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Conditional Distribution (conditional + distribution)
Selected AbstractsTime Series Concepts for Conditional Distributions*OXFORD BULLETIN OF ECONOMICS & STATISTICS, Issue 2003Clive W. J. Granger Abstract The paper asks the question , as time series analysis moves from consideration of conditional mean values and variances to unconditional distributions, do some of the familiar concepts devised for the first two moments continue to be helpful in the more general area? Most seem to generalize fairly easy, such as the concepts of breaks, seasonality, trends and regime switching. Forecasting is more difficult, as forecasts become distributions, as do forecast errors. Persistence can be defined and also common factors by using the idea of a copula. Aggregation is more difficult but causality and controllability can be defined. The study of the time series of quantiles becomes more relevant. [source] Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous RegressorsECONOMETRICA, Issue 4 2005Joseph G. Altonji We propose two new methods for estimating models with nonseparable errors and endogenous regressors. The first method estimates a local average response. One estimates the response of the conditional mean of the dependent variable to a change in the explanatory variable while conditioning on an external variable and then undoes the conditioning. The second method estimates the nonseparable function and the joint distribution of the observable and unobservable explanatory variables. An external variable is used to impose an equality restriction, at two points of support, on the conditional distribution of the unobservable random term given the regressor and the external variable. Our methods apply to cross sections, but our lead examples involve panel data cases in which the choice of the external variable is guided by the assumption that the distribution of the unobservable variables is exchangeable in the values of the endogenous variable for members of a group. [source] A Conditional Likelihood Ratio Test for Structural ModelsECONOMETRICA, Issue 4 2003Marcelo J. Moreira This paper develops a general method for constructing exactly similar tests based on the conditional distribution of nonpivotal statistics in a simultaneous equations model with normal errors and known reduced-form covariance matrix. These tests are shown to be similar under weak-instrument asymptotics when the reduced-form covariance matrix is estimated and the errors are non-normal. The conditional test based on the likelihood ratio statistic is particularly simple and has good power properties. Like the score test, it is optimal under the usual local-to-null asymptotics, but it has better power when identification is weak. [source] Is the Impact of Public Investment Neutral Across the Regional Income Distribution?ECONOMIC GEOGRAPHY, Issue 3 2005Evidence from Mexico Abstract: This article investigates the contribution of public investment to the reduction of regional inequalities, with a specific application to Mexico. We examine the impact of public investment according to the position of each region in the conditional distribution of regional income by using quantile regression as an empirical technique. The results confirm the hypothesis that regional inequalities can indeed be attributed to the regional distribution of public investment; the observed pattern shows that public investment mainly helped to reduce regional inequalities among the richest regions. [source] CEO Pay-For-Performance Heterogeneity Using Quantile RegressionFINANCIAL REVIEW, Issue 1 2010Kevin F. Hallock G3; J33; M52 Abstract We provide some examples of how quantile regression can be used to investigate heterogeneity in pay-firm size and pay-performance relationships for U.S. CEOs. For example, do conditionally (predicted) high-wage managers have a stronger relationship between pay and performance than conditionally low-wage managers? Our results using data over a decade show, for some standard specifications, there is considerable heterogeneity in the returns-to-firm performance across the conditional distribution of wages. Quantile regression adds substantially to our understanding of the pay-performance relationship. This heterogeneity is masked when using more standard empirical techniques. [source] A score test for non-nested hypotheses with applications to discrete data modelsJOURNAL OF APPLIED ECONOMETRICS, Issue 5 2001J. M. C. Santos Silva In this paper it is shown that a convenient score test against non-nested alternatives can be constructed from the linear combination of the likelihood functions of the competing models. This is essentially a test for the correct specification of the conditional distribution of the variable of interest. Given its characteristics, the proposed test is particularly attractive to check the distributional assumptions in models for discrete data. The usefulness of the test is illustrated with an application to models for recreational boating trips. Copyright © 2001 John Wiley & Sons, Ltd. [source] Comparing density forecast models,JOURNAL OF FORECASTING, Issue 3 2007Yong Bao Abstract In this paper we discuss how to compare various (possibly misspecified) density forecast models using the Kullback,Leibler information criterion (KLIC) of a candidate density forecast model with respect to the true density. The KLIC differential between a pair of competing models is the (predictive) log-likelihood ratio (LR) between the two models. Even though the true density is unknown, using the LR statistic amounts to comparing models with the KLIC as a loss function and thus enables us to assess which density forecast model can approximate the true density more closely. We also discuss how this KLIC is related to the KLIC based on the probability integral transform (PIT) in the framework of Diebold et al. (1998). While they are asymptotically equivalent, the PIT-based KLIC is best suited for evaluating the adequacy of each density forecast model and the original KLIC is best suited for comparing competing models. In an empirical study with the S&P500 and NASDAQ daily return series, we find strong evidence for rejecting the normal-GARCH benchmark model, in favor of the models that can capture skewness in the conditional distribution and asymmetry and long memory in the conditional variance.,,Copyright © 2007 John Wiley & Sons, Ltd. [source] Predicting future citation behaviorJOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE AND TECHNOLOGY, Issue 5 2003Quentin L. Burrell In this article we further develop the theory for a stochastic model for the citation process in the presence of obsolescence to predict the future citation pattern of individual papers in a collection. More precisely, we investigate the conditional distribution,and its mean,of the number of citations to a paper after time t, given the number of citations it has received up to time t. In an important parametric case it is shown that the expected number of future citations is a linear function of the current number, this being interpretable as an example of a success-breeds-success phenomenon. [source] A latent Markov model for detecting patterns of criminal activityJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES A (STATISTICS IN SOCIETY), Issue 1 2007Francesco Bartolucci Summary., The paper investigates the problem of determining patterns of criminal behaviour from official criminal histories, concentrating on the variety and type of offending convictions. The analysis is carried out on the basis of a multivariate latent Markov model which allows for discrete covariates affecting the initial and the transition probabilities of the latent process. We also show some simplifications which reduce the number of parameters substantially; we include a Rasch-like parameterization of the conditional distribution of the response variables given the latent process and a constraint of partial homogeneity of the latent Markov chain. For the maximum likelihood estimation of the model we outline an EM algorithm based on recursions known in the hidden Markov literature, which make the estimation feasible also when the number of time occasions is large. Through this model, we analyse the conviction histories of a cohort of offenders who were born in England and Wales in 1953. The final model identifies five latent classes and specifies common transition probabilities for males and females between 5-year age periods, but with different initial probabilities. [source] Exhaustive Structure Generation for Inverse-QSPR/QSARMOLECULAR INFORMATICS, Issue 1-2 2010Tomoyuki Miyao Abstract Chemical structure generation based on quantitative structure property relationship (QSPR) or quantitative structure activity relationship (QSAR) models is one of the central themes in the field of computer-aided molecular design. The objective of structure generation is to find promising molecules, which according to statistical models, are considered to have desired properties. In this paper, a new method is proposed for the exhaustive generation of chemical structures based on inverse-QSPR/QSAR. In this method, QSPR/QSAR models are constructed by multiple linear regression method, and then the conditional distribution of explanatory variables given the desired properties is estimated by inverse analysis of the models using the framework of a linear Gaussian model. Finally, chemical structures are exhaustively generated by a sophisticated algorithm that is based on a canonical construction path method. The usefulness of the proposed method is demonstrated using a dataset of the boiling points of acyclic hydrocarbons containing up to 12 carbon atoms. The QSPR model was constructed with 600 hydrocarbons and their boiling points. Using the proposed method, chemical structures which had boiling points of 100, 150, or 200,°C were exhaustively generated. [source] Under Performers and Over Achievers: A Quantile Regression Analysis of GrowthTHE ECONOMIC RECORD, Issue 248 2004Raul A. Barreto Numerous papers have searched for empirical linkages between long run economic growth and a myriad of economic, socio-political and environmental factors. Most of these studies use ordinary least-squares regression or panel regression analysis on a sample of countries and therefore consider the behaviour of growth around the mean of the conditional distribution. We extend the literature by using quantile regression to analyse long-term growth at a variety of points in the conditional distribution. By using this approach, we identify the determinants of growth for under performing countries relative to those for over achieving countries. [source] Optimal approximations of nonlinear payoffs in static replication,THE JOURNAL OF FUTURES MARKETS, Issue 11 2010Qiang Liu Static replication of nonlinear payoffs by line segments (or equivalently vanilla options) is an important hedging method, which unfortunately is only an approximation. If the strike prices of options are adjustable (for OTC options), two optimal approximations can be defined for replication by piecewise chords. The first is a naive minimum area approach, which seeks a set of strike prices to minimize the area enclosed by the payoff curve and the chords. The second improves on the first by taking the conditional distribution of the underlying into consideration, and minimizes the expected area instead. When the strike prices are fixed (for exchange-traded options), a third or the approach of least expected squares locates the minimum for the expected sum of squared differences between the payoff and the replicating portfolio, by varying the weights or quantities of the options used in the replication. For a payoff of variance swap, minimum expected area and least expected squares are found to produce the best numerical results in terms of cost of replication. Finally, piecewise tangents can also be utilized in static replication, which together with replication by chords, forms a pair of lower or upper bound to a nonlinear payoff. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark [source] The Distributional Heterogeneity of Growth Effects: Some EvidenceTHE MANCHESTER SCHOOL, Issue 4 2003Brendan M. Cunningham This paper applies quantile regression and non-parametric density estimation techniques to international data on long-run economic growth. The approach reveals that previously identified drivers of growth vary in their impact across the conditional distribution of international growth. Specifically, these factors display disparate effects in conditional low-growth and high-growth contexts. The results suggest that there is a general bias underlying prior research. The incumbent drivers of growth exhibit relatively larger coefficients, in absolute value, on the upper tail of the conditional growth distribution. This set of stylized facts identifies factors that might alter the international distribution of growth. [source] Vulnerability to Poverty in Papua New Guinea in 1996ASIAN ECONOMIC JOURNAL, Issue 3 2010Raghbendra Jha C21; C23; C26; I32 This paper uses cross-section data from the 1996 Papua New Guinea Household Survey to assess household vulnerability to poverty in Papua New Guinea. Vulnerability varies across regions, household size, gender and level of education of households. We use a simple empirical model that permits estimation of vulnerability to poverty assuming that households have the same conditional distribution of consumption in a stationary environment. Although this approach does not capture all dimensions of vulnerability, it at least raises the policy interest that vulnerability should be considered alongside poverty. [source] NONPARAMETRIC ESTIMATION OF CONDITIONAL CUMULATIVE HAZARDS FOR MISSING POPULATION MARKSAUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 1 2010Dipankar Bandyopadhyay Summary A new function for the competing risks model, the conditional cumulative hazard function, is introduced, from which the conditional distribution of failure times of individuals failing due to cause,j,can be studied. The standard Nelson,Aalen estimator is not appropriate in this setting, as population membership (mark) information may be missing for some individuals owing to random right-censoring. We propose the use of imputed population marks for the censored individuals through fractional risk sets. Some asymptotic properties, including uniform strong consistency, are established. We study the practical performance of this estimator through simulation studies and apply it to a real data set for illustration. [source] Ancestral Inference in Population Genetics Models with Selection (with Discussion)AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 4 2003Matthew Stephens Summary A new algorithm is presented for exact simulation from the conditional distribution of the genealogical history of a sample, given the composition of the sample, for population genetics models with general diploid selection. The method applies to the usual diffusion approximation of evolution at a single locus, in a randomly mating population of constant size, for mutation models in which the distribution of the type of a mutant does not depend on the type of the progenitor allele; this includes any model with only two alleles. The new method is applied to ancestral inference for the two-allele case, both with genic selection and heterozygote advantage and disadvantage, where one of the alleles is assumed to have resulted from a unique mutation event. The paper describes how the method could be used for inference when data are also available at neutral markers linked to the locus under selection. It also informally describes and constructs the non-neutral Fleming,Viot measure-valued diffusion. [source] Analysis of Misclassified Correlated Binary Data Using a Multivariate Probit Model when Covariates are Subject to Measurement ErrorBIOMETRICAL JOURNAL, Issue 3 2009Surupa Roy Abstract A multivariate probit model for correlated binary responses given the predictors of interest has been considered. Some of the responses are subject to classification errors and hence are not directly observable. Also measurements on some of the predictors are not available; instead the measurements on its surrogate are available. However, the conditional distribution of the unobservable predictors given the surrogate is completely specified. Models are proposed taking into account either or both of these sources of errors. Likelihood-based methodologies are proposed to fit these models. To ascertain the effect of ignoring classification errors and /or measurement error on the estimates of the regression and correlation parameters, a sensitivity study is carried out through simulation. Finally, the proposed methodology is illustrated through an example. [source] A Bayesian Semiparametric Survival Model with Longitudinal MarkersBIOMETRICS, Issue 2 2010Song Zhang Summary We consider inference for data from a clinical trial of treatments for metastatic prostate cancer. Patients joined the trial with diverse prior treatment histories. The resulting heterogeneous patient population gives rise to challenging statistical inference problems when trying to predict time to progression on different treatment arms. Inference is further complicated by the need to include a longitudinal marker as a covariate. To address these challenges, we develop a semiparametric model for joint inference of longitudinal data and an event time. The proposed approach includes the possibility of cure for some patients. The event time distribution is based on a nonparametric Pólya tree prior. For the longitudinal data we assume a mixed effects model. Incorporating a regression on covariates in a nonparametric event time model in general, and for a Pólya tree model in particular, is a challenging problem. We exploit the fact that the covariate itself is a random variable. We achieve an implementation of the desired regression by factoring the joint model for the event time and the longitudinal outcome into a marginal model for the event time and a regression of the longitudinal outcomes on the event time, i.e., we implicitly model the desired regression by modeling the reverse conditional distribution. [source] Bayesian Quantile Regression for Longitudinal Studies with Nonignorable Missing DataBIOMETRICS, Issue 1 2010Ying Yuan Summary We study quantile regression (QR) for longitudinal measurements with nonignorable intermittent missing data and dropout. Compared to conventional mean regression, quantile regression can characterize the entire conditional distribution of the outcome variable, and is more robust to outliers and misspecification of the error distribution. We account for the within-subject correlation by introducing a,,2,penalty in the usual QR check function to shrink the subject-specific intercepts and slopes toward the common population values. The informative missing data are assumed to be related to the longitudinal outcome process through the shared latent random effects. We assess the performance of the proposed method using simulation studies, and illustrate it with data from a pediatric AIDS clinical trial. [source] Uncovering a Latent Multinomial: Analysis of Mark,Recapture Data with MisidentificationBIOMETRICS, Issue 1 2010William A. Link Summary Natural tags based on DNA fingerprints or natural features of animals are now becoming very widely used in wildlife population biology. However, classic capture,recapture models do not allow for misidentification of animals which is a potentially very serious problem with natural tags. Statistical analysis of misidentification processes is extremely difficult using traditional likelihood methods but is easily handled using Bayesian methods. We present a general framework for Bayesian analysis of categorical data arising from a latent multinomial distribution. Although our work is motivated by a specific model for misidentification in closed population capture,recapture analyses, with crucial assumptions which may not always be appropriate, the methods we develop extend naturally to a variety of other models with similar structure. Suppose that observed frequencies,f,are a known linear transformation,f=A,x,of a latent multinomial variable,x,with cell probability vector,,=,(,). Given that full conditional distributions,[, | x],can be sampled, implementation of Gibbs sampling requires only that we can sample from the full conditional distribution,[x | f, ,], which is made possible by knowledge of the null space of A,. We illustrate the approach using two data sets with individual misidentification, one simulated, the other summarizing recapture data for salamanders based on natural marks. [source] A Semiparametric Joint Model for Longitudinal and Survival Data with Application to Hemodialysis StudyBIOMETRICS, Issue 3 2009Liang Li Summary In many longitudinal clinical studies, the level and progression rate of repeatedly measured biomarkers on each subject quantify the severity of the disease and that subject's susceptibility to progression of the disease. It is of scientific and clinical interest to relate such quantities to a later time-to-event clinical endpoint such as patient survival. This is usually done with a shared parameter model. In such models, the longitudinal biomarker data and the survival outcome of each subject are assumed to be conditionally independent given subject-level severity or susceptibility (also called frailty in statistical terms). In this article, we study the case where the conditional distribution of longitudinal data is modeled by a linear mixed-effect model, and the conditional distribution of the survival data is given by a Cox proportional hazard model. We allow unknown regression coefficients and time-dependent covariates in both models. The proposed estimators are maximizers of an exact correction to the joint log likelihood with the frailties eliminated as nuisance parameters, an idea that originated from correction of covariate measurement error in measurement error models. The corrected joint log likelihood is shown to be asymptotically concave and leads to consistent and asymptotically normal estimators. Unlike most published methods for joint modeling, the proposed estimation procedure does not rely on distributional assumptions of the frailties. The proposed method was studied in simulations and applied to a data set from the Hemodialysis Study. [source] Principal Stratification Designs to Estimate Input Data Missing Due to DeathBIOMETRICS, Issue 3 2007Constantine E. Frangakis Summary We consider studies of cohorts of individuals after a critical event, such as an injury, with the following characteristics. First, the studies are designed to measure "input" variables, which describe the period before the critical event, and to characterize the distribution of the input variables in the cohort. Second, the studies are designed to measure "output" variables, primarily mortality after the critical event, and to characterize the predictive (conditional) distribution of mortality given the input variables in the cohort. Such studies often possess the complication that the input data are missing for those who die shortly after the critical event because the data collection takes place after the event. Standard methods of dealing with the missing inputs, such as imputation or weighting methods based on an assumption of ignorable missingness, are known to be generally invalid when the missingness of inputs is nonignorable, that is, when the distribution of the inputs is different between those who die and those who live. To address this issue, we propose a novel design that obtains and uses information on an additional key variable,a treatment or externally controlled variable, which if set at its "effective" level, could have prevented the death of those who died. We show that the new design can be used to draw valid inferences for the marginal distribution of inputs in the entire cohort, and for the conditional distribution of mortality given the inputs, also in the entire cohort, even under nonignorable missingness. The crucial framework that we use is principal stratification based on the potential outcomes, here mortality under both levels of treatment. We also show using illustrative preliminary injury data that our approach can reveal results that are more reasonable than the results of standard methods, in relatively dramatic ways. Thus, our approach suggests that the routine collection of data on variables that could be used as possible treatments in such studies of inputs and mortality should become common. [source] A Censored Quantile Regression Analysis of Vegetable Demand: The Effects of Changes in Prices and Total ExpenditureCANADIAN JOURNAL OF AGRICULTURAL ECONOMICS, Issue 4 2006Geir Wæhler Gustavsen Many diseases are linked to dietary behavior. One major diet-related risk factor is a low consumption of vegetables. The consumption may be increased through public policies. The effects on vegetable purchases of either removing the value added tax on vegetables or a general income support are investigated. Adverse health effects are most serious in households consuming low quantities of vegetables. Therefore, the effects on high- and low-consuming households are estimated by using quantile regressions (QRs). Since many households did not purchase any vegetable during each survey period, censored as well as ordinary QRs are used. Our results suggest that the effects of the policy variables differ in different parts of the conditional distribution of vegetable purchases. None of the proposed policy options is likely to substantially increase vegetable purchases among low-consuming households. Bon nombre de maladies découlent des habitudes alimentaires. La faible consommation de légumes constitue un important facteur de risque liéà l'alimentation. Cette consommation pourrait être accrue par l'instauration de politiques gouvernementales. Nous avons examiné les effets de l'abolition de la taxe sur la valeur ajoutée ou d'un soutien du revenu sur les achats de légumes. Les effets néfastes sur la santé sont plus graves chez les ménages qui consomment de faibles quantités de légumes. Nous avons donc estimé les effets chez les ménages à forte et à faible consommation de légumes à l'aide de régressions par quantile. Comme de nombreux ménages n'ont pas acheté de légumes au cours des périodes sondées, nous avons utilisé des régressions par quantile censurées et des régressions par quantile ordinaires. Nos résultats ont indiqué que les effets des variables concernant les politiques diffèrent dans différentes parties de la distribution conditionnelle des achats de légumes. Aucune des options politiques proposées ne semble susceptible d'accroître substantiellement les achats de légumes chez les ménages qui en consomment peu. [source] Network bias in air quality monitoring designENVIRONMETRICS, Issue 7 2008Nicola Loperfido Abstract We develop a statistical model for the bias resulting from designing an air quality monitoring network with the aim of finding large values, and then using the data obtained in studies of health effects of air quality. Appropriate conditional distributions are shown to be well-known generalizations of the normal one. Theoretical results are applied to an ozone monitoring network in the state of Washington, USA. Copyright © 2008 John Wiley & Sons, Ltd. [source] Maximum entropy inference for mixed continuous-discrete variablesINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 4 2010Hermann Singer We represent knowledge by probability distributions of mixed continuous and discrete variables. From the joint distribution of all items, one can compute arbitrary conditional distributions, which may be used for prediction. However, in many cases only some marginal distributions, inverse probabilities, or moments are known. Under these conditions, a principle is needed to determine the full joint distribution of all variables. The principle of maximum entropy (Jaynes, Phys Rev 1957;106:620,630 and 1957;108:171,190; Jaynes, Probability Theory,The Logic of Science, Cambridge, UK: Cambridge University Press, 2003; Haken, Synergetics, Berlin: Springer-Verlag, 1977; Guiasu and Shenitzer, Math Intell 1985;117:83,106) ensures an unbiased estimation of the full multivariate relationships by using only known facts. For the case of discrete variables, the expert shell SPIRIT implements this approach (cf. Rödder, Artif Intell 2000;117:83,106; Rödder and Meyer, in Proceedings of the 12th Conference on Uncertainty in Artificial Intelligence, San Francisco, CA, 2006; Rödder et al., Logical J IGPL 2006;14(3):483,500). In this paper, the approach is generalized to continuous and mixed continuous-discrete distributions and applied to the problem of credit scoring. © 2010 Wiley Periodicals, Inc. [source] An efficient multivariate approach for estimating preference when individual observations are dependentJOURNAL OF ANIMAL ECOLOGY, Issue 5 2008Steinar Engen Summary 1We discuss aspects of resource selection based on observing a given vector of resource variables for different individuals at discrete time steps. A new technique for estimating preference of habitat characteristics, applicable when there are multiple individual observations, is proposed. 2We first show how to estimate preference on the population and individual level when only a single site- or resource component is observed. A variance component model based on normal scores in used to estimate mean preference for the population as well as the heterogeneity among individuals defined by the intra-class correlation. 3Next, a general technique is proposed for time series of observations of a vector with several components, correcting for the effect of correlations between these. The preference of each single component is analyzed under the assumption of arbitrarily complex selection of the other components. This approach is based on the theory for conditional distributions in the multi-normal model. 4The method is demonstrated using a data set of radio-tagged dispersing juvenile goshawks and their site characteristics, and can be used as a general tool in resource or habitat selection analysis. [source] Treating missing values in INAR(1) models: An application to syndromic surveillance dataJOURNAL OF TIME SERIES ANALYSIS, Issue 1 2010Jonas Andersson Time-series models for count data have found increased interest in recent years. The existing literature refers to the case of data that have been fully observed. In this article, methods for estimating the parameters of the first-order integer-valued autoregressive model in the presence of missing data are proposed. The first method maximizes a conditional likelihood constructed via the observed data based on the k -step-ahead conditional distributions to account for the gaps in the data. The second approach is based on an iterative scheme where missing values are imputed so as to update the estimated parameters. The first method is useful when the predictive distributions have simple forms. We derive in full details this approach when the innovations are assumed to follow a finite mixture of Poisson distributions. The second method is applicable when there are no closed form expression for the conditional likelihood or they are hard to derive. The proposed methods are applied to a dataset concerning syndromic surveillance during the Athens 2004 Olympic Games. [source] Uncovering a Latent Multinomial: Analysis of Mark,Recapture Data with MisidentificationBIOMETRICS, Issue 1 2010William A. Link Summary Natural tags based on DNA fingerprints or natural features of animals are now becoming very widely used in wildlife population biology. However, classic capture,recapture models do not allow for misidentification of animals which is a potentially very serious problem with natural tags. Statistical analysis of misidentification processes is extremely difficult using traditional likelihood methods but is easily handled using Bayesian methods. We present a general framework for Bayesian analysis of categorical data arising from a latent multinomial distribution. Although our work is motivated by a specific model for misidentification in closed population capture,recapture analyses, with crucial assumptions which may not always be appropriate, the methods we develop extend naturally to a variety of other models with similar structure. Suppose that observed frequencies,f,are a known linear transformation,f=A,x,of a latent multinomial variable,x,with cell probability vector,,=,(,). Given that full conditional distributions,[, | x],can be sampled, implementation of Gibbs sampling requires only that we can sample from the full conditional distribution,[x | f, ,], which is made possible by knowledge of the null space of A,. We illustrate the approach using two data sets with individual misidentification, one simulated, the other summarizing recapture data for salamanders based on natural marks. [source] Exploring Dependence with Data on Spatial LatticesBIOMETRICS, Issue 3 2009Mark S. Kaiser Summary The application of Markov random field models to problems involving spatial data on lattice systems requires decisions regarding a number of important aspects of model structure. Existing exploratory techniques appropriate for spatial data do not provide direct guidance to an investigator about these decisions. We introduce an exploratory quantity that is directly tied to the structure of Markov random field models based on one-parameter exponential family conditional distributions. This exploratory diagnostic is shown to be a meaningful statistic that can inform decisions involved in modeling spatial structure with statistical dependence terms. In this article, we develop the diagnostic, illustrate its use in guiding modeling decisions with simulated examples, and reexamine a previously published application. [source] Maximum Likelihood Methods for Nonignorable Missing Responses and Covariates in Random Effects ModelsBIOMETRICS, Issue 4 2003Amy L. Stubbendick Summary. This article analyzes quality of life (QOL) data from an Eastern Cooperative Oncology Group (ECOG) melanoma trial that compared treatment with ganglioside vaccination to treatment with high-dose interferon. The analysis of this data set is challenging due to several difficulties, namely, nonignorable missing longitudinal responses and baseline covariates. Hence, we propose a selection model for estimating parameters in the normal random effects model with nonignorable missing responses and covariates. Parameters are estimated via maximum likelihood using the Gibbs sampler and a Monte Carlo expectation maximization (EM) algorithm. Standard errors are calculated using the bootstrap. The method allows for nonmonotone patterns of missing data in both the response variable and the covariates. We model the missing data mechanism and the missing covariate distribution via a sequence of one-dimensional conditional distributions, allowing the missing covariates to be either categorical or continuous, as well as time-varying. We apply the proposed approach to the ECOG quality-of-life data and conduct a small simulation study evaluating the performance of the maximum likelihood estimates. Our results indicate that a patient treated with the vaccine has a higher QOL score on average at a given time point than a patient treated with high-dose interferon. [source] | |||||||||||||||||||