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Logistic regression models are widely used in case-control data analysis, and testing the goodness-of-fit of their parametric model assumption is a fundamental research problem. In this article, we propose to enhance the power of the goodness-of-fit test by exploiting a monotonic density ratio model, in which the ratio of case and control densities is assumed to be a monotone function. We show that such a monotonic density ratio model is naturally induced by the retrospective case-control sampling design under the alternative hypothesis. The pool-adjacent-violator algorithm is adapted to solve for the constrained nonparametric maximum likelihood estimator under the alternative hypothesis. By measuring the discrepancy between this estimator and the semiparametric maximum likelihood estimator under the null hypothesis, we develop a new Kolmogorov-Smirnov-type statistic to test the goodness-of-fit for logistic regression models with case-control data. A bootstrap resampling procedure is suggested to approximate the p $$ p $$ -value of the proposed test. Simulation results show that the type I error of the proposed test is well controlled and the power improvement is substantial in many cases. Three real data applications are also included for illustration., (© 2024 John Wiley & Sons Ltd.)

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.

To evaluate model fit in confirmatory factor analysis, researchers compare goodness-of-fit indices (GOFs) against fixed cutoff values (e.g., CFI > .950) derived from simulation studies. Methodologists have cautioned that cutoffs for GOFs are only valid for settings similar to the simulation scenarios from which cutoffs originated. Despite these warnings, fixed cutoffs for popular GOFs (i.e., χ 2 , χ 2 /df, CFI, RMSEA, SRMR) continue to be widely used in applied research. We (1) argue that the practice of using fixed cutoffs needs to be abandoned and (2) review time-honored and emerging alternatives to fixed cutoffs. We first present the most in-depth simulation study to date on the sensitivity of GOFs to model misspecification (i.e., misspecified factor dimensionality and unmodeled cross-loadings) and their susceptibility to further data and analysis characteristics (i.e., estimator, number of indicators, number and distribution of response options, loading magnitude, sample size, and factor correlation). We included all characteristics identified as influential in previous studies. Our simulation enabled us to replicate well-known influences on GOFs and establish hitherto unknown or underappreciated ones. In particular, the magnitude of the factor correlation turned out to moderate the effects of several characteristics on GOFs. Second, to address these problems, we discuss several strategies for assessing model fit that take the dependency of GOFs on the modeling context into account. We highlight tailored (or "dynamic") cutoffs as a way forward. We provide convenient tables with scenario-specific cutoffs as well as regression formulae to predict cutoffs tailored to the empirical setting of interest., (© 2023. The Author(s).)

Background: Indigenous communities often have poorer health outcomes and services under traditional models of care. In New Zealand, this holds true for Māori people who are tāngata whenua (the indigenous people). Several barriers exist that decrease the likelihood of indigenous communities often have poorer health outcomes and poor service fit under traditional models of care, including access issues, systemic and provider racism, and a lack of culturally safe and responsive services. Web-based interventions (WBIs) have been shown to be effective in supporting mental health and well-being and can overcome some of these barriers. Despite the large number of WBIs developed, more investigation is needed to know how well WBIs fit with an indigenous worldview and how they meet the needs of indigenous communities so that a digitally based future does not drive social and health inequities., Objective: This study aims to explore the goodness-of-fit of WBIs of Māori individuals, the indigenous people of Aotearoa/New Zealand., Methods: We used interviews (n=3) and focus groups (n=5) with 30 Māori participants to explore their views about WBIs. Interviews were analyzed using reflexive thematic analysis by members of the research team., Results: Overall, there was a perception that the design of WBIs did not align with the Māori worldview, which centers around people, relationships, spirituality, and holistic views of well-being. A total of 4 key themes and several subthemes emerged, indicating that WBIs were generally considered a poor fit for Māori. Specifically, the themes were as follows: (1) WBIs are disconnected from the core values of te ao Māori (the Māori worldview), (2) WBIs could be helpful in the right context, (3) there are significant barriers that may make it harder for Māori to use WBIs than other groups, and (4) ways to improve WBIs to help engagement with Māori., Conclusions: While WBIs are often considered a way to reduce barriers to care, they may not meet the needs of Māori when used as a stand-alone intervention. If WBIs are continued to be offered, developers and researchers need to consider how to develop WBIs that are responsive and engaging to the needs of indigenous communities rather than driving inequities. Ideally, WBIs should be developed by the people they are intended for to fit with those populations' world views., (©Liesje Donkin, Marie-Claire Bidois-Putt, Holly Wilson, Penelope Hayward, Amy Hai Yan Chan. Originally published in JMIR Formative Research (https://formative.jmir.org), 02.05.2024.)

Methods to detect item response theory (IRT) item-level misfit are typically derived assuming fixed test forms. However, IRT is also employed with more complicated test designs, such as the balanced incomplete block (BIB) design used in large-scale educational assessments. This study investigates two modifications of Douglas and Cohen's 2001 nonparametric method of assessing item misfit, based on A) using block total score and B) pooling booklet level scores for analyzing BIB data. Block-level scores showed extreme inflation of Type I error for short blocks containing 5 or 10 items. The pooled booklet method yielded Type I error rates close to nominal α in most conditions and had power to detect misfitting items. The study also found that the Douglas and Cohen procedure is only slightly affected by the presence of other misfitting items in the block. The pooled booklet method is recommended for practical applications of Douglas and Cohen's method with BIB data., Competing Interests: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article., (© The Author(s) 2024.)

Generalized linear models (GLMs) are very widely used, but formal goodness-of-fit (GOF) tests for the overall fit of the model seem to be in wide use only for certain classes of GLMs. We develop and apply a new goodness-of-fit test, similar to the well-known and commonly used Hosmer-Lemeshow (HL) test, that can be used with a wide variety of GLMs. The test statistic is a variant of the HL statistic, but we rigorously derive an asymptotically correct sampling distribution using methods of Stute and Zhu (Scand J Stat 29(3):535-545, 2002) and demonstrate its consistency. We compare the performance of our new test with other GOF tests for GLMs, including a naive direct application of the HL test to the Poisson problem. Our test provides competitive or comparable power in various simulation settings and we identify a situation where a naive version of the test fails to hold its size. Our generalized HL test is straightforward to implement and interpret and an R package is publicly available., Supplementary Information: The online version contains supplementary material available at 10.1007/s11749-023-00912-8., Competing Interests: Conflict of interestThe authors declare no conflict of interest., (© The Author(s) 2023.)

The Hosmer-Lemeshow (HL) test is a commonly used global goodness-of-fit (GOF) test that assesses the quality of the overall fit of a logistic regression model. In this paper, we give results from simulations showing that the type I error rate (and hence power) of the HL test decreases as model complexity grows, provided that the sample size remains fixed and binary replicates (multiple Bernoulli trials) are present in the data. We demonstrate that a generalized version of the HL test (GHL) presented in previous work can offer some protection against this power loss. These results are also supported by application of both the HL and GHL test to a real-life data set. We conclude with a brief discussion explaining the behavior of the HL test, along with some guidance on how to choose between the two tests. In particular, we suggest the GHL test to be used when there are binary replicates or clusters in the covariate space, provided that the sample size is sufficiently large., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.)

In this article, the primary aim is to introduce a new flexible family of circular distributions, namely the wrapped Linnik family which possesses the flexibility to model the inflection points and tail behavior often better than the existing popular flexible symmetric unimodal circular models. The second objective of this article is to obtain a simple and efficient estimator of the index parameter α of symmetric Linnik distribution exploiting the fact that it is preserved in the wrapped Linnik family. This is an interesting problem for highly volatile financial data as has been studied by several authors. Our final aim is to analytically derive the asymptotic distribution of our estimator, not available for other estimator. This estimator is shown to outperform the existing estimator over the range of the parameter for all sample sizes. The proposed wrapped Linnik distribution is applied to some real-life data. A measure of goodness of fit proposed in one of the authors' previous works is used for the above family of distributions. The wrapped Linnik family was found to be preferable as it gave better fit to those data sets rather than the popular von-Mises distribution or the wrapped stable family of distributions., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2023 Informa UK Limited, trading as Taylor & Francis Group.)

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., (© 2023. Springer Nature Limited.)

Copula is a popular method for modeling the dependence among marginal distributions in multivariate censored data. As many copula models are available, it is essential to check if the chosen copula model fits the data well for analysis. Existing approaches to testing the fitness of copula models are mainly for complete or right-censored data. No formal goodness-of-fit (GOF) test exists for interval-censored or recurrent events data. We develop a general GOF test for copula-based survival models using the information ratio (IR) to address this research gap. It can be applied to any copula family with a parametric form, such as the frequently used Archimedean, Gaussian, and D-vine families. The test statistic is easy to calculate, and the test procedure is straightforward to implement. We establish the asymptotic properties of the test statistic. The simulation results show that the proposed test controls the type-I error well and achieves adequate power when the dependence strength is moderate to high. Finally, we apply our method to test various copula models in analyzing multiple real datasets. Our method consistently separates different copula models for all these datasets in terms of model fitness., (© 2022 The International Biometric Society.)

Partly interval-censored event time data arise naturally in medical, biological, sociological and demographic studies. In practice, some patients may be immune from the event of interest, invoking a cure model for survival analysis. Choosing an appropriate parametric distribution for the failure time of susceptible patients is an important step to fully structure the mixture cure model. In the literature, goodness-of-fit tests for survival models are usually restricted to uncensored or right-censored data. We fill in this gap by proposing a new goodness-of-fit test dealing with partly interval-censored data under mixture cure models. Specifically, we investigate whether a parametric distribution can fit the susceptible part by using a Cramér-von Mises type of test, and establish the asymptotic distribution of the test . Empirically, the critical value is determined from the bootstrap resamples. The proposed test, compared to the traditional leveraged bootstrap approach, yields superior practical results under various settings in extensive simulation studies. Two clinical data sets are analyzed to illustrate our method., (© 2022 John Wiley & Sons Ltd.)

Common count distributions, such as the Poisson (binomial) distribution for unbounded (bounded) counts considered here, can be characterized by appropriate Stein identities. These identities, in turn, might be utilized to define a corresponding goodness-of-fit (GoF) test, the test statistic of which involves the computation of weighted means for a user-selected weight function f. Here, the choice of f should be done with respect to the relevant alternative scenario, as it will have great impact on the GoF-test's performance. We derive the asymptotics of both the Poisson and binomial Stein-type GoF-statistic for general count distributions (we also briefly consider the negative-binomial case), such that the asymptotic power is easily computed for arbitrary alternatives. This allows for an efficient implementation of optimal Stein tests, that is, which are most powerful within a given class  F $\mathcal {F}$ of weight functions. The performance and application of the optimal Stein-type GoF-tests is investigated by simulations and several medical data examples., (© 2022 The Authors. Biometrical Journal published by Wiley-VCH GmbH.)

The main aim of this work is to develop a new goodness-of-fit test for the one-sided Lévy distribution. The proposed test is based on the scale-ratio approach in which two estimators of the scale parameter of one-sided Lévy distribution are confronted. The asymptotic distribution of the test statistic is obtained under null hypotheses. The performance of the test is demonstrated using simulated observations from various known distributions. Finally, two real-world datasets are analyzed., (© 2023 Informa UK Limited, trading as Taylor & Francis Group.)

Background: Sub-cohort sampling designs such as a case-cohort study play a key role in studying biomarker-disease associations due to their cost effectiveness. Time-to-event outcome is often the focus in cohort studies, and the research goal is to assess the association between the event risk and risk factors. In this paper, we propose a novel goodness-of-fit two-phase sampling design for time-to-event outcomes when some covariates (e.g., biomarkers) can only be measured on a subgroup of study subjects., Methods: Assuming that an external model, which can be the well-established risk models such as the Gail model for breast cancer, Gleason score for prostate cancer, and Framingham risk models for heart diseases, or built from preliminary data, is available to relate the outcome and complete covariates, we propose to oversample subjects with worse goodness-of-fit (GOF) based on an external survival model and time-to-event. With the cases and controls sampled using the GOF two-phase design, the inverse sampling probability weighting method is used to estimate the log hazard ratio of both incomplete and complete covariates. We conducted extensive simulations to evaluate the efficiency gain of our proposed GOF two-phase sampling designs over case-cohort study designs., Results: Through extensive simulations based on a dataset from the New York University Women's Health Study, we showed that the proposed GOF two-phase sampling designs were unbiased and generally had higher efficiency compared to the standard case-cohort study designs., Conclusion: In cohort studies with rare outcomes, an important design question is how to select informative subjects to reduce sampling costs while maintaining statistical efficiency. Our proposed goodness-of-fit two-phase design provides efficient alternatives to standard case-cohort designs for assessing the association between time-to-event outcome and risk factors. This method is conveniently implemented in standard software., (© 2023. The Author(s).)

We develop new goodness of fit test for uniform distribution based on a conditional moment characterization. We study the asymptotic properties of the proposed test statistic. We also present a goodness of fit test for uniform distribution to incorporate the right censored observations and studied its properties. A Monte Carlo simulation study is carried out to evaluate the finite sample performance of the proposed tests. We illustrate the test procedures using real data sets., (© Korean Statistical Society 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.)

We introduce a simple diagnostic test for assessing the overall or partial goodness of fit of a linear causal model with errors being independent of the covariates. In particular, we consider situations where hidden confounding is potentially present. We develop a method and discuss its capability to distinguish between covariates that are confounded with the response by latent variables and those that are not. Thus, we provide a test and methodology for partial goodness of fit. The test is based on comparing a novel higher-order least squares principle with ordinary least squares. In spite of its simplicity, the proposed method is extremely general and is also proven to be valid for high-dimensional settings. Supplementary materials for this article are available online., Competing Interests: The authors report there are no competing interests to declare., (© 2023 The Author(s). Published with license by Taylor & Francis Group, LLC.)

Probit models are used extensively for inferential purposes in the social sciences as discrete data are prevalent in a vast body of social studies. Among many accompanying model inference problems, a critical question remains unsettled: how to develop a goodness-of-fit measure that resembles the ordinary least square (OLS) R 2 used for linear models. Such a measure has long been sought to achieve 'comparability' of different empirical models across multiple samples addressing similar social questions. To this end, we propose a novel R 2 measure for probit models using the notion of surrogacy - simulating a continuous variable S as a surrogate of the original discrete response (Liu & Zhang, Journal of the American Statistical Association, 113, 845 and 2018). The proposed R 2 is the proportion of the variance of the surrogate response explained by explanatory variables through a linear model, and we call it a surrogate R 2 . This paper shows both theoretically and numerically that the surrogate R 2 approximates the OLS R 2 based on the latent continuous variable, preserves the interpretation of explained variation, and maintains monotonicity between nested models. As no other pseudo R 2 , McKelvey and Zavoina's and McFadden's included, can meet all the three criteria simultaneously, our measure fills this crucial void in probit model inference., (© 2022 The Authors. British Journal of Mathematical and Statistical Psychology published by John Wiley & Sons Ltd on behalf of British Psychological Society.)

In this paper, we introduce a novel framework that allows efficient stochastic process discrimination. The underlying test statistic is based on even empirical moments and generalizes the time-averaged mean-squared displacement framework; the test is designed to allow goodness-of-fit statistical testing of processes with stationary increments and a finite-moment distribution. In particular, while our test statistic is based on a simple and intuitive idea, it enables efficient discrimination between finite- and infinite-moment processes even if the underlying laws are relatively close to each other. This claim is illustrated via an extensive simulation study, e.g., where we confront α-stable processes with stability index close to 2 with their standard Gaussian equivalents. For completeness, we also show how to embed our methodology into the real data analysis by studying the real metal price data.

This paper deals with testing the functional form of the covariate effects in a Cox proportional hazards model with random effects. We assume that the responses are clustered and incomplete due to right censoring. The estimation of the model under the null (parametric covariate effect) and the alternative (nonparametric effect) is performed using the full marginal likelihood. Under the alternative, the nonparametric covariate effects are estimated using orthogonal expansions. The test statistic is the likelihood ratio statistic, and its distribution is approximated using a bootstrap method. The performance of the proposed testing procedure is studied through simulations. The method is also applied on two real data sets one from biomedical research and one from veterinary medicine., (© 2022 The Authors. Biometrical Journal published by Wiley-VCH GmbH.)

Bifactor latent models have gained popularity and are widely used to model construct multidimensionality. When adopting a confirmatory approach, a common practice is to assume that all cross-loadings take zero values. This article presents the results of a simulation study exploring the impact of ignoring non-zero cross-loadings on the performance of confirmatory bifactor analysis. The present work contributes to previous research by including study conditions that had not been examined before. For instance, a wider range of values of the factor loadings both for the group factors and the cross-loadings is considered. Parameter recovery is analyzed, but the focus of the study is on assessing the sensitivity of goodness-of-fit indices to detect the model misspecification that involves ignoring non-zero cross-loadings. Several commonly used SEM fit indices are examined: both biased estimators of the fit index (CFI, GFI, and SRMR) and unbiased estimators (RMSEA and SRMR). Results indicated that parameter recovery worsens when ignoring moderate and large cross-loading values and using small sample sizes, and that commonly used SEM fit indices are not useful to detect such model misspecifications. We recommend the use of the unbiased SRMR index with a cutoff value adjusted by the communality level ( R ), as it is the only fit index sensitive to the model misspecification due to ignoring non-zero cross-loadings in the bifactor model. The results of the present study provide insights into modeling cross-loadings in confirmatory bifactor models but also practical recommendations to researchers.2 ), as it is the only fit index sensitive to the model misspecification due to ignoring non-zero cross-loadings in the bifactor model. The results of the present study provide insights into modeling cross-loadings in confirmatory bifactor models but also practical recommendations to researchers., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Ximénez, Revuelta and Castañeda.)

Goodness of fit tests for two probabilistic multigraph models are presented. The first model is random stub matching given fixed degrees (RSM) so that edge assignments to vertex pair sites are dependent, and the second is independent edge assignments (IEA) according to a common probability distribution. Tests are performed using goodness of fit measures between the edge multiplicity sequence of an observed multigraph, and the expected one according to a simple or composite hypothesis. Test statistics of Pearson type and of likelihood ratio type are used, and the expected values of the Pearson statistic under the different models are derived. Test performances based on simulations indicate that even for small number of edges, the null distributions of both statistics are well approximated by their asymptotic χ 2 -distribution. The non-null distributions of the test statistics can be well approximated by proposed adjusted χ 2 -distributions used for power approximations. The influence of RSM on both test statistics is substantial for small number of edges and implies a shift of their distributions towards smaller values compared to what holds true for the null distributions under IEA. Two applications on social networks are included to illustrate how the tests can guide in the analysis of social structure., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.)

Answer: No. Most goodness-of-fit (GOF) tests attempt to discern a preferred weighting using either absolute or relative errors in the back-calculated calibration x values. However, the former are predisposed to select constant weighting and the latter 1/ x 2 or 1/ y 2 weighting, no matter what the true weighting should be. Here, I use Monte Carlo simulations to quantify the flaws in GOF tests and show why they falsely prefer their predisposition weighting. The weighting problem is solved properly through variance function (VF) estimation from replicate data, conveniently separating this from the problem of selecting a response function (RF). Any weighting other than inverse-variance must give loss of precision in the RF parameters and in the estimates of unknowns x 0 . In particular, the widely used 1/ x 2 weighting, if wrong, not only sacrifices precision but even worse, appears to give better precision at small x , leading to falsely optimistic estimates of detection and quantification limits. Realistic VFs typically become constant in the low- x , low- y limit. Thus, even when 1/ x 2 weighting is correct at large signal, the neglect of the constant variance component at small signal again gives too-small detection and quantification limits. VF estimation has been disparaged as too demanding of data. Why this is not true is demonstrated with Monte Carlo simulations that show only a few percent increase in calibration parameter uncertainties when the VF is estimated from just three replicates at each of six calibration x values. This point is further demonstrated using examples from the recent literature.

We investigated the relevance of the validation principles on the Quantitative Structure Activity Relationship models issued by Organization for Economic and Co-operation and Development. We checked the goodness-of-fit, robustness and predictivity categories in linear and nonlinear models using benchmark datasets. Most of our conclusions are drawn using the sample size dependence of the different validation parameters. We found that the goodness-of-fit parameters misleadingly overestimate the models on small samples. In the case of neural network and support vector models, the feasibility of the goodness-of-fit parameters often might be questioned. We propose to use the simplest y-scrambling method to estimate chance correlation. We found that the leave-one-out and leave-many-out cross-validation parameters can be rescaled to each other in all models and the computationally feasible method should be chosen depending on the model type. We assessed the interdependence of the validation parameters by calculating their rank correlations. Goodness of fit and robustness correlate quite well over a sample size for linear models and one of the approaches might be redundant. In the rank correlation between internal and external validation parameters, we found that the assignment of good and bad modellable data to the training or the test causes negative correlations., (© 2022 The Authors. Molecular Informatics published by Wiley-VCH GmbH.)

Based on the goodness-of-fit theory, the current research examined how parental socialization expectations and socialization practices in infancy predicted child social adjustment in the preschool year dependent on child characteristics in toddlerhood with a longitudinal sample of Chinese families. Participants were 272 Chinese mother-child dyads. Maternal socialization goals of child autonomy and obedience were assessed when the child was 6 months old. Maternal respect for autonomy and negative control were observed in free-plays at 15 months. Mothers reported child compliance and inhibitory control at 25 months and rated child externalizing behaviors at 37 months. Results showed that for children with low levels of compliance or high levels of inhibitory control, obedience socialization goals predicted more externalizing behaviors, whereas for children with high levels of compliance or low levels of inhibitory control, obedience socialization goals predicted fewer externalizing behaviors. Moreover, for children with high levels of inhibitory control, higher levels of respect for autonomy or lower levels of negative control foretold fewer externalizing behaviors. Conversely, for children with low levels of inhibitory control, lower levels of respect for autonomy or higher levels of negative control forecasted fewer externalizing behaviors. Together, our findings demonstrate that socialization expectations, socialization practices, and child characteristics are jointly predictive of social adjustment across early childhood and all the significant interactions are characterized by the pattern of a contrastive effect, therefore congruently supporting the goodness-of-fit hypotheses. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

The objective of this study was to estimate the good-of-fitness and precision of parameters of the Gompertz-Laird, Logistic, Richards, and Von Bertalanffy growth models, using different data collection periods (DCP). Two hundred and sixty-two Mexican Creole chicks (116 females and 146 males), were individually weighed to form the following sets of data for each sex: DCP 1 (weights recorded weekly from hatching to 63 d, and every 2 wk, from 63 to 133 d of age), DCP 2 (weights recorded weekly from hatching to 133 d of age), DCP 3 (weights recorded every third day, from hatching to 63 d, and every 14 d, from 63 to 133 d of age), and DCP 4 (weights recorded every third day, from hatching to 63 d, and weekly, from 63 to 133 d of age). Data were analyzed using the NLIN procedure of SAS (Marquardt algorithm). For all growth models, the width of confidence interval (CI) of each parameter, was estimated (α = 0.05). The adjusted coefficient of determination (AR 2 ), as well as the Akaike (AIC) and Bayesian information criteria (BIC) were used to select the best model. The higher the AR 2 , and the lower the width of CI, as well as the AIC and BIC values, the better the model. The Gompertz-Laird model, more frequently showed the highest AR 2 , and the lowest AIC and BIC values compared to the other models. Moreover, for all models, both sexes and all parameters, most confidence interval widths (all with the Gompertz-Laird model) were the lowest with DCP 3 when compared to the other sets of data. In conclusion, the Gompertz-Laird model was the best provided that the chickens are weighed every third day from hatching until 63 d of age, and every 2 wk thereafter., Competing Interests: Disclosures The authors declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of the study reported., (Copyright © 2022 The Authors. Published by Elsevier Inc. All rights reserved.)

Simple linear regression using ordinary least-squares is the most common function applied in laboratories for analytical calibrations. The determination and/or the correlation coefficients are usually the parameters applied for assessing the goodness-of-fit of a simple linear calibration. However, these parameters are unable to detect the highly biased results at low calibration levels that are obtained with ordinary least-squares. In this study, the use of other parameters based on the relative standard errors of the calculated contents is evaluated. It has been found that these alternative parameters can detect the biased results obtained at low calibration levels with ordinary least-squares, being the relative standard error the one that seems to provide the most adequate results. Ordinary least-squares should only be applied if the lower limit of quantification is set to at least five times above the conventional limit of quantification. For trace analysis, where the lowest possible limit of quantification is required, weighted least-squares should be applied to obtain accurate estimates, especially at low concentrations. One of the greatest advantages of the relative standard error is that this parameter can be determined for all types of regression functions and is not limited to calibrations with linear relationships between the variables., (© 2021 The Authors. Journal of Separation Science published by Wiley-VCH GmbH.)

Gene set-based signal detection analyses are used to detect an association between a trait and a set of genes by accumulating signals across the genes in the gene set. Since signal detection is concerned with identifying whether any of the genes in the gene set are non-null, a goodness-of-fit (GOF) test can be used to compare whether the observed distribution of gene-level tests within the gene set agrees with the theoretical null distribution. Here, we present a flexible gene set-based signal detection framework based on tail-focused GOF statistics. We show that the power of the various statistics in this framework depends critically on two parameters: the proportion of genes within the gene set that are non-null and the degree of separation between the null and alternative distributions of the gene-level tests. We give guidance on which statistic to choose for a given situation and implement the methods in a fast and user-friendly R package, wHC (https://github.com/mqzhanglab/wHC). Finally, we apply these methods to a whole exome sequencing study of amyotrophic lateral sclerosis., (© The Author(s) 2021. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.)

Since COVID-19 outbreak, scientists have been interested to know whether there is any impact of the Bacillus Calmette-Guerin (BCG) vaccine against COVID-19 mortality or not. It becomes more relevant as a large population in the world may have latent tuberculosis infection (LTBI), for which a person may not have active tuberculosis but persistent immune responses stimulated by Mycobacterium tuberculosis antigens, and that means, both LTBI and BCG generate immunity against COVID-19. In order to understand the relationship between LTBI and COVID-19 mortality, this article proposes a measure of goodness of fit, viz., Goodness of Instrumental Variable Estimates (GIVE) statistic, of a model obtained by Instrumental Variables estimation. The GIVE statistic helps in finding the appropriate choice of instruments, which provides a better fitted model. In the course of study, the large sample properties of the GIVE statistic are investigated. As indicated before, the COVID-19 data is analysed using the GIVE statistic, and moreover, simulation studies are also conducted to show the usefulness of the GIVE statistic along with analysis of well-known Card data., (© 2022. The Author(s).)

Stomata play a central role in surface-atmosphere exchange by controlling the flux of water and CO 2 between the leaf and the atmosphere. Representation of stomatal conductance (g sw ) is therefore an essential component of models that seek to simulate water and CO 2 exchange in plants and ecosystems. For given environmental conditions at the leaf surface (CO 2 concentration and vapor pressure deficit or relative humidity), models typically assume a linear relationship between g sw and photosynthetic CO 2 assimilation (A). However, measurement of leaf-level g sw response curves to changes in A are rare, particularly in the tropics, resulting in only limited data to evaluate this key assumption. Here, we measured the response of g sw and A to irradiance in six tropical species at different leaf phenological stages. We showed that the relationship between g sw and A was not linear, challenging the key assumption upon which optimality theory is based-that the marginal cost of water gain is constant. Our data showed that increasing A resulted in a small increase in g sw at low irradiance, but a much larger increase at high irradiance. We reformulated the popular Unified Stomatal Optimization (USO) model to account for this phenomenon and to enable consistent estimation of the key conductance parameters g 0 and g 1 . Our modification of the USO model improved the goodness-of-fit and reduced bias, enabling robust estimation of conductance parameters at any irradiance. In addition, our modification revealed previously undetectable relationships between the stomatal slope parameter g 1 and other leaf traits. We also observed nonlinear behavior between A and g sw in independent data sets that included data collected from attached and detached leaves, and from plants grown at elevated CO 2 concentration. We propose that this empirical modification of the USO model can improve the measurement of g sw parameters and the estimation of plant and ecosystem-scale water and CO 2  fluxes., (© 2022 John Wiley & Sons Ltd.)

Model checking for logistic regression with covariates missing at random is considered. Based on the ideas of Copas (1989) and Osius and Rojek (1992) and studies of Homser et al. (1997), proposed are the two-type goodness-of-fit tests, Pearson chi-squared and unweighted residual sum-of-squares tests, in which their test statistics are centralized by subtracting their estimated mean to be mean-zero-form test statistics via the inverse probability weighting (IPW) and nonparametric multiple imputation (MI) methods to solve the missing value problem. The asymptotic properties of these test statistics are established under the null hypothesis and some regularity conditions. The test statistics conducted by using the IPW and MI estimators are asymptotically equivalent. Proposed are the IPW method and two bootstrap re-sampling approaches for estimation of the variances of the proposed test statistics to solve the issue of underestimating their variances by the MI method of Rubin (1987). Simulation studies are carried out to assess the finite-sample power performances of these proposed tests. Two real data examples are used to illustrate the applicability of the proposed tests.

Pearson's chi-squared test is widely used to test the goodness of fit between categorical data and a given discrete distribution function. When the number of sets of the categorical data, say k , is a fixed integer, Pearson's chi-squared test statistic converges in distribution to a chi-squared distribution with k -1 degrees of freedom when the sample size n goes to infinity. In real applications, the number k often changes with n and may be even much larger than n . By using the martingale techniques, we prove that Pearson's chi-squared test statistic converges to the normal under quite general conditions. We also propose a new test statistic which is more powerful than chi-squared test statistic based on our simulation study. A real application to lottery data is provided to illustrate our methodology., Competing Interests: No potential conflict of interest was reported by the authors., (© 2021 Informa UK Limited, trading as Taylor & Francis Group.)

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., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2022 Informa UK Limited, trading as Taylor & Francis Group.)

Student evaluations of teaching have demonstrated limited validity in traditional classrooms, but there is some evidence that they may be more useful in measuring teaching effectiveness in simulation or clinical environments. Current student evaluations of clinical teaching measure a subset of constructs designed for use by a single profession, which may limit institutional evaluation and make interprofessional evaluations challenging. The purpose of this study was to describe the multi-step creation of the CITES and to establish its internal consistency and goodness of fit for measuring students' perceptions of clinical instructor teaching effectiveness. In its second iteration, the CITES is a 25-item questionnaire that was tested among 161 physical therapy and physician assistant students. Most items, with the exception of item 5, demonstrated goodness of fit, with a standardized coefficient of 0.94. Internal consistency was high, with a Cronbach alpha of 0.96-0.97. Though this tool demonstrates internal consistency and goodness of fit, the test information curve indicated that it would be more useful as a screening tool to detect those who are very poor clinical teachers, rather than a tool to evaluate those who are highly effective at teaching.

We evaluate the validity of a projection-based test checking linear models when the number of covariates tends to infinity, and analyze two gene expression datasets. We show that the test is still consistent and derive the asymptotic distributions under the null and alternative hypotheses. The asymptotic properties are almost the same as those when the number of covariates is fixed as long as p/n → 0 with additional mild assumptions. The test dramatically gains dimension reduction, and its numerical performance is remarkable., (© 2021 John Wiley & Sons Ltd.)

The case-cohort design is commonly used in epidemiological studies due to its cost-effectiveness. The additive hazards model is widely used in survival analysis when the hazards difference is constant. In this article, we propose a class of goodness-of-fit test statistics for the assumption of the additive hazards model with case-cohort data through a class of asymptotically mean-zero multiparameter stochastic processes. We also establish the asymptotic theory of the proposed test statistics and a resampling scheme is adopted to approximate its asymptotic distribution. The performance of the proposed test statistics is evaluated through simulation studies and a real dataset is analyzed to illustrate the proposed method., (© 2020 John Wiley & Sons Ltd.)

In hydrological modelling, a good result for the criterion of goodness of fit does not always imply that the hypothesis of mass conservation is fulfilled, and models can lose their essential physical soundness. We propose a way for detecting this anomaly by accounting the resulting water balance during model simulation and use it to modulate the obtained goodness of fit. We call this anomaly in water balance as "inner balance error of the model". To modulate the goodness of fit values, a penalty function that depends on this error is proposed. In addition, this penalty function is introduced into a multi-criteria objective function, which is also tested. This procedure was followed in modelling the Headwater of the Tagus River (Spain), applying the monthly abcd water balance model. Modulation of the goodness of fit allowed for detecting balance errors in the modelling, revealing that in the simulation of some catchments the model tends to accumulate water in, or release water from, the reservoir that simulates groundwater storage. Although the proposed multi-criteria objective function solves the inner balance error for most catchments, in some cases the error cannot be corrected, indicating that any error in the input and output data is probably related to groundwater flows., Competing Interests: The authors have declared that no competing interests exist.

From our initial screening of applications, we assess that the 10% to 15% of applicants whom we will interview are all academically qualified to complete our residency training program. This initial screening to select applicants to interview includes a personality assessment provided by the personal statement, Dean's letter, and letters of recommendation that, taken together, begin our evaluation of the applicant's cultural fit for our program. While the numerical scoring ranks applicants preinterview, the final ranking into best fit categories is determined solely on the interview day at a consensus conference by faculty and residents. We analyzed data of 819 applicants from 2005 to 2017. Most candidates were US medical graduates (62.5%) with 23.7% international medical graduates, 11.7% Doctors of Osteopathic Medicine (DO), and 2.1% Caribbean medical graduates. Given that personality assessment began with application review, there was excellent correlation between the preinterview composite score and the final categorical ranking in all 4 categories. For most comparisons, higher scores and categorical rankings were associated with applicants subsequently working in academia versus private practice. We found no problem in using our 3-step process employing virtual interviews during the COVID pandemic., Competing Interests: Declaration of Conflicting Interests: The author(s) declared no potential conflicts of interest concerning the research, authorship, and publication of this article., (© The Author(s) 2021.)

Evaluating the goodness of fit of logistic regression models is crucial to ensure the accuracy of the estimated probabilities. Unfortunately, such evaluation is problematic in large samples. Because the power of traditional goodness of fit tests increases with the sample size, practically irrelevant discrepancies between estimated and true probabilities are increasingly likely to cause the rejection of the hypothesis of perfect fit in larger and larger samples. This phenomenon has been widely documented for popular goodness of fit tests, such as the Hosmer-Lemeshow test. To address this limitation, we propose a modification of the Hosmer-Lemeshow approach. By standardizing the noncentrality parameter that characterizes the alternative distribution of the Hosmer-Lemeshow statistic, we introduce a parameter that measures the goodness of fit of a model but does not depend on the sample size. We provide the methodology to estimate this parameter and construct confidence intervals for it. Finally, we propose a formal statistical test to rigorously assess whether the fit of a model, albeit not perfect, is acceptable for practical purposes. The proposed method is compared in a simulation study with a competing modification of the Hosmer-Lemeshow test, based on repeated subsampling. We provide a step-by-step illustration of our method using a model for postneonatal mortality developed in a large cohort of more than 300 000 observations., (© 2020 The International Biometric Society.)

Neural networks have become increasingly popular in the field of machine learning and have been successfully used in many applied fields (e.g., imaging recognition). With more and more research has been conducted on neural networks, we have a better understanding of the statistical proprieties of neural networks. While many studies focus on bounding the prediction error of neural network estimators, limited research has been done on the statistical inference of neural networks. From a statistical point of view, it is of great interest to investigate the statistical inference of neural networks as it could facilitate hypothesis testing in many fields (e.g., genetics, epidemiology, and medical science). In this paper, we propose a goodness-of-fit test statistic based on neural network sieve estimators. The test statistic follows an asymptotic distribution, which makes it easy to use in practice. We have also verified the theoretical asymptotic results via simulation studies and a real data application.

The characterization of covariate effects on model parameters is a crucial step during pharmacokinetic/pharmacodynamic analyses. Although covariate selection criteria have been studied extensively, the choice of the functional relationship between covariates and parameters, however, has received much less attention. Often, a simple particular class of covariate-to-parameter relationships (linear, exponential, etc.) is chosen ad hoc or based on domain knowledge, and a statistical evaluation is limited to the comparison of a small number of such classes. Goodness-of-fit testing against a nonparametric alternative provides a more rigorous approach to covariate model evaluation, but no such test has been proposed so far. In this manuscript, we derive and evaluate nonparametric goodness-of-fit tests for parametric covariate models, the null hypothesis, against a kernelized Tikhonov regularized alternative, transferring concepts from statistical learning to the pharmacological setting. The approach is evaluated in a simulation study on the estimation of the age-dependent maturation effect on the clearance of a monoclonal antibody. Scenarios of varying data sparsity and residual error are considered. The goodness-of-fit test correctly identified misspecified parametric models with high power for relevant scenarios. The case study provides proof-of-concept of the feasibility of the proposed approach, which is envisioned to be beneficial for applications that lack well-founded covariate models., (© 2021 The Authors. CPT: Pharmacometrics & Systems Pharmacology published by Wiley Periodicals LLC on behalf of American Society for Clinical Pharmacology and Therapeutics.)

Classical continuous goodness-of-fit (GOF) testing is employed for examining whether the data come from an assumed parametric model. In many cases, GOF tests assume a uniform null distribution and examine extreme values of the order statistics of the samples. Many of these statistics can be expressed by a function of the order statistics and the p -values amount to a joint probability statement based on the uniform order statistics. In this paper, we utilize Steck's recursion method and propose two high precision computing algorithms to compute the p -values for these GOF statistics. The numerical difficulties in implementing Steck's method are discussed and compared with solutions provided in high precision libraries., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2020 Informa UK Limited, trading as Taylor & Francis Group.)

For the clinical development of a new drug, the determination of dose-proportionality is an essential part of the pharmacokinetic evaluations, which may provide early indications of non-linear pharmacokinetics and may help to identify sub-populations with divergent clearances. Prior to making any conclusions regarding dose-proportionality, the goodness-of-fit of the model must be assessed to evaluate the model performance. We propose the use of simulation-based visual predictive checks to improve the validity of dose-proportionality conclusions for complex designs. We provide an illustrative example and include a table to facilitate review by regulatory authorities., (© 2020 John Wiley & Sons Ltd.)

There have been numerous tests proposed to determine whether or not the exponential model is suitable for a given data set. In this article, we propose a new test statistic based on spacings to test whether the general progressive Type-II censored samples are from exponential distribution. The null distribution of the test statistic is discussed and it could be approximated by the standard normal distribution. Meanwhile, we propose an approximate method for calculating the expectation and variance of samples under null hypothesis and corresponding power function is also given. Then, a simulation study is conducted. We calculate the approximation of the power based on normality and compare the results with those obtained by Monte Carlo simulation under different alternatives with distinct types of hazard function. Results of simulation study disclose that the power properties of this statistic by using Monte Carlo simulation are better for the alternatives with monotone increasing hazard function, and otherwise, normal approximation simulation results are relatively better. Finally, two illustrative examples are presented., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2020 Informa UK Limited, trading as Taylor & Francis Group.)

Background: Two-dimensional personalized medicine (2-PM) models are tools for measuring individual benefits of medical treatments for chronic diseases which have potential applications in personalized medicine. These models assume normality for the distribution of random effects. It is necessary to examine the appropriateness of this assumption. Here, we propose a graphical approach to assessing the goodness-of-fit of 2-PM models with continuous responses., Methods: We propose benefit quantile-quantile (BQQ) plots which compare the empirical quantiles of individual benefits from a patient sample predicted through an empirical Bayes (EB) approach versus the quantiles of the theoretical distribution of individual benefits derived from the assumption of normality for the random effects. We examine the performance of the approach by conducting a simulation study that compared 2-PM models with non-normal distributions for the random effects versus models with comparable normal distributions. Cramer-von Mises discrepancies were used to quantify the performance of the approach. The approach was illustrated with data from a clinical trial of imipramine for patients with depression., Results: Simulations showed that BQQ plots were able to capture deviations from the normality assumption for the random effects and did not show any asymmetric deviations from the y = x line when the random effects were normally distributed. For the depression data, the points of the BQQ plot were scattered around closely to the y = x line, without presenting any asymmetric deviations. This implied the adequacy of the normality assumption for the random effects and the goodness-of-fit of the 2-PM model for the imipramine data., Conclusion: BQQ plots are sensitive to violations of the normality assumption for the random effects, suggesting that the approach is a useful tool for examining the goodness-of-fit of random-effects linear models when the goal is to measure individual treatment benefits.

This paper presents two new model-based goodness-of-fit tests for the ordered stereotype model applied to an ordinal response variable. The proposed tests are based on the Lipsitz test, which partitions the subjects into G groups following the popular Hosmer-Lemeshow test for binary data. The tests construct an alternative model where group effects are added into the null model. If the model fits the data well then the null model is correct, and there should be no group effects. One of the main advantages of the ordered stereotype model is that it allows us to determine a new uneven spacing of the ordinal response categories, dictated by the data. The two proposed tests use this new adjusted spacing. One test uses the form of the original ordered stereotype model, and the other uses an ordinary linear model. We demonstrate the performance of both tests under a variety of scenarios. Finally, the results of the application in three examples are presented.