In many fields of statistical application the fundamental task is to quantify the association between some explanatory variables or covariates and a response or outcome variable through a suitable regression model. The accuracy of such quantification depends on how precisely we measure the relevant covariates. In many instances, we can not measure some of the covariates accurately, rather we can measure noisy versions of them. In statistical terminology this is known as measurement errors or errors in variables. Regression analyses based on noisy covariate measurements lead to biased and inaccurate inference about the true underlying response-covariate associations. In this thesis we investigate some aspects of measurement error modelling in the case of binary logistic regression models. We suggest a flexible parametric approach for adjusting the measurement error bias while estimating the response-covariate relationship through logistic regression model. We investigate the performance of the proposed flexible parametric approach in comparison with the other flexible parametric and nonparametric approaches through extensive simulation studies. We also compare the proposed method with the other competitive methods with respect to a real-life data set. Though emphasis is put on the logistic regression model the proposed method is applicable to the other members of the generalized linear models, and other types of non-linear regression models too. Finally, we develop a new computational technique to approximate the large sample bias that my arise due to exposure model misspecification in the estimation of the regression parameters in a measurement error scenario.

In many fields of statistical application the fundamental task is to quantify the association between some explanatory variables or covariates and a response or outcome variable through a suitable regression model. The accuracy of such quantification depends on how precisely we measure the relevant covariates. In many instances, we can not measure some of the covariates accurately, rather we can measure noisy versions of them. In statistical terminology this is known as measurement errors or errors in variables. Regression analyses based on noisy covariate measurements lead to biased and inaccurate inference about the true underlying response-covariate associations. In this thesis we investigate some aspects of measurement error modelling in the case of binary logistic regression models. We suggest a flexible parametric approach for adjusting the measurement error bias while estimating the response-covariate relationship through logistic regression model. We investigate the performance of the proposed flexible parametric approach in comparison with the other flexible parametric and nonparametric approaches through extensive simulation studies. We also compare the proposed method with the other competitive methods with respect to a real-life data set. Though emphasis is put on the logistic regression model the proposed method is applicable to the other members of the generalized linear models, and other types of non-linear regression models too. Finally, we develop a new computational technique to approximate the large sample bias that my arise due to exposure model misspecification in the estimation of the regression parameters in a measurement error scenario.

In many fields of statistical application the fundamental task is to quantify the association between some explanatory variables or covariates and a response or outcome variable through a suitable regression model. The accuracy of such quantification depends on how precisely we measure the relevant covariates. In many instances, we can not measure some of the covariates accurately, rather we can measure noisy versions of them. In statistical terminology this is known as measurement errors or errors in variables. Regression analyses based on noisy covariate measurements lead to biased and inaccurate inference about the true underlying response-covariate associations. In this thesis we investigate some aspects of measurement error modelling in the case of binary logistic regression models. We suggest a flexible parametric approach for adjusting the measurement error bias while estimating the response-covariate relationship through logistic regression model. We investigate the performance of the proposed flexible parametric approach in comparison with the other flexible parametric and nonparametric approaches through extensive simulation studies. We also compare the proposed method with the other competitive methods with respect to a real-life data set. Though emphasis is put on the logistic regression model the proposed method is applicable to the other members of the generalized linear models, and other types of non-linear regression models too. Finally, we develop a new computational technique to approximate the large sample bias that my arise due to exposure model misspecification in the estimation of the regression parameters in a measurement error scenario. / Science, Faculty of / Statistics, Department of / Graduate

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In epidemiological studies of an exposure-response association, often only a mismeasured exposure is taken on each individual of the population under study. If ignored, exposure measurement error can bias the estimated exposure-response association in question. A reliability study may be carried out to estimate the relation between the mismeasured and true exposure, which could then be used to adjust for measurement error in the attenuated exposure-response relationship. However, taking repeated exposure measurements may be expensive. Given a fixed total study cost, a two-stage design may be a more efficient approach for regression parameter estimation compared to the traditional single-stage design since, in the second-stage, repeated measurement is restricted to a sample of first-stage subjects. Sampling the extremes of the first-stage exposure distribution has been shown to be more efficient than random sampling.

Master of Science / Statistics / Weixing Song / In this report, an improved estimation procedure for the regression parameter in simple linear regression models with the Laplace measurement error is proposed. The estimation procedure is made feasible by a Tweedie type equality established for E(X|Z), where Z = X + U, X and U are independent, and U follows a Laplace distribution. When the density function of X is unknown, a kernel estimator for E(X|Z) is constructed in the estimation procedure. A leave-one-out cross validation bandwidth selection method is designed. The finite sample performance of the proposed estimation procedure is evaluated by simulation studies. Comparison study is also conducted to show the superiority of the proposed estimation procedure over some existing estimation methods.

When only whole years of age are recorded in survey data, children who experienced a birthday since the beginning of the school year may appear to be of school-age when they are not, or vice-versa. This creates an error in estimates of school participation indicators based on such data. This issue is well-known in education statistics, and several procedures attempting to correct for this error have been proposed. The present study critiques current practice and demonstrates that its limitations continue to confound educational research and high-stakes policy conclusions: speculative explanations have been proposed for what is actually a measurement artefact. An alternative adjustment strategy is proposed that coherently exploits all available information and explicitly indicates the remaining uncertainty. The application of the method is illustrated by a number of empirical case studies using recent household survey data. These examples demonstrate that the method is feasible, accurate, and that taking survey timing into account can significantly alter how these data are interpreted.

Thesis advisor: Henry Braun / The measurement of student academic growth is one of the most important statistical tasks in an educational accountability system. The current methods of measuring student growth adopted in most states have various drawbacks in terms of sensitivity, accuracy, and interpretability. In this thesis, we apply the conditional growth chart method, a well-developed diagnostic tool in pediatrics, to student longitudinal test data to produce descriptive and diagnostic statistics about students' academic growth trajectory. We also introduce an innovative simulation-extrapolation (SIMEX) method which corrects for measurement error-induced bias in the estimation of the conditional growth model. Our simulation study shows that the proposed method has an advantage in terms of mean squared error of the estimators, when compared with the growth model that ignores measurement error. Our data analysis demonstrates that the conditional growth chart method, when combined with the SIMEX method, can be a powerful tool in the educational accountability system. It produces more sensitive and accurate measures of student growth than the other currently available methods; it provides diagnostic information that is easily understandable to teachers, parents and students themselves; the individual level growth measures can also be aggregated to school level as an indicator of school growth. / Thesis (PhD) — Boston College, 2009. / Submitted to: Boston College. Lynch School of Education. / Discipline: Educational Research, Measurement, and Evaluation.

The development of a simulation strategy and modelling algorithm with potential application to a variety of food process operations, particularly to thermal processing of canned foodstuffs has been undertaken. A review of published work identified previous efforts in the development of mathematical models for thennal process operations, including their limitations. The review showed that Finite Difference methods have found wide application in modelling conduction heating of canned foods. A similar model would be a useful numerical yardstick for validating any developments in this work. The great diversity of food handling operations have been grouped into a more manageable small number of classes. Such classification recognised that sets of related operations share common characteristics and functions which are the basis for the development of mathematical models for each class of operations. The strategy developed involved hierarchical decomposition of unit operations into assemblies of basic modules and mathematical modelling of these basics. A model of the operation can then be constructed simply by selecting and arranging the required basic units with due consideration to the boundary conditions of the physical problem. For transient operations with positional variation, these elementary modules have been termed "zones". The range of basic zones to model representative units have been identified. This hierarchical zone-model simulation has been demonstrated for heat transfer in a cylindrical container and for batch retort operation. The repeated use of the same unit modules for different operations makes this a flexible and robust strategy. The mathematics of zone-modelling has been developed for heat conduction in foodstuffs in cylindrical containers. To ensure accuracy, the numerical integration steps were rigorously monitored using mathematical procedures well-established for this purpose. The validity of the model has been tested against the analytical and implicit finite difference solutions. Generally, zone models agreed within 1 % of these standard yardsticks with the difference becoming negligible when sufficiently small integration steps or zone sizes were used. The effectiveness of zone-modelling as a simulation tool has been established using experimental data and the various sources of discrepancy between the model and experimental data accounted for. Thermocouple measurement errors have been found to have contributed most significantly to this discrepancy. Detailed analysis and modelling of thermocouple measurement errors has been carried out using zone-modelling to simulate the true experimental system which accounted for the presence of a thermocouple. The result has been an improved agreement between experiment and the zonemodel, and it also demonstrated the flexibility of the modelling technique. Further resuhs have shown that the discrepancy varied with thermocouple size and type. The contributions to error of temperature variability of, and of uncertainty in, thermophysical properties of the food were discussed. , The flexibility and robustness of zone-modelling have been further demonstrated using some practical situations including heat transfer to foodstuff in flexible packaging - such as sausage rolls, heat transfer in a food container with varying headspaces and the consequence of steam interruption during processing. Examples have been discussed of other transient processes that could similarly be modelled using this technique. The main achievements of this work include the application of hierarchical simulation and zonemodelling techniques to food processing and the development of a novel mathematical modelling technique which is more flexible than finite differences. Moreover, the applications of zonemodelling to the study of thermocouple errors, to the study of the consequences of steam interruption during thermal processing, and to heat transfer in foods in flexible containers, are developments of interest in food processing. It is concluded that the hierarchical simulation and zone modelling algorithm are robust and flexible techniques with potential applications in food process simulation .

This thesis deals with the take-up of social security benefits in Britain. It is well documented that not everyone who is entitled to benefits actually claims them. Nontake- up of benefits has been found to be a problem especially for benefits which are means-tested. So, throughout this thesis, we concentrate on Income Support, the main means-tested benefit in Britain. The latest official estimates on the extent of non-takeup (for 1993/94) suggest that up to 1.4 million persons are not receiving close to £1.7 billion of IS in spite of being entitled to it. The main question this thesis addresses IS what are the factors which determine whether an individual will or will not take-up their benefit entitlement? We consider the problem from an economic perspective by constructing suitable models set in both static and dynamic environments. These models provide some interesting insights about the nature of non-take-up. In tum, they also form the basis to a series of econometric models. Previous empirical evidence has shown that the entitlement level itself is one of the key determinants of whether or not an individual will take-up. In addition, it has long been recognized that - due to the complex nature of the benefit system - determining individual entitlements is, in many cases, error-prone with resulting benefit entitlements that are subject to measurement error. Hence, unlike any other studies thus far, we account for the presence of measurement error in the benefit entitlement when modelling the likelihood of take-up. Finally, we shed new light on the dynamics of take-up by using the information contained in our panel data set. In particular, we consider the effect claiming in the past has on the current decision to take-up and how future changes, expected or known with certainty, influence the decision to take-up or not