泊松分布中参数的经典估计与Bayes估计的相等关系

文中证明了泊松分布中未知参数的矩估计和最大似然估计,一定存在一个先验分布,使其贝叶斯估计就是该经典估计的结论.     

略论矩阵逆的误差估计

借助矩阵范数和向量范数的概念,结合矩阵幂级数的有关结论 ,给出了矩阵逆的误差估计。     

Bayesian Inference and Application of Robust Growth Curve Models Using Student's t Distribution

Despite the widespread popularity of growth curve analysis, few studies have investigated robust growth curve models. In this article, the t distribution is applied to model heavy-tailed data and contaminated normal data with outliers for growth curve analysis. The derived robust growth curve models are estimated through Bayesian methods utilizing data augmentation and Gibbs sampling algorithms. The analysis of mathematical development data shows that the robust latent basis growth curve model better describes the mathematical growth trajectory than the corresponding normal growth curve model and can reveal the individual differences in mathematical development. Simulation studies further confirm that the robust growth curve models significantly outperform the normal growth curve models for both heavy-tailed t data and normal data with outliers but lose only slight efficiency for normal data. It appears convincing to replace the normal distribution with the t distribution for growth curve analysis. Three information criteria are evaluated for model selection. Online software is also provided for conducting robust analysis discussed in this study.     

Nonlongitudinal Estimation of Growth Curve Parameters: The Cohort Growth Model

The cohort growth model (CGM) is a method for estimating the parameters of a latent growth model (LGM) based on cross-sectional data. The CGM models the interindividual differences in the growth rate, and it models how subjects’ growth rate is related to their initial status. We derive model identification for the CGM and illustrate, in a simulation study, that the CGM provides unbiased parameter estimates in most simulation conditions. Based on empirical data we compare the estimates of the CGM with the estimates of the LGM. The results were comparable for both models. Although the estimates of the (co)-variances were different, the estimates of both models led to similar conclusions on the developmental change. Finally, we discuss the advantages and limitations of the CGM, and we provide recommendations for its use in empirical research.     

刻度平方误差损失下Pareto分布参数的E Bayes和多层Bayes估计

在对给定容量为n的一个Pareto分布样本X 1,X 2,…,Xn,在刻度平方误差损失函数下,利用先验分布讨论Pareto分布参数λ的E Bayes估计和多层Bayes估计.     

The Impact of Moderate Priors For Bayesian Estimation and Testing of Item Factor Analysis Models When Maximum Likelihood is Unsuitable

In psychological research, available data are often insufficient to estimate item factor analysis (IFA) models using traditional estimation methods, such as maximum likelihood (ML) or limited information estimators. Bayesian estimation with common-sense, moderately informative priors can greatly improve efficiency of parameter estimates and stabilize estimation. There are a variety of methods available to evaluate model fit in a Bayesian framework; however, past work investigating Bayesian model fit assessment for IFA models has assumed flat priors, which have no advantage over ML in limited data settings. In this paper, we evaluated the impact of moderately informative priors on ability to detect model misfit for several candidate indices: posterior predictive checks based on the observed score distribution, leave-one-out cross-validation, and widely available information criterion (WAIC). We found that although Bayesian estimation with moderately informative priors is an excellent aid for estimating challenging IFA models, methods for testing model fit in these circumstances are inadequate.     

增长曲线模型参数阵的唯一线性容许Minimax估计

对于一般增长曲线模型 ,在二次损失函数下分别找到了参数阵的线性可估函数在给定的齐次线性估计类和非齐次线性估计类中的容许Miniarx估计 ,并证明了这两种估计分别是唯一的     

复合LINEX对称损失下Lomax分布形状参数的Bayes估计

文章在复合LINEX对称损失函数下,研究Lomax分布尺度参数已知的情况下,形状参数的Bayes估计,并通过数值模拟来验证其合理性。     

生长曲线模型中回归系数阵的一类线性估计的优良性

设生长曲线模型为Yn×p=An×mBm×kCk×p＋En×p,E～N（0,σ^2In Ip）,当A^TA为病态时,令回归系数阵的最小二乘（LS）解和一类线性估计分别为B^=（A^TA）-A^TYC^T（CC^T）^-1和B^1（A^TA＋p∑）^-1A^TYC^T（CC^T）^-1,其中p〉0为常数,∑为正定阵,分别在A^TA和∑的可交换性未知和已知的情形下证明了在适当条件下B^1,在PC准则下优于B^,并将这一结论推广到A^TA和C^TC都是病态时的情况。     

矩阵之逆的推广及应用

本文在n阶方阵逆的基础上分析非方矩阵逆的存在性,并给出了计算公式和应用实例。     

On the Estimation of Nonlinear Mixed-Effects Models and Latent Curve Models for Longitudinal Data

Nonlinear models are effective tools for the analysis of longitudinal data. These models provide a flexible means for describing data that follow complex forms of change. Exponential and logistic functions that include a parameter to represent an asymptote, for instance, are useful for describing responses that tend to level off with time. There are forms of nonlinear latent curve models and nonlinear mixed-effects model that are equivalent, and so given the same set of data, growth function, distributional assumptions, and method of estimation, the 2 models yield equivalent results. There are also forms that are strikingly different and can yield different interpretations for a given set of data. This article discusses cases in which nonlinear mixed-effects models and nonlinear latent curve models are equivalent and those in which they are different and clarifies the estimation needs of the different models. Examples based on empirical data help to illustrate these points.     

线性约束下增长曲线模型中参数的线性估计的可容许性

利用矩阵的向量化方法,研究了带线性约束的增长曲线模型中可估函数的线性估计在非齐次线性估计类中可容许的充要条件。     

无失效数据下的参数及可靠度估计

对指数分布无失效数据的失效率,在先验分布为Gamma分布时,在引进失效信息后,给出了多层Bayes估计,并给出了可靠度的估计.     

非线性模型中无信息方差和协方差分量Bayes估计

采用Bayes方法从无先验信息出发,得到了非线性模型中方差和协方差分量的估计(包含相关系数),最后通过实例解算,结果表明:非线性模型中方差和协方差分量的估计,与ρ的理论值-0.5偏差不大,当没有先验信息时,该方法是可行的.     

多变量模型参数的贝叶斯估计及其在农业研究中的应用

对于农业研究中多变量线性模型参数的估计,以往常采用经典统计方法。随着计算机技术的进步,贝叶斯统计方法在科学研究的各个领域迅速发展。文章利用贝叶斯统计方法对农业研究中的多变量模型进行参数估计,并与经典统计方法进行比较,验证了贝叶斯方法的有效性。该方法可为农业研究中多变量模型参数的估计提供新的途径和手段。     

Application of Latent Growth Curve Analysis With Categorical Responses in Social Behavioral Research

Latent growth modeling allows social behavioral researchers to investigate within-person change and between-person differences in within-person change. Typically, conventional latent growth curve models are applied to continuous variables, where the residuals are assumed to be normally distributed, whereas categorical variables (i.e., binary and ordinal variables), which do not hold to normal distribution assumptions, have rarely been used. This article describes the latent growth curve model with categorical variables, and illustrates applications using Mplus software that are applicable to social behavioral research. The illustrations use marital instability data from the Iowa Youth and Family Project. We close with recommendations for the specification and parameterization of growth models that use both logit and probit link functions.     

A Comparison of One-Step and Three-Step Approaches for Including Covariates in the Shared Parameter Growth Mixture Model

The shared parameter growth mixture model (SPGMM) has been proposed as a method to handle missing not at random (MNAR) data in longitudinal studies. This Monte Carlo simulation study compared the one-step approach with a three-step approach for adding covariates into the SPGMM. The results showed that performances of one-step and three-step approaches did not differ, but the estimate of the coefficient of the covariate was biased in most conditions with MNAR data. However, means, variances, and covariance of the intercept and slope as well as their standard errors were estimated without bias in most conditions, except for some combinations of small class distances and MNAR dropout missingness that was not related to the underlying growth trajectory. Classification accuracy was similar with both one-step and three-step SPGMM.     

Sensitivity Analysis of the No-Omitted Confounder Assumption in Latent Growth Curve Mediation Models

Latent growth curve mediation models are increasingly used to assess mechanisms of behavior change. For latent growth mediation model, like any another mediation model, even with random treatment assignment, a critical but untestable assumption for valid and unbiased estimates of the indirect effects is that there should be no omitted variable that confounds indirect effects. One way to address this untestable assumption is to conduct sensitivity analysis to assess whether the inference about an indirect effect would change under varying degrees of confounding bias. We developed a sensitivity analysis technique for a latent growth curve mediation model. We compute the biasing effect of confounding on point and confidence interval estimates of the indirect effects in a structural equation modeling framework. We illustrate sensitivity plots to visualize the effects of confounding on each indirect effect and present an empirical example to illustrate the application of the sensitivity analysis.     

Fitting Structural Equation Model Trees and Latent Growth Curve Mixture Models in Longitudinal Designs: The Influence of Model Misspecification

When conducting longitudinal research, the investigation of between-individual differences in patterns of within-individual change can provide important insights. In this article, we use simulation methods to investigate the performance of a model-based exploratory data mining technique—structural equation model trees (SEM trees; Brandmaier, Oertzen, McArdle, & Lindenberger, 2013)—as a tool for detecting population heterogeneity. We use a latent-change score model as a data generation model and manipulate the precision of the information provided by a covariate about the true latent profile as well as other factors, including sample size, under the possible influences of model misspecifications. Simulation results show that, compared with latent growth curve mixture models, SEM trees might be very sensitive to model misspecification in estimating the number of classes. This can be attributed to the lower statistical power in identifying classes, resulting from smaller differences of parameters prescribed by the template model between classes.