Inferential Issues Research Articles

Modeling uncertainty with the truncated zeta distribution in mixture models for ordinal responses

In recent three decades, there has been a rapid increasing interest in the mixture models for ordinal responses, and the classical CUB model as a fundamental one has been extended to different preference and uncertainty models. In this article, based on a response style supported by Zipf’s law, we propose a novel mixture model for ordinal responses via replacing the uncertainty component of the CUB model with a truncated Zeta distribution. Parameters estimation with EM algorithm, inferential issues with respect to the approximation of a truncated Riemann Zeta function and estimators’ variance-covariance information matrix are investigated. The advantages of the proposed model over the CUB model have been illustrated with simulations of two sets of Monte Carlo experiments and practical applications of a health survey and a bicycle use. The intention of the article is to distinguish the respondents’ true preference from the response style of “the higher, the less”, so as to understand more reasonably the formation causes of ordinal responses.

Threshold spatial autoregressive model

In this paper, we consider the estimation and inferential issues of the threshold spatial autoregressive (TSAR) model, which is a hybrid of the threshold and spatial autoregressive models. We use the quasi maximum likelihood (QML) method to estimate the model. In addition, we prove the tightness and the Hájek–Rényi type inequality for a quadratic form and establish a full inferential theory of the QML estimator under the setup that threshold effect shrinks to zero as the sample size increases. We conduct hypothesis testing on the presence of the threshold effect, using three super-type statistics. Their asymptotic behaviors are studied under the Pitman local alternatives. A bootstrap procedure is applied to obtain the asymptotically correct critical value. We also consider hypothesis testing on the threshold value set equal to a prespecified one. We run Monte Carlo simulations to investigate the finite sample performance of the QML estimators and find that the estimators perform well. In an empirical application, we apply the proposed TSAR model to study the relationship between financial development and economic growth, and we find firm evidence to support the TSAR model.

Understanding the dual glass ceiling of selecting and electing women candidates: evidence from Latin American mayoral elections

ABSTRACT Women politicians face two distinct glass ceilings – when becoming candidates and when turning these candidacies into elected offices. While existing research posits important explanatory accounts of both these processes, both stages are often studied separately when the determinants of women’s descriptive representation are analyzed. This generates possible inferential issues, because one stage conditions the other and individual variables might pull in opposing directions in both stages. Drawing on a novel data set of mayoral elections in almost 10,000 municipalities across 15 Latin American countries, we build on existing research to identify the distinct components of glass ceilings at both stages, propose a methodological solution to this problem, illustrate how certain variables have different effects in each stage, and draw implications for theory building in the research on women’s descriptive representation.

FLAT LIKELIHOODS: BINOMIAL CASE

The shape of the likelihood function is often considered as one of the underlying causes of strange or counterintuitive estimation results. However, strange likelihood shapes may be a symptom of inferential issues related with the nature of the model and experimental data. In the cases discussed here, binomial flat likelihoods are related not only to sample size, but also to an embedded Poisson model problem. It is essential to understand the shapes of the likelihood function in order for being able to legitimately criticize likelihood inferences. This is particularly important since the likelihood function is a key ingredient in many inferential methods

Cubic rank transmuted generalized Gompertz distribution: properties and applications

In this paper, we introduce a new lifetime distribution as an alternative to generalized Gompertz, Gompertz distribution and its modified ones. This new distribution is a special case of the family of distributions introduced by Granzotto et al. [D.C.T. Granzotto, F. Louzada and N. Balakrishnan, Cubic rank transmuted distributions: inferential issues and applications., J. Stat. Comput. Simul. 87 (2017), pp. 2760–2778]. We obtain some characteristic properties of suggested distribution such as hazard function, ordinary moments, coefficient of skewness, coefficient of kurtosis, moment generating function, quantile function and median. We discuss three different methods of estimation to estimate the parameters of proposed distribution. A comprehensive Monte Carlo simulation study is performed in order to compare the performances of estimators according to mean square errors and biases. Finally, three real data applications are performed to illustrate usefulness of suggested distribution.

Computer Model Calibration with Time Series Data Using Deep Learning and Quantile Regression

Computer models play a key role in many scientific and engineering problems. One major source of uncertainty in computer model experiment is input parameter uncertainty. Computer model calibration is a formal statistical procedure to infer input parameters by combining information from model runs and observational data. The existing standard calibration framework suffers from inferential issues when the model output and observational data are high-dimensional dependent data such as large time series due to the difficulty in building an emulator and the non-identifiability between effects from input parameters and data-model discrepancy. To overcome these challenges we propose a new calibration framework based on a deep neural network (DNN) with long-short term memory layers that directly emulates the inverse relationship between the model output and input parameters. Adopting the 'learning with noise' idea we train our DNN model to filter out the effects from data model discrepancy on input parameter inference. We also formulate a new way to construct interval predictions for DNN using quantile regression to quantify the uncertainty in input parameter estimates. Through a simulation study and real data application with WRF-hydro model we show that our approach can yield accurate point estimates and well calibrated interval estimates for input parameters.

On the asymptotic properties of the likelihood estimates and some inferential issues related to hidden truncated Pareto (type II) model

The usefulness of a hidden truncated Pareto (type II) model along with its’ inference under both the classical and Bayesian paradigm have been discussed in the literature in great details. In the multivariate set-up, some discussions are made that are primarily based on constructing a multivariate hidden truncated Pareto (type II) models with — single variable truncation or more than one variable truncation. However, in all such previous discussions regarding bivariate hidden truncated Pareto models, in the classical estimation set-up, large bias and standard error values for the truncation parameter(s) as well as for the other parameters have been observed, and no discussion was made to address this issue. In this article, we try to address this issue of large bias values by considering constrained optimization via linear/non-linear transformation of the parameters following the strategy as proposed (the reference is given in Section 3), in efficiently implementing Newton-Raphson optimization algorithm in R. This plays a major motivation for the present paper. We also derive the observed Fisher Information Matrix. For illustrative purposes, we provide a simulation study to address this issue. A real-life data set is also re-analyzed to study the utility of such two-sided hidden truncation Pareto (type II) models.

Making Inferences from Index Numbers (1860–1914)

Index numbers are indirect measurements as well as composite quantities that present particular inferential challenges to the measurer and their intended audiences. The early history of the use of index numbers in British economics (ca. 1860–1914) shows that making inferences using this measuring instrument was rife with problems. Economists grappled with multiple “inferential gaps” in order to make inferences from index numbers. The extent to which these gaps could be bridged depended on the theoretical frameworks and measurement strategies used. However, it is also evident that some inferential issues confronting economists were ideological or political in nature. Two case studies are examined, Stanley Jevons’s price index and the Board of Trade’s cost-of-living index, that sharpen the focus on the accuracy of index numbers. What did index numbers really capture about the deterioration of the monetary standard or standard of living of the working classes? By situating the index numbers within the broader ecology in which they were constructed, the article shows that making inferences was not just a heuristic process (one that eliminated gaps by getting the estimations right) but a cognitive one as well (one that people could accept as being “fit for purpose”).

To the exclusion of all others? DNA profile and transfer mechanics—R v Jones (William Francis) [2020] EWCA Crim 1021 (03 Aug 2020)

This case note deals with doctrinal and inferential issues around the use of DNA in the criminal process, in particular DNA alone, as a case to answer.

Generalized confidence interval for an agreement between raters.

Estimation and inference are two key components toward the solution of any statistical problem; however, the inferential issues of statistical assessment of agreement among two or more raters have not been well developed as compared to the development of estimation procedures in this area. The fundamental reason for this gap is the complex expression of the concordance correlation coefficient (CCC) that is frequently used in assessing agreement among raters. Large sample-based statistical tests for CCC often fail to produce desired results for small samples. Hence, inferential procedures for small samples are urgently needed to evaluate agreement between raters. We argue that hypothesis testing of CCC has little value in practice due to the absence of a gold standard of agreement. In this article, we construct the generalized confidence interval (GCI) for CCC utilizing a bivariate normal distribution of measurements, and also develop a large sample-based confidence interval (LSCI). We establish satisfactory performance of GCI by providing the desired coverage probability (CP) via simulation. Results of GCI and LSCI are illustrated and compared with a data set of a recent study performed at U.S. Department of Veterans Affairs, Hines.

Separation and Rare Events

AbstractWhen separation is a problem in binary dependent variable models, many researchers use Firth's penalized maximum likelihood in order to obtain finite estimates (Firth, 1993; Zorn, 2005; Rainey, 2016). In this paper, I show that this approach can lead to inferences in the opposite direction of the separation when the number of observations are sufficiently large and both the dependent and independent variables are rare events. As large datasets with rare events are frequently used in political science, such as dyadic data measuring interstate relations, a lack of awareness of this problem may lead to inferential issues. Simulations and an empirical illustration show that the use of independent “weakly-informative” prior distributions centered at zero, for example, the Cauchy prior suggested by Gelman et al. (2008), can avoid this issue. More generally, the results caution researchers to be aware of how the choice of prior interacts with the structure of their data, when estimating models in the presence of separation.

A spatial mixed-effects regression model for electoral data

On 4th March 2018, elections took place in Italy for the two Chambers of the Parliament. Many newspapers emphasized the victory of the 5 Star Movement (5SM) and its unprecedented dominance in most of the southern regions of Italy. Aim of this contribution is to analyze the electoral results through an ad hoc statistical model to evaluate the presence and possible impact of spatial structures. The response variable is the percentage of votes got by the 5SM in each electoral district. To handle a bounded continuous outcome with values in the open interval (0, 1), a mixture regression model is used. This model is based on a special mixture of two betas (referred to as flexible beta) sharing the same precision parameter, but displaying two distinct component means subject to an inequality constraint. Advantages of this model are its many theoretical properties which are reflected in its computational tractability. Furthermore, the special mixture structure is designed to represent a wide range of phenomena (bimodality, heavy tails, and outliers). The model is further extended through random effects to account for spatial correlation. Intensive simulation studies are performed to evaluate the fit of the proposed regression model. Inferential issues are dealt with by a (Bayesian) Hamiltonian Monte Carlo algorithm.

A Flexible Parametric Modelling Framework for Survival Analysis

SummaryWe introduce a general, flexible, parametric survival modelling framework which encompasses key shapes of hazard functions (constant; increasing; decreasing; up then down; down then up) and various common survival distributions (log-logistic; Burr type XII; Weibull; Gompertz) and includes defective distributions (cure models). This generality is achieved by using four distributional parameters: two scale-type parameters—one of which relates to accelerated failure time (AFT) modelling; the other to proportional hazards (PH) modelling—and two shape parameters. Furthermore, we advocate ‘multiparameter regression’ whereby more than one distributional parameter depends on covariates—rather than the usual convention of having a single covariate-dependent (scale) parameter. This general formulation unifies the most popular survival models, enabling us to consider the practical value of possible modelling choices. In particular, we suggest introducing covariates through just one or other of the two scale parameters (covering AFT and PH models), and through a ‘power’ shape parameter (covering more complex non-AFT or non-PH effects); the other shape parameter remains covariate independent and handles automatic selection of the baseline distribution. We explore inferential issues and compare with alternative models through various simulation studies, with particular focus on evidence concerning the need, or otherwise, to include both AFT and PH parameters. We illustrate the efficacy of our modelling framework by using data from lung cancer, melanoma and kidney function studies. Censoring is accommodated throughout.

Research Registries: Facts, Myths, and Possible Improvements

The past few decades have ushered in an experimental revolution in economics whereby scholars are now much more likely to generate their own data. While there are virtues associated with this movement, there are concomitant difficulties. Several scientific disciplines, including economics, have launched research registries in an effort to attenuate key inferential issues. This study assesses registries both empirically and theoretically, with a special focus on the AEA registry. We find that over 90% of randomized controlled trials (RCTs) in economics do not register, only 50% of the RCTs that register do so before the intervention begins, and the majority of these preregistrations are not detailed enough to significantly aid inference. Our empirical analysis further shows that using other scientific registries as aspirational examples is misguided, as their perceived success in tackling the main issues is largely a myth. In light of these facts, we advance a simple economic model to explore potential improvements. A key insight from the model is that removal of the (current) option to register completed RCTs could increase the fraction of trials that register. We also argue that linking IRB applications to registrations could further increase registry effectiveness.

A bivariate inverse Weibull distribution and its application in complementary risks model

ABSTRACTIn reliability and survival analysis the inverse Weibull distribution has been used quite extensively as a heavy tailed distribution with a non-monotone hazard function. Recently a bivariate inverse Weibull (BIW) distribution has been introduced in the literature, where the marginals have inverse Weibull distributions and it has a singular component. Due to this reason this model cannot be used when there are no ties in the data. In this paper we have introduced an absolutely continuous bivariate inverse Weibull (ACBIW) distribution omitting the singular component from the BIW distribution. A natural application of this model can be seen in the analysis of dependent complementary risks data. We discuss different properties of this model and also address the inferential issues both from the classical and Bayesian approaches. In the classical approach, the maximum likelihood estimators cannot be obtained explicitly and we propose to use the expectation maximization algorithm based on the missing value principle. In the Bayesian analysis, we use a very flexible prior on the unknown model parameters and obtain the Bayes estimates and the associated credible intervals using importance sampling technique. Simulation experiments are performed to see the effectiveness of the proposed methods and two data sets have been analyzed to see how the proposed methods and the model work in practice.

Bayesian factor analytic model: An approach in multiple environment trials.

One of the main challenges in plant breeding programs is the efficient quantification of the genotype-by-environment interaction (GEI). The presence of significant GEI may create difficulties for breeders in the selection and recommendation of superior genotypes for a wide environmental network. Among the diverse statistical procedures developed for this purpose, we highlight those based on mixed models and factor analysis that are called factor analytic (FA) models. However, some inferential issues are related to the factor analytic model, such as Heywood cases that make the model non-identifiable. Moreover, the representation of the loads and factors in the conventional biplot does not involve any measurement of uncertainty. In this work, we propose dealing with the FA model using the Bayesian framework with direct sampling of factor loadings via spectral decomposition; this guarantees identifiability in the estimation process and eliminates the need for the rotationality of factor loadings or imposition of any ad hoc constraints. We used simulated and real data to illustrate the method’s application in multi-environment trials (MET) and to compare it with traditional FA mixed models on controlled unbalancing. In general, the Bayesian FA model was robust under different simulated unbalanced levels, presenting the superior predictive ability of missing data when compared to competing models, such as those based on FA mixed models. In addition, for some scenarios, the classical FA mixed model failed in estimating the full FA model, illustrating the parametric problems of convergence in these models. Our results suggest that Bayesian factorial models might be successfully used in plant breeding for MET analysis.

On some inferential issues for the destructive COM-Poisson-generalized gamma regression cure rate model

In this paper, we assume the initial number of malignant cells to undergo a destructive process and hence what we record is only from the undamaged portion of the original number of malignant cells. This gives a realistic and practical interpretation of the biological mechanism of the occurrence of a cancerous tumor. We propose to model the initial number of malignant cells by the flexible Conway-Maxwell (COM) Poisson distribution, which includes some of the commonly used discrete distributions as its particular cases. Furthermore, we propose to model the time taken by each active malignant cell after an initial treatment by the wider class of generalized gamma distribution, which includes some of the commonly used lifetime distributions as its particular cases. The main contribution is in developing the likelihood inference based on the expectation maximization algorithm for such a flexible and general destructive cure rate model. An extensive simulation study is carried out to demonstrate the performance of the proposed estimation method. The flexibilities of the COM-Poisson distribution and the generalized gamma distribution are also utilized to carry out a two-way model discrimination using some likelihood-based methods. Finally, a melanoma dataset is analyzed for illustrative purposes.

Rejoinder to the discussion of “The class of cub models: statistical foundations, inferential issues and empirical evidence”

The paper is the rejoinder to a series of Discussions on the class of cub models for rating data. The main topics advanced by Discussants are reviewed and debated, with focus on the most prominent issues. As a result, the trailhead of possible future research developments is outlined.

A review of: The class of CUB models: statistical foundations, inferential issues and empirical evidence by Domenico Piccolo and Rosaria Simone

This discussion consists of six comments to the review paper by Piccolo and Simone. The comments offer an expanded perspective designed to encourage further research in the important class of CUB model.

Comments on The class of cub models: statistical foundations, inferential issues and empirical evidence by D. Piccolo and R. Simone

Comments on The class of cub models: statistical foundations, inferential issues and empirical evidence by D. Piccolo and R. Simone