Consequences Of Model Misspecification Research Articles

Reliability analysis of degrading systems based on time-varying copula

Modern engineering products usually have complex structures and different functions, which means that products may have multiple degradation failure mechanisms. At present, the study of multivariate degradation reliability is mostly limited to copula function with constant parameters. For high-reliability products with multiple degradation processes, a bivariate accelerated degradation reliability estimation method based on time-varying copula is proposed. For accelerated degradation data, the marginal degradation model is constructed by using the nonlinear Wiener process with random effect, and the influence of environmental covariates is considered in combination with the acceleration model. The joint-dependence structure between two degradation processes is described by time-varying copula. A Simulation study validates this approach and the consequences of model misspecification are evaluated too. Furthermore, a real-world example is presented to demonstrate the effectiveness of the method. The results show that this method has some advantages over the existing methods.

Copula-based reliability analysis of degrading systems with dependent failures

Consider a coherent system, in which the degradation processes of its performance characteristics are positively correlated, this paper systematically investigates a bivariate degradation model of such a system. To analyze the accelerated degradation data, a flexible class of bivariate stochastic processes are proposed to incorporate the effects of environmental stress variables and the dependency between two degradation processes is modeled by a copula function. A two-step system reliability analysis approach is developed and it is implemented with the Hamiltonian Monte Carlo algorithm. Simulation studies validate this approach and the consequences of model misspecification are evaluated too. Furthermore, two real-world examples are presented to demonstrate the applicability of the proposed modeling framework of system reliability on correlated degradation processes.

Measuring model misspecification: Application to propensity score methods with complex survey data

Model misspecification is a potential problem for any parametric-model based analysis. However, the measurement and consequences of model misspecification have not been well formalized in the context of causal inference. A measure of model misspecification is proposed, and the consequences of model misspecification in non-experimental causal inference methods are investigated. The metric is then used to explore which estimators are more sensitive to misspecification of the outcome and/or treatment assignment model. Three frequently used estimators of the treatment effect are considered, all of which rely on the propensity score: (1) full matching, (2) 1:1 nearest neighbor matching, and (3) weighting. The performance of these estimators is evaluated under two different sampling designs: (1) simple random sampling (SRS) and (2) a two-stage stratified survey. As the degree of misspecification of either the propensity score or outcome model increases, so does the bias and the root mean square error, while the coverage decreases. Results are similar for the simple random sample and a complex survey design.

The effect of omitted covariates in marginal and partially conditional recurrent event analyses

There have been many advances in statistical methodology for the analysis of recurrent event data in recent years. Multiplicative semiparametric rate-based models are widely used in clinical trials, as are more general partially conditional rate-based models involving event-based stratification. The partially conditional model provides protection against extra-Poisson variation as well as event-dependent censoring, but conditioning on outcomes post-randomization can induce confounding and compromise causal inference. The purpose of this article is to examine the consequences of model misspecification in semiparametric marginal and partially conditional rate-based analysis through omission of prognostic variables. We do so using estimating function theory and empirical studies.

Studying the Strength of Prediction Using Indirect Mixture Modeling: Nonlinear Latent Regression with Heteroskedastic Residuals

We present a latent regression model in which the regression function is possibly nonlinear, and not necessarily smooth (e.g., a step function), and in which the residual variances are not necessarily homoskedastic. Heteroskedasticity is modeled by making the conditional (on the predictor) residual variance a (user-specified) function of the predictor. We use indirect mixture modeling to estimate the parameters by marginal maximum likelihood estimation, as proposed by Bock and Aitken (1981) in the context of item-response theory modeling and Klein and Moosbrugger (2000) in the context of structural equation modeling. We present a small simulation study to evaluate power and the consequences of model misspecification, and an illustration concerning neuroticism and extroversion. The model can be used to evaluate changes in the strength of the prediction as a function of the predictor.

Prior event rate ratio adjustment for hidden confounding in observational studies of treatment effectiveness: a pairwise Cox likelihood approach.

Observational studies provide a rich source of information for assessing effectiveness of treatment interventions in many situations where it is not ethical or practical to perform randomized controlled trials. However, such studies are prone to bias from hidden (unmeasured) confounding. A promising approach to identifying and reducing the impact of unmeasured confounding is prior event rate ratio (PERR) adjustment, a quasi‐experimental analytic method proposed in the context of electronic medical record database studies. In this paper, we present a statistical framework for using a pairwise approach to PERR adjustment that removes bias inherent in the original PERR method. A flexible pairwise Cox likelihood function is derived and used to demonstrate the consistency of the simple and convenient alternative PERR (PERR‐ALT) estimator. We show how to estimate standard errors and confidence intervals for treatment effect estimates based on the observed information and provide R code to illustrate how to implement the method. Assumptions required for the pairwise approach (as well as PERR) are clarified, and the consequences of model misspecification are explored. Our results confirm the need for researchers to consider carefully the suitability of the method in the context of each problem. Extensions of the pairwise likelihood to more complex designs involving time‐varying covariates or more than two periods are considered. We illustrate the application of the method using data from a longitudinal cohort study of enzyme replacement therapy for lysosomal storage disorders. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Item Response Theory Models for Carry-Over Effect Across Different Scales.

It is common in educational and psychological tests or social surveys that the same statement is judged on multiple scales. These multiple responses are linked by the same statement, which may cause local dependence. Considering the way a statement is judged on multiple scales, a new class of item response theory (IRT) models is developed to account for the nonrecursive carry-over effect, in which a response can be affected only by its preceding response rather than by a subsequent response. The parameters of the models can be estimated with the freeware WinBUGS. Two simulation studies were conducted to evaluate the parameter recovery of the new models and the consequences of model misspecification. Results showed that the parameters of the new models were recovered fairly well; fitting unnecessarily complicated models to data that did not have the carry-over effect did little harm to parameter estimation; and ignoring the carry-over effect by fitting standard IRT models yielded biased estimates for the item parameters, the correlation between latent traits, and the test reliability. Two empirical examples with parallel design and sequential design are provided to demonstrate the implications and applications of the new models.

The Multidimensional Testlet-Effect Rasch Model

Testlet design has been widely adopted in educational and psychological assessment. A testlet is a cluster of items that share a common stimulus(e.g., a reading comprehension passage or a figure), and the possible local dependence among items within a testlet is called testlet-effect. Various models have been developed to take into account such testlet effect. Examples included the Rasch testlet model, two-parameter logistic Bayesian testlet model, and higher-order testlet model. However, these existing models all assume that an item is affected by only one single testlet effect. Therefore, they are essentially unidimensional testlet-effect models. In practice, multiple testlet effects may simultaneously affect item responses in a testlet. For example, in addition to common stimulus, items can be grouped according to their domains, knowledge units, or item format, such that multiple testlet effects are involved. In essence, an item measures multiple latent traits, in addition to the target latent trait(s) that the test was designed to measure. Existing unidimensional testlet-effect models become inapplicable when multiple testlet effects are involved. To account for multiple testlet effect, in this study we develop the so-called(within-item) multidimensional testlet-effect Rasch model. The parameters can be estimated with marginal maximum likelihood estimation methods or Bayesian methods with Markov chain Monte Carlo(MCMC) algorithms. In this study, a popular computer program for Rasch models, ConQuest, was used. A series of simulations were conducted to evaluate parameter recovery of the new model, consequences of model misspecification, and the effectiveness of model-data fit statistics. Results show that the parameters of the new model can be recovered fairly well; and ignoring the multiple testlet effects resulted in a biased estimation of item parameters, and an overestimation of test reliability. Additionally, it did little harm on parameter estimation to fit a more complicated model(i.e., the multidimensional testlet-effect Rasch model) to data with a simple structure. In conclusion, the new model is feasible and flexible.

Constructing stock abundance indices from catch and effort data: Some nuts and bolts

Construction of annual indices of stock abundance based on the standardisation of catch and effort data remains central to many fisheries assessments. However, while the use of advanced statistical methods has helped catch rates to be standardised accounting for many explanatory variables, some of the more routine aspects of constructing abundance indices, such as how the index is constructed from the model parameters, receives little explanation in many analyses. This has lead to a lack of understanding as to how the indices are constructed and in some instances incorrect techniques have been applied. This lack of understanding can be a particular issue when interactions are used in the standardising model, especially those which contain interactions with the temporal effects over which the time-series of the abundance index is required. Other issues include the use of weighted model fits, the influence of anomalous data values, how best to impute missing values when required, the consequences of model mis-specification, and the use of random-effects. In this study, the basic approach for constructing abundance indices is outlined and a worked example using simulated data is presented to explore the nature of these issues and several techniques are suggested for dealing with them and to overcome potential biases. Finally, the methods presently used by ICCAT scientists for constructing abundance indices are reviewed.

The Multidimensional Testlet-Effect Rasch Model

Testlet design has been widely adopted in educational and psychological assessment. A testlet is a cluster of items that share a common stimulus(e.g., a reading comprehension passage or a figure), and the possible local dependence among items within a testlet is called testlet-effect. Various models have been developed to take into account such testlet effect. Examples included the Rasch testlet model, two-parameter logistic Bayesian testlet model, and higher-order testlet model. However, these existing models all assume that an item is affected by only one single testlet effect. Therefore, they are essentially unidimensional testlet-effect models. In practice, multiple testlet effects may simultaneously affect item responses in a testlet. For example, in addition to common stimulus, items can be grouped according to their domains, knowledge units, or item format, such that multiple testlet effects are involved. In essence, an item measures multiple latent traits, in addition to the target latent trait(s) that the test was designed to measure. Existing unidimensional testlet-effect models become inapplicable when multiple testlet effects are involved. To account for multiple testlet effect, in this study we develop the so-called(within-item) multidimensional testlet-effect Rasch model. The parameters can be estimated with marginal maximum likelihood estimation methods or Bayesian methods with Markov chain Monte Carlo(MCMC) algorithms. In this study, a popular computer program for Rasch models, ConQuest, was used. A series of simulations were conducted to evaluate parameter recovery of the new model, consequences of model misspecification, and the effectiveness of model-data fit statistics. Results show that the parameters of the new model can be recovered fairly well; and ignoring the multiple testlet effects resulted in a biased estimation of item parameters, and an overestimation of test reliability. Additionally, it did little harm on parameter estimation to fit a more complicated model(i.e., the multidimensional testlet-effect Rasch model) to data with a simple structure. In conclusion, the new model is feasible and flexible.

Higher Order Testlet Response Models for Hierarchical Latent Traits and Testlet-Based Items

Both testlet design and hierarchical latent traits are fairly common in educational and psychological measurements. This study aimed to develop a new class of higher order testlet response models that consider both local item dependence within testlets and a hierarchy of latent traits. Due to high dimensionality, the authors adopted the Bayesian approach implemented in the WinBUGS freeware for parameter estimation. A series of simulations were conducted to evaluate parameter recovery, consequences of model misspecification, and effectiveness of model–data fit statistics. Results show that the parameters of the new models can be recovered well. Ignoring the testlet effect led to a biased estimation of item parameters, underestimation of factor loadings, and overestimation of test reliability for the first-order latent traits. The Bayesian deviance information criterion and the posterior predictive model checking were helpful for model comparison and model–data fit assessment. Two empirical examples of ability tests and nonability tests are given.

A Monte Carlo Study for Pure and Pretest Estimators of a Panel Data Model with Spatially Autocorrelated Disturbances

This paper examines the consequences of model misspecification using a panel data model with spatially autocorrelated disturbances. The performance of several maximum likelihood estimators assuming different specifications for this model are compared using Monte Carlo experiments. These include (i) MLE of a random effects model that ignore the spatial correlation; (ii) MLE described in Anselin (1988) which assumes that the individual effects are not spatially autocorrelated; (iii) MLE described in Kapoor, et al. (2006) which assumes that both the individual effects and the remainder error are governed by the same spatial autocorrelation; (iv) MLE described in Baltagi, et al. (2006) which allows the spatial correlation parameter for the individual effects to be different from that of the remainder error term. The latter model encompasses the other models and allows the researcher to test these specifications as restrictions on the general model using LM and LR tests. In fact, based on these tests, we suggest a pretest estimator which is shown to perform well in Monte Carlo experiments, ranking a close second to the true MLE in mean squared error performance.

Estimation of contingency tables in complex survey sampling using probabilistic expert systems

Abstract In this paper we explore the possibility to use a particular class of models, known as probabilistic expert systems, to define two classes of estimators of a contingency table in case of stratified sampling designs. The two classes are characterized by the different role of the sampling design: in the first, the sampling design is treated as an additional variable; in the second, it is used only for estimation purposes by means of the survey weights. The bias/variance trade off of these estimators is analyzed and the consequences of model misspecification are illustrated. Furthermore, it is shown that the Horvitz–Thompson estimator belongs to both classes of estimators. It comes out that the Horvitz–Thompson estimator is almost always inefficient but robust. Monte Carlo simulations illustrate the efficiency of the proposed estimators.

The applicability of deadline models: Comment on Glickman, Gray, and Morales (2005)

Glickman, Gray, and Morales (this issue) propose a statistical model for measuring the unobserved latency of stimulus-controlled processes. The model accounts for both speed and accuracy and does so by assuming participants set an internal deadline. If a stimulus-controlled response is not produced by the deadline, the participant then guesses. The applicability the model is discussed in this comment. The deadline model yields specific predictions for the case in which stimulus difficulty is manipulated in a within-block manner. In this case, it is reasonable to assume that stimulus difficulty does not affect the deadline. It is shown that in common perceptual and cognitive domains, extant data do not fully meet these predictions. Hence, practitioners need be aware of the possibility and consequences of model misspecification.

Some consequences of model misspecification for t testing in a structural equation

This paper examines the distribution theory relevant to statistics obtained from a single structural equation from a system of simultaneous equations. Attention is focused on t statistics in misspecified models which have been estimated by instrumental variable techniques.

On the Consequences of Model Misspecification in Logistic Regression

Logistic regression models are commonly used to study the association between a binary response variable and an exposure variable. Besides the exposure of interest, other covariates are frequently included in the fitted model in order to control for their effects on outcome. Unfortunately, misspecification of the main exposure variable and the other covariates is not uncommon, and this can adversely affect tests of the association between the exposure and response. We allow the term "misspecification" to cover a broad range of modeling errors including measurement errors, discretizing continuous explanatory variables, and completely excluding covariates from the model. This paper reviews some recent results on the consequences of model misspecification on the large sample properties of likelihood score tests of association between exposure and response.

On the consequences of model misspecification in logistic regression.

Logistic regression models are commonly used to study the association between a binary response variable and an exposure variable. Besides the exposure of interest, other covariates are frequently included in the fitted model in order to control for their effects on outcome. Unfortunately, misspecification of the main exposure variable and the other covariates is not uncommon, and this can adversely affect tests of the association between the exposure and response. We allow the term "misspecification" to cover a broad range of modeling errors including measurement errors, discretizing continuous explanatory variables, and completely excluding covariates from the model. This paper reviews some recent results on the consequences of model misspecification on the large sample properties of likelihood score tests of association between exposure and response.

The Interpretation of Regression Analysis Results in Sex and Race Discrimination Problems

Abstract Linear models are often used to quantify differentials between protected and unprotected groups on variables such as salary. Some consequences of model misspecification are examined. In addition, the effects of preferential selection on linear analysis results are studied.

The Consequences Of Model Misspecification In Regression Analysis.

In ordinary least squares regression analysis the desired property of unbiasedness in estimated coefficients is contingent upon the correspondence of the fitted model with the true underlying data generating process. This paper focuses on developing a systematic characterization of the error forms resulting from model misspecification in single equation models. The consequences of model misspecification, for the error forms identified, are also evaluated.