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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.

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 st...

This paper concerns linear models for grouped data with group‐specific effects. We construct a portmanteau test for the null of no within‐group correlation beyond that induced by the group‐specific effect. The approach allows for heteroskedasticity and is applicable to models with exogenous, predetermined, or endogenous regressors. The test can be implemented as soon as three observations per group are available and is applicable to unbalanced data. A test with such general applicability is not available elsewhere. We provide theoretical results on size and power under asymptotics where the number of groups grows but their size is held fixed. Extensive power comparisons with other tests available in the literature for special cases of our setup reveal that our test compares favorably. In a simulation study we find that, under heteroskedasticity, only our procedure yields a test that is both size correct and powerful. In a large data set on mothers with multiple births we find that infant birthweight is correlated across children even after controlling for mother fixed effects and a variety of prenatal care factors. This suggests that such a strategy may be inadequate to take care of all confounding factors that correlate with the mother's decision to engage in activities that are detrimental to the infant's health, such as smoking.

Inference using difference-in-differences with clustered data requires care. Previous research has shown that, when there are few treated clusters, t -tests based on cluster-robust variance estimators (CRVEs) severely overreject, and different variants of the wild cluster bootstrap can either overreject or underreject dramatically. We study two randomization inference (RI) procedures. A procedure based on estimated coefficients may be unreliable when clusters are heterogeneous. A procedure based on t -statistics typically performs better (although by no means perfectly) under the null, but at the cost of some power loss. An empirical example demonstrates that RI procedures can yield inferences that differ dramatically from those of other methods.

The primary objective of this paper is to introduce a new measure for detecting skewness for grouped data, which is simpler than the current measures in its application. The new proposed coefficient of skewness based on the cumulative frequency data and hence uses more information from the tails of the distribution and thus will be more appropriate to detect asymmetry in the data. Another advantage of the new statistic is that it is bounded by -1 and +1; hence, the coefficients of skewness can be interpreted easily. Simulation study is employed to assess the performance of the proposed coefficient of skewness with three of the classical measure of skewness appeared in the literature using the mean square error (MSE) and mean absolute error (MAE). The simulation study strongly supports the use of the proposed measure for comparing the degrees of skewness of different frequency distributions.

Background The payment card (PC) format and the open-ended (OE) format are common methods in eliciting willingness-to-pay (WTP) of one additional quality-adjusted life year (QALY). The aim of this research is to compare these two formats in eliciting the monetary value of a QALY. Methods A contingent valuation survey was carried out using a pre-designed questionnaire with various hypothetical scenarios. The difference between the PC and the OE formats was evaluated by a two-sample equality test. Furthermore, generalized linear models were carried out to control observed heterogeneity and to test theoretical validity. Results In total, 461 individuals were involved, among whom 235 (51%) answered the PC question, while 226 (49%) answered the OE question. Excluding zero response, the mean WTP values of these two formats for different scenarios varied dramatically, which was from 13,278 to 280,177 RMB for the PC, 18,119 to 620,913 RMB for the OE. The OE format tended to elicit lower values for less serious condition and higher values for more serious condition. However, equality test of mean and median demonstrated insignificant difference of these two formats for all scenarios. For both OE and PC format, most variables were found to have significant effect on the value of WTP/QALY. Moreover, joint estimation indicated a statistically significant positive effect on the OE results. Further analysis demonstrated that the imbalanced zero response distribution caused the main difference of these two formats. Conclusions This research indicated insignificantly different WTP/QALY estimates of the PC format and OE format with the grouped data whereas significantly higher estimates of the OE format from the pooled data. These two formats were found to be valid. More research about the difference and the validity of various WTP eliciting methods would be recommended for a robust estimation of WTP/QALY.

This letter deals with a very simple question: if we have grouped data with a binary-dependent variable and want to include fixed effects in the specification, can we meaningfully compare results using a linear model to those estimated with a logit? The reason to doubt such a comparison is that the linear specification appears to keep all observations, whereas the logit drops the groups where the dependent variable is either all zeros or all ones. This letter demonstrates that a linear specification averages the estimates for all the homogeneous outcome groups (which, by definition, all have slope coefficients of zero) with the slope coefficients for the groups with a mix of zeros and ones. The correct comparison of the linear to logit form is to only look at groups with some variation in the dependent variable. Researchers using the linear specification are urged to report results for all groups and for the subset of groups where the dependent variable varies. The interpretation of the difference between these two results depends upon assumptions which cannot be empirically assessed.

Piecewise-exponential excess-relative-risk (ERR) model is used for analysis of large cohort follow-up grouped data of exposure risk. Estimation method for the expected-acceleration-time (EAT) to fa...

The Lorenz curve, introduced more than 100 years ago, remains as one of the main tools for analysis of inequality. International institutions such as the World Bank collect and publish grou...

The M-estimators for distribution parameters under grouped data are defined. These estimators are compared in terms of asymptotic variance to MLE’s. We show that these estimators are the same as the MLE’s in the case of exponential families. Moreover, the obtained results are illustrated by examples jointly with simulation study.

For statistical evaluations that involve within-group and between-group variance components (denoted σ W 2 and σ B 2 , respectively), there is sometimes a need to monitor for a shift in the mean of time-ordered data. Uncertainty in the estimates σ ^ W 2 and σ ^ B 2 should be accounted for when setting alarm thresholds to check for a mean shift as both σ W 2 and σ B 2 must be estimated. One-way random effects analysis of variance (ANOVA) is the main tool for analysing such grouped data. Nearly all of the ANOVA applications assume that both the within-group and between-group components are normally distributed. However, depending on the application, the within-group and/or between-group probability distributions might not be well approximated by a normal distribution. This review paper uses the same example throughout to illustrate the possible approaches to setting alarm limits in grouped data, depending on what is assumed about the within-group and between-group probability distributions. The example involves measurement data, for which systematic errors are assumed to remain constant within a group, and to change between groups. The false alarm probability depends on the assumed measurement error model and its within-group and between-group error variances, which are estimated while using historical data, usually with ample within-group data, but with a small number of groups (three to 10 typically). This paper illustrates the parametric, semi-parametric, and non-parametric options to setting alarm thresholds in such grouped data.

We derive asymptotic properties of estimators and test statistics to determine—in a grouped data setting—common versus group‐specific factors. Despite the fact that our test statistic for the number of common factors, under the null, involves a parameter at the boundary (related to unit canonical correlations), we derive a parameter‐free asymptotic Gaussian distribution. We show how the group factor setting applies to mixed‐frequency data. As an empirical illustration, we address the question whether Industrial Production (IP) is still the dominant factor driving the U.S. economy using a mixed‐frequency data panel of IP and non‐IP sectors. We find that a single common factor explains 89% of IP output growth and 61% of total GDP growth despite the diminishing role of manufacturing.

The intraclass correlation plays a central role in modeling hierarchically structured data, such as educational data, panel data, or group-randomized trial data. It represents relevant information concerning the between-group and within-group variation. Methods for Bayesian hypothesis tests concerning the intraclass correlation are proposed to improve decision making in hierarchical data analysis and to assess the grouping effect across different group categories. Estimation and testing methods for the intraclass correlation coefficient are proposed under a marginal modeling framework where the random effects are integrated out. A class of stretched beta priors is proposed on the intraclass correlations, which is equivalent to shifted $F$ priors for the between groups variances. Through a parameter expansion it is shown that this prior is conditionally conjugate under the marginal model yielding efficient posterior computation. A special improper case results in accurate coverage rates of the credible intervals even for minimal sample size and when the true intraclass correlation equals zero. Bayes factor tests are proposed for testing multiple precise and order hypotheses on intraclass correlations. These tests can be used when prior information about the intraclass correlations is available or absent. For the noninformative case, a generalized fractional Bayes approach is developed. The method enables testing the presence and strength of grouped data structures without introducing random effects. The methodology is applied to a large-scale survey study on international mathematics achievement at fourth grade to test the heterogeneity in the clustering of students in schools across countries and assessment cycles.

Sampling within a given interval with a constraint has not been previously considered. Standard parametric simulation engines require knowledge of the parameters of the distribution from which a sa...

[PORTUGUESE ABSTRACT] Neste estudo, demonstramos como significância estatística pode variar a partir da comparação de quatro métodos distintos: teste t, ANOVA (seguida de Tukey HSD), modelo linear simples, e modelo linear de efeitos mistos. Em nossa demonstração, modelamos tempos de reação em função de diferentes afixos em dinamarquês, e mostramos como nossas conclusões a respeito do efeito de certos afixos podem mudar categoricamente dependendo de qual dos métodos mencionados acima decidimos utilizar. Por fim, reiteramos o que dizem estudos recentes, e sugerimos que modelos de efeitos mistos devam ser a norma sempre que dados agrupados forem analisados. Esperamos, com este estudo, alertar pesquisadores da área para a importância de decisões analíticas bem informadas e éticas em estudos linguísticos.[ENGLISH ABSTRACT] In this study, we illustrate the potential variability of statistical significance by comparing four different methods, namely, t-test, ANOVA (followed by Tukey HSD), simple linear regression, and mixed effects linear regression. In our demonstration, we model reaction times as a function of different affixes in Danish, and show how our conclusions regarding the effect of certain affixes can change categorically depending on which of the aforementioned methods we choose to use. Finally, we echo recent studies and suggest that mixed effects models be the norm whenever grouped data is analyzed. With our comparison, we hope to raise researchers’ awareness to the need for well-informed and ethical analytical decisions in linguistic studies.

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.

In this chapter, we will introduce the important measures of central tendency and dispersion under the neutrosophic statistics (NS). The measures are the extension of central tendency and dispersion under classical statistics (CS). The purpose of this chapter is to introduce the measures to analyze the data which has been measured under uncertain environments. We will focus on the basic ideas about these measures under the NS, neutrosophic arithmetic mean, neutrosophic geometric mean, neutrosophic harmonic mean, neutrosophic mode, neutrosophic median, the relationship between these measures and quantiles under the NS, neutrosophic range, neutrosophic variance, etc.

Frequency table of continuous quantitative data is arranged so that to describe the data better and convenience of numerical calculations. There are some difficulties to calculate the descriptive statistics of open-ended grouped data. Because the formulations of mean and standard deviation are based on midpoints, and midpoints are based on class intervals, it is necessary to know the lower-most and upper-most categories. In the previous studies, the interquartile, interdecile, interpercentile, and mid-distance ranges were used to estimate the unknown boundaries. This paper proposes four methods to estimate the population mean and standard deviation in open-ended group data. We conduct an extensive Monte Carlo simulation to compare these methods and the results are discussed over CO2 emission data., Verilerin daha iyi açıklanması ve hesaplamaların daha kolay olması amacıyla, sürekli nicel verilerin frekans tabloları düzenlenmektedir. Açık uçlu gruplanmış verinin tanımlayıcı istatistiklerini hesaplamada bazı zorluklar ortaya çıkmaktadır. Ortalama ve standart sapmanın formüllerinin sınıf değerlerine, sınıf değerlerinin de sınıf aralıklarına dayanmasından dolayı, ilk sınıfın alt ve son sınıfın üst sınır değerini bilmek gerekir. Önceki çalışmalarda, bilinmeyen sınırları tahmin etmek için çeyrekler, ondalıklar, yüzdeler ve sınıf ara değerleri arası aralıklar kullanılmıştır. Bu çalışmada, açık uçlu gruplanmış verilerinde kitle ortalaması ve standart sapmasını tahmin etmek amacıyla dört yöntem önerilmiştir. Bu yöntemleri karşılaştırmak amacıyla kapsamlı bir Monte Carlo benzetimi uygulanmış ve sonuçlar CO2 emisyon verileri üzerinden tartışılmıştır.

Poisson regression is a powerful tool for the analysis of incidence rates from cohort survival studies and facilitates simple, straightforward analyses of temporal patterns that may be difficult to assess with other methods. The Kaplan-Meier method, the logrank test, and the Cox model each have their respective parallels in grouped data analysis: instantaneous hazards, the hazard ratio for grouped data, and Poisson regression, grouped by intervals. This approach makes it possible to present the instantaneous speed of occurrence of events that may be more significant for clinicians and to consider more easily some constraints like parameters according to time (like time dependent variables or a time-dependent effect, neither of which are included in the conventional Cox model). However the application of Poisson regression requires that data on individual subjects be organized into event-time tables stratified by time and other factors of interest. This approach therefore requires the use of a large-scale database when small time intervals or many adjustment variables are necessary.

We propose a general framework for Maximum Likelihood (ML) and Bayesian estimation of income distributions based on grouped data information. The asymptotic properties of the ML estimators are derived and Bayesian parameter estimates are obtained by Monte Carlo Markov Chain (MCMC) techniques. A comprehensive simulation experiment shows that obtained estimates of the income distribution are very precise and that the proposed estimation framework improves the statistical precision of parameter estimates relative to the classical multinomial likelihood. The estimation approach is finally applied to a set of countries included in the World Bank database PovcalNet.

Weibull mixture models are widely used in a variety of fields for modeling phenomena caused by heterogeneous sources. We focus on circumstances in which original observations are not available, and...

Background: Mortality data at the population level are often aggregated in age classes, for example 5-year age groups with an open-ended interval for the elderly aged 85+. Capturing detailed age-specific mortality patterns and mortality time trends from such coarsely grouped data can be problematic at older ages, especially where open-ended intervals are used.Methods: We illustrate the penalized composite link model (PCLM) for ungrouping to model cancer mortality surfaces. Smooth age-specific distributions from data grouped in age classes of adjacent calendar years were estimated by constructing a two-dimensional regression, based on B-splines, and maximizing a penalized likelihood. We show the applicability of the proposed model, analysing age-at-death distributions from cancers of all sites in Denmark from 1980 to 2014. Data were retrieved from the Danish Cancer Society and the Human Mortality Database.Results: The main trends captured by PCLM are: (i) a decrease in cancer mortality rates after the 1990s for ages 50-75; (ii) a decrease in cancer mortality in later cohorts for young ages, especially, and very advanced ages. Comparing the raw data by single year of age, with the PCLM-ungrouped distributions, we clearly illustrate that the model fits the data with a high level of accuracy.Conclusions: The PCLM produces detailed smooth mortality surfaces from death counts observed in coarse age groups with modest assumptions, that is Poisson distributed counts and smoothness of the estimated distribution. Hence, the method has great potential for use within epidemiological research when information is to be gained from aggregated data, because it avoids strict assumptions about the actual distributional shape.

This study considers a method of estimating generalized beta (GB) distribution parameters based on grouped data from a Bayesian point of view and explores the possibility of the GB distribution focusing on the goodness-of-fit because the GB distribution is one of the most typical five-parameter distributions. It uses a tailored randomized block Metropolis–Hastings (TaRBMH) algorithm to estimate the GB distribution parameters and this method is then applied to one simulated and two real datasets. Moreover, the fit of the GB distribution is compared with those of the generalized beta distribution of the second kind (GB2 distribution) and Dagum (DA) distribution by using the marginal likelihood. The estimation results of simulated and real datasets show that the GB distributions are preferred to the DA distributions in general, while the GB2 distributions have similar performances to the GB distributions. In other words, the GB2 distribution could be adopted as well as the GB distribution in terms of the smallest possible number of parameters, although our TaRBMH algorithm can estimate the GB distribution parameters efficiently and accurately. The accuracy of the Gini coefficients also suggests the use of the GB2 distributions.

Researchers studying income inequality, economic segregation, and other subjects must often rely on grouped data—that is, data in which thousands or millions of observations have been reduced to counts of units by specified income brackets. The distribution of households within the brackets is unknown, and highest incomes are often included in an open-ended top bracket, such as “$200,000 and above.” Common approaches to this estimation problem include calculating midpoint estimators with an assumed Pareto distribution in the top bracket and fitting a flexible multiple-parameter distribution to the data. The authors describe a new method, mean-constrained integration over brackets (MCIB), that is far more accurate than those methods using only the bracket counts and the overall mean of the data. On the basis of an analysis of 297 metropolitan areas, MCIB produces estimates of the standard deviation, Gini coefficient, and Theil index that are correlated at 0.997, 0.998, and 0.991, respectively, with the parameters calculated from the underlying individual record data. Similar levels of accuracy are obtained for percentiles of the distribution and the shares of income by quintiles of the distribution. The technique can easily be extended to other distributional parameters and inequality statistics.

This paper presents a Bayesian approach, using differential evolution Markov chain method, to estimate the parameters of the failure time distribution and its percentiles based on grouped and non-grouped degradation data. The observed failure times are modeled by linear degradation path model with random degradation rates follow log-logistic distribution. Two Monte Carlo simulation studies are conducted. The first one is devoted to assess the performance of the proposed method with respect to the mean squared error (MSE) for different values of the scale and shape parameters of the degradation model using small, moderate and large sample sizes. The proposed method performs better when applied to non-grouped data compared with grouped data. The second simulation study is conducted to compare the proposed log-logistic model with a Weibull degradation model. More importantly, the log-logistic model outperforms the Weibull model. The proposed methods are demonstrated by modeling real life times of laser devices.

Grouped survival data arise often in studies where the disease status is assessed at regular visits to clinic. The time to the event of interest can only be determined to be between two adjacent visits or is right censored at one visit. In data analysis, replacing the survival time with the endpoint or midpoint of the grouping interval leads to biased estimators of the effect size in group comparisons. Prentice and Gloeckler developed a maximum likelihood estimator for the proportional hazards model with grouped survival data and the method has been widely applied. Previous work on sample size calculation for designing studies with grouped data is based on either the exponential distribution assumption or the approximation of variance under the alternative with variance under the null. Motivated by studies in HIV trials, cancer trials and in vitro experiments to study drug toxicity, we develop a sample size formula for studies with grouped survival endpoints that use the method of Prentice and Gloeckler for comparing two arms under the proportional hazards assumption. We do not impose any distributional assumptions, nor do we use any approximation of variance of the test statistic. The sample size formula only requires estimates of the hazard ratio and survival probabilities of the event time of interest and the censoring time at the endpoints of the grouping intervals for one of the two arms. The formula is shown to perform well in a simulation study and its application is illustrated in the three motivating examples.

SummaryInference based on cluster‐robust standard errors in linear regression models, using either the Student's t‐distribution or the wild cluster bootstrap, is known to fail when the number of treated clusters is very small. We propose a family of new procedures called the subcluster wild bootstrap, which includes the ordinary wild bootstrap as a limiting case. In the case of pure treatment models, where all observations within clusters are either treated or not, the latter procedure can work remarkably well. The key requirement is that all cluster sizes, regardless of treatment, should be similar. Unfortunately, the analogue of this requirement is not likely to hold for difference‐in‐differences regressions. Our theoretical results are supported by extensive simulations and an empirical example.

This short note supplements the paper by Glschossl et al. (Eur Actuar J 1:23–41, 2011) with an efficient method allowing actuaries to include continuous covariates in their life tables, such as the sum insured for instance. Compared to the classical approach based on grouped data adopted in the majority of actuarial mortality studies, individual observations recorded at the policy level are included in the Poisson regression model. The proposed procedure avoids any preliminary, subjective banding of the range of continuous covariates that may bias the resulting life tables. The approach is illustrated on a numerical example demonstrating its advantages when individual mortality data are available.

Taylor’s power law (TPL) can be applied to the mean-variance relationship for various quantities, e.g., population densities over space and time, biomass of plants in the growth processes, developmental rates and growth rates of arthropods at different temperatures, etc. When TPL holds in the grouped data (e.g., the biomass of plants at different investigation times with limited replicates at each investigation), we must consider the heterocedasticity when carrying out the parameter estimation for a given mathematical model. We propose two new target functions based on TPL and attempt to more accurately estimate the model parameter(s). By capturing the mean-variance relationship, the accuracy of parameter estimation and the power of hypothesis testing are improved compared to the traditional methods which assume homogeneous variance. Five approaches, including ordinary least squares (OLS), chi-squared (χ2), weighted least squares (WLS), psi-squared (ψ2) and maximum likelihood estimation (MLE), are compared under both linear and nonlinear scenarios regarding the prediction accuracy using both computer simulations and experimental data. We further simulate irregular measurements on the predictors to examine the robustness of parameter estimation. In computer simulations, psi-squared, WLS, and MLE outperform OLS and chi-squared with respect to parameter estimation. In the simulation study of irregular measurements, psi-squared and MLE outperform WLS when the sample mean is smaller than the population mean. On the other hand, WLS outperforms psi-squared and MLE when the sample mean is larger than the population mean. Psi-squared has an advantage over MLE when large irregular deviations are present. This study strongly suggests using psi-squared and WLS in place of OLS or chi-squared for both linear and nonlinear regressions, the choice of method depending on the observations.

Introduction The proportion of cancer patients cured of the disease is estimated with standard cure models assuming they have the same risk of death as the general population [1] . These patients, however often maintain an extra risk of dying compared to the overall population, which we assume is due to other causes than cancer [2] . The aim of the work was to develop and validate an extended cure model incorporating the estimated patients’ relative risk of death from other causes (α) compared to that observed in the general population. Methods We extended the mixture cure model considering Weibull relative survival of the uncured by including a relative risk αwhich muliptlies the mortality observed in the general population. The parameters were estimated using maximum likelihood method for individual data and unweighted least square for grouped data. The extended model was evaluated through a simulation study of the performance and robustness. The validity of parameters estimated by both the standard and the extended cure models was evaluated on a set of simulations based on scenarios mirroring the behavior of lung and breast cancer from real data with 1000 samples of different sizes (500–20,000 cases each), with different values of α, with different length of follow-up, with set-ups where all the assumptions are verified or where some of them are not verified (survival of uncured patients does not follow a Weibull distribution; extra non-cancer death risk is dependent of age at diagnosis or randomly varies across patients). The models were also applied to real data: colon cancer data from the FRANCIM common database. Results When the assumptions were satisfied, the extended cure models correctly estimated the parameters and their standard errors, providing excellent coverage, in all scenario. The standard model underestimated the proportion of cured by 7% when α = 1.2, and by 40% when α = 2.0. Age effect on the proportion of cured was heavily overestimated. Among the extended models, the maximum likelihood estimation on individual data outperformed the unweighted least square for grouped data. When some of the assumptions were violated, parameter estimates by both extended models appeared fairly robust. Applied to real colon cancer data (e.g. in men), the extended models estimated close values of α respectively 1.28 (95% confidence interval [1.16–1.40] for grouped data and 1.23 [1.12–1.35] for individual data) and cure fraction (respectively 57.2% [54.3–60.1%] and 55.7%[53.3–58.1%]), higher than that of the conventional model (51.0% [48.5–53.5%] for grouped data and 51.6% [50.0–53.3%] for individual data). In individual data analyses, AIC was smaller for the extended model (55748) than for the conventional model (55760). Conclusion The present analysis suggests that conventional indicators overestimate cancer-specific death and underestimate cure fraction for cancer survivors. The extended models are more efficient to estimate net survival in presence of an extra risk of dying.

Although count data are often collected in social, psychological, and epidemiological surveys in grouped and right-censored categories, there is a lack of statistical methods simultaneously taking both grouping and right-censoring into account. In this research, we propose a new generalized Poisson-multinomial mixture approach to model grouped and right-censored (GRC) count data. Based on a mixed Poisson-multinomial process for conceptualizing grouped and right-censored count data, we prove that the new maximum-likelihood estimator (MLE-GRC) is consistent and asymptotically normally distributed for both Poisson and zero-inflated Poisson models. The use of the MLE-GRC, implemented in an R function, is illustrated by both statistical simulation and empirical examples. This research provides a tool for epidemiologists to estimate incidence from grouped and right-censored count data and lays a foundation for regression analyses of such data structure.

This paper deals with non-Bayesian estimation problem of constant-stress Accelerated Life Tests (ALTs) when the lifetime of the items follow truncated Generalized Logistic Distribution (GLD). Some considerations on inference based on the use of asymptotically normality of the ML estimators are presented considering the stress effects on the two scale parameters of the truncated GLD with a k-level constant-stress ALT under progressive type-I censored grouped data. The EM algorithm method is used to obtain the estimators of the unknown parameters. In addition, estimator of the two scale parameters, reliability function under usual conditions and Fisher information matrix of the estimators are given. Finally, we present a Simulation Study to illustrate the proposed procedure.

The Dimensional Change Card Sort (DCCS) task is a widely used measure of preschoolers’ executive function. We combined data for 3,290 3-year-olds from 37 unique studies reporting 130 experimental conditions. Using raw pass/fail counts, we computed the pass rates and chi-squared value for each against chance (50/50) performance. We grouped data according to DCCS variants and computed the standard pass rate and chi-squared and phi for each variant relative to standard. For all standard versions, the mean pass rate was 36%. We compared all other variants to the standard and found robust improvements in performance for manipulations that involved spatial separation of the conflicting dimensions, use of distraction between pre and post-switch, elimination of all conflict, and extra practice. We also found that negative priming offers a better explanation for 3-year-olds’ perseveration than attentional inertia. The results support a theoretical model of 3-year-olds’ performance based on inhibitory control.

This article investigates the problem of simultaneously testing the normality and homoscedasticity assumptions in a linear fixed effects model when we have grouped data. This has been facilitated by the assumption of a smooth alternative to the normal distribution. The smooth alternative is specified using Legendre polynomials, and the score statistic is derived under two scenarios: a common smooth alternative across the different groups, or different smooth alternatives across the different groups. A data-driven approach available in the literature is used for determining the order of the polynomials. For the null distribution of the score statistic, the accuracy of the asymptotic chi-squared distribution is numerically investigated under a one-way fixed effects model with balanced and unbalanced data. The results are illustrated with an example.

We propose a unified approach that is flexibly applicable to various types of grouped data for estimating and testing parametric income distributions. To simplify the use of our approach, we also provide a parametric bootstrap method and show its asymptotic validity. We also compare this approach with existing methods for grouped income data, and assess their finite-sample performance by a Monte Carlo simulation. For empirical demonstrations, we apply our approach to recovering China's income/consumption distributions from a sequence of income/consumption share tables and the U.S. income distributions from a combination of income shares and sample quantiles. Supplementary materials for this article are available online.

Summary In observational epidemiological studies, the exposure that is received by an individual often cannot be precisely observed, resulting in measurement error, and a common approach to dealing with measurement error is regression calibration (RC). Use of RC, which requires assumptions about the distribution of unknown error-free (true) variables, leads to concern about the possibility of bias due to misspecification of that distribution. The simulation–extrapolation (SIMEX) method, in contrast, does not require a distributional assumption. However, analyses of large cohorts may be performed by using grouped or person-year data, and application of SIMEX to grouped data is not straightforward, particularly when there is a mixture of classical and Berkson measurement errors. We compared RC and SIMEX with grouped data analyses to assess robustness of the RC method to misspecification of the true dose distribution. We also applied SIMEX assuming mixtures of classical and Berkson errors and compared the results with those obtained by using RC for classical error only. SIMEX had less bias than RC and performed well regardless of the true dose distribution, whereas RC based on a misspecified true dose distribution showed greater bias than when based on the correctly specified true dose distribution.

The consistency and asymptotic normality of the maximum likelihood estimators (MLEs), based on progressively type-I interval censored (PIC-I) data are proved under appropriate regularity conditions. The information obtained in the PIC-I setup is compared with that of grouped data and also with progressively type-I censored (PC-I) data.

This paper considers a parametric model for grouped data collected via line transect technique. The weighted exponential model is studied and investigated when the data are assumed to be grouped in the intervals. The maximum likelihood method is adopted for purpose of estimation. The resultant estimator of the population abundance is compared with the corresponding estimator that developed for ungrouped data by using the Laake stakes real data.