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Nowadays, the confidentiality of data and information is of great importance for many companies and organizations. For this reason, they may prefer not to release exact data, but instead to grant researchers access to approximate data. For example, rather than providing the exact measurements of their clients, they may only provide researchers with grouped data, that is, the number of clients falling in each of a set of non-overlapping measurement intervals. The challenge is to estimate the mean and variance structure of the hidden ungrouped data based on the observed grouped data. To tackle this problem, this work considers the exact observed data likelihood and applies the Expectation-Maximization (EM) and Monte Carlo EM (MCEM) algorithms for cases where the hidden data follow a univariate, bivariate, or multivariate normal distribution. Simulation studies are conducted to evaluate the performance of the proposed EM and MCEM algorithms. The well-known Galton data set is considered as an application example. [ABSTRACT FROM AUTHOR]

Generalized fused Lasso (GFL) is a powerful method based on adjacent relationships or the network structure of data. It is used in a number of research areas, including clustering, discrete smoothing, and spatio-temporal analysis. When applying GFL, the specific optimization method used is an important issue. In generalized linear models, efficient algorithms based on the coordinate descent method have been developed for trend filtering under the binomial and Poisson distributions. However, to apply GFL to other distributions, such as the negative binomial distribution, which is used to deal with overdispersion in the Poisson distribution, or the gamma and inverse Gaussian distributions, which are used for positive continuous data, an algorithm for each individual distribution must be developed. To unify GFL for distributions in the exponential family, this paper proposes a coordinate descent algorithm for generalized linear models. To illustrate the method, a real data example of spatio-temporal analysis is provided. [ABSTRACT FROM AUTHOR]

Numerous robust estimators exist as alternatives to the maximum likelihood estimator (MLE) when a completely observed ground-up loss severity sample dataset is available. However, the options for robust alternatives to a MLE become significantly limited when dealing with grouped loss severity data, with only a handful of methods, like least squares, minimum Hellinger distance, and optimal bounded influence function, available. This paper introduces a novel robust estimation technique, the Method of Truncated Moments (MTuM), pecifically designed to estimate the tail index of a Pareto distribution from grouped data. Inferential justification of the MTuM is established by employing the central limit theorem and validating it through a comprehensive simulation study. [ABSTRACT FROM AUTHOR]

We introduce a new command, summclust, that summarizes the cluster structure of the dataset for linear regression models with clustered disturbances. The key unit of observation for such a model is the cluster. We therefore propose cluster-level measures of leverage, partial leverage, and influence and show how to compute them quickly in most cases. The measures of leverage and partial leverage can be used as diagnostic tools to identify datasets and regression designs in which cluster–robust inference is likely to be challenging. The measures of influence can provide valuable information about how the results depend on the data in the various clusters. We also show how to calculate two jackknife variance matrix estimators efficiently as a by-product of our other computations. These estimators, which are already available in Stata, are generally more conservative than conventional variance matrix estimators. The summclust command computes all the quantities that we discuss. [ABSTRACT FROM AUTHOR]

The fluctuation experiment, devised by Luria and Delbrück in 1943, remains the method of choice for measuring microbial mutation rates in the laboratory. While most inference problems commonly encountered in a fluctuation experiment can be tackled by existing standard algorithms, investigators from time to time run into nonstandard problems not amenable to any existing algorithms. A major obstacle to solving these nonstandard problems is the construction of confidence intervals for mutation rates. This note describes methods for two important categories of nonstandard problems, namely, pooling data from separate experiments and analyzing grouped mutant count data, focusing on the construction of likelihood ratio confidence intervals. In addition to illustrative examples using real-world data, simulation results are presented to help assess the proposed methods. [ABSTRACT FROM AUTHOR]

Summary: We provide computationally attractive methods to obtain jackknife‐based cluster‐robust variance matrix estimators (CRVEs) for linear regression models estimated by least squares. We also propose several new variants of the wild cluster bootstrap, which involve these CRVEs, jackknife‐based bootstrap data‐generating processes, or both. Extensive simulation experiments suggest that the new methods can provide much more reliable inferences than existing ones in cases where the latter are not trustworthy, such as when the number of clusters is small and/or cluster sizes vary substantially. Three empirical examples illustrate the new methods. [ABSTRACT FROM AUTHOR]

Numerous robust estimators exist as alternatives to the maximum likelihood estimator (MLE) when a completely observed ground-up loss severity sample dataset is available. However, the options for robust alternatives to a MLE become significantly limited when dealing with grouped loss severity data, with only a handful of methods, like least squares, minimum Hellinger distance, and optimal bounded influence function, available. This paper introduces a novel robust estimation technique, the Method of Truncated Moments (MTuM), pecifically designed to estimate the tail index of a Pareto distribution from grouped data. Inferential justification of the MTuM is established by employing the central limit theorem and validating it through a comprehensive simulation study.

Damage from tornadoes imposes substantial costs on society. This study provides an analysis of time trends in the severity of losses from tornadoes in the United States for the period 1954–2018. Based on information provided by the Storm Prediction Centre (SPC) of the U.S. National Weather Service, we create a dataset of normalized losses from tornadoes spanning 65 years. We then analyse patterns and trends in the total annual losses from tornadoes as well as distributional properties of the damage from individual tornadoes. Our approach allows us to combine observations from the period 1954–1996, when losses from tornadoes were typically reported in a range (e.g. $500,000–$5,000,000) with observations from 1997 onwards when an actual estimate of the damage for an event is provided. Our findings suggest an overall national significant decline in normalized losses from tornado events. At the country level, both the severity of damage from individual events and the total annual losses from tornadoes are seen to have reduced over time. We also find spatial variations in time trends for the damage from tornadoes: while for most U.S. states the declining trend in severity is confirmed, an increasing trend of total annual losses from tornadoes is observed for Alabama.

Abstract Introduction Surveys are common research tools, and questionnaires revisions are a common occurrence in longitudinal studies. Revisions can, at times, introduce systematic shifts in measures of interest. We formulate that questionnaire revision are a stochastic process with transition matrices. Thus, revision shifts can be reduced by first estimating these transition matrices, which can be utilized in estimation of interested measures. Materials and method An ideal survey response model is defined by mapping between the true value of a participant’s response to an interval in the grouped data type scale. A population completed surveys multiple times, as modeled with multiple stochastic process. This included stochastic processes related to true values and intervals. While multiple factors contribute to changes in survey responses, here, we explored the method that can mitigate the effects of questionnaire revision. We proposed the Version Alignment Method (VAM), a data preprocessing tool, which can separate the transitions according to revisions from all transitions via solving an optimization problem and using the revision-related transitions to remove the revision effect. To verify VAM, we used simulation data to study the estimation error and a real life MJ dataset containing large amounts of long-term questionnaire responses with several questionnaire revisions to study its feasibility. Result We compared the difference of the annual average between consecutive years. Without adjustment, the difference is 0.593 when the revision occurred, while VAM brought it down to 0.115, where difference between years without revision was in the 0.005, 0.125 range. Furthermore, our method rendered the responses to the same set of intervals, thus comparing the relative frequency of items before and after revisions became possible. The average estimation error in L infinity was 0.0044 which occupied the 95% CI which was constructed by bootstrap analysis. Conclusion Questionnaire revisions can induce different response bias and information loss, thus causing inconsistencies in the estimated measures. Conventional methods can only partly remedy this issue. Our proposal, VAM, can estimate the aggregate difference of all revision-related systematic errors and can reduce the differences, thus reducing inconsistencies in the final estimations of longitudinal studies.

BackgroundTime- and dose-to-event phenotypes used in basic science and translational studies are commonly measured imprecisely or incompletely due to limitations of the experimental design or data collection schema. For example, drug-induced toxicities are not reported by the actual time or dose triggering the event, but rather are inferred from the cycle or dose to which the event is attributed. This exemplifies a prevalent type of imprecise measurement called grouped failure time, where times or doses are restricted to discrete increments. Failure to appropriately account for the grouped nature of the data, when present, may lead to biased analyses.ResultsWe present groupedSurv, an R package which implements a statistically rigorous and computationally efficient approach for conducting genome-wide analyses based on grouped failure time phenotypes. Our approach accommodates adjustments for baseline covariates, and analysis at the variant or gene level. We illustrate the statistical properties of the approach and computational performance of the package by simulation. We present the results of a reanalysis of a published genome-wide study to identify common germline variants associated with the risk of taxane-induced peripheral neuropathy in breast cancer patients.ConclusionsgroupedSurv enables fast and rigorous genome-wide analysis on the basis of grouped failure time phenotypes at the variant, gene or pathway level. The package is freely available under a public license through the Comprehensive R Archive Network.

Introduction: Surveys are common research tools, and questionnaires revisions are a common occurrence in longitudinal studies. Revisions can, at times, introduce systematic shifts in measures of interest. We formulate that questionnaire revision are a stochastic process with transition matrices. Thus, revision shifts can be reduced by first estimating these transition matrices, which can be utilized in estimation of interested measures. Materials and method: An ideal survey response model is defined by mapping between the true value of a participant's response to an interval in the grouped data type scale. A population completed surveys multiple times, as modeled with multiple stochastic process. This included stochastic processes related to true values and intervals. While multiple factors contribute to changes in survey responses, here, we explored the method that can mitigate the effects of questionnaire revision. We proposed the Version Alignment Method (VAM), a data preprocessing tool, which can separate the transitions according to revisions from all transitions via solving an optimization problem and using the revision-related transitions to remove the revision effect. To verify VAM, we used simulation data to study the estimation error and a real life MJ dataset containing large amounts of long-term questionnaire responses with several questionnaire revisions to study its feasibility. Result: We compared the difference of the annual average between consecutive years. Without adjustment, the difference is 0.593 when the revision occurred, while VAM brought it down to 0.115, where difference between years without revision was in the 0.005, 0.125 range. Furthermore, our method rendered the responses to the same set of intervals, thus comparing the relative frequency of items before and after revisions became possible. The average estimation error in L infinity was 0.0044 which occupied the 95% CI which was constructed by bootstrap analysis. Conclusion: Questionnaire revisions can induce different response bias and information loss, thus causing inconsistencies in the estimated measures. Conventional methods can only partly remedy this issue. Our proposal, VAM, can estimate the aggregate difference of all revision-related systematic errors and can reduce the differences, thus reducing inconsistencies in the final estimations of longitudinal studies. [ABSTRACT FROM AUTHOR]

A wide range of machine-learning-based approaches have been developed in the past decade, increasing our ability to accurately model nonlinear and nonadditive response surfaces. This has improved performance for inferential tasks such as estimating average treatment effects in situations where standard parametric models may not fit the data well. These methods have also shown promise for the related task of identifying heterogeneous treatment effects. However, the estimation of both overall and heterogeneous treatment effects can be hampered when data are structured within groups if we fail to correctly model the dependence between observations. Most machine learning methods do not readily accommodate such structure. This paper introduces a new algorithm, stan4bart, that combines the flexibility of Bayesian Additive Regression Trees (BART) for fitting nonlinear response surfaces with the computational and statistical efficiencies of using Stan for the parametric components of the model. We demonstrate how stan4bart can be used to estimate average, subgroup, and individual-level treatment effects with stronger performance than other flexible approaches that ignore the multilevel structure of the data as well as multilevel approaches that have strict parametric forms. [ABSTRACT FROM AUTHOR]

Plain language summary Time to age at first marriage of women is the duration of time until the age at which they started living with their first partner. African women are more likely to marry earlier than other continent women, which causes high fertility due to their long period of exposure to the risk of pregnancy. Even though Sub-Sahara Africa accounts for the highest rate of age at first marriage among countries in the Africa continent, comparably the case is very worse in Ethiopia. Furthermore, there is no study about the determinant of time to age at first marriage in Ethiopia using advanced models like Cox Model with Mixed effects. This model allows for the analysis of data with complex patterns of variability, with a focus on nested sources of variability. Very often it makes sense to use such a model to represent the variability within and between groups. For instance, in this study, our interest is not only knowing the significant effect of determinant factors on time to age at first marriage among women in Ethiopia but also the variability of time to age at first marriage within the region of Ethiopia and between regions of Ethiopia. We have used a dataset for this study from Ethiopia Demography and Health Survey which was conducted in 2016. The study helps to indicate relevant solutions for women's marriage-related problems (predominantly, women's reproductive health problems) in Ethiopia and it provides input for further studies in Ethiopia.

Objective: The aim of this study is to examine the effectiveness of linear mixed-effects (LME) model, one of the traditional models used in the classification of clustered data, and mixed-effects machine learning models, which are the latest approaches. Material and Methods: For the simulation, various data sets were created with different number of groups (250, 500, 1000) and different sample sizes (5000, 10000, 15000). Within the scope of the simulation, LME model, mixed-effects random forest (MERF) and Gaussian process boosting (GPBoost) models were compared in terms of root mean square error (RMSE) on two functions. Results: When the error variance (EV) is 4 for the linear function, sample size is small and the number of groups is high, RMSE of MERF model is smaller. In all other scenarios, RMSE of the linear model was smaller and. In cases where EV for the nonlinear function is 1, the sample size is small and the number of groups is high, RMSE of MERF is smaller. In all other scenarios (while EV was 1), RMSE of GPBoost model was small, p<0.05 for the difference with LME, and p>0.05 for MERF. In cases where EV is 4 for the nonlinear function and the sample size and groups is high, RMSE of MERF is smaller. In all other scenarios (while EV was 4), RMSE of GPBoost model was smaller. Conclusion: As a conclusion, for a nonlinear function, GPBoost performed better than MERF and LME methods in terms of RMSE and time. However, when a linear function is considered, LME gives a better result. [ABSTRACT FROM AUTHOR]

The paper provides a Bayesian alternative to transform the abridged age-specific fertility data into an unabridged one. A model suitable for a binary type of fertility data is considered for the study. The success probabilities of the considered model are assumed to vary in accordance with some established parametric age-specific fertility models. Bayes analysis is done using uniform priors for the unknown parameters of the considered models. Since the posterior analysis involves analytically intractable form of integrals, the paper employs the Gibbs sampler algorithm with intermediate Metropolis-Hastings steps to draw the corresponding posterior samples. Numerical illustration is provided using grouped age-specific fertility rate data. Finally, a few standard Bayesian model comparison tools are used in order to recommend an appropriate model for the data in hand, keeping in view the intended objectives. [ABSTRACT FROM AUTHOR]

Researchers often need to work with categorical income data. The typical nonparametric (including midpoint) and parametric estimation methods used to estimate summary statistics both have advantages, but they carry assumptions that cause them to deviate in important ways from real-world income distributions. The method introduced here, random empirical distribution imputation (REDI), imputes discrete observations using binned income data, while also calculating summary statistics. REDI achieves this through random cold-deck imputation from a real-world reference data set (demonstrated here using the Current Population Survey Annual Social and Economic Supplement). This method can be used to reconcile bins between data sets or across years and handle top incomes. REDI has other advantages for computing values of an income distribution that is nonparametric, bin consistent, area and variance preserving, continuous, and computationally fast. The author provides proof of concept using two years of the American Community Survey. The method is available as the redi command for Stata. [ABSTRACT FROM AUTHOR]

To understand how income inequality affects individuals and communities, researchers must have accurate measures of income inequality at lower geographic levels, such as counties, school districts, and census tracts. Studies of income inequality, however, are constrained by the tabular format in which censuses publish income data. In this article, the author proposes a new method, Lorenz interpolation, for estimating income inequality from binned income data. Using public microsample data from the American Community Survey (ACS), the author shows that Lorenz interpolation produces more accurate and reliable income inequality estimates than do alternative estimation methods. Then, using restricted ACS income data obtained through a Federal Statistical Research Data Center, the author evaluates the accuracy of Lorenz interpolation at the census tract and school district levels. Lorenz interpolation produces reliable school district–level estimates, but the method produces less reliable estimates for some income inequality measures at the tract level. These findings indicate that researchers should refrain from estimating tract-level income inequality measures from tabular data. They also show that aggregating tract income distributions to higher geographic levels can produce valid estimates of income inequality. [ABSTRACT FROM AUTHOR]

We examine the effects of monetary policy on income inequality in Japan. For that purpose, we use a novel Bayesian approach that jointly estimates the Gini coefficient from grouped income data and the dynamics of macroeconomic quantities. Our results indicate different effects on income inequality for different types of households: A monetary tightening decreases inequality when we consider a broad definition of household data that also includes the unemployed and retirees. Higher unemployment and tighter borrowing conditions make the richer (i.e., employed) comparably worse off. The result reverses, if we focus on the subsample of households whose head is employed. Through the same channels, inequality increases if monetary policy is tightened. A counterfactual analysis reveals that indeed the financial channel and the job destruction channel are the most important transmission mechanisms. [ABSTRACT FROM AUTHOR]

The paper argues that household budgets are the best starting point for investigating a number of big questions related to the evolution of the living standards during the last two-three centuries. if one knows where to look, historical family budgets are more abundant than might be suspected. and statistical techniques have been developed to handle the associated problems of small, incomplete, and unrepresentative samples. We introduce the Historical Household Budgets (HHB) Project, aimed at gathering data and sources, but also at creating an informational infrastructure that provides i) reliable storage and easy access to historical family budget data, along with ii) tools to configure the data as it is entered so as to harmonise it with present-day surveys. [ABSTRACT FROM AUTHOR]

Background: Time to age at first marriage of women is the duration of time until the age at which they started living with their first partner. Time to age at first marriage is widely considered a proxy indicator for the age at which women begin to be exposed to the risks inherent in sexual activity. The purpose is to model the determinant of time to age at first marriage among women in Ethiopia using Cox models with mixed effects. Methods: The 2016 Ethiopian Demography and Health survey sample was selected using a two-stage cluster design. The data set in this study were obtained from the Demography and Health survey conducted in Ethiopia in 2016. In this study, we used Cox models with mixed effects. Results: Of all 15,683 women aged 15–49 years, 11,405 (72.72%) were married with the median and mean age at first marriage 17 years and 18 years, respectively. Cox frailty survival model showed that residence, educational level, occupation, work status of women& head education level of households were the most significant factors whereas religion, access to media and wealth index of a household of women were not significant factors at 5% level of significance. The significant clustering effect showed that heterogeneity among the regions on age at first marriage was present. Conclusions: The present study determined the duration of time until the age at first marriage and indicated relevant solutions for marriage-related problems of women aged 15–49 years in Ethiopia. Women residing in rural area of Ethiopia and had lower education level were married earlier. Therefore, programs to reduce the high rate of early marriage in Ethiopia should give attention to women education and women residing in rural area. Plain language summary: Time to age at first marriage of women is the duration of time until the age at which they started living with their first partner. African women are more likely to marry earlier than other continent women, which causes high fertility due to their long period of exposure to the risk of pregnancy. Even though Sub-Sahara Africa accounts for the highest rate of age at first marriage among countries in the Africa continent, comparably the case is very worse in Ethiopia. Furthermore, there is no study about the determinant of time to age at first marriage in Ethiopia using advanced models like Cox Model with Mixed effects. This model allows for the analysis of data with complex patterns of variability, with a focus on nested sources of variability. Very often it makes sense to use such a model to represent the variability within and between groups. For instance, in this study, our interest is not only knowing the significant effect of determinant factors on time to age at first marriage among women in Ethiopia but also the variability of time to age at first marriage within the region of Ethiopia and between regions of Ethiopia. We have used a dataset for this study from Ethiopia Demography and Health Survey which was conducted in 2016. The study helps to indicate relevant solutions for women's marriage-related problems (predominantly, women's reproductive health problems) in Ethiopia and it provides input for further studies in Ethiopia. [ABSTRACT FROM AUTHOR]

When working with grouped data, investigators may choose between "fixed effects" models (FE) with specialized (e.g., cluster-robust) standard errors, or "multilevel models" (MLMs) employing "random effects." We review the claims given in published works regarding this choice, then clarify how these approaches work and compare by showing that: (i) random effects employed in MLMs are simply "regularized" fixed effects; (ii) unmodified MLMs are consequently susceptible to bias—but there is a longstanding remedy; and (iii) the "default" MLM standard errors rely on narrow assumptions that can lead to undercoverage in many settings. Our review of over 100 papers using MLM in political science, education, and sociology show that these "known" concerns have been widely ignored in practice. We describe how to debias MLM's coefficient estimates, and provide an option to more flexibly estimate their standard errors. Most illuminating, once MLMs are adjusted in these two ways the point estimate and standard error for the target coefficient are exactly equal to those of the analogous FE model with cluster-robust standard errors. For investigators working with observational data and who are interested only in inference on the target coefficient, either approach is equally appropriate and preferable to uncorrected MLM. [ABSTRACT FROM AUTHOR]

In medical and social science research, reliability of testing methods measured through inter‐ and intraobserver agreement is critical in disease diagnosis. Often comparison of agreement across multiple testing methods is sought in situations where testing is carried out on the same experimental units rendering the outcomes to be correlated. In this article, we first developed a Bayesian method for comparing dependent agreement measures under a grouped data setting. Simulation studies showed that the proposed methodology outperforms the competing methods in terms of power, while maintaining a decent type I error rate. We further developed a Bayesian joint model for comparing dependent agreement measures adjusting for subject and rater‐level heterogeneity. Simulation studies indicate that our model outperforms a competing method that is used in this context. The developed methodology was implemented on a key measure on a dichotomous rating scale from a study with six raters evaluating three classification methods for chest radiographs for pneumoconiosis developed by the International Labor Office. [ABSTRACT FROM AUTHOR]

For a given sample of grouped and ungrouped (raw) data, the maximum likelihood (ML) estimator is obtained using iterative algorithms such as Newton-Raphson (NR), which may not be converged always. Three-parameter Birnbaum-Saunders (BS) and Weibull distributions are frequently used in forestry and environmental sciences. In this study, we suggest using the expectation-maximization (EM) algorithm to estimate the parameters of BS and Weibull distributions when these models are fitted to grouped data. The EM algorithm is an iterative procedure that is used to obtain the ML estimator and always converges, whereas it is shown through simulation that the NR method may fail to converge. We demonstrate through three illustrations that the EM algorithm applied to the grouped data works efficiently. For the first illustration, the ML estimates of the grouped data exist and they are almost the same as the output of the EM algorithm. In the second and third real data examples that are of small sizes, the ML estimator does not exist for the ungrouped data but, we find it using the EM algorithm applied to the grouped data.

The demand for network visualization of relationships between nodes attributed to different categories grows in various biomedical research scenarios, such as gene regulatory networks, drug-target networks, ligand-receptor interactions and association networks of multi-omics elements. Elegantly visualizing the relationships between nodes with complex metadata of nodes and edges appended may inspire new insights. Here, we developed the crosslink R package, tailored for network visualization of grouped nodes, to provide a series of flexible functions for generating network diagrams. We first designed a CrossLink class for storage of metadata about nodes and edges and manipulation of node coordinates. Then affine transformation and function mapping transformation are implemented to perform fundamental node coordinates transformation by groups, based on which various network layouts can be defined easily. For convenience, we predefined several commonly used layouts, including row, column, arc, polygon and hive, which also can be combined in one layout. Finally, we designed a user-friendly wrapper function to draw network connections, aesthetic mappings of metadata and decoration with related annotation graphs in one interface by taking advantage of the powerful ggplot2 system. Overall, the crosslink R package is easy-to-use for achieving complex visualization of a network diagram of grouped nodes surrounded by associated annotation graphs.Availability and ImplementationCosslink is an open-source R package, freely available from github: https://github.com/zzwch/crosslink; A detailed user documentation can be found in https://zzwch.github.io/crosslink/.

The demand for network visualization of relationships between nodes attributed to different categories grows in various biomedical research scenarios, such as gene regulatory networks, drug-target networks, ligand-receptor interactions and association networks of multi-omics elements. Elegantly visualizing the relationships between nodes with complex metadata of nodes and edges appended may inspire new insights. Here, we developed the crosslink R package, tailored for network visualization of grouped nodes, to provide a series of flexible functions for generating network diagrams. We first designed a CrossLink class for storage of metadata about nodes and edges and manipulation of node coordinates. Then affine transformation and function mapping transformation are implemented to perform fundamental node coordinates transformation by groups, based on which various network layouts can be defined easily. For convenience, we predefined several commonly used layouts, including row, column, arc, polygon and hive, which also can be combined in one layout. Finally, we designed a user-friendly wrapper function to draw network connections, aesthetic mappings of metadata and decoration with related annotation graphs in one interface by taking advantage of the powerful ggplot2 system. Overall, the crosslink R package is easy-to-use for achieving complex visualization of a network diagram of grouped nodes surrounded by associated annotation graphs. Availability and Implementation: Cosslink is an open-source R package, freely available from github: https://github.com/zzwch/crosslink; A detailed user documentation can be found in https://zzwch.github.io/crosslink/. [ABSTRACT FROM AUTHOR]

Grouped data are frequently used in several fields of study. In this work, we use the expectation-maximization (EM) algorithm for fitting the skew-normal (SN) mixture model to the grouped data. Implementing the EM algorithm requires computing the one-dimensional integrals for each group or class. Our simulation study and real data analyses reveal that the EM algorithm not only always converges but also can be implemented in just a few seconds even when the number of components is large, contrary to the Bayesian paradigm that is computationally expensive. The accuracy of the EM algorithm and superiority of the SN mixture model over the traditional normal mixture model in modelling grouped data are demonstrated through the simulation and three real data illustrations. For implementing the EM algorithm, we use the package called ForestFit developed for R environment available at . [ABSTRACT FROM AUTHOR]

Abstract Background Time- and dose-to-event phenotypes used in basic science and translational studies are commonly measured imprecisely or incompletely due to limitations of the experimental design or data collection schema. For example, drug-induced toxicities are not reported by the actual time or dose triggering the event, but rather are inferred from the cycle or dose to which the event is attributed. This exemplifies a prevalent type of imprecise measurement called grouped failure time, where times or doses are restricted to discrete increments. Failure to appropriately account for the grouped nature of the data, when present, may lead to biased analyses. Results We present groupedSurv, an R package which implements a statistically rigorous and computationally efficient approach for conducting genome-wide analyses based on grouped failure time phenotypes. Our approach accommodates adjustments for baseline covariates, and analysis at the variant or gene level. We illustrate the statistical properties of the approach and computational performance of the package by simulation. We present the results of a reanalysis of a published genome-wide study to identify common germline variants associated with the risk of taxane-induced peripheral neuropathy in breast cancer patients. Conclusions groupedSurv enables fast and rigorous genome-wide analysis on the basis of grouped failure time phenotypes at the variant, gene or pathway level. The package is freely available under a public license through the Comprehensive R Archive Network.

We study two cluster-robust variance estimators (CRVEs) for regression models with clustering in two dimensions and give conditions under which t-statistics based on each of them yield asymptotically valid inferences. In particular, one of the CRVEs requires stronger assumptions about the nature of the intra-cluster correlations. We then propose several wild bootstrap procedures and state conditions under which they are asymptotically valid for each type of t-statistic. Extensive simulations suggest that using certain bootstrap procedures with one of the t-statistics generally performs very well. An empirical example confirms that bootstrap inferences can differ substantially from conventional ones. [ABSTRACT FROM AUTHOR]

The paper provides first generation estimates of poverty and inequality rates for three countries in Francophone Africa – Cameroon, Côte d'Ivoire, and Gabon – in the aftermath of independence. Sources – a large collection of historical household budgets – are new, as is the method that allows to connect historical sources to modern household budget surveys, and to deliver nationally representative estimates. The second part of the paper identifies the trend of poverty and inequality in Côte d'Ivoire for the years 1965 to 2015: mean income growth failed to reduce poverty during the 15 years of economic boom post-independence (1965–1979) because of increasing inequality. Conversely, in the following period (1979–2015) poverty changes are mostly guided by the evolution of growth. [ABSTRACT FROM AUTHOR]

This paper investigates the statistical analysis of grouped accelerated temperature cycling test data when the product lifetime follows a Weibull distribution. A log-linear acceleration equation is derived from the Coffin-Manson model. The problem is transformed to a constant-stress accelerated life test with grouped data and multiple acceleration variables. The Jeffreys prior and reference priors are derived. Maximum likelihood estimation and Bayesian estimation with objective priors are obtained by applying the technique of data augmentation. A simulation study shows that both of these two methods perform well when sample size is large, and the Bayesian method gives better performance under small sample sizes. [ABSTRACT FROM AUTHOR]

Virtual power plants (VPPs) of secondary distribution network have come into existence due to the installation of generators in the premises of domestic consumers and the recent legislative emphasis on net‐zero energy operation. A predetermined operation of VPP as required by a system operator is possible only when its power output is assessed beforehand. A simple approach for assessment based on load profiling using descriptive statistical parameters such as z‐scores of the load data is proposed in this study. The proposed method collates historical customer data according to seasons, days of the week and specified time‐intervals of the day. Then, z‐scores are computed for each of the historical load and generator data. The calculated z‐scores are subsequently grouped into specified clusters. The grouped data in each of the clusters are then employed to predict the VPP output. Demonstration of the assessment of VPP output using available Pecan street data is presented to validate the proposed approach. [ABSTRACT FROM AUTHOR]

The observed increase in economic inequality, where the major concern is relative to the huge growth of the highest incomes, motivates to revisit classical measures of inequality and to offer new ways to synthesize the variability of the entire income distribution. The idea is to provide policy makers a way to contrast the economic position of the group of the poorer p percent of the population and to compare their mean income to the one owned by the p percent of the richest. The new measure is still a Lorenz-based one, but the significant focus is based here in equally sized and opposite parts of the population whose difference is so remarkable nowadays. We then highlight the specific information given by the new inequality measure and curve, by comparing it to the widely employed Lorenz curve and Gini index and the more recent Zenga approach, and provide an application to Italian data on household income, wealth, and consumption along the years 1980–2012. The effects of estimating inequality indices and curves from grouped data are also discussed. [ABSTRACT FROM AUTHOR]

Researchers often estimate income statistics from summaries that report the number of incomes in bins such as $0 to 10,000, $10,001 to 20,000, ..., $200,000+. Some analysts assign incomes to bin midpoints, but this treats income as discrete. Other analysts fit a continuous parametric distribution, but the distribution may not fit well. We fit nonparametric continuous distributions that reproduce the bin counts perfectly by interpolating the cumulative distribution function (CDF). We also show how both midpoints and interpolated CDFs can be constrained to reproduce the mean of income when it is known. We evaluate the methods in estimating the Gini coefficients of all 3,221 U.S. counties. Fitting parametric distributions is very slow. Fitting interpolated CDFs is much faster and slightly more accurate. Both interpolated CDFs and midpoints give dramatically better estimates if constrained to match a known mean. We have implemented interpolated CDFs in the "binsmooth" package for R. We have implemented the midpoint method in the "rpme" command for Stata. Both implementations can be constrained to match a known mean.

In studies of clinical phenotypes, such as dementia, disability, and frailty, participants are typically assessed at in-person clinic visits. Thus, the precise time of onset for the phenotype is unknown. The discreteness of the clinic visits yields grouped event time data. We investigate how to perform a risk factor analysis in the case of grouped data. Since visits can be months to years apart, numbers of ties can be large, causing the exact tie-handling method of the Cox model to be computationally infeasible. We propose two, new, computationally efficient approximations to the exact method: Laplace approximation and an analytic approximation. Through extensive simulation studies, we compare these new methods to the Prentice-Gloeckler model and the Cox model using Efron's and Breslow's tie-handling methods. In addition, we compare the methods in an application to a large cohort study (N = 3,605) on the development of clinical frailty in older adults. In our simulations, the Laplace approximation has low bias in all settings, and the analytic approximation has low bias in settings where the regression coefficient is not large in magnitude. Their corresponding confidence intervals also have approximately the nominal coverage probability. In the data application, the results from the approximations are nearly identical to that of the Prentice-Gloeckler model. [ABSTRACT FROM AUTHOR]

Rate regulation plays an important role in the financial service of the auto insurance industry. Modelling the Size of Loss distributions, particularly the large loss distribution at the aggregate level, is a key component of rate regulation to produce a benchmark for the industry. However, traditionally actuarial practice is constructing the group-based Size of Loss with irregular intervals. The frequency values associated with each group are counted to form a frequency distribution. However, this approach is limited by lacking a parametric distribution that can capture the underlying randomness of the Size of Loss. In this work, we propose a de-grouping method based on the simulation of the uniform random variate, with and without constraint on knowing the average incurred loss per claim count. Using the de-grouping method, we simulate the individual observation based on the limited information available from the grouped Size of Loss. We have successfully identified the Exponentiated Weibull distribution as a good candidate as it outperforms other heavy-tailed distributions being considered. Our findings provide critical guidance and direction for the practical use of the proposed de-grouping method in auto insurance rate regulation practice and other fields in business and economics. [ABSTRACT FROM AUTHOR]