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Modified Poisson regression, which estimates the regression parameters in the log-binomial regression model using the Poisson quasi-likelihood estimating equation and robust variance, is a useful tool for estimating the adjusted risk and prevalence ratio in binary outcome analysis. Although several goodness-of-fit tests have been developed for other binary regressions, few goodness-of-fit tests are available for modified Poisson regression. In this study, we proposed several goodness-of-fit tests for modified Poisson regression, including the modified Hosmer-Lemeshow test with empirical variance, Tsiatis test, normalized Pearson chi-square tests with binomial variance and Poisson variance, and normalized residual sum of squares test. The original Hosmer-Lemeshow test and normalized Pearson chi-square test with binomial variance are inappropriate for the modified Poisson regression, which can produce a fitted value exceeding 1 owing to the unconstrained parameter space. A simulation study revealed that the normalized residual sum of squares test performed well regarding the type I error probability and the power for a wrong link function. We applied the proposed goodness-of-fit tests to the analysis of cross-sectional data of patients with cancer. We recommend the normalized residual sum of squares test as a goodness-of-fit test in the modified Poisson regression., Competing Interests: Declaration of conflicting interestsThe author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

This article presents a novel and powerful goodness-of-fit test specifically designed for the Cauchy distribution. The motivation behind our research stems from the need for a more accurate and robust method to assess the fit of the Cauchy distribution to data. This distribution is known for its heavy tails and lack of finite moments. To compute the proposed test statistic, we utilize the maximum likelihood estimators of the unknown parameters, ensuring the test efficiency and reliability. In addition, Monte Carlo simulations are employed to obtain critical points of the test statistic for different sample sizes, enabling precise determination of the threshold for rejecting the null hypothesis. To assess the performance of the proposed test, we conduct power comparisons against several well-known competing tests, considering various alternative distributions. Through extensive simulations, we demonstrate the superiority of our test in the majority of the cases examined, highlighting its effectiveness in distinguishing departures from the Cauchy distribution. The contributions of our study are twofold. Firstly, we introduce a novel goodness-of-fit test tailored specifically for the Cauchy distribution, taking into account its unique characteristics. By incorporating the maximum likelihood estimate and employing Monte Carlo simulations, our test offers improved accuracy and robustness compared to existing methods. Furthermore, we provide practical validation of the proposed test through the analysis of a financial dataset. The application of the test to real-world data underscores its relevance and applicability in practical scenarios. [ABSTRACT FROM AUTHOR]

The recent popularity of models that capture the dynamic coevolution of both network structure and behavior has driven the need for summary indices to assess the adequacy of these models to reproduce dynamic properties of scientific or practical importance. Whereas there are several existing indices for assessing the ability of the model to reproduce network structure over time, to date there are few indices for assessing the ability of the model to reproduce individuals’ behavior patterns. Drawing on the widely used strategy of assessing model adequacy by comparing index values summarizing features of the observed data to the distribution of those index values on simulated data from the fitted model, we propose four goals that a researcher could reasonably expect of a joint structure/behavior model regarding how well it captures behavior and describe indices for assessing each of these. These reasonably simple and easily implemented indices can be used for assessing model adequacy with any dynamic network models jointly working with networks and behavior, including the stochastic actor-based models implemented within software packages such as RSien version 1.2-24. We demonstrate the use of our indices with an empirical example to show how they can be employed in practical settings, with an additional extension to modeling affiliation dynamics in two-mode networks. Key scripts are provided in the Supplemental Document (which can be found at http://smr.sagepub.com/supplemental/).

The typical single-event characteristics of a voltage dip include residual voltage, duration, dip type, point-on-wave and phase-angle jump, which may influence the operation of the sensitive equipment under voltage dip. This operation is the foundation on which the single-event characteristics of a voltage dip can be accurately calculated to mitigate the voltage dip. The challenge of existing studies is that no unified and systematic method to calculate multiple single-event characteristics. This study proposes a robust adaptive method based on Goodness-of-Fit (GoF) test to calculate the characteristics of a voltage dip. First, a calculation method for the transition segment of voltage dip is proposed based on the GoF test. Then, four methods are presented for calculating four different characteristics of the dip based on the detected transition segment. The proposed method is subsequently unified and thus reduces the computation of monitor devices. Moreover, this method can adaptively adjust the critical value according to the sampling rate, avoiding the influence of noise. Finally, this study applies 516 sets of measured voltage dips to verify the performance of the proposed method, comparing the results with that of the existing methods.

Abstract Random-effects (RE) meta-analysis is a crucial approach for combining results from multiple independent studies that exhibit heterogeneity. Recently, two frequentist goodness-of-fit (GOF) tests were proposed to assess the fit of RE model. However, they tend to perform poorly when assessing rare binary events. Under a general binomial-normal framework, we propose a novel GOF test for the meta-analysis of rare events. Our method is based on pivotal quantities that play an important role in Bayesian model assessment. It further adopts the Cauchy combination idea proposed in a 2019 JASA paper, to combine dependent p-values computed using posterior samples from Markov Chain Monte Carlo. The advantages of our method include clear conception and interpretation, incorporation of all data including double zeros without the need for artificial correction, well-controlled Type I error, and generally improved ability in detecting model misfits compared to previous GOF methods. We illustrate the proposed method via simulation and three real data applications.

The common used goodeness-of-fit tests are based on the empirical distributions functions (EDF) where distances between empirical and theoretical hypothesized distributions are compared to critical values. The aim of this paper is to provide for different sample sizes, tables of goodness-of-fit critical values of modified Kolmogorov-Smirnov statistic D n , Anderson-Darling statistic A2, Cramer-Von Mises statistic W 2 , Liao and Shimokawa statistic Ln, and Watson statistic U2 for the competing risks model of Bertholon which is used to describe the reliability of real systems where failure times can have different risks and in medical studies to characterize the survival time of patients who can have risks of death from different causes. The power of these statistics is studied using some alternatives such as the exponential, the inverse Weibull, the exponentiated Weibull and the exponentiated exponential distributions. All the computation are carried out by using matlab software and Monte Carlo method. [ABSTRACT FROM AUTHOR]

Clustered current status data are frequently encountered in biomedical research and other areas that require survival analysis. This paper proposes graphical and formal model assessment procedures to evaluate the goodness of fit of the additive hazards model to clustered current status data. The test statistics proposed are based on sums of martingale-based residuals. Relevant asymptotic properties are established, and empirical distributions of the test statistics can be simulated utilizing Gaussian multipliers. Extensive simulation studies confirmed that the proposed test procedures work well for practical scenarios. This proposed method applies when failure times within the same cluster are correlated, and in particular, when cluster sizes can be informative about intra-cluster correlations. The method is applied to analyze clustered current status data from a lung tumorigenicity study. [ABSTRACT FROM AUTHOR]

This article proposes goodness-of-fit tests for multinomial models using an inverse sampling scheme. From the multiple decision-theoretic perspective, we devise a test statistic and stopping rule that satisfy a prespecified probability level P* and obtain corresponding optimal sample sizes. Incomplete Dirichlet type II distribution functions are used to develop the procedure and to express the probability of correct decisions for various cell configurations for multinomial models. For empirical studies, Monte Carlo experiments are conducted, and for illustrations, various cell configurations of a wheel of fortune are demonstrated. [ABSTRACT FROM AUTHOR]

Species distribution models (SDMs) are numerical tools that combine species occurrence (or abundance) data with environmental variables, to predict the species’ distribution spatially. SDMs are increasingly used for purposes of conservation planning and management of ecosystems. The model performance can be measured as the goodness-of-fit (GOF), which describes how well it fits (e.g., the discrepancy between the statistical model and the data observed). However, there is still a need for a deeper understanding of the ecological characteristics of the modelled species which can affect the accuracy of those models. Here, we compared the goodness-of-fit of SDMs, considering several ecological characteristics of 56 bird species: Most frequently used environment, body mass, home-range, species specialization index (SSI), diet specialization and detectability. All SDMs were performed on the same dataset, and the relative frequency of each species was also incorporated to account for occurrence heterogeneity. GOF of SDMs was not significantly correlated with species’ frequency, home-range, body mass, degree of detectability or level of diet specialization. Overall, the birds with more accurate SDMs (GOF) were species of grasslands and the GOF was positively associated with SSI, indicating that more habitat-specialized species are better predictable. Our findings suggest that is important to focus not only on statistical issues potentially related to model performance but also on ecological characteristics of single species because can improve the performance of modellistic procedures, increasing their predictive power.

Imperfect repair (IR) modelling has attracted a lot of attention during the last decades. To assess and predict repairable systems' reliability, analysts have to choose among a plethora of models: renewal processes, non‐homogeneous Poisson processes (NHPPs), Brown–Proschan, Kijima, ARA, ARI, Quasi‐Renewal (QR), Trend‐Renewal and so forth. Choosing an appropriate model for a given failures, dataset is an important practical issue. The fit of an IR model can be assessed using goodness‐of‐fit (GoF) tests but very few have been proposed and a good fit to past data does not guarantee good reliability predictions. This work proposes general GoF tests for IR models based on sequential (or on‐line) assessment of times‐to‐failures forecasts. The suggested predictive‐sequential (or prequential) GoF tests have a low computational complexity and a common test statistic for several IR models. These tests have been proved to be asymptotically distribution‐free (ADF) for renewal and power‐law processes (PLPs). Our numerical simulations and preliminary theoretical results highly suggest that this ADF property still holds for several other IR models. The prequential tests are much easier to use than the already known bootstrap tests, and a simulation study shows that they are also slightly more powerful. The simulations also show that the prequential tests are powerful to identify classes of similar appropriate models but are much less powerful to distinguish models belonging to the same class. A comparison of MTTF estimates show that models from the same class give close reliability predictions and that the tests are able to reject models which would yield to dramatic errors in reliability predictions. [ABSTRACT FROM AUTHOR]

In this study, we propose a gradient-free statistical goodness-of-fit test for determining if a joint sample (xi,yi)is drawn from p(y|x)πxfor some density πxgiven a conditional distribution. This test is an alternative to Kernel Conditional Stein Discrepancy, which require the computation of model derivatives and are therefore impractical for complex statistical models. Our method, known as Gradient-Free Kernel Conditional Stein Discrepancy, does not require the calculation of derivatives, this makes it a great tool for tackling difficult problems such as evaluating the performance of generative models. It is able to detect convergence and divergence with the same level of accuracy as the gradient-based method. We also discuss the application of this test in importance sampling and compare its performance with two other conventional methods.