Multivariate Adaptive Splines for Analysis of Longitudinal Data

Abstract

An essential feature of longitudinal data is the existence of autocorrelation among the observations from the same unit or subject. Two-stage random-effects linear models are commonly used to analyze longitudinal data. These models are not flexible enough, however, for exploring the underlying data structures and, especially, for describing time trends. Semi-parametric models have been proposed recently to accommodate general time trends. But these semi-parametric models do not provide a convenient way to explore interactions among time and other covariates although such interactions exist in many applications. Moreover, semi-parametric models require specifying the design matrix of the covariates (time excluded). We propose nonparametric models to resolve these issues. To fit nonparametric models, we use the novel technique of the multivariate adaptive regression splines for the estimation of mean curve and then apply an EM-like iterative procedure for covariance estimation. After giving a general algorithm of model building, we show how to design a fast algorithm. We use both simulated and published data to illustrate the use of our proposed method.     

Mode Trees for Multivariate Data

We consider visualizing scales of multivariate density estimates with the help of mode trees. Mode trees visualize the locations of the modes of density estimates, when the smoothing parameter of the estimates ranges over an interval. We define multiframe mode graphs which generalize classical mode trees to the multivariate setting. We give examples of the application of multiframe mode graphs with kernel estimates and with multivariate adaptive histograms.     

多指标面板数据融合聚类分析

针对多指标面板数据的样品分类和历史时期划分问题,从多元统计分析理论角度提出一个多指标面板数据的融合聚类分析方法。该方法改进了多指标面板数据的因子分析和系统聚类方法,依据Fisher有序聚类理论,构造了Frobenius范数形式的离差平方和函数,提出了多指标面板数据的有序聚类方法。实证结果表明,该方法能够满足系统分析的统一性要求,保证指标之间的不相关;能够克服时间维度上均值处理造成的偏误,信息损失较少;能够解决面板数据有序聚类的问题;弥补了单一分析的片面性和局限性。     

Multivariate Percentile Tests for Incomplete Data

In this paper, we consider the percentile test procedures for multivariate and right censored data. Because of the involvement of censoring distribution into the distribution of the proposed test statistic, we study the asymptotic normality using the estimated covariance matrix. Finally, we derive the asymptotic relative efficiency and illustrate our procedures with an example.     

Regression Models for Multivariate Count Data

Data with multivariate count responses frequently occur in modern applications. The commonly used multinomial-logit model is limiting due to its restrictive mean-variance structure. For instance, analyzing count data from the recent RNA-seq technology by the multinomial-logit model leads to serious errors in hypothesis testing. The ubiquity of overdispersion and complicated correlation structures among multivariate counts calls for more flexible regression models. In this article, we study some generalized linear models that incorporate various correlation structures among the counts. Current literature lacks a treatment of these models, partly because they do not belong to the natural exponential family. We study the estimation, testing, and variable selection for these models in a unifying framework. The regression models are compared on both synthetic and real RNA-seq data. Supplementary materials for this article are available online.     

The Dynamical System Approach to Multivariate Data Analysis

In this survey a number of problems arising in multivariate data analysis (MDA) are listed and reformulated as matrix fitting (e.g., least-squares, maximum likelihood, etc.) constrained optimization problems (OPs). The goal is to demonstrate that consideration and solution of these diverse MDA problems can be unified by means of the dynamical system approach. The approach transforms the MDA problems into dynamical systems on a manifold defined by the constraints of the original OP.     

Nonparametric Bayesian Modeling for Multivariate Ordinal Data

This article proposes a probability model for k-dimensional ordinal outcomes, that is, it considers inference for data recorded in k-dimensional contingency tables with ordinal factors. The proposed approach is based on full posterior inference, assuming a flexible underlying prior probability model for the contingency table cell probabilities. We use a variation of the traditional multivariate probit model, with latent scores that determine the observed data. In our model, a mixture of normals prior replaces the usual single multivariate normal model for the latent variables. By augmenting the prior model to a mixture of normals we generalize inference in two important ways. First, we allow for varying local dependence structure across the contingency table. Second, inference in ordinal multivariate probit models is plagued by problems related to the choice and resampling of cutoffs defined for these latent variables. We show how the proposed mixture model approach entirely removes these problems. We illustrate the methodology with two examples, one simulated dataset and one dataset of interrater agreement.     

Reduced-Rank Regularized Multivariate Model for High-Dimensional Data

This article proposes a modeling framework for high-dimensional experimental data, such as brain images or microarrays, that discovers statistically significant structures most relevant to the experimental covariates. To deal with the curse of dimensionality, three regularization schemes are used: a reduced-rank model, penalization of the covariance matrix, and regularization of the basis-expanded predictor set. The latter allows us to flexibly model associations while controlling for overfitting. The modeling framework is derived from a reduced-rank multiresponse linear model, which offers a familiar interface for researchers. The novel regularizations of both sides of the model make it applicable in high-dimensional settings, without a need for prior dimension reduction, and can model nonlinear relationships. An efficient, dual-space algorithm is proposed to estimate its components in low-dimensional space. It permits the use of the bootstrap, to provide pointwise standard error bands on association graphs, and other resampling techniques to optimize hyperparameters. We evaluate the model on a small neuroimaging dataset, and in a simulation study using simple images corrupted by additive Gaussian iid and random field noise components with signal-to-noise ratios below 0.1. Our model compares well with a general linear model (GLM) even when the nonlinear associations are specified explicitly in GLM.     

季节性数据的横断面建模方法

本文提出了一种对季节性数据建立数学模型的新方法──横断面方法．其思想是，把一个季节性时间序列划分成为数相当于一个季节周期长度的若干个子序列，在这些子序列中已完全消除了季节性因素，然后对这些子序列分别建立形式各异的数学模型，最后再把这些子序列的数学模型综合起来就得到了对原始序列的数学模型．     

基于多元统计方法的居民健康体检数据危险因素分析

以邯郸市体检中心2014年居民的健康体检数据为依据,随机抽取了32281名居民的健康体检数据,分析了影响居民健康的危险因素,为有效的了解和掌握邯郸市居民健康状况提供帮助,为健康指导、健康干预策略的制定提供科学依据.     

多元模糊数据的假设检验方法

模糊假设检验对处理模糊概念进行决策分析是很重要的。本文给出了一个模糊多元数据的假设检验方法。因为数据是模糊的,不能在一个清晰的置信水平上接受或拒绝原假设,故本文提出了一个与结果相关联的可信度的概念。为了能应用清晰数据的假设检验,本文引入了模糊数的δ-截概念。     

装备多寿命指标变量现场数据的可靠性分析

在装备使用保障阶段,对于可由多个寿命指标衡量和控制的装备系统,其可靠性评估及维修保障策略制定都具有重要的工程应用价值.通过对飞机寿命指标不同形式的分析,建立了时间特征与使用特征寿命相关时装备系统多寿命指标变量联合可靠性评估模型,并通过实例对比研究,在评估方法的实用性和有效性等方面均有所改进,为装备多寿命指标变量现场可靠性评估提供了一种方法.     

多元比例响应数据的贝叶斯推断及其应用

多元比例响应数据具有有界性、归一性以及分量取值稀疏性等特点。本文在多项分布拟似然框架下基于贝叶斯方法研究多元比例数据的估计及其推断问题。通过引入Polya-Gamma分布的潜在变量,得到了易于后验抽样的Gibbs抽样算法。新方法具有估计稳健性、计算量小、推断效率高等特点,且不需要事先对响应数据作近似或变换。大量的数值模拟分析和两个实例分析验证了所提方法的有效性。     

MCMC Strategies for Computing Bayesian Predictive Densities for Censored Multivariate Data

Traditional criteria for comparing alternative Bayesian hierarchical models, such as cross-validation sums of squares, are inappropriate for nonstandard data structures. More flexible cross-validation criteria such as predictive densities facilitate effective evaluations across a broader range of data structures, but do so at the expense of introducing computational challenges. This article considers Markov chain Monte Carlo strategies for calculating Bayesian predictive densities for vector measurements subject to differential component-wise censoring. It discusses computational obstacles in Bayesian computations resulting from both the multivariate and incomplete nature of the data, and suggests two Monte Carlo approaches for implementing predictive density calculations. It illustrates the value of the proposed methods in the context of comparing alternative models for joint distributions of contaminant concentration measurements.     

Modeling and Exploring Multivariate Spatial Variation: A Test Procedure for Isotropy of Multivariate Spatial Data

In this paper an exploratory technique based on the diagonalization of cross-variogram matrices is described. Through the definition of a model for the analysis and simulation of multivariate spatial data, a test procedure for the assumption of isotropy of multivariate spatial data is proposed. Applications to simulated and real data are reported.     

Asymptotics on Semiparametric Analysis of Multivariate Failure Time Data Under the Additive Hazards Model

Many survival studies record the times to two or more distinct failures on each subject. The failures may be events of different natures or may be repetitions of the same kind of event. In this article, we consider the regression analysis of such multivariate failure time data under the additive hazards model. Simple weighted estimating functions for the regression parameters are proposed, and asymptotic distribution theory of the resulting estimators are derived. In addition, a class of generalized Wald and generalized score statistics for hypothesis testing and model selection are presented, and the asymptotic properties of these statistics are examined.     

Modelling Acid Deposition for Policy Analysis

The acid rain problem is just one amongst many complex environmental issues that are facing policy-makers today. Analytical advice normally takes the form of large and expensive studies, expressed in written reports. The availability of powerful dedicated and interactive computers opens the possibility for the analysis to be represented as an interactive computer program. The computer has considerable potential to improve the quality of the analysis available to a policy-maker.This paper will report on the construction of a decision aid on a powerful personal computer for the British Government, to study the acid deposition problem. As well as describing the technical issues involved in this model, the paper discusses the potential for this approach to policy analysis.