Alvaro J. Flórez, I. Van Keilegom, G. Molenberghs, A. Verhasselt
{"title":"Quantile regression for longitudinal data via the multivariate generalized hyperbolic distribution","authors":"Alvaro J. Flórez, I. Van Keilegom, G. Molenberghs, A. Verhasselt","doi":"10.1177/1471082X211015454","DOIUrl":"https://doi.org/10.1177/1471082X211015454","url":null,"abstract":"While extensive research has been devoted to univariate quantile regression, this is considerably less the case for the multivariate (longitudinal) version, even though there are many potential applications, such as the joint examination of growth curves for two or more growth characteristics, such as body weight and length in infants. Quantile functions are easier to interpret for a population of curves than mean functions. While the connection between multivariate quantiles and the multivariate asymmetric Laplace distribution is known, it is less well known that its use for maximum likelihood estimation poses mathematical as well as computational challenges. Therefore, we study a broader family of multivariate generalized hyperbolic distributions, of which the multivariate asymmetric Laplace distribution is a limiting case. We offer an asymptotic treatment. Simulations and a data example supplement the modelling and theoretical considerations.","PeriodicalId":49476,"journal":{"name":"Statistical Modelling","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1177/1471082X211015454","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42336179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Interactively visualizing distributional regression models with distreg.vis","authors":"Stanislaus Stadlmann, T. Kneib","doi":"10.1177/1471082X211007308","DOIUrl":"https://doi.org/10.1177/1471082X211007308","url":null,"abstract":"A newly emerging field in statistics is distributional regression, where not only the mean but each parameter of a parametric response distribution can be modelled using a set of predictors. As an extension of generalized additive models, distributional regression utilizes the known link functions (log, logit, etc.), model terms (fixed, random, spatial, smooth, etc.) and available types of distributions but allows us to go well beyond the exponential family and to model potentially all distributional parameters. Due to this increase in model flexibility, the interpretation of covariate effects on the shape of the conditional response distribution, its moments and other features derived from this distribution is more challenging than with traditional mean-based methods. In particular, such quantities of interest often do not directly equate the modelled parameters but are rather a (potentially complex) combination of them. To ease the post-estimation model analysis, we propose a framework and subsequently feature an implementation in R for the visualization of Bayesian and frequentist distributional regression models fitted using the bamlss, gamlss and betareg R packages.","PeriodicalId":49476,"journal":{"name":"Statistical Modelling","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1177/1471082X211007308","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43253762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Kangjie Zhang, Juxin Liu, Yang Liu, Peng Zhang, R. Carroll
{"title":"Bayesian adjustment for measurement error in an offset variable in a Poisson regression model","authors":"Kangjie Zhang, Juxin Liu, Yang Liu, Peng Zhang, R. Carroll","doi":"10.1177/1471082X211008011","DOIUrl":"https://doi.org/10.1177/1471082X211008011","url":null,"abstract":"Fatal car crashes are the leading cause of death among teenagers in the USA. The Graduated Driver Licensing (GDL) programme is one effective policy for reducing the number of teen fatal car crashes. Our study focuses on the number of fatal car crashes in Michigan during 1990–2004 excluding 1997, when the GDL started. We use Poisson regression with spatially dependent random effects to model the county level teen car crash counts. We develop a measurement error model to account for the fact that the total teenage population in the county level is used as a proxy for the teenage driver population. To the best of our knowledge, there is no existing literature that considers adjustment for measurement error in an offset variable. Furthermore, limited work has addressed the measurement errors in the context of spatial data. In our modelling, a Berkson measurement error model with spatial random effects is applied to adjust for the error-prone offset variable in a Bayesian paradigm. The Bayesian Markov chain Monte Carlo (MCMC) sampling is implemented in rstan. To assess the consequence of adjusting for measurement error, we compared two models with and without adjustment for measurement error. We found the effect of a time indicator becomes less significant with the measurement-error adjustment. It leads to our conclusion that the reduced number of teen drivers can help explain, to some extent, the effectiveness of GDL.","PeriodicalId":49476,"journal":{"name":"Statistical Modelling","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1177/1471082X211008011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44696177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Mixed effect modelling and variable selection for quantile regression","authors":"H. Bar, J. Booth, M. Wells","doi":"10.1177/1471082X211033490","DOIUrl":"https://doi.org/10.1177/1471082X211033490","url":null,"abstract":"It is known that the estimating equations for quantile regression (QR) can be solved using an EM algorithm in which the M-step is computed via weighted least squares, with weights computed at the E-step as the expectation of independent generalized inverse-Gaussian variables. This fact is exploited here to extend QR to allow for random effects in the linear predictor. Convergence of the algorithm in this setting is established by showing that it is a generalized alternating minimization (GAM) procedure. Another modification of the EM algorithm also allows us to adapt a recently proposed method for variable selection in mean regression models to the QR setting. Simulations show that the resulting method significantly outperforms variable selection in QR models using the lasso penalty. Applications to real data include a frailty QR analysis of hospital stays, and variable selection for age at onset of lung cancer and for riboflavin production rate using high-dimensional gene expression arrays for prediction.","PeriodicalId":49476,"journal":{"name":"Statistical Modelling","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47055947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modelling changes over time in a multivariate paired comparison: An application to window display design","authors":"A. Grand, R. Dittrich","doi":"10.1177/1471082X21995675","DOIUrl":"https://doi.org/10.1177/1471082X21995675","url":null,"abstract":"This article proposes an alternative method of making comparative judgements in multivariate paired comparisons (PCs) where judgements about change are made directly by comparing an object at two time points for each of a series of attributes. The application deals with the design of shop window displays where products should be arranged by teams of vocational students according to aesthetic principles (attributes). The photos of the students’ window displays at time 1 (before feedback) and at time 2 (after feedback) were compared by judging each attribute as to whether it was fulfilled better at time 1 or at time 2. An advantage of this PC approach over an alternative of a scoring system is the possibility to assess even subtle changes of various aspects of attractiveness, which cannot easily be measured using a score. To analyse these data, we used earlier work which developed both a multivariate PC pattern model for multi-attribute data and a PC model over time and defined a multivariate PC model of changes (MPCC). The model can be fitted as a non-standard Poisson log-linear model and provides estimates of change for the three attributes for time 2 and we were able to check for possible interaction effects between these attributes.","PeriodicalId":49476,"journal":{"name":"Statistical Modelling","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1177/1471082X21995675","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42838067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Volkmann, Almond Stöcker, F. Scheipl, S. Greven
{"title":"Multivariate functional additive mixed models","authors":"A. Volkmann, Almond Stöcker, F. Scheipl, S. Greven","doi":"10.1177/1471082X211056158","DOIUrl":"https://doi.org/10.1177/1471082X211056158","url":null,"abstract":"Multivariate functional data can be intrinsically multivariate like movement trajectories in 2D or complementary such as precipitation, temperature and wind speeds over time at a given weather station. We propose a multivariate functional additive mixed model (multiFAMM) and show its application to both data situations using examples from sports science (movement trajectories of snooker players) and phonetic science (acoustic signals and articulation of consonants). The approach includes linear and nonlinear covariate effects and models the dependency structure between the dimensions of the responses using multivariate functional principal component analysis. Multivariate functional random intercepts capture both the auto-correlation within a given function and cross-correlations between the multivariate functional dimensions. They also allow us to model between-function correlations as induced by, for example, repeated measurements or crossed study designs. Modelling the dependency structure between the dimensions can generate additional insight into the properties of the multivariate functional process, improves the estimation of random effects, and yields corrected confidence bands for covariate effects. Extensive simulation studies indicate that a multivariate modelling approach is more parsimonious than fitting independent univariate models to the data while maintaining or improving model fit.","PeriodicalId":49476,"journal":{"name":"Statistical Modelling","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48199296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Semi-supervised clustering of time-dependent categorical sequences with application to discovering education-based life patterns","authors":"Yingying Zhang, Volodymyr Melnykov, Igor Melnykov","doi":"10.1177/1471082X21989170","DOIUrl":"https://doi.org/10.1177/1471082X21989170","url":null,"abstract":"A new approach to the analysis of heterogeneous categorical sequences is proposed. The first-order Markov model is employed in a finite mixture setting with initial state and transition probabilities being expressed as functions of time. The expectation–maximization algorithm approach to parameter estimation is implemented in the presence of positive equivalence constraints that determine which observations must be placed in the same class in the solution. The proposed model is applied to a dataset from the British Household Panel Survey to evaluate the association between the education background and life outcomes of study participants. The analysis of the survey data reveals many interesting relationships between the level of education and major life events.","PeriodicalId":49476,"journal":{"name":"Statistical Modelling","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1177/1471082X21989170","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49177583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Reflections on Murray Aitkin's contributions to nonparametric mixture models and Bayes factors","authors":"A. Agresti, F. Bartolucci, A. Mira","doi":"10.1177/1471082X20981312","DOIUrl":"https://doi.org/10.1177/1471082X20981312","url":null,"abstract":"We describe two interesting and innovative strands of Murray Aitkin's research publications, dealing with mixture models and with Bayesian inference. Of his considerable publications on mixture models, we focus on a nonparametric random effects approach in generalized linear mixed modelling, which has proven useful in a wide variety of applications. As an early proponent of ways of implementing the Bayesian paradigm, Aitkin proposed an alternative Bayes factor based on a posterior mean likelihood. We discuss these innovative approaches and some research lines motivated by them and also suggest future related methodological implementations.","PeriodicalId":49476,"journal":{"name":"Statistical Modelling","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1177/1471082X20981312","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44826179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Statistical ModellingPub Date : 2021-02-01Epub Date: 2020-07-27DOI: 10.1177/1471082x20933363
Fan Zhang, Ming-Hui Chen, Xiuyu Julie Cong, Qingxia Chen
{"title":"Assessing Importance of Biomarkers: a Bayesian Joint Modeling Approach of Longitudinal and Survival Data with Semicompeting Risks.","authors":"Fan Zhang, Ming-Hui Chen, Xiuyu Julie Cong, Qingxia Chen","doi":"10.1177/1471082x20933363","DOIUrl":"https://doi.org/10.1177/1471082x20933363","url":null,"abstract":"<p><p>Longitudinal biomarkers such as patient-reported outcomes (PROs) and quality of life (QOL) are routinely collected in cancer clinical trials or other studies. Joint modeling of PRO/QOL and survival data can provide a comparative assessment of patient-reported changes in specific symptoms or global measures that correspond to changes in survival. Motivated by a head and neck cancer clinical trial, we develop a class of trajectory-based models for longitudinal and survival data with disease progression. Specifically, we propose a class of mixed effects regression models for longitudinal measures, a cure rate model for the disease progression time (<i>T</i> <sub><i>P</i></sub> ), and a Cox proportional hazards model with time-varying covariates for the overall survival time (<i>T</i> <sub><i>D</i></sub> ) to account for <i>T</i> <sub><i>P</i></sub> and treatment switching. Under the semi-competing risks framework, the disease progression is the nonterminal event, the occurrence of which is subject to a terminal event of death. The properties of the proposed models are examined in detail. Within the Bayesian paradigm, we derive the decompositions of the deviance information criterion (DIC) and the logarithm of the pseudo marginal likelihood (LPML) to assess the fit of the longitudinal component of the model and the fit of each survival component, separately. We further develop ΔDIC as well as ΔLPML to determine the importance and contribution of the longitudinal data to the model fit of the <i>T</i> <sub><i>P</i></sub> and <i>T</i> <sub><i>D</i></sub> data.</p>","PeriodicalId":49476,"journal":{"name":"Statistical Modelling","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1177/1471082x20933363","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39258068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}