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While ecologists know that models require assumptions, the consequences of their violation become vague as model complexity increases. Integrated population models (IPMs) combine several datasets to inform a population model and to estimate survival and reproduction parameters jointly with higher precision than is possible using independent models. However, accuracy actually depends on an adequate fit of the model to datasets. We first investigated bias of parameters obtained from integrated population models when specific assumptions are violated. For instance, a model may assume that all females reproduce although there are non-breeding females in the population. Our second goal was to identify which diagnostic tests are sensitive to detect violations of the assumptions of IPMs. We simulated data mimicking a short- and a long-lived species under five scenarios in which a specific assumption is violated. For each simulated scenario, we fitted an IPM that violates the assumption (simple IPM) and an IPM that does not violate each specific assumption. We estimated bias and uncertainty of parameters and performed seven diagnostic tests to assess the fit of the models to the data. Our results show that the simple IPM was quite robust to violation of many assumptions and only resulted in small bias of the parameter estimates. Yet, the applied diagnostic tests were not sensitive to detect such small bias. The violation of some assumptions such as the absence of immigrants resulted in larger bias to which diagnostic tests were more sensitive. The parameters informed by the least amount of data were the most biased in all scenarios. We provide guidelines to identify misspecified models and to diagnose the assumption being violated. Simple models should often be sufficient to describe simple population dynamics, and when data are abundant, complex models accounting for specific processes will be able to shed light on specific biological questions. &nbsp

The Campbell and Vuolteenaho (Am Econ Rev 94(5):1249–1275, 2004) two–beta model decomposes the systematic risk in the sensitivity of cash flow and discount rate change. We employed this model, which we call the Two Beta Decomposition Model (TBDM) and found that this model is useful to compute the cost of capital for unlisted companies (UCs) via a proxy from listed companies. This model includes not only the accounting return reaction to long-term changes in consumption, but also links fundamental reactions to temporal changes in risk aversion. We test this model along with three traditional alternatives that are potentially useful in computing the cost of equity for UCs: accounting betas (AB), unlevered betas (UB), and operational betas (OB). Our results show that AB, UB and TBDM can partially explain the cross-sectional variations of stock returns. Additionally, using a series of non-parametric ranking test along with several statistics of goodness of fit, we found that the TBDM is the model that produces the best fit among competing models followed by the UB which is currently the most used among proxy methods.

Measuring the spread of disease during a pandemic is critically important for accurately and promptly applying various lockdown strategies, so to prevent the collapse of the medical system. The latest pandemic of COVID-19 that hits the world death tolls and economy loss very hard, is more complex and contagious than its precedent diseases. The complexity comes mostly from the emergence of asymptomatic patients and relapse of the recovered patients which were not commonly seen during SARS outbreaks. These new characteristics pertaining to COVID-19 were only discovered lately, adding a level of uncertainty to the traditional SEIR models. The contribution of this paper is that for the COVID-19 epidemic, which is infectious in both the incubation period and the onset period, we use neural networks to learn from the actual data of the epidemic to obtain optimal parameters, thereby establishing a nonlinear, self-adaptive dynamic coefficient infectious disease prediction model. On the basis of prediction, we considered control measures and simulated the effects of different control measures and different strengths of the control measures. The epidemic control is predicted as a continuous change process, and the epidemic development and control are integrated to simulate and forecast. Decision-making departments make optimal choices. The improved model is applied to simulate the COVID-19 epidemic in the United States, and by comparing the prediction results with the traditional SEIR model, SEAIRD model and adaptive SEAIRD model, it is found that the adaptive SEAIRD model's prediction results of the U.S. COVID-19 epidemic data are in good agreement with the actual epidemic curve. For example, from the prediction effect of these 3 different models on accumulative confirmed cases, in terms of goodness of fit, adaptive SEAIRD model (0.99997) approximate to SEAIRD model (0.98548) > Classical SEIR model (0.66837); in terms of error value: adaptive SEAIRD model (198.6563) < < SEAIRD model(4739.8577) < < Classical SEIR model (22,652.796); The objective of this contribution is mainly on extending the current spread prediction model. It incorporates extra compartments accounting for the new features of COVID-19, and fine-tunes the new model with neural network, in a bid of achieving a higher level of prediction accuracy. Based on the SEIR model of disease transmission, an adaptive model called SEAIRD with internal source and isolation intervention is proposed. It simulates the effects of the changing behaviour of the SARS-CoV-2 in U.S. Neural network is applied to achieve a better fit in SEAIRD. Unlike the SEIR model, the adaptive SEAIRD model embraces multi-group dynamics which lead to different evolutionary trends during the epidemic. Through the risk assessment indicators of the adaptive SEAIRD model, it is convenient to measure the severity of the epidemic situation for consideration of different preventive measures. Future scenarios are projected from the trends of various indicators by running the adaptive SEAIRD model.

Background Estimates of future survival can be a key evidence source when deciding if a medical treatment should be funded. Current practice is to use standard parametric models for generating extrapolations. Several emerging, more flexible, survival models are available which can provide improved within-sample fit. This study aimed to assess if these emerging practice models also provided improved extrapolations. Methods Both a simulation study and a case-study were used to assess the goodness of fit of five classes of survival model. These were: current practice models, Royston Parmar models (RPMs), Fractional polynomials (FPs), Generalised additive models (GAMs), and Dynamic survival models (DSMs). The simulation study used a mixture-Weibull model as the data-generating mechanism with varying lengths of follow-up and sample sizes. The case-study was long-term follow-up of a prostate cancer trial. For both studies, models were fit to an early data-cut of the data, and extrapolations compared to the known long-term follow-up. Results The emerging practice models provided better within-sample fit than current practice models. For data-rich simulation scenarios (large sample sizes or long follow-up), the GAMs and DSMs provided improved extrapolations compared with current practice. Extrapolations from FPs were always very poor whilst those from RPMs were similar to current practice. With short follow-up all the models struggled to provide useful extrapolations. In the case-study all the models provided very similar estimates, but extrapolations were all poor as no model was able to capture a turning-point during the extrapolated period. Conclusions Good within-sample fit does not guarantee good extrapolation performance. Both GAMs and DSMs may be considered as candidate extrapolation models in addition to current practice. Further research into when these flexible models are most useful, and the role of external evidence to improve extrapolations is required.

It has been observed that certain economic and financial variables commonly exhibit switching behavior depending on their magnitude. This phenomenon in general cannot be naturally captured by the linear regression (LR), which assumes a linear relationship between the dependent and explanatory variables. To decipher investor behavior more appropriately by accounting for this observation, a switching-regime regression (SRR) is proposed and applied to the S&P 500 market return with respect to seven explanatory variables. It is shown that, compared with LR, the new regression results in a significantly improved adjusted $$R^2$$ , increasing from less than $$4\%$$ to over $$50\%$$ . In addition, SRR yields better out-of-sample forecasting performance, besides that the fitted values from the new regression even resemble the dip during the 2008 financial crisis, while those from LR do not. The study thus indicates that the switching-regime regression improves significantly the statistical properties including the goodness of fit as well as conforms more to investor behavior theory.

Suppose we have a location-scale regression model where the location is the conditional mean and the scale is the conditional standard deviation; the response is possibly right-censored, the covariate is fully observed, and the error is independent of the covariate. We propose new goodness-of-fit testing procedures for the conditional mean and variance based on an integrated regression function technique which uses artificial data points. We obtain the weak convergence of the resulting processes and study their finite sample behavior via simulations. Finally, we analyze a data set about unemployment in Galicia.

We propose two families of tests for the classical goodness-of-fit problem to univariate normality. The new procedures are based on $L^2$-distances of the empirical zero-bias transformation to the normal distribution or the empirical distribution of the data, respectively. Weak convergence results are derived under the null hypothesis, under fixed alternatives as well as under contiguous alternatives. Empirical critical values are provided and a comparative finite-sample power study shows the competitiveness to classical procedures.

Numerous multivariate time series encountered in real applications display seasonal behavior. In this paper we consider portmanteau tests for testing the adequacy of structural multiplicative seasonal vector autoregressive moving-average (SVARMA) models under the assumption that the errors are uncorrelated but not necessarily independent (i.e. weak SVARMA). We study the asymptotic distributions of residual autocorrelations at seasonal lags of multiple of the length of the seasonal period under weak assumptions on the noise. We deduce the asymptotic distribution of the proposed multivariate portmanteau statistics, which can be quite different from the usual chi-squared approximation used under independent and identically distributed (iid) assumptions on the noise. A set of Monte Carlo experiments and an application of U.S. monthly housing starts and housing sold are presented.

Most statistical methods are based on models, but most practical applications ignore the fact that the results depend on the model as well as on the data. This paper examines the size of this model dependence, and finds that there can be very considerable variation between the results of fitting different models to the same data, even if the models being considered are restricted to those which give an acceptable fit to the data. Under reasonable regularity conditions, we show that different empirically acceptable models can give rise to non-overlapping confidence intervals for the same parameter. Application papers need to recognize that the validity of conventional statistical results rests on the assumption that the underlying model is known to be correct, and that this is a much stronger requirement than merely confirming that the model gives a good fit to the data. The problem of model dependence is only partially resolved by using formal methods of model selection or model averaging.

Given the recent growth of bicycle-sharing systems (BSS) around the world, it is of interest to BSS operators/analysts to identify contributing factors that influence individuals’ decision processes in adoption and usage of bicycle-sharing systems. The current study contributes to research on BSS by examining user behavior at a trip level. Specifically, we study the decision process involved in identifying destination locations after picking up the bicycle at a BSS station. In the traditional destination/location choice approaches, the model frameworks implicitly assume that the influence of exogenous factors on the destination preferences is constant across the entire population. We propose a finite mixture multinomial logit (FMMNL) model that accommodates such heterogeneity by probabilistically assigning trips to different segments and estimate segment-specific destination choice models for each segment. Unlike the traditional destination choice based multinomial logit (MNL) model or mixed multinomial logit (MMNL), in an FMMNL model, we can consider the effect of fixed attributes across destinations such as users’ or origins’ attributes in the decision process. Using data from New York City bicycle-sharing system (CitiBike) for 2014, we develop separate models for members and non-members. We validate our models using hold-out samples and compare our proposed FMMNL model results with the traditional MNL and MMNL model results. The proposed FMMNL model provides better results in terms of goodness of fit measures, explanatory power and prediction performance.

We generalize a recent class of tests for univariate normality that are based on the empirical moment generating function to the multivariate setting, thus obtaining a class of affine invariant, consistent and easy-to-use goodness-of-fit tests for multinormality. The test statistics are suitably weighted $L^2$-statistics, and we provide their asymptotic behavior both for i.i.d. observations as well as in the context of testing that the innovation distribution of a multivariate GARCH model is Gaussian. We study the finite-sample behavior of the new tests, compare the criteria with alternative existing procedures, and apply the new procedure to a data set of monthly log returns., 27 pages, 2 figures. arXiv admin note: text overlap with arXiv:1706.03029

Evapotranspiration is difficult to measure and, when measured, its spatial variability is not usually taken into account. The recommended method to estimate evapotranspiration, Penman-Monteith FAO, requires variables not available in most weather stations. Simplified but less accurate methods, as Hargreaves equation, are normally used. Several approaches have been proposed to improve Hargreaves equation accuracy. In this work, 14 calibrations of the Hargreaves equation are compared. Three goodness of fit statistics were used to select the optimal, in terms of simplicity and accuracy. The best option was an annual linear regression. Its parameters were interpolated using regression-kriging combining Random Forest and Ordinary Kriging. Twelve easy to obtain ancillary variables were used as predictors. The same approach was used to interpolate Hargreaves and Penman-Monteith-FAO ET0 on a daily basis; the Hargreaves ET0 layers and the parameter layers were used to obtain calibrated ET0 estimations. To compare the spatial patterns of the three estimations the daily layers were integrated into annual layers. The results of the proposed calibration are much more similar to Penman-Monteith FAO results than those obtained with Hargreaves equation. The research was conducted in south-east Spain with 79 weather stations with data from 01/01/2003 to 31/12/2014.

Extreme rainfall data are usually scarce due to the low frequency of these events. However, prior knowledge of the precipitation depth and return period of a design event is crucial to water resource management and engineering. This study presents a model-based selection approach associated with regional frequency analysis to examine the lack of maximum daily rainfall data in Brazil. A generalized extreme values (GEV) distribution was hierarchically fitted using a Bayesian approach and data that were collected from rainfall gauge stations. The GEV model parameters were submitted to a model-based cluster analysis, resulting in regions of homogeneous rainfall regimes. Time-series data of the individual rainfall gauges belonging to each identified region were joined into a new dataset, which was divided into calibration and validation sets to estimate new GEV parameters and to evaluate model performance, respectively. The results identified two distinct rainfall regimes in the region: more and less intense rainfall extremes in the southeast and northwest regions, respectively. According to the goodness of fit measures that were used to evaluate the models, the aggregation level of the parameters in clustering influenced their performance.

The paper is devoted to the supremum-type multivariate goodness-of-fit tests based on the empirical characteristic function. Particular attention is devoted to the composite hypothesis of normality and Gaussian distribution mixture model. An analytical way to approximate the null asymptotic distributions of the considered test statistics is discussed applying the theory of large excursions of differentiable Gaussian random fields. The produced comparative Monte Carlo power study shows that the considered tests are powerful competitors to the existing classical criteria, clearly dominating in verification of the goodness-of-fit hypotheses against the specific types of alternatives.

In ecology and evolutionary biology, controlled animal experiments are often conducted to measure time to metamorphosis which is possibly censored by the competing risk of death and the follow-up end. This paper considers the problem of estimating the survival function of time-to-event when it is subject to dependent censoring. When the censorship is due to competing risks, the traditional assumption of independent censorship may not be satisfied, and hence, the usual application of the Kaplan–Meier estimator yields a biased estimation for the survival function of the event time. This paper follows an assumed copula approach (Zheng and Klein in Biometrika 82(1):127–138, 1995) to adjust for dependence between the event time of interest and the competing event time. While the literature on an assumed copula approach has mostly focused on semiparametric settings, we alternatively consider a parametric approach with piecewise exponential models for fitting the survival function. We develop maximum likelihood estimation under the piecewise exponential models with an assumed copula. A goodness-of-fit procedure is also developed, which touches upon the identifiability issue of the copula. We conduct simulations to examine the performance of the proposed method and compare it with an existing semiparametric method. The method is applied to real data analysis on time to metamorphosis for salamander larvae living in Hokkaido, Japan (Michimae et al. in Evol Ecol Res 16:617–629, 2014).

When a statistically significant mean difference is found, the magnitude of the difference is judged qualitatively using an effect size such as Cohen's d. In contrast, in a structural equation model (SEM), the result of the statistical test of model fit is often disregarded if significant, and inferences are drawn using "close" models retained based on point estimates of sample statistics (goodness-of-fit indices). However, when a SEM cannot be retained using a test of exact fit, all substantive inferences drawn from it are suspect. It is therefore important to determine the size of the model misfit. Standardized residual covariances and residual correlations provide standardized effect sizes of the misfit of SEM models. They can be summarized using the Standardized Root Mean Squared Residual (SRMSR) and the Correlation Root Mean Squared Residual (CRMSR) which can be used as overall effect sizes of the misfit. Statistical theory is provided that allows the construction of confidence intervals and tests of close fit based on the SRMSR and CRMSR. It is hoped that the use of standardized effect sizes of misfit will help reconcile current practices in SEM and elsewhere in statistics.

This paper studies goodness-of-fit tests and specification tests for an extension of the Log-GARCH model, which is both asymmetric and stable by scaling. A Lagrange-multiplier test is derived for testing the extended Log-GARCH against more general formulations taking the form of combinations of Log-GARCH and exponential GARCH (EGARCH). The null assumption of an EGARCH is also tested. Portmanteau goodness-of-fit tests are developed for the extended Log-GARCH. An application to real financial data is proposed.

The application of the nonparametric Anderson–Darling, Cramer–Mises–Smirnov, Kuiper, Watson, Kolmogorov, and Zhang goodness-of-fit tests in verification of simple and composite hypotheses is considered. Based on an investigation of the power, it is shown for the first time that there exist pairs of competing hypotheses which these tests are not able to distinguish in the case of small sample sizes n and type 1 error probabilities. It is shown that the reason for this lies in the bias of the tests in corresponding situations.

Integrated models for multiple decision variables, not necessarily from the same family, are becoming possible thanks to the advances in econometrics and in the estimation techniques. Recently, probit type models have been proposed to model joint decisions for the flexibility offered by the multivariate normal to capture correlations across the different dependent variables. Ordered probit models are in general preferred to unordered probit for the saving in computational costs deriving from the closed mathematical form of the choice probabilities. In this study, we compare results obtained from unordered probit models estimated with simulation and numerical computation to those obtained from ordered discrete–continuous probit. The analysis is performed on household decisions concerning vehicle holding and mileage travelled and using data extracted from the 2009 National Household Travel Survey. Estimation results show that discrete–continuous unordered probit are superior to ordered structures in terms of goodness of fit, but produce comparable results when applied to predict behavioral changes. Model applications for policy analysis also reveal that income and density only affects marginally vehicle holding decisions and annual miles driven, while driving cost has a more significant effect on annual household mileage.

We explore the properties of the squared Euclidean interpoint distances (IDs) drawn from multinomial distributions. We consider the distances within one sample and across two samples and obtain their means, variances, covariances and distributions. We discuss applications of IDs for testing goodness of fit, the equality of high dimensional multinomial distributions, classification, and outliers detection. A simulation study compares the performance of the $$\chi ^2$$ and the likelihood ratio statistics for testing equality of distributions, with methods based on the IDs.

Power-law distributions can be generated by a variety of theoretical processes and have been found in many areas of economics and finance. This paper demonstrates that the distribution of cumulative oil and gas recovery in Texas is best described by a power-law distribution, with exponent approximately equal to 1.1 for oil production and 1.6 for gas production. Estimation is carried out using lease and well-level data from a cross section of over 600,000 observations gathered by DrillingInfo. The goodness of fit of the hypothesized power law is verified with regression-based and likelihood ratio tests, as well as nested and composite hypotheses. Results are significant because they show that production data are heavy tailed, that empirical variance estimates do not converge, and that 1 % of oil leases are responsible for 70 % of cumulative recovery. The distribution has consequences for efficient management and implications about peak oil because wells close to the mean account for so little of the cumulative distribution of recovery.

Analysis of censored environmental data has been of special interest to many scientists and practitioners for the recent years. Numerous works have been published on modeling bivariate environmental data when variables of interest are below some detection limits. Depending on the problem, one of the variables or both variables may be unobserved. These situations especially arise in modeling the joint distributions of environmental variables such as flood, drought and epidemiological. Some of these variables cannot be observed as they are too small to be detected below certain threshold points. Because of this censored structure, it is difficult to assess the validity of proposed bivariate distributions. Moreover, there is a wide need for a simple goodness-of-fit test for researchers working on practical environmental problems. This motivates us to propose a goodness-of-fit test for location-scale type bivariate distributions with censored data. The asymptotic distribution of the proposed test is shown to have a Chi-square distribution. A simulation study is carried out to show the power performances of the test. A real environmental data from the literature is analyzed to illustrate the efficacy of our proposed test.

This study primarily investigated the forecasting of the growth trend in renewable energy consumption in China. Only 22 samples were acquired for this study because renewable energy is an emerging technology. Because historical data regarding renewable energy were limited in sample size and the data were not normally distributed, forecasting methods used for analyzing large amounts of data were unsuitable for this study. Grey system theory is applied to system models involving incomplete information, unclear behavioral patterns, and unclear operating mechanisms. In addition, it can be used to perform comprehensive analyses, observe developments and changes in systems, and conduct long-term forecasts. The most prominent feature of this theory is that a minimum of only four data sets are required for establishing a model and that making stringent assumptions regarding the distribution of the sample population is not required. However, to address the limitations of previous studies on grey forecasting and to enhance the forecasting accuracy, this study adopted the grey model (1, 1) [GM(1, 1)] and the nonlinear grey Bernoulli model (1, 1) [(NGBM)] for theoretical derivation and verification. Subsequently, the two models were compared with a regression analysis model to determine the models’ predictive accuracy and goodness of fit. According to the indexes of mean absolute error, mean square error, and mean absolute percentage error, NGBM(1, 1) exhibited the most accurate forecasts, followed by GM(1, 1) and regression analysis model. The results indicated that the modified NGBM(1, 1) grey forecasting models demonstrated superior predictive abilities among the compared models.

The paper introduces a new approach for testing the validity of a model’s forecasts and it is established that the proposed test is exact for location–scale family. The results are used to introduce goodness-of-fit tests for the normal, exponential, uniform and Laplace distributions. Through Monte Carlo simulation, the power values of the proposed test under various alternatives are compared with the other tests. The proposed test has higher power than the competing tests against some alternatives. The use of the proposed test is shown in real examples.

The Reconnaissance Drought Index (RDI) is obtained by fitting a lognormal probability density function (PDF) to the ratio of accumulated precipitation over potential evapotranspiration values (αk) at different time scales. This paper aims to address the question of how a probability distribution may fit better to the αk values than a lognormal distribution and how RDI values may change in shorter (i.e.,3-month, and 6-month) and longer (i.e., 9-month, and annual) time scales during 1960–2010 period over various climate conditions (arid, semi-arid, and humid) in Iran. For this purpose, the series of RDI were initially computed by fitting a lognormal PDF to the αk values and the Kolmogorov–Smirnov (K-S) test was implemented to choose the best probability function in different window sizes from 3 to 12-months. The corresponding RDI values for the best distribution were then deriven based on an equiprobability transformation function. The differences between RDI values (the lognormal (RDIlog) and the best (RDIApp) distributions) were compared based on Nash-Sutcliffe efficiency (NSE) criterion. The results of goodness of fit test based on threshold value in the K-S test showed that the goodness of fit in the lognormal distribution may not be rejected at 0.01 and 0.05 significance levels while may only be rejected in a short term (Apr.-Jun.) period at humid station (Rasht station), and three-month (Oct.-Dec. and Apr.-Jun.) and six-month (Apr.-Sep.) periods in semi-arid station (Shiraz station) at significance levels of 0.10 and 0.20, correspondingly. Further a difference between RDIlog and RDIApp performed that RDI values may change if the best distribution employs and this may therefore lead to significant discrepant and/or displacement of drought severity classes in the RDI estimation.

In risk theory with application to insurance, the identification of the relevant distributions for both the counting and the claim size processes from given observations is of major importance. In some situations left-truncated distributions can be used to model, not only the single claim severity, but also the inter-arrival times between two consecutive claims. We show that left-truncated Weibull distributions are particularly relevant, especially for the claim severity distribution. For that, we first demonstrate how the parameters can be estimated consistently from the data, and then show how a Kolmogorov-Smirnov goodness-of-fit test can be set up using modified critical values. These critical values are universal to all left-truncated Weibull distributions, independent of the actual Weibull parameters. To illustrate our findings we analyse three applications using real insurance data, one from a Swiss excess of loss treaty over automobile insurance, another from an American private passenger automobile insurance and a third from earthquake inter-arrival times in California.. info:eu-repo/semantics/publishedVersion

Household members often interact with each other during their daily activity- and travel-related decision-making process. In the context of social and recreational activities, these interactions lead to decisions about pursuing such episodes either independently or jointly with others. The substantial focus of the study is on the operationalizing household interactions in various modeling mechanisms by the ways of seeking to maximize the utility of each household member in an interdependent fashion. Florida add-on samples from the 2009 National Household Travel Survey are utilized. The results indicate that household income, age of male, engagement of mandatory activities, engagement of maintenance activities, day of the week, and whether raining have strong impacts on the choice of social-recreational activity participations. Overall, no one model turned out to be a clear “winner” in terms of statistical goodness of fit and predictive abilities, rather on the behavioral insights, the multi-linear logit and parallel constrained logit models do highlight differences in the “power” across household heads, and the trivariate binary probitmodels capture strong correlations in the choices across the male and female and between solo and joint choices.

Multistate models provide important methods of analysis for many life history processes, and this is an area where John Klein made numerous contributions. When individuals in a study group are observed continuously so that all transitions between states, and their times, are known, estimation and model checking is fairly straightforward. However, individuals in many studies are observed intermittently, and only the states occupied at the observation times are known. We review methods of estimation and assessment for Markov models in this situation. Numerical studies that show the effects of inter-observation times are provided, and new methods for assessing fit are given. An illustration involving viral load dynamics for HIV-positive persons is presented.

EQ-5D-3L scoring algorithms vary amongst countries, not only in the values of regression coefficients but also in the independent variables included in the regression model (hereafter referred to as model specification). It is unclear how much of this variation is due to differences in health state selection, the relative frequencies with which health states were valued, and model diagnostics, rather than to genuine differences in population preferences. Using aggregate data from a recent review, we noted all model specifications that were used. For each country the country’s own model was re-fitted, as were all other model specifications. This was done twice: once using all valued health states for each country, and again using a common set of 17 health states for all countries. Goodness of fit was assessed using the following model diagnostics: mean absolute error (MAE), mean squared error (MSE) and rho (the Pearson correlation coefficient between predicted and observed mean utilities), both with and without leave-one-out cross-validation. Thirteen countries contributed data. Even when using a common set of health states, the preferred model varied across countries. However, choice of health states did impact the preferred model specification: when using cross-validation, the preferred specification changed in five of ten countries when moving from 17 health states to all valued health states. The relative frequency with which health states were valued had little impact on the preferred model. Variation in choices of health states to value is responsible for some, but not all, of the observed heterogeneity in model specification. Relative frequency of health state valuation and choice of model diagnostic has a limited impact on model preference, however, use of cross-validation has a substantial impact. The use of cross-validation, implemented through omitting health states rather than respondents, is recommended as one approach to assessing model fit.

As the size and complexity of models grow, the choice of the best model becomes a difficult and challenging task. Once the best model is specified, the goodness of fit of the model needs to be examined first. A highly complex model may provide a good fit, but giving no consideration to model complexity could result in incorrect estimates of parameter values and predictions. In order to improve the model selection process, model complexity needs to be defined clearly. This article studies different aspects of model complexity and discusses the extent to which they can be measured. The most common attribute that is usually ignored from many complexity measures is the parameter prior, which is an inherent part of the model and could impact the complexity significantly. The concept of parameter prior and its connection to model complexity are therefore discussed here, and some relationships to the entropy measure elements are also addressed.

Over the years, social scientists have amassed an impressive body of knowledge on state repression. Despite our improved understanding, this body of research implicitly assumes that the relationships between the independent variables and state sponsored repression are stationary over space. Current approaches, like OLS regression, cannot capture the spatial heterogeneity of the relationships and may lead to public policy inferences that are poorly specified or completely wrong for some countries. The purpose of the paper is to reexamine the repression model using geographically-weighted regression. We found significant variation in the goodness of fit of the model and strength of coefficients. A closer evaluation of the geographically varying results reveals that these variations have a distinct spatial trend, suggesting processes that might otherwise have gone undetected due to traditional ‘global’ results.

Goodness-of-fit tests are proposed for the innovation distribution in INAR models. The test statistics incorporate the joint probability generating function of the observations. Special emphasis is given to the INAR(1) model and particular instances of the procedures which involve innovations from the general family of Poisson stopped-sum distributions. A Monte Carlo power study of a bootstrap version of the test statistic is included as well as a real data example. Generalizations of the proposed methods are also discussed.

This study investigates six water quality monitoring stations in the watershed of the Feitsui Reservoir. It uses nine parameters of water quality collected in an interval of two and half years for factor analyses, which was first conducted to determine four types of factors, respectively, those for organic pollution, eutrophication, seasonal influence, and sediment pollution. The analysis results effectively help to determine water quality in the watershed of the reservoir. The authors reutilize analysis of moment structures (AMOS) to acquire further results in order to confirm the goodness of fit of the previous factor analysis model. During the confirmation, we examine the hypothesized orthogonal results as well as utilize oblique rotation to explore the goodness of fit of the reflective indicators of the orthogonal rotation. As shown in the algorithm results, as long as the covariance curve is included in the four factors, no related issues are detected in the goodness of fit of reflective indicators and interior and external quality is reported with excellence. The orthogonal model, thus, stands. Additionally, when the analysis of structural equation modeling (SEM) is conducted, sample data mismatches the hypotheses of multivariate normality. Therefore, this study adopts the generalized least square (GLS) for an algorithm. Research results of this study have been submitted to the reservoir management authorities in Taiwan for the improvement of statistical application and strategic evaluation of water quality monitoring data in order to strengthen the managerial effectiveness of water quality in watersheds.

When performing a population pharmacokinetic modelling analysis covariates are often added to the model. Such additions are often justified by improved goodness of fit and/or decreased in unexplained (random) parameter variability. Increased goodness of fit is most commonly measured by the decrease in the objective function value. Parameter variability can be defined as the sum of unexplained (random) and explained (predictable) variability. Increase in magnitude of explained parameter variability could be another possible criterion for judging improvement in the model. The agreement between these three criteria in diagnosing covariate-parameter relationships of different strengths and nature using stochastic simulations and estimations as well as assessing covariate-parameter relationships in four previously published real data examples were explored. Total estimated parameter variability was found to vary with the number of covariates introduced on the parameter. In the simulated examples and two real examples, the parameter variability increased with increasing number of included covariates. For the other real examples parameter variability decreased or did not change systematically with the addition of covariates. The three criteria were highly correlated, with the decrease in unexplained variability being more closely associated with changes in objective function values than increases in explained parameter variability were. The often used assumption that inclusion of covariates in models only shifts unexplained parameter variability to explained parameter variability appears not to be true, which may have implications for modelling decisions.

The extensions of the entropy and Kullback–Leibler (KL) information to the cumulative distribution function have been recently studied because they are well defined on the empirical distribution function. In this paper, we generalize the extended KL information to the censored case and propose a censored cumulative residual KL information. We estimate the censored cumulative residual KL information based on the empirical distribution function and evaluate its performance as a goodness of fit test statistic for the censored data.

This is an examination of models of statistical distributions and tables of percentage points for application of the Kuiper and Watson tests of goodness-of-fit for composite hypotheses belonging to samples with different parametric models of their probability distributions. An interactive simulation method is presented which can be used for the construction and use of a statistical distribution of a test in the course of the statistical analysis associated with hypothesis testing.

The so-called fuzzy representations of real-valued random variables are reviewed. They are used to visualize or/and characterize distributions through fuzzy sets. Various fuzzy representations useful to explore or test about different characteristics of real distributions are described. The main developments concerning the representation, goodness-of-fit, equality of distribution and asymmetry are overviewed. New inferential strategies for the equality of two-paired distributions based on bootstrap techniques are introduced. They are analyzed theoretically and empirically.

Historically, the National Agricultural Statistics Service crop forecasts and estimates have been determined by a group of commodity experts called the Agricultural Statistics Board (ASB). The corn yield forecasts for the “speculative region,” ten states that account for approximately 85 % of corn production, are based on two sets of monthly surveys, a farmer interview survey and a field measurement survey. The members of the ASB subjectively determine a forecast on the basis of a discussion of the survey data and auxiliary information about weather, average planting dates, and crop maturity. The ASB uses an iterative procedure, where initial state estimates are adjusted so that the weighted sum of the final state estimates is equal to a previously-determined estimate for the speculative region. Deficiencies of the highly subjective ASB process are lack of reproducibility and a measure of uncertainty. This paper describes the use of Bayesian methods to model the ASB process in a way that leads to objective forecasts and estimates of the corn yield. First, we use small area estimation techniques to obtain state-level forecasts. Second, we describe a way to adjust the state forecasts so that the weighted sum of the state forecasts is equal to a previously-determined regional forecast. We use several diagnostic techniques to assess the goodness of fit of various models and their competitors. We use Markov chain Monte Carlo methods to fit the models to both historic and current data from the two monthly surveys. Our results show that our methodology can provide reasonable and objective forecasts of corn yields for states in the speculative region.

This survey intends to collect the developments on Goodness-of-Fit for regression models during the last 20 years, from the very first origins with the proposals based on the idea of the tests for density and distribution, until the most recent advances for complex data and models. Far from being exhaustive, the contents in this paper are focused on two main classes of tests statistics: smoothing-based tests (kernel-based) and tests based on empirical regression processes, although other tests based on Maximum Likelihood ideas will be also considered. Starting from the simplest case of testing a parametric family for the regression curves, the contributions in this field provide also testing procedures in semiparametric, nonparametric, and functional models, dealing also with more complex settings, as those ones involving dependent or incomplete data.

A survey on the new developments in goodness-of-fit testing in regression models isvery welcome and the authors have done an excellent job reviewing the recent litera-ture. I would like to complement this nearly exhaustive exposition by focusing on twofurther issues in the context of testing model assumptions for regression models. Thefirst refers to hypothesis testing in nonparametric quantile regression models, whilethe second discusses goodness-of-fit tests in inverse regression models.

First of all I would like to congratulate the authors for writing this very interesting, timely and thorough review paper. It is an almost impossible task to review the very extensive literature on smoothing-based goodness-of-fit tests in regression in one single paper. Nevertheless, the paper contains a very rich collection of the contributions over the last 10–20 years, not only about goodness-of-fit tests for the regression function, but also regarding the variance function, the error distribution, the case of incomplete or dependent data, and much more. A comprehensive book on goodnessof-fit tests in regression using smoothing-based approaches is somewhat missing in the literature, and I hope that the authors will use this paper as a starting point for a more extensive book on this topic. In this discussion I would like to comment on three issues, which the authors did not consider in their review: (1) Goodness-of-fit tests for the coefficient of variation; (2) tests for the independence between the error term and the covariates; and (3) some open questions and comments.

First for all, we would like to thank the discussants for reading our paper and fortaking time to prepare such interesting and valuable contributions. The feeling, afterrevising the discussions and going back to the original version of the paper, is thatthere is still too much to say about Goodness-of-Fit (GoF) tests for regression modelsand the discussants have given a good proof of this. Although they qualify the reviewas

We discuss the following two particular aspects of the paper of Gonzalez-Manteiga and Crujeiras ( 10.1007/s11749-013-0327-5 ): First, what changes if the null hypothesis is non- or semiparametric? For example, Rodriguez-Poo et al. (A practical test for misspecification in regression: functional form, separability, and distribution. Econom. Theory, 2013, under revision) considered optimal rates of adaptive nonparametric tests when the null model is semiparametric. A second, though related question is, how serious are the bandwidth and calibration problems? Sperlich (On the choice of regularization parameters in specification testing: a critical discussion. Empir. Econ., 2013, forthcoming) has shown that the unsolved bandwidth selection problems, in particular when calibrating, render nonparametric specification tests useless in practice. Two additional questions are only raised briefly and concern (a) the computational aspects, and (b) the problem that asymptotically, nonparametric omnibus tests might reject almost any null hypothesis as probably no parametric or semiparametric model is 100 % correct. But it is maybe a reasonable and useful approximation. To this aim we recall the idea of testing the problem of so-called ‘precise hypotheses’ as outlined in Dette (Ann. Stat. 27:1012–1040, 1999) for nonparametric goodness-of-fit tests.

This paper presents a goodness-of-fit test for the volatility function of a SDE driven by a Gaussian process with stationary and centered increments. Under rather weak assumptions on the Gaussian process, we provide a procedure for testing whether the unknown volatility function lies in a given linear functional space or not. This testing problem is highly non-trivial, because the volatility function is not identifiable in our model. The underlying fractional diffusion is assumed to be observed at high frequency on a fixed time interval and the test statistic is based on weighted power variations. Our test statistic is consistent against any fixed alternative.

As an indispensable energy source, lignite is almost exclusively used in power generation in Turkey. To assess the quality level of Turkish lignite, a multivariate statistical analysis was conducted. The relationship among the lignite quality parameters has been investigated using a response method that is the logistic regression method. The analysis determines the effect of multiple predictor variables such as moisture, ash and sulphur presented simultaneously to predict membership of the two calorific value categories. By this way, a reliable binary response regression structure was constructed considering all the lignite fields in Turkey. Both the experiments on identifying the influential measurements and the measure of goodness of fit indicated that the overall model has a big capability to exhibit the relationship among the parameters of the Turkish lignite.

This article studies the robustness of confidence interval construction for the intraclass kappa statistic based on a dichotomous response when the assumption of marginal homogeneity across two raters is violated. Two methods of construction are considered: the goodness-of-fit approach and the modified Wald method. Evaluation was done by exact calculation of the confidence interval coverage produced by these approaches. It was found that under mild departures from marginal homogeneity (differences in rater success rates of $$

Empirical research often requires a method how to convert a deterministic economic theory into an econometric model. A popular method is to add a random error term on the utility scale. This method, however, ignores stochastic dominance. A modification of this method is proposed to account for stochastic dominance. The modified model compares favorably to other existing models in terms of goodness of fit to experimental data. The modified model can rationalize the preference reversal phenomenon. An intuitive axiomatic characterization of the modified model is provided. Important microeconomic concept of risk aversion is well defined in the modified model.

A new modelling approach for analysing data from discrete-choice experiments (DCEs) has been recently developed in transport economics based on the notion of regret minimization-driven choice behaviour. This so-called Random Regret Minimization (RRM) approach forms an alternative to the dominant Random Utility Maximization (RUM) approach. The RRM approach is able to model semi-compensatory choice behaviour and compromise effects, while being as parsimonious and formally tractable as the RUM approach. Our objectives were to introduce the RRM modelling approach to healthcare-related decisions, and to investigate its usefulness in this domain. Using data from DCEs aimed at determining valuations of attributes of osteoporosis drug treatments and human papillomavirus (HPV) vaccinations, we empirically compared RRM models, RUM models and Hybrid RUM–RRM models in terms of goodness of fit, parameter ratios and predicted choice probabilities. In terms of model fit, the RRM model did not outperform the RUM model significantly in the case of the osteoporosis DCE data (p = 0.21), whereas in the case of the HPV DCE data, the Hybrid RUM–RRM model outperformed the RUM model (p

The main objective of this study is to investigate the joint distribution of rainfall severity and rainfall duration in the state of Victoria, Australia, based on monthly rainfall data from selected rain-gauge stations which are located in the north-eastern and south-western parts of the state, during the period from 1950 to 2010. Traditional approach for considering the joint distribution of rainfall characteristics using standard bivariate modeling presents some limitations that can be circumvented by using Copula models. Archimedean and extreme-value copulas will be used to obtain the bivariate distribution of rainfall severity and duration. The Standard Precipitation Index (SPI), which is employed extensively to quantify rainfall severity, will be discussed in detail. Several goodness of fit tests will be performed to find the best fitting copulas and the results will be summarized. The final fitted copulas will then be applied to obtain the joint and conditional return periods from a minimum of two years to one hundred years of rainfall events in Victoria.

Radiation-related risks of cancer can be transported from one population to another population at risk, for the purpose of calculating lifetime risks from radiation exposure. Transfer via excess relative risks (ERR) or excess absolute risks (EAR) or a mixture of both (i.e., from the life span study (LSS) of Japanese atomic bomb survivors) has been done in the past based on qualitative weighting. Consequently, the values of the weights applied and the method of application of the weights (i.e., as additive or geometric weighted means) have varied both between reports produced at different times by the same regulatory body and also between reports produced at similar times by different regulatory bodies. Since the gender and age patterns are often markedly different between EAR and ERR models, it is useful to have an evidence-based method for determining the relative goodness of fit of such models to the data. This paper identifies a method, using Akaike model weights, which could aid expert judgment and be applied to help to achieve consistency of approach and quantitative evidence-based results in future health risk assessments. The results of applying this method to recent LSS cancer incidence models are that the relative EAR weighting by cancer solid cancer site, on a scale of 0-1, is zero for breast and colon, 0.02 for all solid, 0.03 for lung, 0.08 for liver, 0.15 for thyroid, 0.18 for bladder and 0.93 for stomach. The EAR weighting for female breast cancer increases from 0 to 0.3, if a generally observed change in the trend between female age-specific breast cancer incidence rates and attained age, associated with menopause, is accounted for in the EAR model. Application of this method to preferred models from a study of multi-model inference from many models fitted to the LSS leukemia mortality data, results in an EAR weighting of 0. From these results it can be seen that lifetime risk transfer is most highly weighted by EAR only for stomach cancer. However, the generalization and interpretation of radiation effect estimates based on the LSS cancer data, when projected to other populations, are particularly uncertain if considerable differences exist between site-specific baseline rates in the LSS and the other populations of interest. Definitive conclusions, regarding the appropriate method for transporting cancer risks, are limited by a lack of knowledge in several areas including unknown factors and uncertainties in biological mechanisms and genetic and environmental risk factors for carcinogenesis; uncertainties in radiation dosimetry; and insufficient statistical power and/or incomplete follow-up in data from radio-epidemiological studies.