing repeated measures of a continuous random variable we discuss modelling the mean vector and covariance structure statistical efficiency regression diagnostics and discrepancies between longitudinal and cross sectional methods we illustrate key points with examples and discuss areas requiring further development

restricted unbiased iterative generalized least squares estimation summary it is shown that the iterative least squares procedure for estimating the parameters in a general multilevel random coefficients linear model can be modified to produce unbiased estimates of the random parameters in the multivariate normal case these are equivalent to restricted maximum likelihood estimates

multilevel mixed linear model analysis using iterative generalized least squares summary models for the analysis of hierarchically structured data are discussed an iterative generalized least squares estimation procedure is given and shown to be equivalent to maximum likelihood in the normal case there is a discussion of applications to complex surveys longitudinal data and estimation in multivariate models with missing responses an example is given using educational data

conditional quantile analysis when covariates are functions with application to growth data summary motivated by the conditional growth charts problem we develop a method for conditional quantile analysis when predictors take values in a functional space the method proposed aims at estimating conditional distribution functions under a generalized functional regression framework this approach facilitates balancing of model flexibility and the curse of dimensionality for the infinite dimensional functional predictors its good performance in comparison with other methods both for sparsely and for densely observed functional covariates is demonstrated through theory as well as in simulations and an application to growth curves where the method proposed can for example be used to assess the entire growth pattern of a child by relating it to the predicted quantiles of adult height

describing the elephant structure and function in multivariate data there is a unity underlying the diversity of models for the analysis of multivariate data essentially they constitute a family models most generally nonlinear for structural functional relations between variables drawn from a behavior domain

multilevel analysis of structural equation models summary this paper considers the multilevel analysis of structural equation models with unbalanced sampling designs the analysis is based on the maximum likelihood and the generalized least squares approaches basic statistical results for inference such as the asymptotic distribution of the estimators goodness of fit test statistics for the validity of the model and functional constraints are developed computationally the applications of the scoring algorithm and the gauss newton algorithm are discussed

fast moment based estimation for hierarchical models summary hierarchical models allow for heterogeneous behaviours in a population while simultaneously borrowing estimation strength across all subpopulations unfortunately existing likelihood based methods for fitting hierarchical models have high computational demands and these demands have limited their adoption in large scale prediction and inference problems the paper proposes a moment based procedure for estimating the parameters of a hierarchical model which has its roots in a method originally introduced by cochran in 1937 the method trades statistical efficiency for computational efficiency it gives consistent parameter estimates competitive prediction error performance and substantial computational improvements when applied to a large scale recommender system application and compared with a standard maximum likelihood procedure the method delivers competitive prediction performance while reducing the sequential computation time from hours to minutes

a general model for two level data with responses missing at random a general model for two level multivariate data with responses possibly missing at random is described the model combines regressions on fixed explanatory variables with structured residual covariance matrices the likelihood function is reduced to a form enabling computational methods for estimating the model to be devised

evaluation of diagnostic scores with adjustment for covariates diagnostic tests yield measurements on very different types of scales quantitative scales may consist of non negative integers either unbounded or bounded with a fixed number of different values or they may consist of continuous or percentage values remembering a different threshold value for each diagnostic variable would be cumbersome in particular if covariates have to be taken into account as a convenient way to overcome such problems we propose to compute z scores for all measurements they will be adjusted for covariates so that any individual can be judged on any test result on one single scale with an appropriate standard normal quantile as threshold two issues need to be addressed selection of covariates in the regression model which delivers the adjustment and normality of the residuals the first will be treated by cross validation and the latter by applying an appropriate transformation we apply this methodology to neuropsychological tests and adjust for age length of education and sex normality of residuals is needed on the diagnostically relevant side only this allows to use parametric transformations which can be easily implemented e g in database systems since we have measurements at baseline and at follow up we also analyze change values in a similar manner for ease of interpretation we transform the resulting z scores back to the original scale

generalized multilevel structural equation modeling a unifying framework for generalized multilevel structural equation modeling is introduced the models in the framework called generalized linear latent and mixed models gllamm combine features of generalized linear mixed models glmm and structural equation models sem and consist of a response model and a structural model for the latent variables the response model generalizes glmms to incorporate factor structures in addition to random intercepts and coefficients as in glmms the data can have an arbitrary number of levels and can be highly unbalanced with different numbers of lower level units in the higher level units and missing data a wide range of response processes can be modeled including ordered and unordered categorical responses counts and responses of mixed types the structural model is similar to the structural part of a sem except that it may include latent and observed variables varying at different levels for example unit level latent variables factors or random coefficients can be regressed on cluster level latent variables special cases of this framework are explored and data from the british social attitudes survey are used for illustration maximum likelihood estimation and empirical bayes latent score prediction within the gllamm framework can be performed using adaptive quadrature in gllamm a freely available program running in stata

contextually specific effects and other generalizations of the hierarchical linear model for comparative analysis abstract contextually specific differences among members of a context pose substantive and methodological problems in multilevel analysis an important example is ethnic identity in comparative studies involving different societies ethnic and religious group membership in many societies is a basis not only for differentiation among members but also for the identification and maintenance of deeply rooted integrative ties so important is ethnicity that the existence of different groups within societies sometimes delays or prohibits the taking of censuses moreover even when ethnic information is available in national statistical data sources researchers are sometimes prohibited from reporting the results of analyses that contain ethnic detail despite these constraints information on ethnicity is often available for pluralistic societies where it is available ethnicity poses a challenging analytic problem for comparative analysis if researchers wish to compare different societies how is ethnicity

some mathematical models for deciding the number of examination questions on computerized adaptive tests abstract the computerized adaptive test cat was developed to obtain an efficient estimate of an examinee s ability in traditional paper and pencil tests all examinees had to answer the same number of questions this kind of test was not fair for every examinee consequently the cat plays an important role in fair and adaptive examinations however the basic and necessary requirements in the cat are the databases and computer operation rules of the examination system this paper presents some mathematical algorithms dealing with the number of questions for the examination system the algorithms are feasible and can determine the reasonable number of questions for a cat system

multiplicative effects in mixed model analysis of variance summary a class of two way mixed analysis of variance models is proposed in which the fixed and random effects enter multiplicatively equations are developed for iterative computation of maximum likelihood estimates via a scoring algorithm parameter estimation and hypothesis testing are illustrated on a set of plant genetics data

order statistics of rosenstock s trapping problem in disordered media the distribution of times t j n elapsed until the first j independent random walkers from a set of n ensuremath gg 1 all starting from the same site are trapped by a quenched configuration of traps randomly placed on a disordered lattice is investigated in doing so the cumulants of the distribution of the territory explored by n independent random walkers s n t and the probability ensuremath phi n t that no particle of an initial set of n is trapped by time t are considered simulation results for the two dimensional incipient percolation aggregate show that the ratio between the nth cumulant and the nth moment of s n t is for large n i very large in comparison with the same ratio in euclidean media and ii almost constant the first property implies that in contrast with euclidean media approximations of the order higher than the standard zeroth order rosenstock approximation are required to provide a reasonable description of the trapping order statistics fortunately the second property which has a geometric origin can be exploited to build these higher order rosenstock approximations simulation results for the two dimensional incipient percolation aggregate confirm the predictions of our approach

trapping and survival probability in two dimensions institut fu r festkorperforschung forschungszentrum julich gmbh d 52425 ju lich germany received 28 january 2000 published 19 january 2001 we investigate the survival probability f n c of particles performing a random walk on a two dimensionallattice that contains static traps which are randomly distributed with a concentration c as a function of thenumber of steps n f n c is analyzed in terms of a scaling ansatz which allows us to locate quantitatively thecrossover between the rosenstock approximation valid only at early times and the asymptotic donsker varadhan behavior valid only at long times while the existence of the crossover has been postulated before its exact location has not been known our scaling hypothesis is based on the mean value of the quantity s

on muthen s maximum likelihood for two level covariance structure models data in social and behavioral sciences are often hierarchically organized special statistical procedures that take into account the dependence of such observations have been developed among procedures for 2 level covariance structure analysis muthen s maximum likelihood muml has the advantage of easier computation and faster convergence when data are balanced muml is equivalent to the maximum likelihood procedure simulation results in the literature endorse the muml procedure also for unbalanced data this paper studies the analytical properties of the muml procedure in general the results indicate that the muml procedure leads to correct model inference asymptotically when level 2 sample size goes to infinity and the coefficient of variation of the level 1 sample sizes goes to zero the study clearly identifies the impact of level 1 and level 2 sample sizes on the standard errors and test statistic of the muml procedure analytical results explain previous simulation results and will guide the design or data collection for the future applications of muml

constructing time specific reference ranges reference ranges which take time such as age into account are often required in medicine but simple systematic and efficient statistical methods for constructing them are lacking a method is described which is based on low order polynomial curves linear quadratic or occasionally cubic together with guidelines for when and how to apply a logarithmic transformation to the variable analysed testing for departures from normality and assessment of the adequacy of the reference range which is constructed from the regression line plus or minus a multiple of the standard deviation standard statistical packages may be used to carry out the calculations the question of comparing two or more groups of patients is addressed three examples are discussed in detail

determination of finite automata accepting subregular languages we investigate the descriptional complexity of the nondeterministic finite automaton nfa to the deterministic finite automaton dfa conversion problem for automata accepting subregular languages such as combinational languages definite languages and variants thereof strictly locally testable languages star free languages ordered languages prefix suffix and infix closed languages and prefix suffix and infix free languages most of the bounds for the conversion problem are shown to be tight in the exact number of states that is the number is sufficient and necessary in the worst case otherwise tight bounds in order of magnitude are shown

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

weighting for unequal selection probabilities in multilevel models when multilevel models are estimated from survey data derived using multistage sampling unequal selection probabilities at any stage of sampling may induce bias in standard estimators unless the sources of the unequal probabilities are fully controlled for in the covariates this paper proposes alternative ways of weighting the estimation of a two level model by using the reciprocals of the selection probabilities at each stage of sampling consistent estimators are obtained when both the sample number of level 2 units and the sample number of level 1 units within sampled level 2 units increase scaling of the weights is proposed to improve the properties of the estimators and to simplify computation variance estimators are also proposed in a limited simulation study the scaled weighted estimators are found to perform well although non negligible bias starts to arise for informative designs when the sample number of level 1 units becomes small the variance estimators perform extremely well the procedures are illustrated using data from the survey of psychiatric morbidity

multi level models for longitudinal growth norms multi level models for estimating conditional and unconditional longitudinal growth norms are presented the procedure involves transforming the original growth measurements to normality and modelling these with a two level random coefficient model growth norms for any desired time interval and function can be derived height and weight data are used for illustration

dirichlet process mixed generalized linear models abstract although generalized linear models glm s are an attractive and widely used class of models they are limited in the range of density shapes that they can provide for instance they are unimodal exponential families of densities in the response variable with tail behavior determined by the implicit mean variance relationship dirichlet process dp mixing adds considerable flexibility to these models using such mixing we develop models that we call dpmglm s which still retain the glm character with regard to the mean overdispersed glm s oglm s provide an alternative class of models to cope with extra variability in samples we show that how oglm s may be dp mixed leading to what we call dpmoglm s these models are extremely rich moreover recent computational advances enable them to be fitted straightforwardly we illustrate this with both simulated and real datasets we also address the question of choosing between the glm oglm dpmglm and dpmoglm finally we consider extensions by

multi level modelling under informative sampling we consider a model dependent approach for multi level modelling that accounts for informative probability sampling of first and lower level population units the proposed approach consists of first extracting the hierarchical model holding for the sample data given the selected sample as a function of the corresponding population model and the first and lower level sample selection probabilities and then fitting the resulting sample model using bayesian methods an important implication of the use of the model holding for the sample is that the sample selection probabilities feature in the analysis as additional data that possibly strengthen the estimators a simulation experiment is carried out in order to study the performance of this approach and compare it to the use of design based methods the simulation study indicates that both approaches perform in general equally well in terms of point estimation but the model dependent approach yields confidence credibility intervals with better coverage properties another simulation study assesses the impact of misspecification of the models assumed for the sample selection probabilities the use of maximum likelihood estimation is also considered

estimating and testing variance components in a multi level glm most analysis of multi subject fmri data is concerned with determining whether there exists a significant population wide activation in a comparison between two or more conditions this is typically assessed by testing the average value of a contrast of parameter estimates cope against zero in a general linear model glm analysis however important information can also be obtained by testing whether there exist significant individual differences in effect magnitude between subjects i e whether the variance of a cope is significantly different from zero intuitively such a test amounts to testing whether inter individual differences are larger than would be expected given the within subject error variance we compare several methods for estimating variance components including a a naive estimate using ordinary least squares ols b linear mixed effects in r lmer c a novel matlab implementation of iterative generalized least squares igls and its restricted maximum likelihood variant rigls all methods produced reasonable estimates of within and between subject variance components with igls providing an attractive balance between sensitivity and appropriate control of false positives finally we use the igls method to estimate inter subject variance in a perfusion fmri study n 18 of social evaluative threat and show evidence for significant inter individual differences in ventromedial prefrontal cortex vmpfc amygdala hippocampus and medial temporal lobes insula and brainstem with predicted inverse coupling between vmpfc and the midbrain periaqueductal gray only when high inter individual variance was used to define the seed for functional connectivity analyses in sum tests of variance provides a way of selecting regions that show significant inter individual variability for subsequent analyses that attempt to explain those individual differences

enumeration and generation with a string automata representation the representation of combinatorial objects is decisive for the feasibility of several enumerative tasks in this work we present a unique string representation for complete initially connected deterministic automata icdfas with n states over an alphabet of k symbols for these strings we give a regular expression and show how they are adequate for exact and random generation allow an alternative way for enumeration and lead to an upper bound for the number of icdfas the exact generation algorithm can be used to partition the set of icdfas in order to parallelize the counting of minimal automata and thus of regular languages a uniform random generator for icdfas is presented that uses a table of pre calculated values based on the same table an optimal coding for icdfas is obtained

some contributions to efficient statistics in structural models specification and estimation of moment structures current practice in structural modeling of observed continuous random variables is limited to representation systems for first and second moments e g means and covariances and to distribution theory based on multivariate normality in psychometrics the multinormality assumption is often incorrect so that statistical tests on parameters or model goodness of fit will frequently be incorrect as well it is shown that higher order product moments yield important structural information when the distribution of variables is arbitrary structural representations are developed for generalizations of the bentler weeks joreskog keesling wiley and factor analytic models some asymptotically distribution free efficient estimators for such arbitrary structural models are developed limited information estimators are obtained as well the special case of elliptical distributions that allow nonzero but equal kurtoses for variables is discussed in some detail the argument is made that multivariate normal theory for covariance structure models should be abandoned in favor of elliptical theory which is only slightly more difficult to apply in practice but specializes to the traditional case when normality holds many open research areas are described

the power to detect differences in average rates of change in longitudinal studies with considerable current interest in longitudinal epidemiologic studies little is available regarding sample size requirements this paper considers a method for analysis of longitudinal data where one compares the mean rates of change for two or more groups and proposes a statistic for use in determining sample size requirements one calculates individual rates of change with least squares estimates of slopes of individuals responses regressed over time the assumption of linear change over time while clearly not applicable for some data applies to many biological measurements either as recorded or with some transformation the variances of these estimated slopes have two components within individual variability based on measurement error and length and frequency of follow up and true between individual slope variability it is assumed that measurement error is the same for all subjects so that the total variances differ due to differences in follow up the question addressed is when can one use the usual anova f statistic to compare group means of estimated slopes expected mean squares demonstrate that this f is appropriate when either each group has the same number of subjects or when each subject has the same length and frequency of follow up a procedure for computing power and sample size is presented where one can specify the maximum detectable difference in any two average slopes moment estimation and maximum likelihood estimation of variance components from prior data are discussed

regional optimization of fertilization using a hierarchical linear model utilization of regional data for optimizing fertilizer strategy is considered it is argued that a hierarchical mixed effects model is a reasonable parsimonious way to model the data such models take into account the correlations between yield responses at the same site also they conveniently let one model the differences between years or between sites as a function of year and site characteristics we specifically develop the case of a linear in the parameters response model but hierarchical models could also be based on nonlinear response functions given the estimated parameters the calculation of an optimal fertilizer strategy which depends on the site and year characteristics is usually straightforward a number of measures of the quality of this strategy are proposed among these are the risk which measures yield loss caused by using estimated rather than true parameter values another measure of interest is the potential gain from having a model that explains all the between year or all the between site variability the effect of potassium on sown prairies in france is treated as an example

residual plots for repeated measures multivariate data are difficult to analyse partly because of difficulty in looking at the data repeated measures data have a special structure that makes the parallel plot1 2 particularly effective for viewing the data in this paper we use parallel plots to display not just raw data but also residuals from standard models fit to repeated measures data the plots are useful for determining how well a particular model fits the data identifying outlying observations and suggesting terms missing from the linear predictor

factor analysis for clustered observations classical factor analysis assumes a random sample of vectors of observations for clustered vectors of observations such as data for students from colleges or individuals within households it may be necessary to consider different within group and between group factor structures such a two level model for factor analysis is defined and formulas for a scoring algorithm for estimation with this model are derived a simple noniterative method based on a decomposition of the total sums of squares and crossproducts is discussed this method provides a suitable starting solution for the iterative algorithm but it is also a very good approximation to the maximum likelihood solution extensions for higher levels of nesting are indicated with judicious application of quasi newton methods the amount of computation involved in the scoring algorithm is moderate even for complex problems in particular no inversion of matrices with large dimensions is involved the methods are illustrated on two examples

maximum likelihood estimation of two level latent variable models with mixed continuous and polytomous data summary two level data with hierarchical structure and mixed continuous and polytomous data are very common in biomedical research in this article we propose a maximum likelihood approach for analyzing a latent variable model with these data the maximum likelihood estimates are obtained by a monte carlo em algorithm that involves the gibbs sampler for approximating the e step and the m step and the bridge sampling for monitoring the convergence the approach is illustrated by a two level data set concerning the development and preliminary findings from an aids preventative intervention for filipina commercial sex workers where the relationship between some latent quantities is investigated

calculation of unconditional and conditional reference intervals for foetal size and growth from longitudinal measurements methods for estimating unconditional and conditional reference intervals for foetal size and growth based on longitudinal observations are presented the methods are based on simple random effects regression models and involve transforming both the response and the covariate timepoint a dataset from a designed longitudinal study of foetal size is analysed in detail as a motivating example

a general model for the analysis of multilevel data a general model is developed for the analysis of multivariate multilevel data structures special cases of the model include repeated measures designs multiple matrix samples multilevel latent variable models multiple time series and variance and covariance component models

inference for the association between coefficients in a multivariate growth curve model this paper generalizes the work of blomqvist 1977 journal of the american statistical association 72 746 749 on inference for the relationship between the individual specific slope and the individual specific intercept in a linear growth curve model the paper deals with longitudinal data involving one or more response variables and irregular follow up times with each response variable postulated to follow a linear growth curve model the problem considered is inference concerning the association between one growth curve coefficient and another for example the slope and intercept for a selected response variable or the two slopes for two different response variables after adjusting for all remaining coefficients among all of the response variables an inferential approach based on the method of moments and an inferential approach based on maximum likelihood are described and the asymptotic properties of these procedures are presented extensions of the methodology to allow polynomial growth curves and baseline covariates are outlined the methodology is illustrated with a practical example arising from a clinical trial in lung disease

on normal theory based inference for multilevel models with distributional violations data in social and behavioral sciences are often hierarchically organized though seldom normal yet normal theory based inference procedures are routinely used for analyzing multilevel models based on this observation simple adjustments to normal theory based results are proposed to minimize the consequences of violating normality assumptions for characterizing the distribution of parameter estimates sandwich type covariance matrices are derived standard errors based on these covariance matrices remain consistent under distributional violations implications of various covariance estimators are also discussed for evaluating the quality of a multilevel model a rescaled statistic is given for both the hierarchical linear model and the hierarchical structural equation model the rescaled statistic improving the likelihood ratio statistic by estimating one extra parameter approaches the same mean as its reference distribution a simulation study with a 2 level factor model implies that the rescaled statistic is preferable

conditional growth charts growth charts are often more informative when they are customized per subject taking into account prior measurements and possibly other covariates of the subject we study a global semiparametric quantile regression model that has the ability to estimate conditional quantiles without the usual distributional assumptions the model can be estimated from longitudinal reference data with irregular measurement times and with some level of robustness against outliers and it is also flexible for including covariate information we propose a rank score test for large sample inference on covariates and develop a new model assessment tool for longitudinal growth data our research indicates that the global model has the potential to be a very useful tool in conditional growth chart analysis

generalized least squares taylor series linearization and fisher s scoring in multivariate nonlinear regression in this article we consider a general multivariate nonlinear regression setting in which the marginal mean and variance covariance structure share a common set of regression parameters estimation is carried out via iteratively reweighted generalized least squares irgls that entails repeated application of taylor series linearization and estimated generalized least squares egls under normality this irgls procedure is equivalent to fisher s method of scoring and hence maximum likelihood estimation mle however estimates from this procedure are also shown to minimize a bias corrected generalized least squares objective function that does not require the assumption of normality under fairly mild regularity conditions the resulting estimates are consistent asymptotically normal and under normality assumptions asymptotically efficient the estimates are compared against those obtained as solutions to the usual generalized estimating equations gee using both simulation and numerical examples

incomplete operational transition complexity of regular languages abstract the state complexity of basic operations on regular languages considering complete deterministic finite automata dfa has been extensively studied in the literature but if incomplete dfas are considered transition complexity is also a significant measure in this paper we study the incomplete deterministic state and transition complexity of some operations for regular and finite languages for regular languages we give a new tight upper bound for the transition complexity of the union which refutes the conjecture presented by y gao et al for finite languages we correct the published state complexity of concatenation for complete dfas and provide a tight upper bound for the case when the right operand is larger than the left one we also present some experimental results to test the behavior of those operations on the average case and we conjecture that for many operations and in practical applications the worst case complexity is seldom reached

efficient parametrisations for normal linear mixed models summary the generality and easy programmability of modern sampling based methods for maximisation of likelihoods and summarisation of posterior distributions have led to a tremendous increase in the complexity and dimensionality of the statistical models used in practice however these methods can often be extremely slow to converge due to high correlations between or weak identifiability of certain model parameters we present simple hierarchical centring reparametrisations that often give improved convergence for a broad class of normal linear mixed models in particular we study the two stage hierarchical normal linear model the laird ware model for longitudinal data and a general structure for hierarchically nested linear models using analytical arguments simulation studies and an example involving clinical markers of acquired immune deficiency syndrome aids we indicate when reparametrisation is likely to provide substantial gains in efficiency

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

transition to localization of biased walkers in a randomly absorbing environment abstract we study biased random walkers on lattices with randomly dispersed static traps in one two and three dimensions as the external bias is increased from zero the system undergoes a phase transition most clearly manifested in the asymptotic drift velocity of survivors which is zero below a critical bias this transition is second order in one dimension but of first order in higher dimensions the model can be mapped to a stretched polymer with attractive interaction between monomers and this phase transition would then describe sudden unfolding of the polymer when the stretching force exceeds a critical value we also present precise simulations of the zero bias case where we show unambiguously that the transition between the rosenstock rs and donsker varadhan dv regimes is first order in dimension 2