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用贝叶斯逻辑回归多重插补人口普查行业与职业编码AI 解读

We describe methods used to create a new Census data base that can be used to study comparability of industry and occupation classification systems. This project represents the most extensive application of multiple imputation to date, and the modeling effort was considerable as well—hundreds of logistic regressions were estimated. One goal of this article is to summarize the strategies used in the project so that researchers can better understand how the new data bases were…

通过多重插补对粗化数据推断：年龄堆积的应用AI 解读

Multiple imputation is applied to a demographic data set with coarse age measurements for Tanzanian children. The heaped ages are multiply imputed with plausible true ages using (a) a simple naive model and (b) a new, relatively complex model that relates true age to the observed values of heaped age, sex, and anthropometric variables. The imputed true ages are used to create valid inferences under the models and compare inferences across models, thereby revealing…

缺失数据的统计分析AI 解读

Preface.PART I: OVERVIEW AND BASIC APPROACHES.Introduction.Missing Data in Experiments.Complete-Case and Available-Case Analysis, Including Weighting Methods.Single Imputation Methods.Estimation of Imputation Uncertainty.PART II: LIKELIHOOD-BASED APPROACHES TO THE ANALYSIS OF MISSING DATA.Theory of Inference Based on the Likelihood Function.Methods Based on Factoring the Likelihood, Ignoring the Missing-Data Mechanism.Maximum Likelihood for General Patterns of Missing Data:…

可忽略无响应下简单随机样本的多重插补区间估计AI 解读

Several multiple imputation techniques are described for simple random samples with ignorable nonresponse on a scalar outcome variable. The methods are compared using both analytic and Monte Carlo results concerning coverages of the resulting intervals for the population mean. Using m = 2 imputations per missing value gives accurate coverages in common cases and is clearly superior to single imputation (m = 1) in all cases. The performances of the methods for various m can…

利用调整权重与多重插补的文件拼接进行统计匹配AI 解读

Statistically matched files are created in an attempt to solve the practical problem that exists when no single file has the full set of variables needed for drawing important inferences. Previous methods of file matching are reviewed, and the method of file concatenation with adjusted weights and multiple imputations is described and illustrated on an artificial example. A major benefit of this approach is the ability to display sensitivity of inference to untestable…

有限混合模型中的估计与假设检验AI 解读

SUMMARY Finite mixture models are a useful class of models for application to data. When sample sizes are not large and the number of underlying densities is in question, likelihood ratio tests based on joint maximum likelihood estimation of the mixing parameter, λ, and the parameter of the underlying densities, θ, are problematical. Our approach places a prior distribution on λ and estimates θ by maximizing the likelihood of the data given θ with λ integrated out.…

回归中的舍入误差：Sheppard 修正的适用性AI 解读

SUMMARY We consider three simple approaches to rounding error in least squares regression. The first treats the rounded data as if they were unrounded, the second adds an adjustment to the diagonal of the covariance matrix of the variables and the third subtracts an adjustment from the diagonal. The third, Sheppard's corrections, can be motivated as maximum likelihood with small rounding error and either (1) joint normal data or (2) normal residuals, “regular” independent…

倾向得分在观察性因果效应研究中的核心作用AI 解读

The propensity score is the conditional probability of assignment to a particular treatment given a vector of observed covariates. Both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates. Applications include: (i) matched sampling on the univariate propensity score, which is a generalization of discriminant matching, (ii) multivariate adjustment by subclassification on the propensity…

用 EM 算法求解结构化协方差矩阵的最大似然估计AI 解读

Some patterned covariance matrices used to model multivariate normal data that do not have explicit maximum likelihood estimates can be viewed as submatrices of larger patterned covariance matrices that do have explicit maximum likelihood estimates. In such cases, the smaller covariance matrix can be viewed as the covariance matrix for observed variables and the larger covariance matrix can be viewed as the covariance matrix for both observed and missing variables. The…

利用 EM 算法求结构化协方差矩阵的极大似然估计AI 解读

Some patterned covariance matrices used to model multivariate normal data that do not have explicit maximum likelihood estimates can be viewed as submatrices of larger patterned covariance matrices that do have explicit maximum likelihood estimates. In such cases, the smaller covariance matrix can be viewed as the covariance matrix for observed variables and the larger covariance matrix can be viewed as the covariance matrix for both observed and missing variables. The…

贝叶斯自助法AI 解读

The Bayesian bootstrap is the Bayesian analogue of the bootstrap. Instead of simulating the sampling distribution of a statistic estimating a parameter, the Bayesian bootstrap simulates the posterior distribution of the parameter; operationally and inferentially the methods are quite similar. Because both methods of drawing inferences are based on somewhat peculiar model assumptions and the resulting inferences are generally sensitive to these assumptions, neither method…

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利用多变量匹配抽样与回归调整控制观察性研究偏差AI 解读

Monte Carlo methods are used to study the efficacy of multivariate matched sampling and regression adjustment for controlling bias due to specific matching variables X when dependent variables are moderately nonlinear in X. The general conclusion is that nearest available Mahalanobis metric matching in combination with regression adjustment on matched pair differences is a highly effective plan for controlling bias due to X.

因果效应的贝叶斯推断：随机化的作用AI 解读

Causal effects are comparisons among values that would have been observed under all possible assignments of treatments to experimental units. In an experiment, one assignment of treatments is chosen and only the values under that assignment can be observed. Bayesian inference for causal effects follows from finding the predictive distribution of the values under the other assignments of treatments. This perspective makes clear the role of mechanisms that sample experimental…

缺失数据方差分析的非迭代最小二乘估计、标准误与 F 检验AI 解读

Summary This article generalizes Rubin's method of least squares estimation of missing values in an analysis of variance. The general method produces not only least squares estimates of all parameters and the residual mean square, but also the correct least squares standard error and t-test for each contrast as well as the least squares sum of squares and F-test for each collection of contrasts. The method is non-iterative and requires only those subroutines designed to…

回归解的可接受性：重新审视计算精度AI 解读

Longley [10] proposed a set of data for use in testing regression programs. This paper shows that the numerically accurate solution in this example was probably an unreasonable estimate of the regression coefficients. This is true because the accuracy of the data and appropriateness of the model may affect the solution more than the computational method. An easily computed index is derived that can be used to indicate such computational instability. The basic conclusion is…

推断与缺失数据AI 解读

When making sampling distribution inferences about the parameter of the data, θ, it is appropriate to ignore the process that causes missing data if the missing data are ‘missing at random’ and the observed data are ‘observed at random’, but these inferences are generally conditional on the observed pattern of missing data. When making direct-likelihood or Bayesian inferences about θ, it is appropriate to ignore the process that causes missing data if the missing data are…

使用估计权重组合独立估计量的方差AI 解读

Consider k independent unbiased estimators of a common parameter τ. Let t* be the linear combination of the k estimators with minimum variance, and let t∩ be any linear combination whose weights sum to unity and are independent of the k estimators. Then t∩ is unbiased for τ and the variance of t∩ depends only on the variance of t* and the mean squared error of the weights as estimates of the optimum weights.

使用估计权重组合独立估计量时的方差AI 解读

Consider k independent unbiased estimators of a common parameter τ. Let t* be the linear combination of the k estimators with minimum variance, and let t∩ be any linear combination whose weights sum to unity and are independent of the k estimators. Then t∩ is unbiased for τ and the variance of t∩ depends only on the variance of t* and the mean squared error of the weights as estimates of the optimum weights.

不完整数据问题中参数估计的结构刻画AI 解读

A framework is given for organizing and understanding the problems of estimating the parameters of a multivariate data set which contains blocks of missing observations. The basic technique is to decompose the original estimation problem into smaller estimation problems by factoring the likelihood of the observed data into a product of likelihoods. The result is summarized in a “factorization table,” which identifies the “complete-data” factors whose parameters may be…