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In this paper, a new approach is presented to fit a fuzzy regression model with the fuzzy coefficients when the explanatory variables and the response variable are as fuzzy numbers. In this approach, a nonlinear function is introduced to predict the response variables based on the kernel function. To estimate the parameters of regression model, the objective function is calculated using the quantile loss function on fuzzy numbers. To evaluate the goodness of fit of the optimal quantile fuzzy regression models, two indices are introduced using the similarity measures. Based on the presented results, the proposed fuzzy regression models have the perfect performances on the original data and also in the presences of different types of outliers. [ABSTRACT FROM AUTHOR]

The inequality in leaf and fruit size distribution per plant can be quantified using the Gini index, which is linked to the Lorenz curve depicting the cumulative proportion of leaf (or fruit) size against the cumulative proportion of the number of leaves (or fruits). Prior researches have predominantly employed empirical models—specifically the original performance equation (PE‐1) and its generalized counterpart (GPE‐1)—to fit rotated and right‐shifted Lorenz curves. Notably, another potential performance equation (PE‐2), capable of generating similar curves to PE‐1, has been overlooked and not systematically compared with PE‐1 and GPE‐1. Furthermore, PE‐2 has been extended into a generalized version (GPE‐2). In the present study, we conducted a comparative analysis of these four performance equations, evaluating their applicability in describing Lorenz curves related to plant organ (leaf and fruit) size. Leaf area was measured on 240 culms of dwarf bamboo (Shibataea chinensis Nakai), and fruit volume was measured on 31 field muskmelon plants (Cucumis melo L. var. agrestis Naud.). Across both datasets, the root‐mean‐square errors of all four performance models were consistently smaller than 0.05. Paired t‐tests indicated that GPE‐1 exhibited the lowest root‐mean‐square error and Akaike information criterion value among the four performance equations. However, PE‐2 gave the best close‐to‐linear behavior based on relative curvature measures. This study presents a valuable tool for assessing the inequality of plant organ size distribution. [ABSTRACT FROM AUTHOR]

The goodness of fit (GOF) test is an intensely crucial and meaningful issue in scientific research because it is widely applied in sciences such as statistics, applied mathematics, economics, finance, engineering, and so on. To the extent of this article, we first revisit the GOF test for the logistic model, and then we propose the GOF test for the zero-inflated Bernoulli (ZIBer) model. We seek to establish Karl Pearson's chi-square test and unweighted residual sum of square test for this model. Afterward, we demonstrate that both tests have an asymptotic normal distribution with a mean and standard deviation that they derived. Simulation studies and an actual data set are also studied to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Objective: The aim of this study is to introduce and analyze the Topp-Leone Kumaraswamy Fréchet (TLKFr) distribution a new probability distribution model. This model extends the classical Fréchet distribution by introducing three additional positive shape parameters to enhance flexibility and robustness. Material and Methods: The novel distribution is based on the Topp-Leone Kumaraswamy generalized distribution family, incorporating three shape parameters. This foundation allows for the derivation of both the cumulative distribution function and probability density function for the new distribution. The study also extensively explores the mathematical properties of this distribution, including the survival, hazard, and quantile functions. Parameter estimation is conducted using the maximum likelihood estimation (MLE) technique. Results: The study introduces the TLKFr distribution, providing mathematical expressions for key statistical measures. Parameters were estimated using MLE technique. Plots illustrate the distribution's characteristics, showing positive skewness and reliable survival analysis predictions. Simulation analysis indicates decreasing bias and root mean square error (RMSE) with larger sample sizes, emphasizing reliability. Application to two real-life datasets, demonstrates the TLKFr distribution consistently outperforming rival models, supported by goodness-of-fit statistics. Conclusion: The study introduces and analyzes the TLKFr distribution, enhancing the traditional Fréchet distribution with three additional shape parameters. Mathematical characteristics are explored, employing MLE for parameter estimation. A simulation study underscores the distribution's strong reliability, evident in decreasing bias and RMSE with increasing sample size. When tested with real datasets, the TLKFr distribution outperforms alternative models, highlighting its significance in representing real-world phenomena and validating its applicability to the two datasets examined in this study. [ABSTRACT FROM AUTHOR]

In data analysis, we cannot expect the data under study to always follow a symmetric probability distribution; they can have a skewed probability distribution. Modeling skewed data is a challenging task for data scientists. A mixture of probability distributions is a better option for modelling skewed data. In this study, we generated a few mixtures of probability distributions using the exponential as the first fixed component and Gompertz, Lindley, and log-normal distributions as the second component for modelling skewed data. We also examined the characteristics of mixed probability distributions. The maximum likelihood method was used to estimate the unknown parameters. As a result, all three mixture models have a right-skewed pattern, which provides a better fit than existing distributions. Finally, we used real-time datasets to model skewed data. [ABSTRACT FROM AUTHOR]

This research fitted a discrete distribution for modeling count data. Specifically, Zero-Inflated Poisson (ZIP) regression was used to model plant protein consumption by 400 randomly sampled individuals in Wukari. The data was collected by questionnaire. The ZIP regression model was used based on its ability to model data with excess zeros present in the collected data. Variables considered and used for the analysis are Age, Body Mass Index, Blood Pressure, Occupation, Gender, Weight, Height, Body Reaction, and Consumption Class. The parameters of the ZIP model were estimated using the maximum likelihood estimation technique. The model was tested for Goodness of Fit (GoF) using deviance, scaled deviance, Pearson–χ2 and scaled Pearson–χ2 statistics. The results obtained showed that Age, Gender, and Reaction were significant at 5%, and the GoF tests revealed that the Zero-Inflated Poisson regression produces a good fit and is a good model for overcoming the overdispersion effect. [ABSTRACT FROM AUTHOR]

In this study, we introduce a new four-parameter continuous probability distribution known as the Topp-Loene Gompertz Inverse Rayleigh (TLGoIRa) distribution. This novel model extends the Gompertz Inverse Rayleigh distribution. We present various mathematical properties of the distribution, including moments, moment generating functions, quantile functions, survival functions, hazard functions, reversed hazard functions, and odd functions. We also derive the distribution of order statistics, yielding both the maximum and minimum order statistics. This process of parameter estimation using the maximum likelihood estimation method is discussed. Furthermore, we present two real-life applications that illustrate the effectiveness and robustness of the TLGoIRa distribution when compared to several considered lifetime models. Our analysis reveals that the TLGoIRa distribution demonstrates superior robustness in comparison to the competing lifetime models. Additionally, the study highlights the distribution’s efficacy in fitting biomedical datasets. [ABSTRACT FROM AUTHOR]

This work presents a new model and estimation procedure for the illness–death survival data where the hazard functions follow accelerated failure time (AFT) models. A shared frailty variate induces positive dependence among failure times of a subject for handling the unobserved dependency between the nonterminal and the terminal failure times given the observed covariates. The motivation behind the proposed modeling approach is to leverage the well‐known interpretability advantage of AFT models with respect to the observed covariates, while also benefiting from the simple and intuitive interpretation of the hazard functions. A semiparametric maximum likelihood estimation procedure is developed via a kernel smoothed‐aided expectation‐maximization algorithm, and variances are estimated by weighted bootstrap. We consider existing frailty‐based illness–death models and place particular emphasis on highlighting the contribution of our current research. The breast cancer data of the Rotterdam tumor bank are analyzed using the proposed as well as existing illness–death models. The results are contrasted and evaluated based on a new graphical goodness‐of‐fit procedure. Simulation results and data analysis nicely demonstrate the practical utility of the shared frailty variate with the AFT regression model under the illness–death framework. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Inflated models are used whenever there are too many frequencies at a given count. In this regard, Poisson moment exponential distribution and a distribution to a point mass at zero are used to create a zeroinflated model namely Zero-Inflated Poisson Moment Exponential Distribution. Its distributional and reliability characteristics are investigated in some detail. A simulation exercise is undertaken to evaluate the effectiveness of the maximum likelihood estimators. The adaptability of the suggested distribution is demonstrated using three real datasets from various domains (e.g., vaccine adverse events, medical science data, epileptic seizure counts). The suggested distribution and the Poisson moment exponential distribution are distinguished by using the two different test procedures. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Specification of a parametric model for the intensity function is a fundamental task in statistics for spatial point processes. It is, therefore, crucial to be able to assess the appropriateness of a suggested model for a given point pattern dataset. For this purpose, we develop a new class of semiparametric goodness-of-fit tests for the specified parametric first-order intensity, without assuming a full data generating mechanism that is needed for the existing popular Monte Carlo tests. The proposed tests crucially rely on accurate nonparametric estimation of the second-order properties of a point process. To address this we propose a new nonparametric pair correlation function (PCF) estimator for clustered spatial point processes under some mild shape constraints, which is shown to achieve uniform consistency. The proposed test statistics are computationally efficient owing to closed-form asymptotic distributions and achieve the nominal size even for testing composite hypotheses. In practice, the proposed estimation and testing procedures provide effective tools to improve parametric intensity function modeling, which is demonstrated through extensive simulation studies as well as a real data analysis of street crime activity in Washington DC. for this article are available online. [ABSTRACT FROM AUTHOR]

Currently, two-level Mokken scale analysis for clustered test data is being developed. This paper contributes to this development by providing model-fit procedures for two-level Mokken scale analysis. New theoretical insights suggested that the existing model-fit procedure from traditional (one-level) Mokken scale analyses can be used for investigating model fit at both level 1 (respondent level) and level 2 (cluster level) of two-level Mokken scale analysis. However, the traditional model-fit procedure requires some modifications before it can be used at level 2. In this paper, we made these modifications and investigated the resulting model-fit procedure. For two model assumptions, monotonicity and invariant item ordering, we investigated the false-positive count and the sensitivity count of the level 2 model-fit procedure, with respect to the number of model violations detected, and the number of detected model violations deemed statistically significant. For monotonicity, the detection of model violations was satisfactory, but the significance test lacked power. For invariant item ordering, both aspects were satisfactory. [ABSTRACT FROM AUTHOR]

Rayleigh–Taylor (RT) interfacial mixing plays an important role in nature and technology, including atmospheric flows. In this work, we identify the physics properties of Rayleigh–Taylor mixing through the analysis of unprocessed experimental data. We consider the fluctuations spectra of the specific kinetic energy of each of the velocity components, and identify their spectral shapes, by employing the group theory guided foundations and the rigorous statistical method. We find the spectral shape parameters, including their mean values and relative errors, and apply the Anderson–Darling test to inspect the residuals and the goodness-of-fit. We scrupulously study the effect of the fitting window and identify, for each velocity component, the best fit interval, where the relative errors are small and the goodness of fit is excellent. We reveal that the fluctuations spectra in RT mixing experiments can be described by a compound function, being a product of a power-law and an exponential. The data analysis results unambiguously discovered the dynamic anisotropy and the dynamic bias of RT mixing and displayed the necessity to improve the design of experiments on RT mixing. [ABSTRACT FROM AUTHOR]

This paper considers a new lifetime distribution called Gamma-Shanker distribution which is a compound of Gamma and Shanker distribution. Many important properties of the suggested distribution including its shape, Inverse moments, hazard rate function, reversed hazard rate function, quantile function and stress-strength reliability have been discussed. The estimation of its parameters has been discussed using maximum likelihood estimation. Goodness of fit of the proposed distribution has been explained with two examples of real lifetime data from biomedical sciences and it shows that the proposed distribution gives much closure fit over the considered distributions. [ABSTRACT FROM AUTHOR]

In the literature of modern psychometric modeling, mostly related to item response theory (IRT), the fit of model is evaluated through known indices, such as χ2, M2, and root mean square error of approximation (RMSEA) for absolute assessments as well as Akaike information criterion (AIC), consistent AIC (CAIC), and Bayesian information criterion (BIC) for relative comparisons. Recent developments show a merging trend of psychometric and machine learnings, yet there remains a gap in the model fit evaluation, specifically the use of the area under curve (AUC). This study focuses on the behaviors of AUC in fitting IRT models. Rounds of simulations were conducted to investigate AUC's appropriateness (e.g., power and Type I error rate) under various conditions. The results show that AUC possessed certain advantages under certain conditions such as high-dimensional structure with two-parameter logistic (2PL) and some three-parameter logistic (3PL) models, while disadvantages were also obvious when the true model is unidimensional. It cautions researchers about the dangers of using AUC solely in evaluating psychometric models. [ABSTRACT FROM AUTHOR]

The Tucker–Lewis index (TLI; Tucker & Lewis, 1973), also known as the non-normed fit index (NNFI; Bentler & Bonett, 1980), is one of the numerous incremental fit indices widely used in linear mean and covariance structure modeling, particularly in exploratory factor analysis, tools popular in prevention research. It augments information provided by other indices such as the root-mean-square error of approximation (RMSEA). In this paper, we develop and examine an analogous index for categorical item level data modeled with item response theory (IRT). The proposed Tucker–Lewis index for IRT (TLIRT) is based on Maydeu-Olivares and Joe's (2005) M 2 family of limited-information overall model fit statistics. The limited-information fit statistics have significantly better Chi-square approximation and power than traditional full-information Pearson or likelihood ratio statistics under realistic situations. Building on the incremental fit assessment principle, the TLIRT compares the fit of model under consideration along a spectrum of worst to best possible model fit scenarios. We examine the performance of the new index using simulated and empirical data. Results from a simulation study suggest that the new index behaves as theoretically expected, and it can offer additional insights about model fit not available from other sources. In addition, a more stringent cutoff value is perhaps needed than Hu and Bentler's (1999) traditional cutoff criterion with continuous variables. In the empirical data analysis, we use a data set from a measurement development project in support of cigarette smoking cessation research to illustrate the usefulness of the TLIRT. We noticed that had we only utilized the RMSEA index, we could have arrived at qualitatively different conclusions about model fit, depending on the choice of test statistics, an issue to which the TLIRT is relatively more immune. [ABSTRACT FROM AUTHOR]

Simple Summary: The current study was conducted to predict the live body weight using body length, heart girth, rump height and withers height of 173 Savanna goats from a stud breeder at Bysteel, Polokwane municipality, South Africa. A multivariate adaptive regression splines algorithm was used, along with the different proportions of the test and training sets to predict body weight. The body weight was best predicted from the training dataset with body weight influenced by withers height and heart girth, respectively. The interaction of withers height and body length with withers height and heart girth also influenced body weight. In conclusion, it could be suggested that the multivariate adaptive regression splines algorithm might allow Savanna goat breeders to find the best population and examine the body measurements affecting body weight as indirect selection criteria for describing the breed description of Savanna goats and aiding sustainable meat production. The Savanna goat breed is an indigenous goat breed in South Africa that is reared for meat production. Live body weight is an important tool for livestock management, selection and feeding. The use of multivariate adaptive regression splines (MARS) to predict the live body weight of Savanna goats remains poorly understood. The study was conducted to investigate the influence of linear body measurements on the body weight of Savanna goats using MARS. In total, 173 Savanna goats between the ages of two and five years were used to collect body weight (BW), body length (BL), heart girth (HG), rump height (RH) and withers height (WH). MARS was used as a data mining algorithm for data analysis. The best predictive model was achieved from the training dataset with the highest coefficient of determination and Pearson's correlation coefficient (0.959 and 0.961), respectively. BW was influenced positively when WH > 63 cm and HG >100 cm with a coefficient of 0.51 and 2.71, respectively. The interaction of WH > 63 cm and BL < 75 cm, WH < 68 cm and HG < 100 cm with a coefficient of 0.28 and 0.02 had a positive influence on Savanna goat BW, while male goats had a negative influence (−4.57). The findings of the study suggest that MARS can be used to estimate the BW in Savanna goats. This finding will be helpful to farmers in the selection of breeding stock and precision in the day-to-day activities such as feeding, marketing and veterinary services. [ABSTRACT FROM AUTHOR]

Exponential-family Random Graph Models (ERGMs) have long been at the forefront of the analysis of relational data. The exponential-family form allows complex network dependencies to be represented. Models in this class are interpretable, flexible and have a strong theoretical foundation. The availability of powerful user-friendly open-source software allows broad accessibility and use. However, ERGMs sometimes suffer from a serious condition known as near-degeneracy, in which the model exhibits unrealistic probabilistic behavior or a severe lack-of-fit to real network data. Recently, Fellows and Handcock proposed a new model class, the Tapered ERGM, which circumvents the issue of near-degeneracy while maintaining the desirable features of ERGMs. However, the question of how to determine the proper amount of tapering needed for any model was heretofore left unanswered. This article develops a new methodology for how to determine the necessary level of tapering and as such provides a new approach to inference for the Tapered ERGM class. Noting that a Tapered ERGM can always be made nondegenerate, we offer data-driven approaches for determining the amount of tapering necessary. The mean-value parameter estimates are unaffected by tapering, and we show that the natural parameter estimates are numerically weakly varying by the level of tapering. We then apply the Tapered ERGM to two published networks to demonstrate its effectiveness in cases where typical ERGMs fail and present the case for Tapered ERGMs replacing ERGMs entirely. [ABSTRACT FROM AUTHOR]

This paper assesses the performance of regularized generalized least squares (RGLS) and reweighted least squares (RLS) methodologies in a confirmatory factor analysis model. Normal theory maximum likelihood (ML) and generalized least squares (GLS) statistics are based on large sample statistical theory. However, ML and GLS goodness-of-fit tests often make incorrect decisions on the true model, when sample size is small. The novel methods RGLS and RLS aim to correct the over-rejection by ML and under-rejection by GLS. Both methods outperform ML and GLS when samples are small, yet no studies have compared their relative performance. A Monte Carlo simulation study was carried out to examine the statistical performance of these two methods. We find that RLS and RGLS have equivalent performance when N ≥ 70; whereas when N < 70, RLS outperforms RGLS. Both methods clearly outperform ML and GLS with N ≤ 400. Nonetheless, adopting mean and variance adjusted test for non-normal data, RGLS slightly outperforms RLS. Power analyses found that RLS generally showed small loss in power compared to ML and performed better than RGLS. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Orientation: Ethical leadership is crucial in fostering work engagement among employees in organisations. Research purpose: This study aimed to empirically validate a theoretical model explicating the structural relationships between ethical leadership, ethical climate and work engagement. Motivation for the study: The central role of work engagement in sustaining competitive advantage calls for an analysis of the role of ethical leadership and climate in enhancing an engaged workforce. Research approach/design and method: A non-probability convenience sample consisting of 304 participants was drawn from 10 selected private security companies. Main findings: High levels of reliability were found, and the unidimensionality of the subscales was confirmed through exploratory factor analyses. A good fit with the data was found for the measurement models through confirmatory factor analysis. Structural equation modelling showed a reasonable fit for the structural model. Positive relationships were found between ethical leadership, climate and work engagement. Practical/managerial implications: The findings emphasise the role of ethical leadership and climate in work engagement. Ethical leadership fosters work engagement if employees perceive their leaders as ethical and if there is provision of favourable, transparent policies and procedures. Contribution/value-add: Ethical leadership alone may not be a sufficient condition for employee work engagement; other variables such as a positive ethical climate also play a role. The study suggests specific variables that may also combine with leadership to positively influence work engagement. [ABSTRACT FROM AUTHOR]

The goodness of fit (GOF) test plays an important role to determine whether a data set comes from an assumed distribution (with possibly unknown parameters). Many approaches have been proposed to perform the goodness of fit test, such as Chi-square, Kolmogorov-Smirnov, Cramér-Von Mises, and Anderson Darling test statistics, but most of those are proposed for univariate data. In this paper, we propose a new class of goodness of fit tests for assessing multivariate normal mixtures (with multivariate normality as a special case) based on dimension reduction. The new method allows us to directly employ existing univariate GOF tests to perform multivariate GOF tests after linearly projecting multivariate data to univariate data. The new GOF statistic is defined as the maximum of some one-dimensional GOF test statistics. We propose a bootstrap procedure to approximate the distribution of the new GOF statistic. Our approach is simple, general and can be easily extended to perform GOF tests for many other multivariate distributions. The effectiveness of our proposed new GOF tests for multivariate normal mixture models is demonstrated via simulation studies and a real data application. [ABSTRACT FROM AUTHOR]

A two-parameter quasi Suja distribution which contains Suja distribution as particular case has been proposed for extreme right skewed data. Its statistical properties including moments, skewness, kurtosis, hazard rate function, mean residual life function, stochastic ordering, mean deviations, Bonferroni and Lorenz curves, Renyi entropy measures, and stress-strength reliability have been derived and studied. The estimation of parameters using method of moments and maximum likelihood has been discussed. A simulation study has been presented to know the performance of maximum likelihood estimation. The goodness of fit of the proposed distribution has been presented. [ABSTRACT FROM AUTHOR]

Previous research on bootstrapped p-values for the chi-square test of model fit has been limited to small models (around 10 variables), revealing that these p-values are accurate provided the sample size is not too small. For small sample sizes (N < 100), usual p-values, obtained using asymptotic methods, are more accurate. However, as the number of variables increases asymptotic p-values incorrectly suggest that models fit poorly. We investigate whether Bollen-Stine (1992) bootstrapped p-values can overcome this problem using normal and non-normal data. We found that as model size increases, Bollen-Stine bootstrapped p-values become too conservative and less accurate than asymptotic p-values obtained using robust methods (i.e., mean and variance corrections). Bollen-Stine p-values cannot be recommended to assess model fit. [ABSTRACT FROM AUTHOR]

In this paper, we introduced a new probability distribution named as inverse power Maxwell distribution. The proposal distribution can be seen as an extension of the Maxwell distribution with more flexibility in modeling upside-down lifetime data. Some statistical properties of this distribution are derived. In estimation viewpoint, five methods are used for estimating the unknown parameters of the distribution and these methods are performed through the simulation study. Finally, two real data sets were analyzed to illustrate the applicability of the proposed distribution, proving that it fits each real data set much better than some other existing distributions. [ABSTRACT FROM AUTHOR]

To develop a mechanistic-empirical pavement design system for Norwegian conditions, this paper evaluates the influence of the adoption of different models and shifting techniques on the determination of dynamic modulus master curves of asphalt mixtures. Two asphalt mixture types commonly used in Norway, namely Asphalt Concrete (AC) and Stone Mastic Asphalt (SMA) containing neat bitumen and polymer-modified bitumen, were prepared by the roller compactor, and their dynamic moduli were determined by the cyclic indirect tensile test. The dynamic modulus master curves were constructed using the standard logistic sigmoidal model, a generalized logistic sigmoidal model and the Christensen–Anderson–Marasteanu model. The shifting techniques consisted of log-linear, quadratic polynomial function, Arrhenius, William–Landel–Ferry and Kaelble methods. The absolute error, normalised square error and goodness-of-fit statistics encompassing standard error ratio and coefficient of determination were used to appraise the models and shifting methods. The results showed that the standard logistic sigmoidal model and the Williams–Landel–Ferry equation had the most suitable fits for the specimens tested. The asphalt mixtures containing neat bitumen had a better fit than the ones containing polymer-modified bitumen. The Kaelble equation and log-linear equation led to similar results. These findings provide a relevant recommendation for the mechanistic-empirical pavement design system. [ABSTRACT FROM AUTHOR]

The goodness‐of‐fit model, which proposes that developmental outcomes result from combinations of environmental and children's factors, has contributed substantially to the recognition of person × environment processes. However, which pattern of person × environment interactions characterizes this model remains unclear, making it difficult to test or compare with other models (e.g., the differential‐susceptibility model). In this article, we offer solutions for these issues. We propose that a contrastive effect pattern best summarizes both goodness of fit and poorness of fit. We outline methodological considerations that help determine whether a person × environment interaction supports the goodness‐of‐fit model. We then discuss how person × environment interactions can be culturally specific, an issue aligned with the goodness‐of‐fit model but not other models. We illustrate cultural specificities in socialization‐by‐temperament interactions with evidence from different sociocultural groups. These theoretical and methodological refinements help clarify how person × environment interactions can be interpreted and predicted by the goodness‐of‐fit model. [ABSTRACT FROM AUTHOR]

In general, varieties of any cultivated species can differ in many aspects. One of the desirable traits in breeding new varieties is high yield, which can be significantly reduced by plant diseases. This study is an extension of previous research about the resistance of seed pea lines to downy mildew, and provides an extended analysis of this type of experiment. The probability of a degree of infection is determined based on a logistic model with a multinomial distribution. In the analysis the impact of a fixed effect of variety and random environmental effects is considered. It is shown that the environmental effects (combinations of years and location – macro-environments) significantly influence the resistance to diseases, and the differences among environments are larger than the variability of differences among genotypes over all environments. For two types of soils (light and rich) the most resistant varieties, which are significantly different from the control variety, are indicated. [ABSTRACT FROM AUTHOR]

In this paper, an alternative mixed Poisson distribution is proposed by amalgamating Poisson distribution and a modification of the Quasi Lindley distribution. Some fundamental structural properties of the new distribution, namely the shape of the distribution and moments and related measures, are explored. It was noted that the new distribution to be either unimodal or bimodal, and over-dispersed. Further, it has a tendency to accommodate various right tail behaviors and variance-to-mean ratios. Its unknown parameter estimation by using the maximum likelihood estimation method is examined by a simulation study based on the asymptotic theory. Finally, two real-world data sets are used to illustrate the flexibility and potentiality of the new distribution. [ABSTRACT FROM AUTHOR]

The Cramer-von Mises test is commonly used to determine how well-observed sample data fits a given model. The existing Cramer-von Mises test under traditional statistics is commonly used when sample data in reliability work are resolute and precise. In this paper, we introduced a Neutrosophic Cramer-von Mises (NCVM) test under neutrosophic statistics. The necessary measures and procedures are presented to perform the test. For the application purpose, we consider the real-life data sets of failure time batteries and ball bearings. It is inferred that the NCVM test is more instructive than the classical CVM test under indeterminacy. [ABSTRACT FROM AUTHOR]

This work utilized three years of measured satellite radio beacons to examine the statistical and temporal characteristics of tropospheric scintillation intensity and amplitude on the earth-space link over Akure, Southwest Nigeria (7.17 °N, 5.18 °E, 358 m). The signal measurement from Eutelsat W4/W7 satellite was taken between January 2016 and December 2018. The instrument used is Tektronix Y400 NetTek spectrum analyzer at a sampling rate of 1-s, downlink frequency 12.254 GHz, and path elevation of 036°E. Analysis involving cumulative distribution and probability density functions was performed over seven sampling intervals for characterizing the distribution of scintillation phenomenon on an annual and sub-annual basis. The results show scintillation intensity (σχ) to be well approximated by lognormal, Gamma, and generalized extreme value (GEV) distributions, while scintillation amplitude (χ) was suitably described by Gaussian distribution model. Also, as the sampling interval increased, the accuracy of the distribution models decreased. Analysis of mean and standard deviation equally revealed that scintillation intensities measured over longer intervals are less variable. Finally, a two-part exponential model developed for scintillation intensity prediction performed well as indicated by a least R2 value of 0.97 just as highest sum of square error (SSE) and root-mean-square error (RMSE) values of 0.192 and 0.087, respectively, were returned for both the goodness of fit and goodness of validation tests. [ABSTRACT FROM AUTHOR]

We introduce the special section on nonparametric item response theory (IRT) in Quality of Life Research. Starting from the well-known Rasch model, we provide a brief overview of nonparametric IRT models and discuss the assumptions, the properties, and the investigation of goodness of fit. We provide references to more detailed texts to help readers getting acquainted with nonparametric IRT models. In addition, we show how the rather diverse papers in the special section fit into the nonparametric IRT framework. Finally, we illustrate the application of nonparametric IRT models using data from a questionnaire measuring activity limitations in walking. The real-data example shows the quality of the scale and its constituent items with respect to dimensionality, local independence, monotonicity, and invariant item ordering. [ABSTRACT FROM AUTHOR]

In a linear regression, the coefficient of determination, R2, is a relevant measure that represents the percentage of variation in the dependent variable that is explained by a set of independent variables. Thus, it measures the predictive ability of the estimated model. For an ordinary least squares (OLS) estimator, this coefficient is calculated from the decomposition of the sum of squares. However, when the model presents collinearity problems (a strong linear relation between the independent variables), the OLS estimation is unstable, and other estimation methodologies are proposed, with the ridge estimation being the most widely applied. This paper shows that the decomposition of the sum of squares is not verified in the ridge regression and proposes how the coefficient of determination should be calculated in this case. [ABSTRACT FROM AUTHOR]

In this article, a new class of weighted exponential distribution called Entropy-Based Exponential weighted distribution (EBEWD) is proposed. The main idea of the new lifetime distribution is in using the Shannon entropy measure as a weighted function. The mathematical properties of the EBEWD, such as reliability measures, moment measures, variability measures, shapes measures, entropy measures and Fisher's information, were derived. The unknown parameters of the proposed distribution were estimated using the maximum likelihood estimation method. The efficiency and flexibility of the EBEWD were examined numerically and then by a real-life data application. The results revealed that the EBEWD outperforms some existing distributions in terms of their test statistics. [ABSTRACT FROM AUTHOR]

Replication provides a confrontation of psychological theory, not only in experimental research, but also in model-based research. Goodness of fit (GOF) of the original model to the replication data is routinely provided as meaningful evidence of replication. We demonstrate, however, that GOF obscures important differences between the original and replication studies. As an alternative, we present Bayesian prior predictive similarity checking: a tool for rigorously evaluating the degree to which the data patterns and parameter estimates of a model replication study resemble those of the original study. We apply this method to original and replication data from the National Comorbidity Survey. Both data sets yielded excellent GOF, but the similarity checks often failed to support close or approximate empirical replication, especially when examining covariance patterns and indicator thresholds. We conclude with recommendations for applied research, including registered reports of model-based research, and provide extensive annotated R code to facilitate future applications of prior predictive similarity checking. [ABSTRACT FROM AUTHOR]

Models for forecasting various ecosystem properties have great potential that comes with a need for model validation. Before we can perform such validation, we need to define what it means for the model to perform well, which depends on the question being asked. Often, it seems easy to ignore the model question and take a standard well-known error measure for comparing the model to the available data. The question is whether this practice is adequate. Here, we defined different types of model-data mismatches that may be more or less relevant to different types of questions. We show that error measures differ in their sensitivity to the type of mismatch and robustness to sparse and noisy data. The results imply that a careful selection of error measures, using a clearly defined ecological question as a starting point, is vital to proper model evaluation. While we present our results as generally applicable to the validation of any type of forecasting model, we also illustrate them using cyanobacterial bloom modelling as a detailed example of a case where different questions could be asked of the same model. • We show the need for a well-defined model question before model evaluation. • Error measures differ with respect to the question they ask the model. • Error measures differ in their robustness to sparse and noisy data. • The choice of error measure can strongly affect the model training/validation outcome. • The above is illustrated with a detailed example of cyanobacterial bloom modelling. [ABSTRACT FROM AUTHOR]

In this paper, we obtain an analytic and explicit estimator of the scale parameter using pivotal method and propose two new goodness of fit tests for the scale family based on general progressively Type-II censored samples. The properties about the test statistics are studied. Furthermore, we apply our methods to some specific life distributions for illustration. Moreover, we obtain critical values by simulations and compare the power of the two tests against various alternatives under many censoring schemes. We also obtain the empirical significance levels thorough Monte Carlo simulation. We do the comparison of the proposed estimator with the existing estimators given in the literature by means of a power study. The influence of the parameter in the alternative distribution to power is explored. The simulation results are presented using data visualization. We conclude that the estimator we derive and tests we propose perform well in many cases. Finally, a numerical example is presented. [ABSTRACT FROM AUTHOR]

We develop factor copula models to analyse the dependence among mixed continuous and discrete responses. Factor copula models are canonical vine copulas that involve both observed and latent variables, hence they allow tail, asymmetric and nonlinear dependence. They can be explained as conditional independence models with latent variables that do not necessarily have an additive latent structure. We focus on important issues of interest to the social data analyst, such as model selection and goodness of fit. Our general methodology is demonstrated with an extensive simulation study and illustrated by reanalysing three mixed response data sets. Our studies suggest that there can be a substantial improvement over the standard factor model for mixed data and make the argument for moving to factor copula models. [ABSTRACT FROM AUTHOR]

Making informed decisions about model adequacy has been an outstanding issue for regression models with discrete outcomes. Standard assessment tools for such outcomes (e.g., deviance residuals) often show a large discrepancy from the hypothesized pattern even under the true model and are not informative, especially when data are highly discrete (e.g., binary). To fill this gap, we propose a quasi-empirical residual distribution function for general discrete (e.g., ordinal and count) outcomes that serves as an alternative to the empirical distribution function of Cox–Snell residuals. The assessment tool we propose is a principled approach and does not require injecting noise into the data. When at least one continuous covariate is available, we show asymptotically that the proposed function converges uniformly to the identity function under the correctly specified model, even with highly discrete outcomes. Through simulation studies, we demonstrate empirically that the proposed quasi-empirical residual distribution function outperforms commonly used residuals for various model assessment tasks, since it is close to the hypothesized pattern under the true model and significantly departs from this pattern under model misspecification, and is thus an effective assessment tool. for this article are available online. [ABSTRACT FROM AUTHOR]

The logit binomial logistic dose response model is commonly used in applied research to model binary outcomes as a function of the dose or concentration of a substance. This model is easily tailored to assess the relative potency of two substances. Consequently, in instances where two such dose response curves are parallel so one substance can be viewed as a dilution of the other, the degree of that dilution is captured in the relative potency model parameter. It is incumbent that experimental researchers working in fields including biomedicine, environmental science, toxicology and applied sciences choose efficient experimental designs to run their studies to both fit their dose response curves and to garner important information regarding drug or substance potency. This article provides far-reaching practical design strategies for dose response model fitting and estimation of relative potency using key illustrations. These results are subsequently extended here to handle situations where the assessment of parallelism and the proper dose-scale are also of interest. Conclusions and recommended strategies are supported by both theoretical and simulation results. [ABSTRACT FROM AUTHOR]

Two main approaches are considered when building statistical models for football outcomes: (1) the goal-based approach, where the number of goals scored by two competing teams is modelled, and (2) the result-based approach, where a three-category outcome (win–draw–loss) is modelled. The debate about which approach is preferable is still ongoing, although the general agreement is that any direct comparison between the forecasting abilities of the two approaches should be based on the quality of the forecasts. Alternatively, a greater emphasis can be given to diagnostic measures in order to judge the quality of model specifications, as is more customary in statistical modelling. In this paper, we develop a broad comparison of four possible Bayesian models, focusing on model checking and calibration and then using Markov chain Monte Carlo replications to explore the predictive performance over future matches. Although inconclusive, we believe our set of comparison tools may be beneficial for future scholars in differentiating the two approaches. [ABSTRACT FROM AUTHOR]

This study examined the role of temperament type and gender of adolescents and teachers in adolescents' well‐being in school. The sample consisted of 677 Finnish students and 56 classroom teachers. Parents rated adolescent temperament and teachers rated their own temperament in autumn of Grade 6. Self‐reports of school well‐being among adolescents were obtained in autumn and the fall of Grade 6. The results showed that being a girl and having resilient temperament type predicted higher school well‐being. In turn, boys with undercontrolled temperament, who were otherwise at risk for decreased school well‐being, particularly benefited from having a female teacher with resilient temperament. Overall, the results suggest that both adolescent temperament type and gender play important roles in adolescents' well‐being in school. [ABSTRACT FROM AUTHOR]

The foundations of the criteria to assess the goodness of quantile estimators for continuous random variables are reviewed and the probabilistic justification for a novel bin-criterion is presented. It is shown that the bin-criterion is a more appropriate measure of goodness of a quantile estimator than those based on minimizing the bias of the quantiles or the parameters of the distribution. [ABSTRACT FROM AUTHOR]

Under the Bayesian approach, posterior predictive model checking (PPMC) has become a popular tool for fit assessment of item response theory (IRT) models. In this study, we propose the use of the Hellinger distance within PPMC to quantify the distance between the realized and the predictive distribution of the model-based covariance for item pairs. Specifically, the case of multidimensional data analyzed with a unidimensional approach is taken into account. The results of the simulation study show the effectiveness of the method in detecting model misfit and the sensitivity to the trait correlations. An application to real data on tourism perceptions shows the feasibility of the method in practice and especially the capability of detecting potential misfit attributed to specific items. [ABSTRACT FROM AUTHOR]

In this paper, the problem of goodness of fit test for the inverse Rayleigh distribution based on progressively Type-II censored samples is studied. We develop two test statistics via entropy and propose one new non-entropy test statistic via a pivotal method. We also study the properties of these test statistics. Critical values are obtained by simulations. Then, we do power analysis of these test statistics against various alternatives under different censoring schemes. We conclude that the tests we proposed perform well against various alternatives, especially for non-monotone hazard alternatives. Finally, one real data set is analyzed. [ABSTRACT FROM AUTHOR]

Abd El‐Monsef, Sweilam and Sabry [Quality and Reliability Engineering International, 2020, doi: 10.1002/qre.2780] proposed a four‐parameter exponentiated power Lomax distribution, derived its properties and illustrated three data applications. In this note, we show that several properties expressed in terms of infinite sums can be simplified to a known special function. We also show that certain one‐parameter distributions can provide better fits to at least two of the data sets considered. [ABSTRACT FROM AUTHOR]

Among milk traits, fat-to-protein ratio (FPR) is considered a potential measure of a cow's energy status and is one of the selection criteria necessary to improve metabolic stability. Further genetic analyses require an appropriate model that describes the pattern of FPR changes throughout lactation. The objective of the study was to examine five mathematical functions to describe the lactation curve for FPR in the first three lactations of Polish Holstein-Friesians. The dataset contained FPR records for 5690 cows in the first lactation, 4081 cows in the second, and 2636 cows in the third lactation based on 48908, 34706, and 22097 test-day (TD) records, respectively. Using the MIXED procedure of SAS statistical analytics software, ten linear models (five with fixed effects only, and five with the additional random effect of cow) were fitted to the TD records. The goodness of fit was tested with Akaike's information criterion, residual variances and the correlation coefficient between the actual and estimated values. The model proposed by Ali and Schaeffer (1987) had the best fit to FPR in the first three parities, and the model of Wilmink (1987) provided the worst fit. The correlation coefficient between the actual and the estimated values of FPR was higher for models that included the random cow effect compared with models without this effect. [ABSTRACT FROM AUTHOR]

The geometric distribution is one of the most widely used count distributions. Novel goodness of fit tests for this distribution are suggested taking advantage of a characterization of that distribution in terms of a differential equation involving its probability generating function. Several ways of looking at the characterization allow us to derive six test statistics. The connection between some of these test statistics and the ratio-plot device is stated. The asymptotic null distributions of these test statistics are derived. However, they depend on the unknown parameter of the geometric law. A suitable parametric bootstrap is used to estimate consistently each null distribution. Moreover, the almost sure limits of the test statistics under alternatives are obtained. The finite sample performance of the bootstrap approximation is assessed via simulation. The powers of the new tests are numerically compared with that of some existing ones, exhibiting competitive behaviour. Some real-life data set applications are included. [ABSTRACT FROM AUTHOR]