Benchmark Dose Calculation for Ordered Categorical Responses

The use of benchmark dose (BMD) calculations for dichotomous or continuous responses is well established in the risk assessment of cancer and noncancer endpoints. In some cases, responses to exposure are categorized in terms of ordinal severity effects such as none, mild, adverse, and severe. Such responses can be assessed using categorical regression (CATREG) analysis. However, while CATREG has been employed to compare the benchmark approach and the no‐adverse‐effect‐level (NOAEL) approach in determining a reference dose, the utility of CATREG for risk assessment remains unclear. This study proposes a CATREG model to extend the BMD approach to ordered categorical responses by modeling severity levels as censored interval limits of a standard normal distribution. The BMD is calculated as a weighted average of the BMDs obtained at dichotomous cutoffs for each adverse severity level above the critical effect, with the weights being proportional to the reciprocal of the expected loss at the cutoff under the normal probability model. This approach provides a link between the current BMD procedures for dichotomous and continuous data. We estimate the CATREG parameters using a Markov chain Monte Carlo simulation procedure. The proposed method is demonstrated using examples of aldicarb and urethane, each with several categories of severity levels. Simulation studies comparing the BMD and BMDL (lower confidence bound on the BMD) using the proposed method to the correspondent estimates using the existing methods for dichotomous and continuous data are quite compatible; the difference is mainly dependent on the choice of cutoffs for the severity levels.     

On Small Samples Testing for Frailty Through Homogeneity Test

We derive a test in order to examine the need of modeling survival data using frailty models based on the likelihood ratio (LR) test for homogeneity. Test is developed for both complete and censored samples from a family of baseline distributions that satisfy a closure property. Approach motivated by I-divergence distance is used in order to determine “credible” regions for all parameters of baseline distribution for which homogeneity hypothesis is not rejected. Proposed test outperforms the usual asymptotic LR test both in very small samples with known frailty and for all small sample sizes under misspecified frailty.     

Finite-sample properties of limited-iinformation estimators in misspecified simultaneous equation models

The two most common limited-information estimators in Simultaneous Equation Models are the two-stage least squares and limited-information maximum likelihood estimators. As both of these estimators are complicated functions of the underlying random variables, their exact distributions are difficult to derive. Consequently, their use was first justified on the basis of large sample criteria, such as consistency and asymptotic efficiency. However, in the early 1960s the analysis of the exact distributions and moments of these estimators began, and since this time substantial progress has been made. Although these estimators are asymptotically equivalent, recent research has shown that their finite-sample properties are substantially different. However, the majority of this research has simply concentrated on a correctly specified system of equations, even though, since typically in applied studies theory provides some guidance but falls short of specifying the precise form of structural relationship, the possibilities for misspecification in simultaneous equation models are numerous. The objective of this paper is to extend the finite-sample analysis of these two estimators to include various cases of misspecification.     

Robust likelihood functions in Bayesian inference

In order to deal with mild deviations from the assumed parametric model, we propose a procedure for accounting for model uncertainty in the Bayesian framework. In particular, in the derivation of posterior distributions, we discuss the use of robust pseudo-likelihoods, which offer the advantage of preventing the effects caused by model misspecifications, i.e. when the underlying distribution lies in a neighborhood of the assumed model. The influence functions of posterior summaries, such as the posterior mean, are investigated as well as the asymptotic properties of robust posterior distributions. Although the use of a pseudo-likelihood cannot be considered orthodox in the Bayesian perspective, it is shown that, also through some illustrative examples, how a robust pseudo-likelihood, with the same asymptotic properties of a genuine likelihood, can be useful in the inferential process in order to prevent the effects caused by model misspecifications.     

Nonparametric Testing for Asymmetric Information

Asymmetric information is an important phenomenon in many markets and in particular in insurance markets. Testing for asymmetric information has become a very important issue in the literature in the last two decades. Almost all testing procedures that are used in empirical studies are parametric, which may yield misleading conclusions in the case of misspecification of either functional or distributional relationships among the variables of interest. Motivated by the literature on testing conditional independence, we propose a new nonparametric test for asymmetric information, which is applicable in a variety of situations. We demonstrate that the test works reasonably well through Monte Carlo simulations and apply it to an automobile insurance dataset and a long-term care insurance (LTCI) dataset. Our empirical results consolidate Chiappori and Salanié’s findings that there is no evidence for the presence of asymmetric information in the French automobile insurance market. While Finkelstein and McGarry found no positive correlation between risk and coverage in the LTCI market in the United States, our test detects asymmetric information using only the information that is available to the insurance company, and our investigation of the source of asymmetric information suggests some sort of asymmetric information that is related to risk preferences as opposed to risk types and thus lends support to Finkelstein and McGarry.     

TESTING THE STABILITY OF REGRESSION COEFFICIENTS USING GENERALIZED RECURSIVE RESIDUALS

Simple but flexible methods to detect deviations from the assumption of constant coefficients in linear regression are presented. Based on recursive residuals a runs test is developed as an alternative to CUSUM- and MOSUM-techniques. Finally a simulation study gives insight into the new method.     

Explained Variation and Predictive Accuracy in General Parametric Statistical Models: The Role of Model Misspecification

When studying a regression model measures of explained variation are used to assess the degree to which the covariates determine the outcome of interest. Measures of predictive accuracy are used to assess the accuracy of the predictions based on the covariates and the regression model. We give a detailed and general introduction to the two measures and the estimation procedures. The framework we set up allows for a study of the effect of misspecification on the quantities estimated. We also introduce a generalization to survival analysis.     

Model Misspecification Effects Within A Family of Alternative Discrete Reliability-Growth Models

We describe a family of related discrete reliability-growth methodologies potentially applicable to one-shot systems undergoing a test-analyze-and-fix development process. The common feature shared by the models is their connection to Duane's renowned learning-curve property. The major difference, however, lies in their applicability in the context of two intrinsically different sampling schemes. For each model, a summary of the statistical properties of various estimators of the parameters as well as the reliability of the system, are reported. For purposes of assessing model misspecification, a particular test execution scenario conforming to a inverse sampling scheme is adopted. In reliability applications, it is not an uncommon practice to borrow inference results from models which are inappropriate in this setting. A detailed study of the potential impact of such misspecification on the estimation of system reliability is presented. This revised version was published online in July 2006 with corrections to the Cover Date.     

Estimation of the average causal effect via multiple propensity score stratification

Suppose we are interested in estimating the average causal effect (ACE) for the population mean from observational study. Because of simplicity and ease of interpretation, stratification by a propensity score (PS) is widely used to adjust for influence of confounding factors in estimation of the ACE. Appropriateness of the estimation by the PS stratification relies on correct specification of the PS. We propose an estimator based on stratification with multiple PS models by clustering techniques instead of model selection. If one of them correctly specifies, the proposed estimator removes bias and thus is more robust than the standard PS stratification.     

Quantification of model risk that is caused by model misspecification

In this paper, we suggest a technique to quantify model risk, particularly model misspecification for binary response regression problems found in financial risk management, such as in credit risk modelling. We choose the probability of default model as one instance of many other credit risk models that may be misspecified in a financial institution. By way of illustrating the model misspecification for probability of default, we carry out quantification of two specific statistical predictive response techniques, namely the binary logistic regression and complementary log–log. The maximum likelihood estimation technique is employed for parameter estimation. The statistical inference, precisely the goodness of fit and model performance measurements, are assessed. Using the simulation dataset and Taiwan credit card default dataset, our finding reveals that with the same sample size and very small simulation iterations, the two techniques produce similar goodness-of-fit results but completely different performance measures. However, when the iterations increase, the binary logistic regression technique for balanced dataset reveals prominent goodness of fit and performance measures as opposed to the complementary log–log technique for both simulated and real datasets.