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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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

This article reflects on the foundational contributions of Rosalie A. Kane to the rise of assisted living in the 1980s and 90s. The author, called the founder of the "Oregon model of assisted living," offers an insider's perspective of how Dr. Kane's insights – and personality–inspired a shift in the options for long term care from a model based on safety and medical treatment to one based on personal choice and independence. Along the way, the article offers an example of how sustained dialogue between theory and practice can spark concrete change. The article also assesses the personality traits that made Rosalie Kane a gifted collaborator and a generator of ideas that reached beyond the academy into real life. A brief glance at Dr. Kane's unfinished agenda speaks to her vision for today's gerontologists and social workers. [ABSTRACT FROM AUTHOR]

Residual analysis is a useful tool for checking lack of fit and for providing insight into model improvement. However, literature on residual analysis and the goodness of fit for hidden Markov models (HMMs) is limited. As HMMs with complex structures are increasingly used to accommodate different types of data, there is a need for further tools to check the validity of models applied to real world data. We review model checking methods for HMMs and develop new methods motivated by a particular case study involving a two-dimensional HMM developed for time series with many null events. We propose new residual analysis and stochastic reconstruction methods, which are adapted from model checking techniques for point process models. We apply the new methods to the case study model and discuss their adequacy. We find that there is not one "best" test for diagnostics but that our new methods have some advantages over previously developed tools. The importance of multiple tests for complex HMMs is highlighted and we use the results of our model checking to provide suggestions for possible improvements to the case study model. for this article are available online. [ABSTRACT FROM AUTHOR]

Multilevel structural equation models (MSEM) are typically evaluated on the basis of goodness of fit indices. A problem with these indices is that they pertain to the entire model, reflecting simultaneously the degree of fit for all levels in the model. Consequently, in cases that lack model fit, it is unclear which level model is misspecified. Although some researchers have suggested that model fit be assessed separately at all levels, this is not always ideal as it depends on the choice of fit indices, cutoff points, and magnitude of the intraclass correlation. Equivalence testing has recently been recommended as a superior way to evaluate the goodness of fit of models. The approach has also been heralded as a way to advance the inferential nature of structural equation modeling as a confirmatory tool. The purpose of this paper is to illustrate the use of equivalence testing for assessing multilevel model fit in educational research. Although the described procedures can be easily generalized to models with more than two levels, for simplicity we explicitly consider only two-level models. [ABSTRACT FROM AUTHOR]

Despite flotation kinetic modeling is well discussed in the literature, its evaluation from overfitting, the number of model parameters and model complexities have not been adequately addressed. Flotation kinetic behavior of two deposits including an elevated-pyritic (Cu/S = 0.21) complex copper sulfide ore and a high-grade carbonaceous sedimentary apatite (P2O5 ≥ 25%) ore were investigated. The flotation kinetic experiments were carried out in a mechanically agitated batch flotation cell. Different flotation kinetic models including seven common empirical and initially four mathematical models were applied to the experimental data. In addition to assessment of the goodness of fit (GOF) for each model, a factor of model complexity was considered using advanced statistical techniques (i.e. Bayesian information (BIC), low of iterated logarithm (LILC) and Akaike information (AIC) indices). The results confirmed that flotation kinetic modeling significantly depends on the feed type. The empirical models were found more sensitive than the mathematical ones to the ore properties and the mineral types. Furthermore, the mathematical models demonstrated relatively favorable results than the practical models concerning the variation of ore properties due to the consideration of more parameters in the modeling. Finally, it was concluded that the IC indices must be applied to the process of model selection owing to consideration of GOF, the complexity of a model and model consistency. The IC was introduced as a more reliable indicator than the common regression approach for evaluating, sequential ordering and selecting the suitable flotation kinetic models. Further studies are required for model's generalizability from a statistical point of view. [ABSTRACT FROM AUTHOR]

Informally testing the fit of a probability distribution model is educationally a desirable precursor to formal methods for senior secondary school students. Limited research on how to teach such an informal approach, lack of statistically sound criteria to enable drawing of conclusions, as well as New Zealand assessment requirements led to this study. Focusing on the Poisson distribution, the criteria used by ten Grade 12 teachers for informally testing the fit of a probability distribution model was investigated using an online task-based interview procedure. It was found that criteria currently used by the teachers were unreliable as they could not correctly assess model fit, in particular, sample size was not taken into account. The teachers then used an interactive goodness of fit simulation-based visual inference tool (GFVIT) developed by the first author to determine if the teachers developed any new understandings about goodness of fit. After using GFVIT teachers reported a deeper understanding of model fit and that the tool had allowed them to take into account sample size when testing the fit of the probability distribution model through the visualization of expected distributional shape variation. Hence, a new informal test for the fit of a probability distribution is proposed. [ABSTRACT FROM AUTHOR]

Partial Robust M (PRM) is a partial robust regression estimator using robust M-estimators. The aim of this study is to see the effects of using alternative Iteratively Reweighted Least Squares (IRLS) weight functions instead of Fair weight function used in original robust Partial Least Squares Regression (PLSR) method PRM, furthermore, is to examine the effects of soft, semi-hard and hard weightings on this algorithm in terms of efficiency, goodness of fit and prediction. Hence, classical SIMPLS, original PRM algorithm using Fair weight function and four alternative PRM algorithms named as PRMBSQR, PRMCHY, PRMHBR, PRMTLWRTH (obtained using Bisquare, Cauchy, Huber and Talworth weight functions) are compared. The simulation results and a real data application show the original PRM and PRMCHY, both of using soft weighting functions, are the leading algorithms in terms of efficiency and prediction for both low and high dimensional data sets in case of moderate outliers existence. However, when the proportion of outliers is getting higher, semi-hard weighting PRMBSQR or a hard weighting PRMTLWRTH could be good alternatives. Moreover, real data application showed that generally original PRM and PRMCHY, PRMBSQR and PRMTLWRTH algorithms have better performances in terms of outlier detection than both PRMHBR and classical SIMPLS algorithms. [ABSTRACT FROM AUTHOR]

When using univariate models, goodness of fit can be assessed through many different methods, including graphical tools such as half-normal plots with a simulation envelope. This is straightforward due to the notion of ordering of a univariate sample, which can readily reveal possible outliers. In the bivariate case, however, it is often difficult to detect extreme points and verify whether a sample of residuals is a reasonable realization from a fitted model. We propose a new framework, implemented as the bivrp R package, available on CRAN. Our framework uses the same principles of the simulation envelope in a half-normal plot, but as a simulation polygon for each point in a bivariate sample. By using algorithms of convex hull construction and polygon area reduction, we describe how our method works and illustrate its functionality with examples using simulated bivariate normal data and real bivariate count data. We show how different model diagnostics can produce different results and pinpoint potential drawbacks of our approach, such as the limitations in terms of computational burden. for this article are available online. [ABSTRACT FROM AUTHOR]

The coefficient of determination R2 and Pearson correlation coefficient ρ = R are standard metrics in hydrology for the evaluation of the goodness of fit between model simulations and observations, and as measures of the degree of dependence of one variable upon another. We show that the standard product moment estimator of ρ, termed r, while well-behaved for bivariate normal data, is upward biased and highly variable for bivariate non-normal data. We introduce three alternative estimators of ρ which are nearly unbiased and exhibit much less variability than r for non-normal data. We also document remarkable upward bias and tremendous increases in variability associated with r using both synthetic data and daily streamflow simulations from 905 calibrated rainfall–runoff models. We show that estimators of ρ = R accounting for skewness are needed for daily streamflow series because they exhibit high variability and skewness compared to, for example, monthly/annual series, where r should perform well. [ABSTRACT FROM AUTHOR]

In this paper, a pivot function which is in terms of the sample and the underlying population distribution is introduced. It is assumed that the population distribution is continuous and strictly increasing on its support. Then, the martingale central limit theorem is applied to prove that limiting distribution of the pivot function is the standard normal. Interestingly, this result provides a unified procedure that can be applied for the goodness of fit, and for the purpose of parametric and nonparametric inferences, for the populations having distribution functions that are continuous and strictly increasing on their supports. The method is fairly simple and can be easily applied. [ABSTRACT FROM AUTHOR]

In comprehending flood model results, we performed sensitivity analyses and evaluated how different combinations of digital elevation model (DEM) resolution and Manning's roughness affect flood maps produced from a 2D hydraulic model. Moreover, we analysed how the estimation of accuracy can further be influenced by the performance measure and the area's topography. Various combinations of DEM and Manning's n produced different results, in terms of quantified performance in relation to actual flood extent and the generated flood boundaries. High-resolution DEMs performed better with higher Manning's n , while lower n values were better for lower resolution DEMs. Furthermore, although lower resolution DEMs (25 and 50 m) received higher quantified performances, there are more discrepancies in the flood maps and water surface elevations (WSE) produced by them. The current statistical estimators of model performance do not necessarily provide an accurate estimate of which combination of DEM resolution and roughness are more suitable for application to modelling. Different statistical estimates have different assumptions, which can affect the model selection. Therefore, a more holistic approach towards model selection should be adopted that gives equal importance to statistical estimators, as well as the quality of flood inundation extents. [ABSTRACT FROM AUTHOR]

A probability property that connects the skew normal (SN) distribution with the normal distribution is used for proposing a goodness-of-fit test for the composite null hypothesis that a random sample follows an SN distribution with unknown parameters. The random sample is transformed to approximately normal random variables, and then the Shapiro–Wilk test is used for testing normality. The implementation of this test does not require neither parametric bootstrap nor the use of tables for different values of the slant parameter. An additional test for the same problem, based on a property that relates the gamma and SN distributions, is also introduced. The results of a power study conducted by the Monte Carlo simulation show some good properties of the proposed tests in comparison to existing tests for the same problem. [ABSTRACT FROM AUTHOR]

It is well known that there exist multiple roots of the likelihood equations for finite normal mixture models. Selecting a consistent root for finite normal mixture models has long been a challenging problem. Simply using the root with the largest likelihood will not work because of the spurious roots. In addition, the likelihood of normal mixture models with unequal variance is unbounded and thus its maximum likelihood estimate (MLE) is not well defined. In this paper, we propose a simple root selection method for univariate normal mixture models by incorporating the idea of goodness of fit test. Our new method inherits both the consistency properties of distance estimators and the efficiency of the MLE. The new method is simple to use and its computation can be easily done using existing R packages for mixture models. In addition, the proposed root selection method is very general and can be also applied to other univariate mixture models. We demonstrate the effectiveness of the proposed method and compare it with some other existing methods through simulation studies and a real data application. [ABSTRACT FROM AUTHOR]

Abstract–The additive hazards model provides benefits in interpretation and theoretical properties over the proportional hazards model, particularly in noninferiority trials. We describe techniques for designing and analyzing trials with a score-type test using the additive hazards model, with a focus on noninferiority trials. Accordingly, the techniques are illustrated using two noninferiority trials, the SPORTIF III trial of anti-coagulants for patients with atrial fibrillation, and the CPORT-E trial evaluating percutaneous coronary intervention in different clinical setting. We also derive a powerful test, which can be conducted using standard statistical software to distinguish between the additive and proportional hazards models. This test is shown to be effective in simulated data and applied to data from a study of melanoma as well as a study of colon cancer. [ABSTRACT FROM AUTHOR]

In this review the state of the art in metrics for single crystal diffraction data and suggested new developments are described. The focus is on how these metrics can help or prevent not only to describe the data but also to give hints towards unresolved modelling problems, identifying systematic errors and their sources. [ABSTRACT FROM AUTHOR]

Over the last few decades, many robust statistics have been proposed in order to assess the fit of structural equation models. To date, however, no clear recommendations have emerged as to which test statistic performs best. It is likely that no single statistic will universally outperform all contenders across all conditions of data, sample size, and model characteristics. In a real-world situation, a researcher must choose which statistic to report. We propose a bootstrap selection mechanism that identifies the test statistic that exhibits the best performance under the given data and model conditions among any set of candidates. This mechanism eliminates the ambiguity of the current practice and offers a wide array of test statistics available for reporting. In a Monte Carlo study, the bootstrap selector demonstrated promising performance in controlling Type I errors compared to current test statistics. [ABSTRACT FROM AUTHOR]

Because model misspecification can lead to inconsistent and inefficient estimators and invalid tests of hypotheses, testing for misspecification is critically important. We focus here on several general purpose goodness-of-fit tests which can be applied to assess the adequacy of a wide variety of parametric models without specifying an alternative model. Parametric bootstrap is the method of choice for computing the p-values of these tests however the proof of its consistency has never been rigourously shown in this setting. Using properties of locally asymptotically normal parametric models, we prove that under quite general conditions, the parametric bootstrap provides a consistent estimate of the null distribution of the statistics under investigation. [ABSTRACT FROM AUTHOR]

Ordinal outcomes are common in scientific research and everyday practice, and we often rely on regression models to make inference. A long-standing problem with such regression analyses is the lack of effective diagnostic tools for validating model assumptions. The difficulty arises from the fact that an ordinal variable has discrete values that are labeled with, but not, numerical values. The values merely represent ordered categories. In this article, we propose a surrogate approach to defining residuals for an ordinal outcome Y. The idea is to define a continuous variable S as a “surrogate” of Y and then obtain residuals based on S. For the general class of cumulative link regression models, we study the residual’s theoretical and graphical properties. We show that the residual has null properties similar to those of the common residuals for continuous outcomes. Our numerical studies demonstrate that the residual has power to detect misspecification with respect to (1) mean structures; (2) link functions; (3) heteroscedasticity; (4) proportionality; and (5) mixed populations. The proposed residual also enables us to develop numeric measures for goodness of fit using classical distance notions. Our results suggest that compared to a previously defined residual, our residual can reveal deeper insights into model diagnostics. We stress that this work focuses on residual analysis, rather than hypothesis testing. The latter has limited utility as it only provides a single p-value, whereas our residual can reveal what components of the model are misspecified and advise how to make improvements. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

In this article, an additive rate model is proposed for clustered recurrent event with a terminal event. The subjects are clustered by some property. For the clustered subjects, the recurrent event is precluded by the death. An estimating equation is developed for the model parameter and the baseline rate function. The asymptotic properties of the resulting estimators are established. In addition, a goodness-of-fit test is presented to assess the adequacy of the model. The finite-sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a bladder cancer data is illustrated. [ABSTRACT FROM AUTHOR]

This paper presents some powerful omnibus tests for multivariate normality based on the likelihood ratio and the characterizations of the multivariate normal distribution. The power of the proposed tests is studied against various alternatives via Monte Carlo simulations. Simulation studies show our tests compare well with other powerful tests including multivariate versions of the Shapiro–Wilk test and the Anderson–Darling test. [ABSTRACT FROM AUTHOR]

We consider a linear combination of two logarithms of cumulative hazard functions and propose a general class of flexible Weibull distribution functions which includes some well-known modified Weibull distributions (MWDs). We suggest avery flexible Weibull distribution, which belongs to the class, and show that its hazard function is monotone, bathtub-shaped, modified bathtub-shaped, or even upside-down bathtub-shaped. We also discuss the methods of least square estimation and maximum likelihood estimation of the unknown parameters. We take two illustrated examples to compare the suggested distribution with some current MWDs, and show that the suggested distribution shows good performances. [ABSTRACT FROM AUTHOR]

Transformation of variables has been recommended for addressing deviations from regression assumptions of normality, constant variance, and linearity. Though the log transformation has become the most commonly used transformation in biomedical, public health, and psychosocial research, challenges arise when the variable to be transformed has zero values. One suggested solution is adding constants. The constants added are usually chosen based on what is commonly used in a given field and have been shown to affect statistical inference. In this article, we examine the effect of the added constants in log transformation of independent variables and propose an approach to improve the choice of the added constant by considering it as a parameter to be estimated simultaneously with other model parameters. We reveal that the constants that are added to deal with zero values when log-transforming independent variables have profound effects on the goodness-of-fit of regression models. Arbitrary chosen values for constants may therefore result in poor fitting models. In contrast, considering the added constant as a model parameter optimizes the model fit. [ABSTRACT FROM AUTHOR]

This study treats an asymptotic distribution for measures of predictive power for generalized linear models (GLMs). We focus on theregression correlation coefficient(RCC) that is one of the measures of predictive power. The RCC, proposed by Zheng and Agresti is a population value and a generalization of the population value for the coefficient of determination. Therefore, the RCC is easy to interpret and familiar. Recently, Takahashi and Kurosawa provided an explicit form of the RCC and proposed a new RCC estimator for a Poisson regression model. They also showed the validity of the new estimator compared with other estimators. This study discusses the new statistical properties of the RCC for the Poisson regression model. Furthermore, we show an asymptotic normality of the RCC estimator. [ABSTRACT FROM AUTHOR]

For a single-index autoregressive conditional heteroscedastic (ARCH-M) model, estimators of the parametric and non parametric components are proposed by the profile likelihood method. The research results had shown that all the estimators have consistency and the parametric estimators have asymptotic normality. We extend this line of research by deriving the asymptotic normality of the non parametric estimator. Based on the asymptotic properties, we propose Wald statistic and generalized likelihood ratio statistic to investigate the testing problems for ARCH effect and goodness of fit, respectively. A simulation study is conducted to evaluate the finite-sample performance of the proposed estimation methodology and testing procedure. [ABSTRACT FROM AUTHOR]

Count data consists of discrete non-negative integer values. Poisson regression model is one of the most popular model used to model count data. This model assumes that response variable has Poisson distribution. The purpose of this article is to assess distributional assumption of this model by using some goodness of fit tests. These tests are compared in respect to type I error and power rates of tests with different samples, parameters and sample sizes. Simulation study suggests that the most powerful tests are generally Dean-Lawless and Cameron-Trivedi score tests. [ABSTRACT FROM AUTHOR]

In this article, we take a brief overview of different functional forms of generalized Poisson distribution (GPD) and various methods of its parameter estimation found in the literature. We compare the method of moment estimation (ME) and maximum likelihood estimation (MLE) of parameters of GPD through simulation study in terms of bias, MSE and covariance. To simulate random numbers from GPD, we develop a Matlab functiongpoissrnd(). The simulation study leads to the important conclusion that the ME performs better or equally good as compared to MLE when sample size is small. Further we fit the GPD to various datasets in literature using both estimation methods and observe that the results do not differ significantly even though the sample size is large. Overall, we conclude that for GPD, use of ME in place of MLE will lead to almost similar results. The computational simplicity in calculation of ME as compared to MLE also gives support to the use of ME in case of GPD for practitioners. [ABSTRACT FROM AUTHOR]

This article discusses applications of Charlier polynomials when checking how well classic Poisson model fits the data. We show that smooth components pertaining to the polynomials can be effectively used in preliminary analysis of data at hand and we propose and discuss some tests based on them. Our extensive simulations shed new light on power behavior of the best tests in the area. [ABSTRACT FROM AUTHOR]

Fuzzy least-square regression can be very sensitive to unusual data (e.g., outliers). In this article, we describe how to fit an alternative robust-regression estimator in fuzzy environment, which attempts to identify and ignore unusual data. The proposed approach concerns classical robust regression and estimation methods that are insensitive to outliers. In this regard, based on the least trimmed square estimation method, an estimation procedure is proposed for determining the coefficients of the fuzzy regression model for crisp input-fuzzy output data. The investigated fuzzy regression model is applied to bedload transport data forecasting suspended load by discharge based on a real world data. The accuracy of the proposed method is compared with the well-known fuzzy least-square regression model. The comparison results reveal that the fuzzy robust regression model performs better than the other models in suspended load estimation for the particular dataset. This comparison is done based on a similarity measure between fuzzy sets. The proposed model is general and can be used for modeling natural phenomena whose available observations are reported as imprecise rather than crisp. [ABSTRACT FROM AUTHOR]

In this article, we propose a robust statistical approach to select an appropriate error distribution, in a classical multiplicative heteroscedastic model. In a first step, unlike to the traditional approach, we do not use any GARCH-type estimation of the conditional variance. Instead, we propose to use a recently developed nonparametric procedure [31]: the local adaptive volatility estimation. The motivation for using this method is to avoid a possible model misspecification for the conditional variance. In a second step, we suggest a set of estimation and model selection procedures (Berk–Jones tests, kernel density-based selection, censored likelihood score, and coverage probability) based on the so-obtained residuals. These methods enable to assess the global fit of a set of distributions as well as to focus on their behaviour in the tails, giving us the capacity to map the strengths and weaknesses of the candidate distributions. A bootstrap procedure is provided to compute the rejection regions in this semiparametric context. Finally, we illustrate our methodology throughout a small simulation study and an application on three time series of daily returns (UBS stock returns, BOVESPA returns and EUR/USD exchange rates). [ABSTRACT FROM AUTHOR]

We examine three approaches for testing goodness of fit in ordinal logistic regression models: an ordinal version of the Hosmer–Lemeshow test (), the Lipsitz test, and the Pulkstenis–Robinson (PR) tests. The properties of these tests have previously been investigated for the proportional odds model. Here, we extend the tests to two other commonly used models: the adjacent-category and the constrained continuation-ratio models. We use a simulation study to assess null distributions and power. All three tests work well and can detect several types of lack of fit under both the adjacent-category and constrained continuation-ratio models. Theand Lipsitz tests are best suited to detect lack of fit associated with continuous covariates, whereas the PR tests excel at detecting lack of fit associated with categorical covariates. We illustrate the use of the tests with data from a study of aftercare placement of psychiatrically hospitalized adolescents. Based on the results here and previous research, we can make a joint recommendation for testing goodness of fit in proportional odds, adjacent-category, and constrained continuation-ratio logistic regression models: because the tests may detect different types of lack of fit, a thorough assessment of goodness of fit requires use of all three approaches. [ABSTRACT FROM AUTHOR]

This note presents the original Steiger-Lind (1980) handout entitled, “Statistically-Based Tests for the Number of Common Factors”, distributed to all in attendance at the talk given at the annual meeting of the Psychometric Society in Iowa City, Iowa. [ABSTRACT FROM PUBLISHER]

The Lindley distribution has been used recently for modeling lifetime data and studying some stress-strength problems. In this paper, a new three-parameter Lindley distribution is introduced. The added location parameter offers more flexibility in fitting some real data against other common distributions. Several statistical and reliability properties are discussed. A simulation study has been carried to examine the MSE, bias, and coverage probability for the parameters. A real data set is used to illustrate the flexibility of the proposed distribution. [ABSTRACT FROM AUTHOR]

The rootogram is a graphical tool associated with the work of J.W. Tukey that was originally used for assessing goodness of fit of univariate distributions. Here, we extend the rootogram to regression models and show that this is particularly useful for diagnosing and treating issues such as overdispersion and/or excess zeros in count data models. We also introduce a weighted version of the rootogram that can be applied out of sample or to (weighted) subsets of the data, for example, in finitemixture models. An empirical illustration revisiting a well-known dataset from ethology is included, for which a negative binomial hurdle model is employed. Supplementary materials providing two further illustrations are available online: the first, using data from public health, employs a two-component finite mixture of negative binomial models; the second, using data from finance, involves underdispersion. An R implementation of our tools is available in the R package countreg. It also contains the data and replication code. [ABSTRACT FROM AUTHOR]

The Goodness-of-Fit model [Thomas, A., & Chess, S. (1977).Temperament and development. New York: Brunner/Mazel] proposes that a child's temperament interacts with the environment to influence child outcomes. In the past, researchers have shown how the association between the quality of the teacher–child relationship in daycare and child behaviour is moderated by temperament [Vitiello, V., Moas, O., Henderson, H., Greenfield, D., & Munis, P. (2012). Goodness of fit between children and classrooms: Effects of child temperament and preschool classroom quality on achievement trajectories.Early Education and Development,23, 302–322.]. Our goal was to examine how teacher–child relationship quality is associated with prosocial behaviour in preschool children and the moderating role of temperament. Information about 60 children (n = 60) in preschool daycare within Eastern Canada was provided by daycare teachers. Children were classified into temperament categories (undercontrolled, overcontrolled, and resilient) and rated on prosocial behaviour. Results revealed that temperament significantly moderates the association between teacher–child relationship and prosocial behaviour. Goodness of fit was supported, in that having a good fit between teacher–child relationship and temperament was predictive of increased prosocial behaviour. Relevance to goodness of fit is further discussed with relation to previous research. [ABSTRACT FROM AUTHOR]

Nakagami distribution is one of the most common distributions used to model positive valued and right skewed data. In this study, we interest goodness of fit problem for Nakagami distribution. Thus, we propose smooth tests for Nakagami distribution based on orthonormal functions. We also compare these tests with some classical goodness of fit tests such as Cramer–von Mises, Anderson–Darling, and Kolmogorov–Smirnov tests in respect to type-I error rates and powers of tests. Simulation study indicates that smooth tests give better results than these classical tests give in respect to almost all cases considered. [ABSTRACT FROM AUTHOR]