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Cognitive diagnosis models (CDMs) are an increasingly popular method to assess mastery or nonmastery of a set of fine-grained abilities in educational or psychological assessments. Several inference techniques are available to quantify the uncertainty of model parameter estimates, to compare different versions of CDMs, or to check model assumptions. However, they require a precise estimation of the standard errors (or the entire covariance matrix) of the model parameter estimates. In this article, it is shown analytically that the currently widely used form of calculation leads to underestimated standard errors because it only includes the item parameters but omits the parameters for the ability distribution. In a simulation study, we demonstrate that including those parameters in the computation of the covariance matrix consistently improves the quality of the standard errors. The practical importance of this finding is discussed and illustrated using a real data example.

A large literature on persistence finds that many modern outcomes strongly reflect characteristics of the same places in the distant past. These studies typically combine unusually high t statistics with severe spatial autocorrelation in residuals, suggesting that some findings may be artefacts of underestimating standard errors or of fitting spatial trends. For 25 studies in leading journals, I apply three basic robustness checks against spatial trends and find that effect sizes typically fall by over half, leaving most well known results insignificant at conventional levels. Turning to standard errors, there is currently no data-driven method for selecting an appropriate HAC spatial kernel. The paper proposes a simple procedure where a kernel with a highly flexible functional form is estimated by maximum likelihood. After correction, standard errors tend to rise substantially for cross sectional studies but to fall for panels. Overall, credible identification strategies tend to perform no better than naive regressions. Although the focus here is on historical persistence, the methods apply to regressions using spatial data more generally.

Kinetic mapping via mixture analysis[8], [10] involves comprehensive voxel-level analysis of dynamic PET data. Bootstrapping from the fitted mixture model gives the ability to directly simulate statistical copies of the 4-D PET data, and following suitable analysis, subsequent simulations of the associated kinetic maps. This gives the ability to numerically evaluate uncertainties in inferences associated with kinetic information. We provide a simple introduction to the concept of the model-based bootstrap and an illustration of the use of the approach for kinetic mapping from dynamic PET using results from recent work in Huang et al.[4]. The illustration is from a PET flow-metabolism imaging study in a breast cancer patient. It involves separate dynamic PET imaging following injections of O-15 H2O and F-18 FDG. The bootstrapped data is created in the image domain rather than the projection domain, so there is no reconstruction requirement involved.

When a scanner is installed and begins to be used operationally, its actual performance may deviate somewhat from the predictions made at the design stage. Thus it is recommended that routine quality assurance (QA) measurements be used to provide an operational understanding of scanning properties. While QA data are primarily used to evaluate sensitivity and bias patterns, there is a possibility to also make use of such data sets for a more refined understanding of the 3-D scanning properties. Building on some recent work on analysis of the distributional characteristics of iteratively reconstructed PET data, we construct an auto-regression model for analysis of the 3-D spatial auto-covariance structure of iteratively reconstructed data, after normalization. Appropriate likelihood-based statistical techniques for estimation of the auto-regression model coefficients are described. The fitted model leads to a simple process for approximate simulation of scanner performance—one that is readily implemented in an [Formula: see text] script. The analysis provides a practical mechanism for evaluating the operational error characteristics of iteratively reconstructed PET images. Simulation studies are used for validation. The approach is illustrated on QA data from an operational clinical scanner and numerical phantom data. We also demonstrate the potential for use of these techniques, as a form of model-based bootstrapping, to provide assessments of measurement uncertainties in variables derived from clinical FDG-PET scans. This is illustrated using data from a clinical scan in a lung cancer patient, after a 3-minute acquisition has been re-binned into three consecutive 1-minute time-frames. An uncertainty measure for the tumor SUV(max) value is obtained. The methodology is seen to be practical and could be a useful support for quantitative decision making based on PET data.

Background: The Chiang method is the most widely accepted standard for estimating life expectancy (LE) at subnational scales; it is the only method that provides an equation for the LE variance. However, the Chiang variance formula incorrectly omits the contribution of the last age interval. This error is largely unknown to practitioners, and its impact has not been rigorously assessed. Objective: We aim to demonstrate the potentially substantial role of the last age interval on LE variance. We further aim to provide formulae and tools for corrected variance estimation. Methods: The delta method is used to derive variance formulae for a range of variance models of the last age interval. Corrected variances are tested on 291 empirical, abridged life tables drawn from Canadian data (2004-2008) spanning provincial, regional, and intra-regional scales. Results: The last age interval death count can contribute substantially to the LE variance, leading to overestimates of precision and false positives in statistical tests when using the uncorrected Chiang variance. Overdispersion amplifies the contribution while error in population counts has minimal impact. Conclusions: Use of corrected variance formulae is essential for studies that use the Chiang LE. The important role of the last age interval , and hence the life table closure method, on LE variance is demonstrated. These findings extend to other LE-derived metrics such as health expectancy. Contribution: We demonstrate that the last age interval death count can contribute substantially to the LE variance, thus resolving an ambiguity in the scientific literature. We provide heretofore-unavailable formulae for correcting the Chiang LE variance equation.

Markov chain Monte Carlo (MCMC) algorithms are used to estimate features of interest of a distribution. The Monte Carlo error in estimation has an asymptotic normal distribution whose multivariate nature has so far been ignored in the MCMC community. We present a class of multivariate spectral variance estimators for the asymptotic covariance matrix in the Markov chain central limit theorem and provide conditions for strong consistency. We examine the finite sample properties of the multivariate spectral variance estimators and its eigenvalues in the context of a vector autoregressive process of order 1.

The question of the validity of procedures used to analyze forensic evidence was raised many years ago by Stephen Fienberg, most notably when he chaired the National Academy of Sciences’ Committee that issued the report The Polygraph and Lie Detection [National Research Council (2003) The National Academies Press]; his role in championing this cause and drawing other statisticians to these issues continued throughout his life. We investigate the validity of three standards related to different test methods for forensic comparison of glass (micro $X$-ray fluorescence ($\mu $-XRF) spectrometry, ICP-MS, LA-ICP-MS], all of which include a series of recommended calculations from which “it may be concluded that [the samples] did not originate from the same source.” Using publicly available data and data from other sources, we develop statistical models based on estimates of means and covariance matrices of the measured trace element concentrations recommended in these standards, leading to population-based estimates of error rates for the comparison procedures stated in the standards. Our results therefore do not depend on internal comparisons between pairs of glass samples, the representativeness of which cannot be guaranteed: our results apply to any collection of glass samples that have been or can be measured via these technologies. They suggest potentially higher false positive rates than have been reported, and we propose alternative methods that will ensure lower error rates.

Sample size determination is a fundamental step in the design of experiments. Methods for sample size determination are abundant for univariate analysis methods, but scarce in the multivariate case. Omics data are multivariate in nature and are commonly investigated using multivariate statistical methods, such as principal component analysis (PCA) and partial least-squares discriminant analysis (PLS-DA). No simple approaches to sample size determination exist for PCA and PLS-DA. In this paper we will introduce important concepts and offer strategies for (minimally) required sample size estimation when planning experiments to be analyzed using PCA and/or PLS-DA.

Penalized regression methods such as the lasso and elastic net (EN) have become popular for simultaneous variable selection and coefficient estimation. Implementation of these methods require selection of the penalty parameters. We propose an empirical Bayes (EB) methodology for selecting these tuning parameters as well as computation of the regularization path plots. The EB method does not suffer from the “double shrinkage problem” of frequentist EN. Also it avoids the difficulty of constructing an appropriate prior on the penalty parameters. The EB methodology is implemented by efficient importance sampling method based on multiple Gibbs sampler chains. Since the Markov chains underlying the Gibbs sampler are proved to be geometrically ergodic, Markov chain central limit theorem can be used to provide asymptotically valid confidence band for profiles of EN coefficients. The practical effectiveness of our method is illustrated by several simulation examples and two real life case studies. Although this article considers lasso and EN for brevity, the proposed EB method is general and can be used to select shrinkage parameters in other regularization methods.

For a general class of hidden Markov models that may include time-varying covariates, we illustrate how to compute the observed information matrix, which may be used to obtain standard errors for the parameter estimates and check model identifiability. The proposed method is based on the Oakes' identity and, as such, it allows for the exact computation of the information matrix on the basis of the output of the expectation-maximization (EM) algorithm for maximum likelihood estimation. In addition to this output, the method requires the first derivative of the posterior probabilities computed by the forward-backward recursions introduced by Baum and Welch. Alternative methods for computing exactly the observed information matrix require, instead, to differentiate twice the forward recursion used to compute the model likelihood, with a greater additional effort with respect to the EM algorithm. The proposed method is illustrated by a series of simulations and an application based on a longitudinal dataset in Health Economics.

When test forms are calibrated separately, item response theory parameters are not comparable because they are expressed on different measurement scales. The equating process includes the conversion of item parameter estimates on a common scale and the determination of comparable test scores. Various statistical methods have been proposed to perform equating between two test forms. This paper provides a generalization to multiple test forms of the mean-geometric mean, the mean-mean, the Haebara, and the Stocking–Lord methods. The proposed methods estimate simultaneously the equating coefficients that permit the scale transformation of the parameters of all forms to the scale of the base form. Asymptotic standard errors of the equating coefficients are derived. A simulation study is presented to illustrate the performance of the methods.

We study the design of two-level experiments with N runs and n factors large enough to estimate the interaction model, which contains all the main effects and all the two-factor interactions. Yet, an effect hierarchy assumption suggests that main effect estimation should be given more prominence than the estimation of two-factor interactions. Orthogonal arrays (OAs) favor main effect estimation. However, complete enumeration becomes infeasible for cases relevant for practitioners. We develop a partial enumeration procedure for these cases and we establish upper bounds on the D-efficiency for the interaction model based on arrays that have not been generated by the partial enumeration. We also propose an optimal design procedure that favors main effect estimation. Designs created with this procedure have smaller D-efficiencies for the interaction model than D-optimal designs, but standard errors for the main effects in this model are improved. Generated OAs for 7–10 factors and 32–72 runs are smaller or have a higher D-efficiency than the smallest OAs from the literature. Designs obtained with the new optimal design procedure or strength-3 OAs (which have main effects that are not correlated with two-factor interactions) are recommended if main effects unbiased by possible two-factor interactions are of primary interest. D-optimal designs are recommended if interactions are of primary interest. Supplementary materials for this article are available online. © 2017 American Statistical Association and the American Society for Quality.

Леса играют важную роль в снижении количества парниковых газов в атмосфере и предотвращении изменения климата. Одним из способов количественной оценки углеродного обмена в лесном покрове является определение изменений в запасах его фитомассы и углерода со временем. Запас фитомассы на единице площади начинается с определения его на уровне отдельных деревьев. Известно строгое и устойчивое аллометрическое соотношение между фитомассой дерева и его диаметром (простая аллометрия), или между фитомассой дерева и несколькими массообразующими (морфометрическими) показателями (многофакторная аллометрия). В настоящее время в разных странах и континентах проводятся интенсивные исследования применимости так называемых «всеобщих» аллометрических моделей (generic, generalized, common models), которые обеспечивали бы аллометрической модели приемлемую точность при оценке фитомассы насаждений. В статье на основе сформированной базы данных о фитомассе деревьев Picea в количестве 1065 определений построены аллометрические модели четырёх видов, включающие в себя фиктивные переменные, которые дают возможность дать региональные оценки их фитомассы по известным морфометрическим показателям (диаметр ствола и кроны, высота дерева). Предложенные аллометрические модели свидетельствуют об их адекватности фактическим данным (коэффициент детерминации от 0,959 до 0,984) и могут применяться при региональных оценках фитомассы деревьев ели. Однако всеобщие аллометрические модели, построенные по всему массиву фактических данных, дают в экорегионах слишком большие стандартные ошибки (до 402%) и неприемлемые смещения обоих знаков (от +311 до -86%), что исключает воз-можность их применения на региональных уровнях. Forests play an important role in reducing the amount of greenhouse gases in the atmosphere and preventing climate change. One way to quantify сarbon exchange in forest cover is estimating changes in its biomass and carbon pools over time. Biomass estimating on the unit of area starts with harvesting sample trees and weighing their biomass. It is known the strong and sustainable relationship between tree biomass and its diameter (simple allometry), or between tree biomass and a number of mass-forming (morphometric) indices (multi-factor allometry). At present, in different countries and continents, the studies of the applicability of the so-called generic (generalized, common) allometric models are intensified that would give acceptable accuracy in estimating forest biomass. In the article on the basis of the compiled database of tree biomass of Picea at a number of 1065 trees, allometric models of the four modifications are designed, which include the block of independent dummy variables. These models provide an opportunity to give regional estimates of tree biomass when using some known mass-forming indices (stem and crown diameter and tree height). Allometric models proposed are indicative of their adequacy for the actual data (coefficients of determination are 0,959 to 0,984) and can be applied in regional estimating of spruce tree biomass. However, generic allometric models built using the total quantity of actual data give in different ecoregions too large standard errors (up to 402%) and unacceptable both positive and negative biases (from + 311 to -86%), that excludes any possibility of their application at regional levels

На основе сформированной базы данных о биомассе деревьев двух- и пятихвойных сосен и пихт в количестве 1234 определений построены аллометрические модели четырёх структурных форм, включающие в себя фиктивные переменные, которые дают возможность дать региональные оценки их надземной биомассы по известным морфометрическим показателям (диаметр ствола и кроны, высота дерева). Предложенные аллометрические модели свидетельствуют об их адекватности фактическим данным с коэффициентом детерминации от 0,725 до 0,990 (исключение составила зависимость надземной биомассы от диаметра кроны пихты с коэффициентом детерминации 0,430) и могут применяться при региональных оценках биомассы деревьев трёх древесных пород. Однако всеобщие аллометрические модели, построенные по всему массиву фактических данных, дают в экорегионах слишком большие стандартные ошибки (до 572%) и неприемлемые смещения обоих знаков (от +315 до -92%), что исключает возможность их применения на региональных уровнях. Оn the basis of the compiled database of tree biomass of 2- or 5-needled pines and firs at a number of 1234 trees, allometric models of the four modifications are designed, which include the block of independent dummy variables. These models provide an opportunity to give regional estimates of tree above-ground biomass when using some known mass-forming indices (stem and crown diameter and tree height). Allometric models proposed are indicative of their adequacy for the actual data having the coefficients of determination between 0,725 and 0,990 (the only exception was the dependence of fir biomass upon crown diameter with a coefficient of determination 0,430) and can be applied in regional estimating above-ground biomass of the above-mentioned tree species. However, generic allometric models built using the total quantity of actual data give in different ecoregions too large standard errors (up to 572%) and unacceptable both positive and negative biases (from + 315 to -92%), that excludes any possibility of their application at regional levels.

The linear regression model is widely used in empirical work in Economics, Statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We give inference methods that allow for many covariates and heteroskedasticity. Our results are obtained using high-dimensional approximations, where the number of included covariates are allowed to grow as fast as the sample size. We find that all of the usual versions of Eicker-White heteroskedasticity consistent standard error estimators for linear models are inconsistent under this asymptotics. We then propose a new heteroskedasticity consistent standard error formula that is fully automatic and robust to both (conditional) heteroskedasticity of unknown form and the inclusion of possibly many covariates. We apply our findings to three settings: parametric linear models with many covariates, linear panel models with many fixed effects, and semiparametric semi-linear models with many technical regressors. Simulation evidence consistent with our theoretical results is also provided. The proposed methods are also illustrated with an empirical application.

Non-response in establishment surveys is a very important problem that can bias results of statistical analysis. The bias can be considerable when the survey data is used to do multivariate analysis that involve several variables with different response rates, which can reduce the effective sample size considerably. Fixing the non-response, however, could potentially cause other econometric problems. This paper uses an operational approach to analyze the sensitivity of results of multivariate analysis to multiple imputation procedures applied to the U.S. Census Bureau/NSF‘s Business Research and Development and Innovation Survey (BRDIS) to address item non-response. Multiple imputation is first applied using data from all survey units and periods for which there is data, presenting scenario 1. A scenario 2 involves separate imputation for units that have participated in the survey only once and those that repeat. Scenario 3 involves no imputation. Sensitivity analysis is done by comparing the model estimates and their standard errors, and measures of the additional uncertainty created by the imputation procedure. In all cases, unit non-response is addressed by using the adjusted weights that accompany BRDIS micro data. The results suggest that substantial benefit may be derived from multiple imputation, not only because it helps provide more accurate measures of the uncertainty due to item non-response but also because it provides alternative estimates of effect sizes and population totals.

Although the effects of insecurity are believed to be important, these have never been directly measured. Previous estimates of the costs of conflict have only captured the joint effect of violence and insecurity. The distinction is important for understanding the origins of the costs and for policy design. Spatially disaggregated measures of insecurity are created based on the spatial-temporal variation in the placement of violence. These are used to generate the first estimates of the relative causal contributions of the risk and experience of violence. The article also provides the first micro-data based counterpart to the cross-country literature on the costs of conflict.