Effect Of Model Misspecification Research Articles

Sandwich corrected standard errors in family-based genome-wide association studies.

Given the availability of genotype and phenotype data collected in family members, the question arises which estimator ensures the most optimal use of such data in genome-wide scans. Using simulations, we compared the Unweighted Least Squares (ULS) and Maximum Likelihood (ML) procedures. The former is implemented in Plink and uses a sandwich correction to correct the standard errors for model misspecification of ignoring the clustering. The latter is implemented by fast linear mixed procedures and models explicitly the familial resemblance. However, as it commits to a background model limited to additive genetic and unshared environmental effects, it employs a misspecified model for traits with a shared environmental component. We considered the performance of the two procedures in terms of type I and type II error rates, with correct and incorrect model specification in ML. For traits characterized by moderate to large familial resemblance, using an ML procedure with a correctly specified model for the conditional familial covariance matrix should be the strategy of choice. The potential loss in power encountered by the sandwich corrected ULS procedure does not outweigh its computational convenience. Furthermore, the ML procedure was quite robust under model misspecification in the simulated settings and appreciably more powerful than the sandwich corrected ULS procedure. However, to correct for the effects of model misspecification in ML in circumstances other than those considered here, we propose to use a sandwich correction. We show that the sandwich correction can be formulated in terms of the fast ML method.

Item Response Theory Models for Performance Decline During Testing

Sometimes, test‐takers may not be able to attempt all items to the best of their ability (with full effort) due to personal factors (e.g., low motivation) or testing conditions (e.g., time limit), resulting in poor performances on certain items, especially those located toward the end of a test. Standard item response theory (IRT) models fail to consider such testing behaviors. In this study, a new class of mixture IRT models was developed to account for such testing behavior in dichotomous and polytomous items, by assuming test‐takers were composed of multiple latent classes and by adding a decrement parameter to each latent class to describe performance decline. Parameter recovery, effect of model misspecification, and robustness of the linearity assumption in performance decline were evaluated using simulations. It was found that the parameters in the new models were recovered fairly well by using the freeware WinBUGS; the failure to account for such behavior by fitting standard IRT models resulted in overestimation of difficulty parameters on items located toward the end of the test and overestimation of test reliability; and the linearity assumption in performance decline was rather robust. An empirical example is provided to illustrate the applications and the implications of the new class of models.

Mis-specification analysis of linear Wiener process–based degradation models for the remaining useful life estimation

The linear Wiener process–based degradation model is commonly used for the lifetime assessment and remaining useful life estimation. This article addresses the effects of model mis-specification of the linear Wiener process for the remaining useful life estimation. First, we study the model mis-specification effects on the parameters’ estimation and the lifetime distribution. Then, the effects of model mis-specification on the remaining useful life estimation and the predictive maintenance decision-making are analysed through some numerical examples and a case study. The results show that mis-specifying the linear Wiener process without measurement error as that with measurement error is negligible. However, under the inverse condition, the mis-specification could result in premature maintenances or failure maintenances, which increases the maintenance costs.

Robust control, informational frictions, and international consumption correlations

In this paper we examine the effects of model misspecification (robustness or RB) on international consumption correlations in an otherwise standard small open economy model with endogenous capital accumulation. We show that in the presence of capital mobility in financial markets, RB lowers the international consumption correlations by generating heterogeneous responses of consumption to productivity shocks across countries facing different macroeconomic uncertainty. In addition, we show that RB can also improve the model's predictions in three other moments of consumption dynamics: the relative volatility of consumption to income, the persistence of consumption, and the correlation between consumption and output. After calibrating the RB parameter using the detection error probabilities, we show that the model can explain the observed international consumption correlations as well as the other consumption moments quantitatively. Finally, we show that the main conclusions of our benchmark model do not change in an extension in which the agent cannot observe the state perfectly due to finite information-processing capacity.

The Robustness of ME/I Evaluations to Among-Group Dependence

This study evaluates the robustness of multisample confirmatory factor analysis approaches to measurement equivalence/invariance (ME/I) evaluations under a specific model misspecification: when independence among the groups is assumed, but groups are dependent. Monte Carlo simulation is used to investigate the robustness of several ME/I evaluation procedures including the likelihood ratio test (), ΔCFI, ΔSRMR, and ΔRMSEA. The effect of this model misspecification on the factor loadings and their standard errors is also considered. Assuming the groups are independent when they are not is shown to have no practical effect on the results of the , ΔCFI, ΔSRMR, or ΔRMSEA procedures because the effect of model misspecification is canceled out through differencing. Similarly, the estimated factor loadings and standard errors are not significantly affected by incorrectly assuming among-group dependence. These results are used to develop recommendations for researchers who conduct multigroup analyses using structural equation models with samples in which independence is unclear.

The Effects of Model Misspecification on Tests of Price Discovery

The Effects of Model Misspecification on Tests of Price Discovery

A Nonparametric Approach to Cognitive Diagnosis by Proximity to Ideal Response Patterns

A trend in educational testing is to go beyond unidimensional scoring and provide a more complete profile of skills that have been mastered and those that have not. To achieve this, cognitive diagnosis models have been developed that can be viewed as restricted latent class models. Diagnosis of class membership is the statistical objective of these models. As an alternative to latent class modeling, a nonparametric procedure is introduced that only requires specification of an item-by-attribute association matrix, and classifies according to minimizing a distance measure between observed responses, and the ideal response for a given attribute profile that would be implied by the item-by-attribute association matrix. This procedure requires no statistical parameter estimation, and can be used on a sample size as small as 1. Heuristic arguments are given for why the nonparametric procedure should be effective under various possible cognitive diagnosis models for data generation. Simulation studies compare classification rates with parametric models, and consider a variety of distance measures, data generation models, and the effects of model misspecification. A real data example is provided with an analysis of agreement between the nonparametric method and parametric approaches.

Some Sampling Properties of Common Phase Estimators

The instantaneous phase of neural rhythms is important to many neuroscience-related studies. In this letter, we show that the statistical sampling properties of three instantaneous phase estimators commonly employed to analyze neuroscience data share common features, allowing an analytical investigation into their behavior. These three phase estimators-the Hilbert, complex Morlet, and discrete Fourier transform-are each shown to maximize the likelihood of the data, assuming the observation of different neural signals. This connection, explored with the use of a geometric argument, is used to describe the bias and variance properties of each of the phase estimators, their temporal dependence, and the effect of model misspecification. This analysis suggests how prior knowledge about a rhythmic signal can be used to improve the accuracy of phase estimates.

Robust Control, Informational Frictions, and International Consumption Correlations

In this paper we examine the effects of model misspecification (robustness or RB) on international consumption correlations in two otherwise standard small open economy models: one with perfect state observation and the other with imperfect state observation. We show that in the presence of capital mobility in financial markets, RB lowers the international consumption correlations by generating heterogeneous responses of consumption to income shocks across countries facing different macroeconomic uncertainty. However, the calibrated RB model with perfect state observation cannot explain the observed consumption correlations quantitatively. We then show that the RB model with imperfect state observation is capable of matching the behavior of international consumption quantitatively via two channels: (i) the gradual response to income shocks that increases the correlations and (ii) the presence of the common noise shocks that reduce the correlations.

Stochastic errors vs. modeling errors in distance based phylogenetic reconstructions.

BackgroundDistance-based phylogenetic reconstruction methods use evolutionary distances between species in order to reconstruct the phylogenetic tree spanning them. There are many different methods for estimating distances from sequence data. These methods assume different substitution models and have different statistical properties. Since the true substitution model is typically unknown, it is important to consider the effect of model misspecification on the performance of a distance estimation method.ResultsThis paper continues the line of research which attempts to adjust to each given set of input sequences a distance function which maximizes the expected topological accuracy of the reconstructed tree. We focus here on the effect of systematic error caused by assuming an inadequate model, but consider also the stochastic error caused by using short sequences. We introduce a theoretical framework for analyzing both sources of error based on the notion of deviation from additivity, which quantifies the contribution of model misspecification to the estimation error. We demonstrate this framework by studying the behavior of the Jukes-Cantor distance function when applied to data generated according to Kimura’s two-parameter model with a transition-transversion bias. We provide both a theoretical derivation for this case, and a detailed simulation study on quartet trees.ConclusionsWe demonstrate both analytically and experimentally that by deliberately assuming an oversimplified evolutionary model, it is possible to increase the topological accuracy of reconstruction. Our theoretical framework provides new insights into the mechanisms that enables statistically inconsistent reconstruction methods to outperform consistent methods.

Optimal Design for Degradation Tests Based on Gamma Processes With Random Effects

Degradation models are usually used to provide information about the reliability of highly reliable products that are not likely to fail within a reasonable period of time under traditional life tests, or even accelerated life tests. The gamma process is a natural model for describing degradation paths, which exhibit a monotone increasing pattern, while the commonly used Wiener process is not appropriate in such a case. We discuss the problem of optimal design for degradation tests based on a gamma degradation process with random effects. To conduct a degradation experiment efficiently, several decision variables (such as the sample size, inspection frequency, and measurement numbers) need to be determined carefully. These decision variables affect not only the experimental cost, but also the precision of the estimates of lifetime parameters of interest. Under the constraint that the total experimental cost does not exceed a pre-specified budget, the optimal decision variables are found by minimizing the asymptotic variance of the estimate of the 100p-th percentile of the lifetime distribution of the product. Laser data are used to illustrate the proposed method. Moreover, we assess analytically the effects of model mis-specification that occur when the random effects are not taken into consideration in the gamma degradation model. The numerical results of these effects reveal that the impact of model mis-specification on the accuracy and precision of the prediction of percentiles of the lifetimes of products are somewhat serious for the tail probabilities. A simulation study also shows that the simulated values are quite close to the asymptotic values.

Missing data techniques for multilevel data: implications of model misspecification

When modeling multilevel data, it is important to accurately represent the interdependence of observations within clusters. Ignoring data clustering may result in parameter misestimation. However, it is not well established to what degree parameter estimates are affected by model misspecification when applying missing data techniques (MDTs) to incomplete multilevel data. We compare the performance of three MDTs with incomplete hierarchical data. We consider the impact of imputation model misspecification on the quality of parameter estimates by employing multiple imputation under assumptions of a normal model (MI/NM) with two-level cross-sectional data when values are missing at random on the dependent variable at rates of 10%, 30%, and 50%. Five criteria are used to compare estimates from MI/NM to estimates from MI assuming a linear mixed model (MI/LMM) and maximum likelihood estimation to the same incomplete data sets. With 10% missing data (MD), techniques performed similarly for fixed-effects estimates, but variance components were biased with MI/NM. Effects of model misspecification worsened at higher rates of MD, with the hierarchical structure of the data markedly underrepresented by biased variance component estimates. MI/LMM and maximum likelihood provided generally accurate and unbiased parameter estimates but performance was negatively affected by increased rates of MD.

Maximum likelihood estimator for cumulative incidence functions under proportionality constraint

This paper deals with a model of possibly dependent competing risks in the presence of additional independent censoring. Under the assumption that the cumulative incidence functions are proportional or equivalently that the cause-specific cumulative hazard functions are proportional, we derive a maximum likelihood estimator for the cumulative incidence functions. Asymptotic results are derived for our estimator namely strong consistency, convergence rate, weak convergence and strong approximation. Pointwise confidence bands are then constructed. Simulation results are carried out to assess the accuracy of the pointwise confidence bands and to investigate the effect of model misspecification. We also briefly consider the case of independent competing risks with proportional net cumulative hazard functions in the presence of independent censoring.

Mis-specification analyses of gamma and Wiener degradation processes

Degradation models are widely used these days to assess the lifetime information of highly reliable products if there exist some quality characteristics (QC) whose degradation over time can be related to the reliability of the product. In this study, motivated by a laser data, we investigate the mis-specification effect on the prediction of product's MTTF (mean-time-to-failure) when the degradation model is wrongly fitted. More specifically, we derive an expression for the asymptotic distribution of quasi-MLE (QMLE) of the product's MTTF when the true model comes from gamma degradation process, but is wrongly assumed to be Wiener degradation process. The penalty for the model mis-specification can then be addressed sequentially. The result demonstrates that the effect on the accuracy of the product's MTTF prediction strongly depends on the ratio of critical value to the scale parameter of the gamma degradation process. The effects on the precision of the product's MTTF prediction are observed to be serious when the shape and scale parameters of the gamma degradation process are large. We then carry out a simulation study to evaluate the penalty of the model mis-specification, using which we show that the simulation results are quite close to the theoretical ones even when the sample size and termination time are not large. For the reverse mis-specification problem, i.e., when the true degradation is a Wiener process, but is wrongly assumed to be a gamma degradation process, we carry out a Monte Carlo simulation study to examine the effect of the corresponding model mis-specification. The obtained results reveal that the effect of this model mis-specification is negligible.

The Effect of Model Misspecification on Semi-Supervised Classification

Semi-supervised classification--training both on labeled and unlabeled observations--can yield improved performance compared to the classifier based on only the labeled observations. Unlabeled observations are always beneficial to classification if the model we assume is correct. However, they may degrade the classifier performance when the model is misspecified. In the classical classification problem setting, many factors affect the semi-supervised performance, including training data, model specification, estimation method, and the classifier itself. For concreteness, we consider maximum likelihood estimation in finite mixture models and the Bayes plug-in classifier, due to their ubiquitousness and tractability. In this specific setting, we examine the effect of model misspecification on semi-supervised classification performance and shed some light on when and why performance degradation occurs.

Discrimination measures for survival outcomes: Connection between the AUC and the predictiveness curve

Finding out biomarkers and building risk scores to predict the occurrence of survival outcomes is a major concern of clinical epidemiology, and so is the evaluation of prognostic models. In this paper, we are concerned with the estimation of the time-dependent AUC--area under the receiver-operating curve--which naturally extends standard AUC to the setting of survival outcomes and enables to evaluate the discriminative power of prognostic models. We establish a simple and useful relation between the predictiveness curve and the time-dependent AUC--AUC(t). This relation confirms that the predictiveness curve is the key concept for evaluating calibration and discrimination of prognostic models. It also highlights that accurate estimates of the conditional absolute risk function should yield accurate estimates for AUC(t). From this observation, we derive several estimators for AUC(t) relying on distinct estimators of the conditional absolute risk function. An empirical study was conducted to compare our estimators with the existing ones and assess the effect of model misspecification--when estimating the conditional absolute risk function--on the AUC(t) estimation. We further illustrate the methodology on the Mayo PBC and the VA lung cancer data sets.

Signal Extraction Revision Variances as a Goodness-of-Fit Measure

Typically, model misspecification is addressed by statistics relying on model-residuals, i.e., on one-step ahead forecasting errors. In practice, however, users are often also interested in problems involving multi-step ahead forecasting performances, which are not explicitly addressed by traditional diagnostics. In this article, we consider the topic of misspecification from the perspective of signal extraction. More precisely, we emphasize the connection between models and real-time (concurrent) filter performances by analyzing revision errors instead of one-step ahead forecasting errors. In applications, real-time filters are important for computing trends, for performing seasonal adjustment or for inferring turning-points towards the current boundary of time series. Since revision errors of real-time filters generally rely on particular linear combinations of one- and multi-step ahead forecasts, we here address a generalization of traditional diagnostics. Formally, a hypothesis testing paradigm for the empirical revision measure is developed through theoretical calculations of the asymptotic distribution under the null hypothesis, and the method is assessed through real data studies as well as simulations. In particular, we analyze the effect of model misspecification with respect to unit roots, which are likely to determine multi-step ahead forecasting performances. We also show that this framework can be extended to general forecasting problems by defining suitable artificial signals.

Signal Extraction Revision Variances as a Goodness-of-Fit Measure

Typically, model misspecification is addressed by statistics relying on model-residuals, i.e., on one-step ahead forecasting errors. In practice, however, users are often also interested in problems involving multi-step ahead forecasting performances, which are not explicitly addressed by traditional diagnostics. In this article, we consider the topic of misspecification from the perspective of signal extraction. More precisely, we emphasize the connection between models and real-time (concurrent) filter performances by analyzing revision errors instead of one-step ahead forecasting errors. In applications, real-time filters are important for computing trends, for performing seasonal adjustment or for inferring turning-points towards the current boundary of time series. Since revision errors of real-time filters generally rely on particular linear combinations of one- and multi-step ahead forecasts, we here address a generalization of traditional diagnostics. Formally, a hypothesis testing paradigm for the empirical revision measure is developed through theoretical calculations of the asymptotic distribution under the null hypothesis, and the method is assessed through real data studies as well as simulations. In particular, we analyze the effect of model misspecification with respect to unit roots, which are likely to determine multi-step ahead forecasting performances. We also show that this framework can be extended to general forecasting problems by defining suitable artificial signals.

Fear of Model Misspecification and the Robustness Premium

Robust decision making implies welfare costs or robustness premia when the approximating model is the true data generating process. To examine the importance of these premia at the aggregate level we employ a simple two-sector dynamic general equilibrium model with human capital and introduce an additional form of precautionary behavior. The latter arises from the robust decision maker s ability to reduce the effects of model misspecification through allocating time and existing human capital to this end. We find that the extent of the robustness premia critically depends on the productivity of time relative to that of human capital. When the relative efficiency of time is low, despite transitory welfare costs, there are gains from following robust policies in the long-run. In contrast, high relative productivity of time implies misallocation costs that remain even in the long-run. Finally, depending on the technology used to reduce model uncertainty, we fi nd that while increasing the fear of model misspecfication leads to a net increase in precautionary behavior, investment and output can fall.

Maximum studentized score tests for the detection of outliers in time series regression models

Efficient score tests exist among others, for testing the presence of additive and/or innovative outliers that are the result of the shifted mean of the error process under the regression model. A sample influence function of autocorrelation-based diagnostic technique also exists for the detection of outliers that are the result of the shifted autocorrelations. The later diagnostic technique is however not useful if the outlying observation does not affect the autocorrelation structure but is generated due to an inflation in the variance of the error process under the regression model. In this paper, we develop a unified maximum studentized type test which is applicable for testing the additive and innovative outliers as well as variance shifted outliers that may or may not affect the autocorrelation structure of the outlier free time series observations. Since the computation of the p-values for the maximum studentized type test is not easy in general, we propose a Satterthwaite type approximation based on suitable doubly non-central F-distributions for finding such p-values [F.E. Satterthwaite, An approximate distribution of estimates of variance components, Biometrics 2 (1946), pp. 110–114]. The approximations are evaluated through a simulation study, for example, for the detection of additive and innovative outliers as well as variance shifted outliers that do not affect the autocorrelation structure of the outlier free time series observations. Some simulation results on model misspecification effects on outlier detection are also provided.