Effect Of Model Misspecification Research Articles

Effects of model misspecification in estimating covariate effects in survival analysis for small sample sizes

The results of a Monte Carlo study of the size and power of parametric and semi-parametric approaches to inference on covariate effects in survival (time-to-events) models in the presence of model misspecification and an independent censoring mechanism are reported. Basic models employed are a parametric model, where both a baseline distribution and the dependence structure of covariates on the failure times are fully specified (exponential, Weibull, log logistic, log normal, and normal regression models are studied), and a semi-parametric approach (due to Cox) in which the baseline distribution is unspecified. The Cox model performs very well compared to the parametric models for distributions with proportional hazard rates and appears to be with regard to the proportional hazards assumption. Appropriate parametric models have the potential of improving the size and power of the tests, although overall they are not appreciably better than the Cox model. In comparing the small sample performance of three statistical tests, the likelihood ratio and Wald tests closely agree with each other (likelihood ratio having a slight advantage), while the score test tends to perform much poorer since it inflates the size and power more than the other two.

Effects of model misspecification in the estimation of variance components and intraclass correlation for paired data

Paired data occur in many experimental situations. When one views the subjects as a random sample from some large population, it may seem reasonable to model the data according to the typical one-way random effects analysis of variance (ANOVA). It is then usually of interest to estimate variance components and intraclass correlation. These estimators can be biased if key assumptions are violated, leading to erroneous interpretations and conclusions. We focus upon assumptions about the equality or inequality of means and/or variances of the two measures on each subject. In the framework of the one-way random effects ANOVA model, and three generalizations of it, we document estimators obtained as solutions to the likelihood equations. We consider the potentially serious effects of mistaken assumptions. Our findings suggest that the most general model considered is most desirable if consistent and efficient estimation of the between-subject variance component and intraclass correlation is the main goal. We also briefly connect our exposition to the study of reliability or agreement.

Nonparametric Tests for Monopsonistic Market Power Exertion

Measurement of market power exerted in imperfectly competitive markets has received considerable attention in recent years. This literature has become known as the New Empirical Industrial Organization (NEIO). Bresnahan (1989) provides an extensive review of these studies. Most often, empirical work relies on estimating monopoly market power exertion from first-order profit maximization conditions using aggregate industry data. Estimates of market power exertion depend on the functional forms selected for aggregate supply and demand. Importantly, econometric identification of the market power parameter estimated from the first-order conditions depends critically on second-order curvature properties of the functions selected (Bresnahan 1982, Lau). Little is known about the effects of model misspecification on estimated market power parameters. While most of the NEIO market power literature focuses on monopoly power, it is likely that firms with potential market power in agricultural and natural resource markets more of-

Application of optimal sampling theory to the determination of metacycline pharmacokinetic parameters: effect of model misspecification.

Use of optimal sampling theory (OST) in pharmacokinetic studies allows the number of sampling times to be greatly reduced without loss in parameter estimation precision. OST has been applied to the determination of the bioavailability parameters (area under the curve (AUC), maximal concentration (Cmax), time to reach maximal concentration (Tmax), elimination half-life (T1/2), of metacycline in 16 healthy volunteers. Five different models were used to fit the data and to define the optimal sampling times: one-compartment first-order, two-compartment first-order, two-compartment zero-order, two-compartment with Michaelis-Menten absorption kinetics, and a stochastic model. The adequacy of these models was first evaluated in a 6-subject pilot study. Only the stochastic model with zero-order absorption kinetics was adequate. Then, bioavailability parameters were estimated in a group of 16 subjects by means of noncompartmental analysis (with 19 samples per subject) using each optimal sampling schedule based procedure (with 6 to 9 samples depending on the model). Bias (PE) and precision (RMSE) of each bioavailability parameter estimation were calculated by reference to noncompartmental analysis, and were satisfactory for the 3 adequate models. The most relevant criteria for discrimination of the best model were the coefficient of determination, the standard deviation, and the mean residual error vs. time plot. Additional criteria were the number of required sampling times and the coefficient of variation of the estimates. In this context, the stochastic model was superior and yielded very good estimates of the bioavailability parameters with only 8 samples per subject.

Non-linear models for the analysis of longitudinal data.

Given the importance of longitudinal studies in biomedical research, it is not surprising that considerable attention has been given to linear and generalized linear models for the analysis of longitudinal data. A great deal of attention has also been given to non-linear models for repeated measurements, particularly in the field of pharmacokinetics. In this article, a brief overview of non-linear models for the analysis of repeated measures is given. Particular emphasis is placed on mixed-effects non-linear models and on various estimation procedures proposed for such models. Several of these estimation procedures are compared via a simulation study. In addition, simulation is used to investigate the effects of model misspecification, particularly with respect to one's choice of random-effects. A relatively straightforward measure useful in selecting an appropriate set of random effects is investigated and found to perform reasonably well.

Designs for population pharmacodynamics: Value of pharmacokinetic data and population analysis

Analyses of simulated data from pharmacokinetic/pharmacodynamic (PK/PD) studies varying with respect to the amount and timing of observations were undertaken to assess the value of these design choices. The simulation models assume mono- or biexponential drug disposition, and Emax-type pharmacodynamics. Data analysis uses a combined PK/PD population analysis or a hybrid, individual-PK/population-PD analysis. Assuming that the goal of the PK/PD studies is to estimate population PD, performance of designs is judged by comparing the precision of estimates of population mean PD parameters and of their interindividual variability. The simulations reveal that (i) PK data, even in small number (2 points per person from as few as 25-50% of persons) are very valuable for estimating population PD; (ii) designs involving more individuals, even if many are sparsely sampled, dominate designs calling for more complete study of fewer persons; (iii) the population analysis is generally superior to the hybrid analysis, especially when the PK model is misspecified (biexponential assumed to be monoexponential for analysis); (iv) varying sampling times and doses among subjects protects against the ill effects of model misspecification. In general, the results are quite encouraging about the usefulness of sparse data designs to estimate population dose response.

Estimation of the annual maximum distribution from samples of maxima in separate seasons

Quantile estimates of the annual maximum distribution can be obtained by fitting theoretical distributions to the maxima in separate seasons, e.g. to the monthly maxima. In this paper, asymptotic expressions for the bias and the variance of such estimates are derived for the case that the seasonal maxima follow a Gumbel distribution. Results from these expressions are presented for a situation with no seasonal variation and for maximum precipitation depths at Uccle/Ukkel (Belgium). It is shown that the bias is often negligible and that the variance reduction by using seasonal maxima instead of just the annual maxima strongly depends on the seasonal variation in the data. A comparison is made between the asymptotic standard error of quantile estimates from monthlymaxima with those from a partial duration series. Much attention is paid to the effect of model misspecification on the resulting quantile estimates of the annual maximum distribution. The use of seasonal maxima should be viewed with caution when the upper tail of this distribution is of interest.

On maximum likelihood estimation of parameters in incorrectly specified models of covariance for spatial data

The analysis of, and from, models of spatial data usually proceeds under the assumption, often implicit, that the correct model has been specified. However, any model identification procedures based on sample data are subject to error, and consequences of such errors then permeate subsequent analysis. Thus, an attempt to quantify some of these consequences is of interest. A standard framework for analysis is extended here, by introduction of information theory, to permit the study of effects of model misspecification on maximum likelihood estimators of parameters of model covariance. Asymptotically valid theoretical results are presented, and the relevance of these results to samples of finite sizes met in practice is assessed in a series of simulation experiments. The effect of model misspecification, and use of estimators of parameters of misspecified covariance models, on the practical problem of prediction at a previously unsampled location is considered briefly, and further areas for possible investigation are outlined.

Uncertain Population Forecasting

Abstract Errors in population forecasts arise from errors in the jump-off population and errors in the predictions of future vital rates. The propagation of these errors through the linear (“Leslie”) growth model is studied, and prediction intervals for future population are developed. For U.S. national forecasts, the prediction intervals are compared with the U.S. Census Bureau's high—low intervals. To assess the accuracy of the predictions of future vital rates, we derive the predictions from a parametric statistical model and estimate the extent of model misspecification and errors in parameter estimates. Subjective, “expert” opinion, so important in real forecasting, is incorporated with the technique of mixed estimation. A robust regression model is used to assess the effects of model misspecification.

Estimation of regression coefficients under model misspecification and non-normality of errors

The effects of model misspecification and non-normality of errors on estimates of coefficients are investigated in the multiple regression model.The expressions for the asymptotic expectation and variance of the M estimators, based on the Huber function, and a modified version of the M estimators are presented for a misspecified multiple regression model. The small sample properties of the least squares, M and modified M estimators are examined by Monte Carlo techniques when the true model is quadratic but a simple linear model is assumed and the errors are non-normal. Results show that the M estimators are sensitive to the misspecification in terms of their bias and variance where the degree of sensitivity is dependent on the choice of design, values of the misspecified parameters, and the error distribution. For the situations examined, the modified M estimators achieved the best overall performance.

On minimum distance estimation of location based on the kolmogorov statistic

The asymptotic distribution is derived for the minimum distance estimator of a location parameter based on the Kolmogorov goodness of fit statistic. The distribution is expressed in terms of the distribution of a functional of a Brownian bridge. An upper bound is obtained for the length of the confidence interval based on the Kolmogorov statistic. A simulation study with sample sizes 10 and 20 compares the length of the interval based on the Kolmogorov statistic to the length of the interval based on the maximum likelihood estimator. Another simulation shows the effect of model misspecification on the coverage probabilities of the interval based on the Kolmogorov statistic.

Preposterior Analysis of Bayes Estimators of Mean Life

In considering life test experiments from a behaviouristic Bayes point of view, one may speculate on the effect of model misspecification on the posterior mean under alternative stopping rulers. Of coures, under the life distribution model, we expect the mean of the posterior to equal the mean of the prior. However, if we think the model may have been misspecified, we would no longer expect this equality. It is shown that for Bayes estimators of mean life under the exponential model and general priors on mean life, we expect, based on a preposterior analysis, that the mean of the posterior will increase with sample size when the true model has an increasing faliure rate and certian fixed stopping rules are used. Also, we show that for Bayes estimators of mean life based on the natural conjugate prior for the exponential model and complete samples, the Bayes risk is less when the coefficient of variation is less than for the exponential model. Recommendations relative to use of life test sampling plans based on an exponential model are made.

Preposterior analysis of Bayes estimators of mean life

Abstract : In considering life test experiments from a behavioristic Bayes point of view, we may speculate on the effect of model misspecification on the posterior mean under alternative stopping rules. Of course, under the life distribution model, we expect the mean of the posterior to equal the mean of the prior. However, if we think the model may have been misspecified, we would no longer expect this equality. We show that for Bayes estimators of mean life under the exponential model and general priors on mean life, we expect, based on a preposterior analysis, that the mean of the posterior will increase with sample size when the true model has an increasing failure rate and certain fixed stopping rules are used. Also, we show that for Bayes estimators of mean life based on the natural conjugate prior for the exponential model and complete samples, the Bayes risk is less when the coefficient of variations is less than for the exponential model. Recommendations relative to use of life test sampling plans based on an exponential model are made. (Author)

A Model-Based Approach to Estimation for Small Subgroups of a Population

Abstract Sample surveys rarely provide enough data to permit accurate estimation for small subgroups of the population by using the standard methods based on the selection probabilities. In this case a possible procedure is to base the required estimate on data from the subgroup concerned, supplemented by that from similar subgroups. Such an approach makes implicit use of the population structure. This article attempts to model that structure explicitly and obtains estimates within a predictive framework. The effect of model misspecification on the bias of the estimators is also examined.

The Effect of Model Misspecification on Tests of the Efficient Market Hypothesis

The Journal of FinanceVolume 32, Issue 1 p. 57-66 Article THE EFFECT OF MODEL MISSPECIFICATION ON TESTS OF THE EFFICIENT MARKET HYPOTHESIS Menachem Brenner, Menachem BrennerHebrew University, Jerusalem. This paper is extracted from my Ph.D. thesis at Cornell University. I wish to express my indebtness to my thesis committee, Seymour Smidt, Bernell Stone, and John McClain. Special thanks are due to Professor Seymour Smidt for his help and insightful comments. This research has been partially supported by a grant from the Lady Davis Foundation.Search for more papers by this author Menachem Brenner, Menachem BrennerHebrew University, Jerusalem. This paper is extracted from my Ph.D. thesis at Cornell University. I wish to express my indebtness to my thesis committee, Seymour Smidt, Bernell Stone, and John McClain. Special thanks are due to Professor Seymour Smidt for his help and insightful comments. This research has been partially supported by a grant from the Lady Davis Foundation.Search for more papers by this author First published: March 1977 https://doi.org/10.1111/j.1540-6261.1977.tb03241.xCitations: 15 Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume32, Issue1March 1977Pages 57-66 RelatedInformation

THE EFFECT OF MODEL MISSPECIFICATION ON TESTS OF THE EFFICIENT MARKET HYPOTHESIS

TESTS OF THE Efficient Market Hypothesis (EMH) are in general weak tests. The null hypothesis has always been that the market is efficient with no specific alternative of inefficiency. Thus, the power of these tests is not known. The tests usually rely on a certain market model without questioning the validity of the model that was used. A misspecified model may provide test statistics that indicate that the market is efficient when it is not efficient and vice versa. The possibility that the EMH has not been rejected because the wrong market model was used, was never adequately considered. This paper is concerned with the theoretical effect of model misspecification on tests of the efficient market hypothesis. Since tests of the EMH usually use a certain market model, the conclusions are based on the assumption that the model is correctly specified. By deriving the possible biases due to model misspecification, we are actually concerned with the power (or validity) of the EMH tests. Tests of the EMH generally proceed in two stages: First, we estimate the relevant parameters using a certain market model; second, we use the estimated parameters for prediction and use the prediction errors, also called residuals,' to test market efficiency. The statistical properties of the parameters, estimated in the first stage, depend on how well the market model describes the true underlying stochastic process. Serious misspecifications may yield biased and/or inefficient parameter estimates. This in turn may result in biased and/or inefficient estimates of the residuals in the second stage. The extent to which these misspecifications affect our conclusion about market efficiency depends on the way we use these residuals in testing the EMH. Under certain circumstances (to be specified later) the misspecifications, no matter how serious, will not affect our conclusions with regard to market efficiency. In the remainder of this paper we first consider general cases of misspecification, their effect on parameter estimates and on residual estimates. Then we consider the effects of misspecification in some specific cases. Finally we present the effect of ,B changes on residual estimates.