multiple imputation and posterior simulation for multivariate missing data in longitudinal studies summary this paper outlines a multiple imputation method for handling missing data in designed longitudinal studies a random coefficients model is developed to accommodate incomplete multivariate continuous longitudinal data multivariate repeated measures are jointly modeled specifically an i i d normal model is assumed for time independent variables and a hierarchical random coefficients model is assumed for time dependent variables in a regression model conditional on the time independent variables and time with heterogeneous error variances across variables and time points gibbs sampling is used to draw model parameters and for imputations of missing observations an application to data from a study of startle reactions illustrates the model a simulation study compares the multiple imputation procedure to the weighting approach of robins rotnitzky and zhao 1995 journal of the american statistical association90 106 121 that can be used to address similar data structures

maximum likelihood estimation for n mixture models summary the focus of this article is on the nature of the likelihood associated with n mixture models for repeated count data it is shown that the infinite sum embedded in the likelihood associated with the poisson mixing distribution can be expressed in terms of a hypergeometric function and thence in closed form the resultant expression for the likelihood can be readily computed to a high degree of accuracy and is algebraically tractable specifically the likelihood equations can be simplified to some advantage the concentrated likelihood in the probability of detection formulated and problematic cases identified the results are illustrated by means of a simulation study and a real world example the study is extended to n mixture models with a negative binomial mixing distribution and results similar to those for the poisson case obtained n mixture models with mixing distributions which accommodate excess zeros and separately with a beta binomial distribution rather than a binomial used to model the intra site counts are also investigated however the results for these settings while computationally attractive do not provide insight into the nature of the maximum likelihood estimates

simulating multivariate nonnormal distributions a method for generating multivariate nonnormal distributions with specified intercorrelations and marginal means variances skews and kurtoses is proposed as an example the method is applied to the generation of simulated scores on three psychological tests administered to a single group of individuals

models for estimating abundance from repeated counts of an open metapopulation summary using only spatially and temporally replicated point counts royle 2004b biometrics 60 108 115 developed an n mixture model to estimate the abundance of an animal population when individual animal detection probability is unknown one assumption inherent in this model is that the animal populations at each sampled location are closed with respect to migration births and deaths throughout the study in the past this has been verified solely by biological arguments related to the study design as no statistical verification was available in this article we propose a generalization of the n mixture model that can be used to formally test the closure assumption additionally when applied to an open metapopulation the generalized model provides estimates of population dynamics parameters and yields abundance estimates that account for imperfect detection probability and do not require the closure assumption a simulation study shows these abundance estimates are less biased than the abundance estimate obtained from the original n mixture model the proposed model is then applied to two data sets of avian point counts the first example demonstrates the closure test on a single season study of mallards anas platyrhynchos and the second uses the proposed model to estimate the population dynamics parameters and yearly abundance of american robins turdus migratorius from a multi year study

illustration of bayesian inference in normal data models using gibbs sampling abstract the use of the gibbs sampler as a method for calculating bayesian marginal posterior and predictive densities is reviewed and illustrated with a range of normal data models including variance components unordered and ordered means hierarchical growth curves and missing data in a crossover trial in all cases the approach is straightforward to specify distributionally and to implement computationally with output readily adapted for required inference summaries

sur les groupes de transformations birationnelles des surfaces ni agissant par transformations bi rationnelles sur les surfaces complexes compactes kahl eriennes nous mon trons a que le groupe des transformations birationnelles d une surface satisfait l alternative de tits b que les actions birationnelles de groupes de kazhdan sur les surfaces sont toutes birationnellement conjugu eesa des actions homographiques sur le plan projectif et c que si f et g sont deux transformations birationnelles de surfaces qui commutent alors ou bien f pr eserve un pinceau de courbes ou bien l un des it er es g m de g m 0 concide avec un it er e f n de f n 2 z let s be any compact complex kahler surface and bir s the group of birational transformations of s we study the structure of nitely genera ted subgroups of bir s and prove three main results a bir s satises the tits alternative b if a group with kazhdan property t acts on a compact kahler surface by birational transformations then the action is conjugate to an action by linear projective transformations on the projec tive plane and c if f is an element of bir s which does not preserve any pencil of curves and if g commutes with f then a positive iterate of g coincides with an iterate of f the second statement provides a positive answer to zimmer s conjecture for birational actions on surfaces

imputation of missing categorical data by maximizing internal consistency this paper suggests a method to supplant missing categorical data by reasonable replacements these replacements will maximize the consistency of the completed data as measured by guttman s squared correlation ratio the text outlines a solution of the optimization problem describes relationships with the relevant psychometric theory and studies some properties of the method in detail the main result is that the average correlation should be at least 0 50 before the method becomes practical at that point the technique gives reasonable results up to 10 15 missing data

simulation of massive public health data by power polynomials situations in which multiple outcomes and predictors of different distributional types are collected are becoming increasingly common in public health practice and joint modeling of mixed types has been gaining popularity in recent years evaluation of various statistical techniques that have been developed for mixed data in simulated environments necessarily requires joint generation of multiple variables most massive public health data sets include different types of variables for instance in clustered or longitudinal designs often multiple variables are measured or observed for each individual or at each occasion this work is motivated by a need to jointly generate binary and possibly non normal continuous variables we illustrate the use of power polynomials to simulate multivariate mixed data on the basis of a real adolescent smoking study we believe that our proposed technique for simulating such intensive data has potential to be a handy methodological addition to public health researchers toolkit

on the reliability of n mixture models for count data n mixture models describe count data replicated in time and across sites in terms of abundance n and detectability p they are popular because they allow inference about n while controlling for factors that influence p without the need for marking animals using a capture recapture perspective we show that the loss of information that results from not marking animals is critical making reliable statistical modeling of n and p problematic using just count data one cannot reliably fit a model in which the detection probabilities are distinct among repeat visits as this model is overspecified this makes uncontrolled variation in p problematic by counter example we show that even if p is constant after adjusting for covariate effects the constant p assumption scientifically plausible alternative models in which n or its expectation is non identifiable or does not even exist as a parameter lead to data that are practically indistinguishable from data generated under an n mixture model this is particularly the case for sparse data as is commonly seen in applications we conclude that under the constant p assumption reliable inference is only possible for relative abundance in the absence of questionable and or untestable assumptions or with better quality data than seen in typical applications relative abundance models for counts can be readily fitted using poisson regression in standard software such as r and are sufficiently flexible to allow controlling for p through the use covariates while simultaneously modeling variation in relative abundance if users require estimates of absolute abundance they should collect auxiliary data that help with estimation of p

gaussianization based quasi imputation and expansion strategies for incomplete correlated binary responses new quasi imputation and expansion strategies for correlated binary responses are proposed by borrowing ideas from random number generation the core idea is to convert correlated binary outcomes to multivariate normal outcomes in a sensible way so that re conversion to the binary scale after performing multiple imputation yields the original specified marginal expectations and correlations this conversion process ensures that the correlations are transformed reasonably which in turn allows us to take advantage of well developed imputation techniques for gaussian outcomes we use the phrase quasi because the original observations are not guaranteed to be preserved we argue that if the inferential goals are well defined it is not necessary to strictly adhere to the established definition of multiple imputation our expansion scheme employs a similar strategy where imputation is used as an intermediate step it leads to proportionally inflated observed patterns forcing the data set to a complete rectangular format the plausibility of the proposed methodology is examined by applying it to a wide range of simulated data sets that reflect alternative assumptions on complete data populations and missing data mechanisms we also present an application using a data set from obesity research we conclude that the proposed method is a promising tool for handling incomplete longitudinal or clustered binary outcomes under ignorable non response mechanisms

an asymptotic approximation to the n mixture model for the estimation of disease prevalence n mixture models are probability models that estimate abundance using replicate observed counts while accounting for imperfect detection in this article we propose an asymptotic approximation to the n mixture model which efficiently estimates large abundances without the computational limitations of the generalized n mixture model introduced by dail and madsen in 2011 it has been suggested in the literature that n mixture models do not perform well when counts from the same sites show weak patterns of population dynamics our proposed model addresses this issue by using the asymptotic information matrix to diagnose model parameter estimability and to derive parameter standard errors a simulation study show that this model performs almost as well as the dail madsen generalized n mixture model at low abundances and improves on it at higher abundances we illustrate the procedure using two data sets the american robin data from dail and madsen 2011 and counts of chlamydia cases in the state of oregon from 2007 2016 the chlamydia data exhibit very large abundances and demonstrate the potential usefulness of the proposed model for disease surveillance data

multiple imputation under bayesianly smoothed pattern mixture models for non ignorable drop out conventional pattern mixture models can be highly sensitive to model misspecification in many longitudinal studies where the nature of the drop out and the form of the population model are unknown interval estimates from any single pattern mixture model may suffer from undercoverage because uncertainty about model misspecification is not taken into account in this article a new class of bayesian random coefficient pattern mixture models is developed to address potentially non ignorable drop out instead of imposing hard equality constraints to overcome inherent inestimability problems in pattern mixture models we propose to smooth the polynomial coefficient estimates across patterns using a hierarchical bayesian model that allows random variation across groups using real and simulated data we show that multiple imputation under a three level linear mixed effects model which accommodates a random level due to drop out groups can be an effective method to deal with non ignorable drop out by allowing model uncertainty to be incorporated into the imputation process

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

topologies and structures of the cremona groups we study the algebraic structure of the n dimensional cremona group and show that it is not an algebraic group of innite dimension ind group if n 2 we describe the obstruction to this which is of a topological nature by contrast we show the existence of a euclidean topology on the cremona group which extends that of its classical subgroups and makes it a topological group

dynamical degrees of birational transformations of projective surfaces the dynamical degree lambda f of a birational transformation f measures the exponential growth rate of the degree of the formulae that define the n th iterate of f we study the set of all dynamical degrees of all birational transformations of projective surfaces and the relationship between the value of lambda f and the structure of the conjugacy class of f for instance the set of all dynamical degrees of birational transformations of the complex projective plane is a closed and well ordered set of algebraic numbers

an imputation strategy for incomplete longitudinal ordinal data a new quasi imputation strategy for correlated ordinal responses is proposed by borrowing ideas from random number generation the essential idea is collapsing ordinal levels to binary ones and converting correlated binary outcomes to multivariate normal outcomes in a sensible way so that re conversion to the binary and then ordinal scale after conducting multiple imputation yields the original marginal distributions and correlations this conversion process ensures that the correlations are transformed reasonably which in turn allows us to take advantage of well developed imputation techniques for gaussian outcomes we use the phrase quasi because the original observations are not guaranteed to be preserved we present an application using a data set from psychiatric research we conclude that the proposed method may be a promising tool for handling incomplete longitudinal or clustered ordinal outcomes

on degenerations of plane cremona transformations this article studies the possible degenerations of cremona transformations of the plane of some degree into maps of smaller degree

an application of a mixed effects location scale model for analysis of ecological momentary assessment ema data for longitudinal data mixed models include random subject effects to indicate how subjects influence their responses over repeated assessments the error variance and the variance of the random effects are usually considered to be homogeneous these variance terms characterize the within subjects i e error variance and between subjects i e random effects variance variation in the data in studies using ecological momentary assessment ema up to 30 or 40 observations are often obtained for each subject and interest frequently centers around changes in the variances both within and between subjects in this article we focus on an adolescent smoking study using ema where interest is on characterizing changes in mood variation we describe how covariates can influence the mood variances and also extend the standard mixed model by adding a subject level random effect to the within subject variance specification this permits subjects to have influence on the mean or location and variability or square of the scale of their mood responses additionally we allow the location and scale random effects to be correlated these mixed effects location scale models have useful applications in many research areas where interest centers on the joint modeling of the mean and variance structure

computational aspects of n mixture models the n mixture model is widely used to estimate the abundance of a population in the presence of unknown detection probability from only a set of counts subject to spatial and temporal replication royle 2004 biometrics 60 105 115 we explain and exploit the equivalence of n mixture and multivariate poisson and negative binomial models which provides powerful new approaches for fitting these models we show that particularly when detection probability and the number of sampling occasions are small infinite estimates of abundance can arise we propose a sample covariance as a diagnostic for this event and demonstrate its good performance in the poisson case infinite estimates may be missed in practice due to numerical optimization procedures terminating at arbitrarily large values it is shown that the use of a bound k for an infinite summation in the n mixture likelihood can result in underestimation of abundance so that default values of k in computer packages should be avoided instead we propose a simple automatic way to choose k the methods are illustrated by analysis of data on hermann s tortoise testudo hermanni

maximum likelihood estimation of models for residual covariance in spatial regression we describe the maximum likelihood method for fitting the linear model when residuals are correlated and when the covariance among the residuals is determined by a parametric model containing unknown parameters observations are assumed to be gaussian we give conditions which ensure consistency and asymptotic normality of the estimators our main concern is with the analysis of spatial data and in this context we describe some simulation experiments to assess the small sample behaviour of estimators we also discuss an application of the spectral approximation to the likelihood for processes on a lattice

restoring definiteness via shrinking with an application to correlation matrices with a fixed block indefinite approximations of positive semidefinite matrices arise in various data analysis applications involving covariance matrices and correlation matrices we propose a method for restoring positive semidefiniteness of an indefinite matrix m 0 that constructs a convex linear combination s alpha alpha m 1 1 alpha m 0 of m 0 and a positive semidefinite target matrix m 1 in statistics this construction for improving an estimate m 0 by combining it with new information in m 1 is known as shrinking we make no statistical assumptions about m 0 and define the optimal shrinking parameter as alpha min alpha in 0 1 s alpha is positive semidefinite we describe three alg s for computing alpha one algorithm is based on the bisection method with the use of cholesky factorization to test definiteness a second employs newton s method and a third finds the smallest eigenvalue of a symmetric definite generalized eigenvalue problem we show that weights that r

on the variety of automorphisms of the affine plane abstract the main subject of our study is ga2 n the variety of automophisms of the affine plane of degree bounded by a positive integern after detailing some definitions and notations in section 1 we give in section 2 an algorithm to decide whether an endomorphism of the affine plane over an integral domain is a tame automorphism then by applying this algorithm to the nagata automorphism we recover easily its known results in section 6 we compute the number of irreducible components of ga2 nwhenn 9 and we show that ga2 nis reducible whenn 4 our proofs are based on a precise decomposition theorem for automorphisms given in section 3 and a characterization of length one automorphisms given in section 5 finally in section 7 we give some details on the casen 4

a family of multivariate binary distributions for simulating correlated binary variables with specified marginal means and correlations summary we introduce a family of multivariate binary distributions with certain conditional linear property this family is particularly useful for efficient and easy simulation of correlated binary variables with a given marginal mean vector and correlation matrix

n mixture models for estimating population size from spatially replicated counts spatial replication is a common theme in count surveys of animals such surveys often generate sparse count data from which it is difficult to estimate population size while formally accounting for detection probability in this article i describe a class of models n mixture models which allow for estimation of population size from such data the key idea is to view site specific population sizes n as independent random variables distributed according to some mixing distribution e g poisson prior parameters are estimated from the marginal likelihood of the data having integrated over the prior distribution for n carroll and lombard 1985 journal of american statistical association 80 423 426 proposed a class of estimators based on mixing over a prior distribution for detection probability their estimator can be applied in limited settings but is sensitive to prior parameter values that are fixed a priori spatial replication provides additional information regarding the parameters of the prior distribution on n that is exploited by the n mixture models and which leads to reasonable estimates of abundance from sparse data a simulation study demonstrates superior operating characteristics bias confidence interval coverage of the n mixture estimator compared to the caroll and lombard estimator both estimators are applied to point count data on six species of birds illustrating the sensitivity to choice of prior on p and substantially different estimates of abundance as a consequence

on the length of polynomial automorphisms of the affine plane the automorphism group of the affine plane is a mysterious and challenging object although we know that it is an amalgamated product of two well known subgroups many questions are still unsolved moreover the group has the structure of an infinite dimensional algebraic group but the interactions between these two structures are not yet clear in this paper we study the length of an element defined using the amalgamated structure with respect to the algebraic structure if the ground field is of characteristic zero we prove that the length is a lower semicontinuous function on the group