Effect Of Model Misspecification Research Articles

Parametric Estimation of Quality Adjusted Lifetime (QAL) Distribution in Simple Illness-Death Model

We discuss parametric estimation of quality adjusted lifetime distribution in simple illness-death model. Model parameters are estimated by maximum likelihood method. The distribution of QAL is estimated by replacing the parameters by their estimates. A regression model is also considered. A simulation study investigates bias and precision of the estimate of QAL distribution and compares it with an existing nonparametric estimate. Another simulation study investigates the effect of model misspecification. Application of our methodology has been illustrated using the Stanford heart transplant data.

Negative Market Volatility Risk Premium: Evidence from the LIFFE Equity Index Options*

AbstractWe provide non‐parametric empirical evidence regarding negative volatility risk premium using LIFFE equity index options. In addition, we incorporate the moment‐adjusted option delta hedge ratio to mitigate the effect of model misspecification. From the results, we observe several interesting phenomena. First, the delta‐hedged gains are negative. Second, with a correction for model misspecification, higher‐order moments measures show less significance and the volatility risk premium still plays a key role in affecting delta‐hedged gains. All empirical evidence supports the existence of negative volatility risk premium in LIFFE equity index options.

Mis-Specification Analysis of Linear Degradation Models

Degradation models are widely used to assess the lifetime information of highly reliable products if there exists quality characteristics whose degradation over time can be related to reliability. The performance of a degradation model depends strongly on the appropriateness of the model describing a product's degradation path. In this paper, motivated by laser data, we propose a general linear degradation path in which the unit-to-unit variation of all test units can be considered simultaneously with the time-dependent structure in degradation paths. Based on the proposed degradation model, we first derive an implicit expression of a product's lifetime distribution, and its corresponding mean-time-to-failure (MTTF). By using the profile likelihood approach, maximum likelihood estimation of parameters, a product's MTTF, and their confidence intervals can be obtained easily. In addition, laser degradation data are used to illustrate the proposed procedure. Furthermore, we also address the effects of model mis-specification on the prediction of the product's MTTF. It shows that the effect of the model mis-specification on the predictions of a product's MTTF is not critical under the case of large samples. However, when the sample size and the termination time are not large enough, a simulation study shows that these effects are not negligible.

Conditional inference in linear versus nonlinear models for binary time series

The modelling of discrete such as binary time series, unlike the continuous time series, is not easy. This is due to the fact that there is no unique way to model the correlation structure of the repeated binary data. Some models may also provide a complicated correlation structure with narrow ranges for the correlations. In this paper, we consider a nonlinear dynamic binary time series model that provides a correlation structure which is easy to interpret and the correlations under this model satisfy the full−1 to 1 range. For the estimation of the parameters of this nonlinear model, we use a conditional generalized quasilikelihood (CGQL) approach which provides the same estimates as those of the well-known maximum likelihood approach. Furthermore, we consider a competitive linear dynamic binary time series model and examine the performance of the CGQL approach through a simulation study in estimating the parameters of this linear model. The model mis-specification effects on estimation as well as forecasting are also examined through simulations.

Ambiguity Shifts and the 2007-2008 Financial Crisis

I analyze the effects of model misspecification on default swap spreads and equity prices for firms that are not perfectly transparent to the investors. The agents in the economy are misspecification-averse and thus assign higher probabilities to lower utility states. This leads to higher CDS rates, lower equity prices and lower expected times to default. Estimating the model using data on financial institutions, I find that the sudden increase in credit spreads in the summer of 2007 can be partially explained by agents' mistrust of the signals observed in the market. The bailout of Bear Stearns in March 2008 and the liquidation of Lehman Brothers in September 2008 further exacerbated the agents' doubts about signals quality and introduced mistrust about the agents' pricing models, accounting for the further increases in credit spreads after these events.

On a Unified Generalized Quasi-likelihood Approach for Familial-Longitudinal Non-Stationary Count Data

In this paper, conditional on random family effects, we consider an auto-regres- sion model for repeated count data and their corresponding time-dependent covariates, collected from the members of a large number of independent families. The count responses, in such a set up, unconditionally exhibit a non-stationary familial-longitudinal correlation structure. We then take this two-way correlation structure into account, and develop a generalized quasilikelihood (GQL) approach for the estimation of the regression effects and the familial correlation index para- meter, whereas the longitudinal correlation parameter is estimated by using the well-known method of moments. The performance of the proposed estimation approach is examined through a simula- tion study. Some model mis-specification effects are also studied. The estimation methodology is illustrated by analysing real life healthcare utilization count data collected from 36 families of size four over a period of 4 years.

Model‐based linkage analysis with imprinting for quantitative traits: ignoring imprinting effects can severely jeopardize detection of linkage

Genes with imprinting (parent-of-origin) effects express differently when inheriting from the mother or from the father. Some genes for development and behavior in mammals are known to be imprinted. We developed parametric linkage analysis that accounts for imprinting effects for continuous traits, implementing it in MORGAN. To study misspecification of imprinting on linkage analysis, we simulated eight markers over a 35 cM region with phenotypes where imprinting contributes 0, 25, 50, and 75% of the variance of a quantitative trait locus (QTL) effect and analyzed them under all four models. Multipoint lod scores were computed and maximized over the same 35 cM region. Our most important finding is the dramatic lod score improvement under the correct imprinting model over the no-imprinting model. For data with minor QTL allele frequency 0.05, the correct model provided the highest lod scores with maximum expected lod scores over 4 in all settings. Ignoring imprinting provided the lowest lod scores with maximum expected lod scores between -9.9 and 2.4. In the extreme scenario, cases with max lod > or =3 from the correct imprinting model and max lod < or =-2 from the no-imprinting model occurred in 86% of replications. Models with misspecified imprinting produced lod scores intermediate between those with correct imprinting and with no imprinting. The effects of model misspecification were less pronounced for singlepoint analysis. Our multipoint results illustrate that ignoring true imprinting severely impairs detection of linkage and erroneously excludes genomic regions (with max lod <-2), whereas accounting for it can substantially improve linkage detection.

Endowment Assurance Products: Effectiveness of Risk-Minimizing Strategies under Model Risk

This paper analyzes and discusses the effects of model misspecification associated with both interest rate and mortality risk on the hedging decisions of insurance companies. We consider hedging strategies in different instruments (zero bonds) which are risk- (variance-) minimizing with respect to an assumed model. In this case, the associated expected costs and the variance of the costs are the same for all strategies. While the introduction of model risk, i.e. a deviation of assumed from true models, has the same effect on the expected costs, this is not true with respect to the variance. It turns out that the choice of hedging instruments has a crucial impact on the robustness of the strategies. In addition, the results of the paper can be used to emphasize the necessity to use a combined hedging model. In terms of robust hedging, a separate specification of interest rate model and mortality model is inconvenient, even in the case that interest rate and mortality are assumed to be independent.

Endowment Assurance Products: Effectiveness of Risk-Minimizing Strategies under Model Risk

This paper analyzes and discusses the effects of model misspecification associated with both interest rate and mortality risk on the hedging decisions of insurance companies. We consider hedging strategies in different instruments (zero bonds) which are risk- (variance-) minimizing with respect to an assumed model. In this case, the associated expected costs and the variance of the costs are the same for all strategies. While the introduction of model risk, i.e. a deviation of assumed from true models, has the same effect on the expected costs, this is not true with respect to the variance. It turns out that the choice of hedging instruments has a crucial impact on the robustness of the strategies. In addition, the results of the paper can be used to emphasize the necessity to use a combined hedging model. In terms of robust hedging, a separate specification of interest rate model and mortality model is inconvenient, even in the case that interest rate and mortality are assumed to be independent.

Using Copulas in Hydrology: Benefits, Cautions, and Issues

This paper discusses the bivariate modeling of extreme tails of correlated hydrological random variables. We take a copula approach and model the dependence structure independently of the marginal distributions. We apply results from the classical extreme value theory to choose marginal distributions for excesses of high thresholds and consider six copula families to capture the dependence structure of these excesses. While copulas can differ somewhat in the degree of association that they provide, differences in which part of the distribution this association is more pronounced can be substantial. We discuss certain pertinent properties of copulas and give some insight to assist the practitioner in their selection. We examine the effects of model misspecification and the impact of the chosen method of estimation, targeting the estimated quantities frequently used by hydrologists. A simulation study shows not only the dangers of improper copula selection, but also the possible benefits of using a bivariate approach to estimate univariate quantities. We apply the methodology to the study of low-flow events and analyze two Canadian hydrometric data sets.

On Reduced Amino Acid Alphabets for Phylogenetic Inference

We investigate the use of Markov models of evolution for reduced amino acid alphabets or bins of amino acids. The use of reduced amino acid alphabets can ameliorate effects of model misspecification and saturation. We present algorithms for 2 different ways of automating the construction of bins: minimizing criteria based on properties of rate matrices and minimizing criteria based on properties of alignments. By simulation, we show that in the absence of model misspecification, the loss of information due to binning is found to be insubstantial, and the use of Markov models at the binned level is found to be almost as effective as the more appropriate missing data approach. By applying these approaches to real data sets where compositional heterogeneity and/or saturation appear to be causing biased tree estimation, we find that binning can improve topological estimation in practice.

Bayesian Analysis of DSGE Models by S. An and F. Schorfheide

The paper that An and Schorfheide have written is an excellent piece of work and will become a useful reference for teaching and consultation purposes. The paper discusses in an articulate and convincing manner almost everything that one could think of covering in such a review. This makes the task of the commentator difficult. Nevertheless, I will attempt to add few insights on three issues which, in my opinion, play an important role in applied work and in the interpretation of the estimation result. In particular, I will discuss a) the sensitivity of posterior distributions to prior spreads; b) the effects of model misspecification and an approach to model respecification; c) parameter identification and its consequences for posterior inference.

Latent-model robustness in structural measurement error models

SUMMARY We present methods for diagnosing the effects of model misspecification of the true predictor distribution in structural measurement error models. We first formulate latent model robustness theoretically. Then we provide practical techniques for examining the adequacy of an assumed latent predictor model. The methods are illustrated via analytical examples, application to simulated data and with data from a study of coronary heart disease.

Model misspecification effects in clustered count data analysis

Clustered count data are usually analysed using Poisson mixed models based on the assumptions of either gamma distributed or log-normal distributed random effects. As it is difficult to anticipate the true mixed model, the researchers tend to make an arbitrary choice between the assumption of gamma or log-normal distribution for the random effects. This arbitrary choice may not affect the estimation of the regression parameters of the model but the efficiency of the estimates of the variance component of the random effects may however be affected to a great extent. This paper addresses this issue by examining the misspecification effects of the distributional assumptions for the random effects in the clustered data.

Exploring Local Item Dependence Using a Random-Effects Facet Model

The random-effects facet model that deals with local item dependence in many-facet contexts is presented. It can be viewed as a special case of the multidimensional random coefficients multinomial logit model (MRCMLM) so that the estimation procedures for the MRCMLM can be directly applied. Simulations were conducted to examine parameter recovery and effects of model misspecification. Results indicated that the item and person parameters as well as the random effects could be recovered very accurately when the data were analyzed using the generating random-effects facet model. When local item dependence was ignored and the standard facet model was used, the parameter estimates were shrunken and the test reliability was overestimated. Two empirical examples about journal quality ratings and rater effects are given to illustrate implications and applications of the proposed random-effects facet model.

On the simultaneous effects of model misspecification and errors in variables

AbstractModel misspecification and noisy covariate measurements are two common sources of inference bias. There is considerable literature on the consequences of each problem in isolation. In this paper, however, the author investigates their combined effects. He shows that in the context of linear models, the large‐sample error in estimating the regression function may be partitioned in two terms quantifying the impact of these sources of bias. This decomposition reveals trade‐offs between the two biases in question in a number of scenarios. After presenting a finite‐sample version of the decomposition, the author studies the relative impacts of model misspecification, covariate imprecision, and sampling variability, with reference to the detectability of the model misspecification via diagnostic plots.

Effects of Model Misspecification on Tests of No Randomized Treatment Effect Arising From Cox’s Proportional Hazards Model

Summary We examine the asymptotic and small sample properties of model-based and robust tests of the null hypothesis of no randomized treatment effect based on the partial likelihood arising from an arbitrarily misspecified Cox proportional hazards model. When the distribution of the censoring variable is either conditionally independent of the treatment group given covariates or conditionally independent of covariates given the treatment group, the numerators of the partial likelihood treatment score and Wald tests have asymptotic mean equal to 0 under the null hypothesis, regardless of whether or how the Cox model is misspecified. We show that the model-based variance estimators used in the calculation of the model-based tests are not, in general, consistent under model misspecification, yet using analytic considerations and simulations we show that their true sizes can be as close to the nominal value as tests calculated with robust variance estimators. As a special case, we show that the model-based log-rank test is asymptotically valid. When the Cox model is misspecified and the distribution of censoring depends on both treatment group and covariates, the asymptotic distributions of the resulting partial likelihood treatment score statistic and maximum partial likelihood estimator do not, in general, have a zero mean under the null hypothesis. Here neither the fully model-based tests, including the log-rank test, nor the robust tests will be asymptotically valid, and we show through simulations that the distortion to test size can be substantial.

The Effect of Model Misspecification on Classification Decisons Made Using a Computerized Test

Many computerized testing algorithms require the fitting of some item response theory (IRT) model to examinees’ responses to facilitate item selection, the determination of test stopping rules, and classification decisions. Some IRT models are thought to be particularly useful for small volume certification programs that wish to make the transition to computerized adaptive testing (CAT). The one‐parameter logistic model (1‐PLM) is usually assumed to require a smaller sample size than the three‐parameter logistic model (3‐PLM) for item parameter calibrations. This study examined the effects of model misspecification on the precision of the decisions made using the sequential probability ratio test (SPRT). For this comparison, the 1‐PLM was used to estimate item parameters, even though the items’ characteristics were represented by a 3‐PLM. Results demonstrated that the 1‐PLM produced considerably more decision errors under simulation conditions similar to a real testing environment, compared to the true model and to a fixed‐form standard reference set of items.

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 text 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.

Estimation and Model Selection in Pharmacokinetics: The Effect of Model Misspecification

A physiologically based computer model of drug and tracer kinetics in humans was constructed. It includes detailed models of drug distribution kinetics in organs arranged according to the circulatory structure of the body. The system does not contain well-mixed compartments. Basic pharmacokinetic parameters were estimated by fitting a sum of three to fife exponentials to error-free data using different weights in a weighted least squares analysis. The effect of model misspecification was minimised by weighting proponional to l/C2i and/or by an increase of the number of exponential terms.