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An important problem in the field of bioinformatics is to identify interactive effects among profiled variables for outcome prediction. In this paper, a logistic regression model with pairwise interactions among a set of binary covariates is considered. Modeling the structure of the interactions by a graph, our goal is to recover the interaction graph from independently identically distributed (i.i.d.) samples of the covariates and the outcome. When viewed as a feature selection problem, a simple quantity called influence is proposed as a measure of the marginal effects of the interaction terms on the outcome. For the case when the underlying interaction graph is known to be acyclic, it is shown that a simple algorithm that is based on a maximum-weight spanning tree with respect to the plug-in estimates of the influences not only has strong theoretical performance guarantees, but can also outperform generic feature selection algorithms for recovering the interaction graph from i.i.d. samples of the covariates and the outcome. Our results can also be extended to the model that includes both individual effects and pairwise interactions via the help of an auxiliary covariate.

This article presents methods for constructing an asymptotic hyperbolic band under the multiple logistic regression model when the predictor variables are restricted to a specific region $\mathscr{X}$. Scheff\'{e}'s method yields unnecessarily wide, and hence conservative, bands if the predictor variables can be restricted to a certain region. Piegorsch and Casella (1988) developed a procedure to build an asymptotic confidence band for the multiple logistic regression model over particular regions. Those regions are shown to be special cases of the region $\mathscr{X}$, which was first investigated by Seppanen and Uusipaikka (1992) in the multiple linear regression context. This article also provides methods for constructing conservative confidence bands when the restricted region is not of the specified form. Particularly, rectangular restricted regions, which are commonly encountered in practice, are considered. Two examples are given to illustrate the proposed methodology, and one example shows that the proposed procedure outperforms the method given by Piegorsch and Casella (1988).

This article presents methods for the construction of two-sided and one-sided simultaneous hyperbolic bands for the logistic and probit regression models when the predictor variable is restricted to a given interval. The bands are constructed based on the asymptotic properties of the maximum likelihood estimators. Past articles have considered building two-sided asymptotic confidence bands for the logistic model, such as Piegorsch and Casella (1988). However, the confidence bands given by Piegorsch and Casella are conservative under a single interval restriction, and it is shown in this article that their bands can be sharpened using the methods proposed here. Furthermore, no method has yet appeared in the literature for constructing one-sided confidence bands for the logistic model, and no work has been done for building confidence bands for the probit model, over a limited range of the predictor variable. This article provides methods for computing critical points in these areas.

This document studied optimally bounded score functions for estimating regression parameters in a generalized linear model. This work extends results obtained by Krasker & Welsch (1982) for the linear model and provides a simple proof of Krasker and Welsch's first order condition for strong optimality. The application of these results to logistic regression is studied in some detail with an example given comparing the bounded influence estimator with maximum likelihood. Additional keywords: Outliers; Robustness; Influentral points. (Author)

The proportional odds (PO) model, which is also called cumulative odds model (Agresti, 1996, 2002 ; Armstrong & Sloan, 1989; Long, 1997, Long & Freese, 2006; McCullagh, 1980; McCullagh & Nelder, 1989; Powers & Xie, 2000; O'Connell, 2006), is one of the most commonly used models for the analysis of ordinal categorical data and comes from the class of generalized linear models. Researchers currently have a variety of options when choosing statistical software packages that can perform ordinal logistic regression analyses. However, statistical software, such as Stata, SAS, and SPSS, may use different techniques to estimate the parameters. The purpose of this article is to: (1) illustrate the use of Stata, SAS and SPSS to fit proportional odds models using educational data; and (2) compare the features and results for fitting the proportional odds model using Stata OLOGIT, SAS PROC LOGISTIC (ascending and descending), and SPSS PLUM. The assumption of the proportional odds was tested, and the results of the fitted models were interpreted. The data of a survey instrument Teachers' Perceptions of Grading Practices (Liu, 2004; Liu, O'Connell & McCoach, 2006) is used to demonstrate the PO analysis. This demonstration clarifies some of the issues that researchers must consider in using different statistical packages for analysis of ordinal data. (Contains 3 tables and 8 figures.)

Logistic and Cox regression methods are practical tools used to model the relationships between certain student learning outcomes and their relevant explanatory variables. The logistic regression model fits an S-shaped curve into a binary outcome with data points of zero and one. The Cox regression model allows investigators to study the duration and timeline of the critical events, which are also a binary and dichotomous measure. This paper introduces logistic and Cox regression models by illustrating examples, implementing step-by-step SPSS procedures, and further comparing the similarities and differences of the model characteristics. Logistic regression analysis was conducted to investigate the effects of the explanatory variables such as pre-admission variables, college cumulative GPAs, and curriculum tracks on student licensure examination. Moreover, logistic regression analysis was employed to quantify the effect (odds or odds ratio) of specific explanatory variables on the binary outcome holding other variables constant. With regards to Cox regression analysis, the outcome variable of interest was the timing of experiencing academic difficulty--dismissal, withdrawal, and leave of absence. The Cox regression model was used to detect when students were most likely to experience academic difficulty beyond their matriculation. The model also allowed the investigators to measure the effect (relative hazard or hazard ratio) of specific risk factors on the academic difficulty after adjusting for other factors. Identifying the occurrence of critical events along with the explanatory variables, college administrators and faculty could implement intervention strategies to ensure student success. (Contains 1 figure and 6 tables.)

Most large Brazilian institutions working with credit concession use credit models to evaluate the risk of consumer loans. Any improvement in the techniques that may bring about greater precision of a prediction model will provide financial returns to the institution. The first phase of this study introduces concepts of credit and risk. Subsequently, with a sample set of applicants from a large Brazilian financial institution, three credit scoring models are built applying these distinct techniques: Logistic Regression, Neural Networks and Genetic Algorithms. Finally, the quality and performance of these models are evaluated and compared to identify the best. Results obtained by the logistic regression and neural network models are good and very similar, although the first is slightly better. Results obtained with the genetic algorithm model are also good, but somewhat inferior. This study shows the procedures to be adopted by a financial institution to identify the best credit model to evaluate the risk of consumer loans. Use of the best fitted model will favor the definition of an adequate business strategy thereby increasing profits.

While it is imperative that attempts be made to assess the predictive accuracy of any prediction model, traditional measures of predictive accuracy have been criticized as suffering from "the base rate problem." The base rate refers to the relative frequency of occurrence of the event being studied in the population of interest, and the problem stems from the fact that statistical prediction models often are not valid when applied to populations with a different base rate than the population for which the prediction model was constructed. This study tested alternative predictive accuracy models, two of which account for base rate levels, to determine the degree to which they are base rate invariant. The indices were the three indices recommended by S. Menard (1995), the Relative Improvement over Change (RIOC) method, and the percentage correct classification indices. A Monte Carlo simulation study was undertaken to generate two types of logistic regression models, one with a dichotomous predictor and a continuously measured predictor and the other with two dichotomous predictors. Four reliabilities, three base rate conditions, and two sample sizes were used. All three of Menard's indices were found to be sensitive to fluctuations in the base rate. Conditions under which these indices and the RIOC may be used are summarized in a table. It is recommended that researchers compute all three of Menard's indices and then compare the values across the three to get an indication of the underlying base rate of the sample. (Contains 3 tables and 26 references.) (SLD)

Cost growth remains a concern for cost analysts, program managers, senior DoD decision-makers, Congress, and even the American public. All of these people have a vested interest in the cost of DoD programs and most would like to see those costs decrease; as such, we need additional tools to help combat cost growth. Previous research creates the foundation for the use of a two-step methodology to help predict cost growth, which we follow closely. First, utilizing logistic regression we analyze whether specific program characteristics predict cost growth within the Engineering and Manufacturing Development (EMD) phase for combined RDT&E and procurement budgets. The second step uses this answer (i.e., a positive response) to find cost growth predictor variables. Specifically, we perform a multiple regression analysis and determine the amount of cost growth incurred by these DoD programs. Through these two steps, we seek to unearth any predictive relationships within the data in order to build a predictive cost growth model. The final models predict whether a program will have cost growth and what the potential amount of the cost growth will be for the combined RDT&E and procurement budgets within the EMD phase of acquisition.

Since its establishment the Naval Space Surveillance Command (NAVSPASUR) in Dalhgren Virginia has been providing surveillance data (NAVSPASUR data sets) for thousands of space objects in a near earth orbit. To date, very little statistical analysis of these data sets in the form of a system performance evaluation has been conducted. The objective of this thesis is to provide NAVSPASUR with a statistical method to evaluate the system performance in terms of its capability of detecting space objects. In this thesis six individual station models, as well as a system-wide model are estimated. Optimal probability levels for classifying predictions are additionally provided. The results being provided are obtained through the implementation of Logistic Regression analysis. The system-wide model estimated in this thesis, is superior in its prediction accuracy when compared to the previous model provided to NAVSPASUR in a September 1991, Naval Postgraduate School Master's Thesis. Finally an implementation program written in FORTRAN is given. This program provides a user friendly interface capability for predicting system performance in terms of its detection ability.

Maximum likelihood estimates for errors-in-variables models are not always root-N consistent. We provide an example of this for logistic regression. (Author)

The challenges for the construction of a pandemic confrontation agenda by COVID-19 in Brazil come up against social inequalities, as a reflection of the segregation of access to comprehensive basic sanitation services and public health assistance programs. The objective of this work is to analyze the profile of deaths and recoveries by COVID-19 in the state of Minas Gerais, based on socio-environmental predictors, using a logistic regression model and classification tree (CHAID). Data on recovered individuals and confirmed deaths for COVID-19 were obtained from the Minas Gerais State Department of Health, containing records of age, sex, race, comorbidity and municipality of residence. The data regarding municipal basic sanitation were obtained from Instituto Trata Brasil. The Minitab and SPSS software were used in the elaboration of the logistic regression models and classification tree, respectively. The probability of death from COVID-19 in the state is significantly higher in males, over the age of 60 years old, with some comorbidity, declared black and brown, living in municipalities located in the poorest macro-regions of the state, where classes prevail inadequate or inadequate basic sanitation. The classification tree for deaths by COVID-19, differentiates young blacks and browns without comorbidity, and the elderly with comorbidity not assisted by a comprehensive basic sanitation network. It is concluded that the worsening of the pandemic in the state is related to aspects of social vulnerability, and that the implementation of inclusive public policies is urgent.

This is a note on logistic regression models and logistic kernel machine models. It contains derivations to some of the expressions in a paper -- SNP Set Analysis for Detecting Disease Association Using Exon Sequence Data -- submitted to BMC proceedings by these authors.

In this paper a robust version of the classical Wald test statistics for linear hypothesis in the logistic regression model is introduced and its properties are explored. We study the problem under the assumption of random covariates although some ideas with non random covariates are also considered. The family of tests considered is based on the minimum density power divergence estimator instead of the maximum likelihood estimator and it is referred to as the Wald-type test statistic in the paper. We obtain the asymptotic distribution and also study the robustness properties of the Wald type test statistic. The robustness of the tests is investigated theoretically through the influence function analysis as well as suitable practical examples. It is theoretically established that the level as well as the power of the Wald-type tests are stable against contamination, while the classical Wald type test breaks down in this scenario. Some classical examples are presented which numerically substantiate the theory developed. Finally a simulation study is included to provide further confirmation of the validity of the theoretical results established in the paper.

In this paper, we used simulations to compare the performance of classical and Bayesian estimations in logistic regression models using small samples. In the performed simulations, conditions were varied, including the type of relationship between independent and dependent variable values (i.e., unrelated and related values), the type of variable (i.e., binary and continuous), and different Binomial distribution values and symmetry (i.e., symmetry and positive asymmetry). Iteratively re-weighted least squares was used as the estimate method to fit the models in both the classical and Bayesian estimations. A weakly informative default distribution was chosen as the prior distribution for Bayesian estimation. The simulation results demonstrate that Bayesian estimations provide more stable distributions but are not able to solve problems generated by asymmetric distributions based on small samples. Additional research using different kinds of priors that is addressed at solving problems caused by asymmetry is needed. (Contains 2 tables, 2 figures and 1 footnote.)

In this paper, we used simulations to compare the performance of classical and Bayesian estimations in logistic regression models using small samples. In the performed simulations, conditions were varied, including the type of relationship between independent and dependent variable values (i.e., unrelated and related values), the type of variable (i.e., binary and continuous), and different Binomial distribution values and symmetry (i.e., symmetry and positive asymmetry). Iteratively re-weighted least squares was used as the estimate method to fit the models in both the classical and Bayesian estimations. A weakly informative default distribution was chosen as the prior distribution for Bayesian estimation. The simulation results demonstrate that Bayesian estimations provide more stable distributions but are not able to solve problems generated by asymmetric distributions based on small samples. Additional research using different kinds of priors that is addressed at solving problems caused by asymmetry is needed. (Contains 2 tables, 2 figures and 1 footnote.)

Molecular profiling data (e.g., gene expression) has been used for clinical risk prediction and biomarker discovery. However, it is necessary to integrate other prior knowledge like biological pathways or gene interaction networks to improve the predictive ability and biological interpretability of biomarkers. Here, we first introduce a general regularized Logistic Regression (LR) framework with regularized term $\lambda \|\bm{w}\|_1 + \eta\bm{w}^T\bm{M}\bm{w}$, which can reduce to different penalties, including Lasso, elastic net, and network-regularized terms with different $\bm{M}$. This framework can be easily solved in a unified manner by a cyclic coordinate descent algorithm which can avoid inverse matrix operation and accelerate the computing speed. However, if those estimated $\bm{w}_i$ and $\bm{w}_j$ have opposite signs, then the traditional network-regularized penalty may not perform well. To address it, we introduce a novel network-regularized sparse LR model with a new penalty $\lambda \|\bm{w}\|_1 + \eta|\bm{w}|^T\bm{M}|\bm{w}|$ to consider the difference between the absolute values of the coefficients. And we develop two efficient algorithms to solve it. Finally, we test our methods and compare them with the related ones using simulated and real data to show their efficiency.

Penalized regression is an attractive framework for variable selection problems. Often, variables possess a grouping structure, and the relevant selection problem is that of selecting groups, not individual variables. The group lasso has been proposed as a way of extending the ideas of the lasso to the problem of group selection. Nonconvex penalties such as SCAD and MCP have been proposed and shown to have several advantages over the lasso; these penalties may also be extended to the group selection problem, giving rise to group SCAD and group MCP methods. Here, we describe algorithms for fitting these models stably and efficiently. In addition, we present simulation results and real data examples comparing and contrasting the statistical properties of these methods.

This paper investigates correct variable selection in finite samples via $\ell_1$ and $\ell_1+\ell_2$ type penalization schemes. The asymptotic consistency of variable selection immediately follows from this analysis. We focus on logistic and linear regression models. The following questions are central to our paper: given a level of confidence $1-\delta$, under which assumptions on the design matrix, for which strength of the signal and for what values of the tuning parameters can we identify the true model at the given level of confidence? Formally, if $\widehat{I}$ is an estimate of the true variable set $I^*$, we study conditions under which $\mathbb{P}(\widehat{I}=I^*)\geq 1-\delta$, for a given sample size $n$, number of parameters $M$ and confidence $1-\delta$. We show that in identifiable models, both methods can recover coefficients of size $\frac{1}{\sqrt{n}}$, up to small multiplicative constants and logarithmic factors in $M$ and $\frac{1}{\delta}$. The advantage of the $\ell_1+\ell_2$ penalization over the $\ell_1$ is minor for the variable selection problem, for the models we consider here. Whereas the former estimates are unique, and become more stable for highly correlated data matrices as one increases the tuning parameter of the $\ell_2$ part, too large an increase in this parameter value may preclude variable selection.

We propose a new prior distribution for classical (nonhierarchical) logistic regression models, constructed by first scaling all nonbinary variables to have mean 0 and standard deviation 0.5, and then placing independent Student-$t$ prior distributions on the coefficients. As a default choice, we recommend the Cauchy distribution with center 0 and scale 2.5, which in the simplest setting is a longer-tailed version of the distribution attained by assuming one-half additional success and one-half additional failure in a logistic regression. Cross-validation on a corpus of datasets shows the Cauchy class of prior distributions to outperform existing implementations of Gaussian and Laplace priors. We recommend this prior distribution as a default choice for routine applied use. It has the advantage of always giving answers, even when there is complete separation in logistic regression (a common problem, even when the sample size is large and the number of predictors is small), and also automatically applying more shrinkage to higher-order interactions. This can be useful in routine data analysis as well as in automated procedures such as chained equations for missing-data imputation. We implement a procedure to fit generalized linear models in R with the Student-$t$ prior distribution by incorporating an approximate EM algorithm into the usual iteratively weighted least squares. We illustrate with several applications, including a series of logistic regressions predicting voting preferences, a small bioassay experiment, and an imputation model for a public health data set.

We propose a new prior distribution for classical (nonhierarchical) logistic regression models, constructed by first scaling all nonbinary variables to have mean 0 and standard deviation 0.5, and then placing independent Student-$t$ prior distributions on the coefficients. As a default choice, we recommend the Cauchy distribution with center 0 and scale 2.5, which in the simplest setting is a longer-tailed version of the distribution attained by assuming one-half additional success and one-half additional failure in a logistic regression. Cross-validation on a corpus of datasets shows the Cauchy class of prior distributions to outperform existing implementations of Gaussian and Laplace priors. We recommend this prior distribution as a default choice for routine applied use. It has the advantage of always giving answers, even when there is complete separation in logistic regression (a common problem, even when the sample size is large and the number of predictors is small), and also automatically applying more shrinkage to higher-order interactions. This can be useful in routine data analysis as well as in automated procedures such as chained equations for missing-data imputation. We implement a procedure to fit generalized linear models in R with the Student-$t$ prior distribution by incorporating an approximate EM algorithm into the usual iteratively weighted least squares. We illustrate with several applications, including a series of logistic regressions predicting voting preferences, a small bioassay experiment, and an imputation model for a public health data set.

Diabetic Mellitus is a disease of inadequate control of level of glucose in blood.  It is also happened by disorder of carbohydrate metabolism by impaired ability to produce insulin in blood.  In this article, I have to discuss about how to find risk factors and how much its influence in the progression of Diabetic Retinopathy (DR), to identify the presence of DR and its progression by formulating some mathematical equations with suitable variables and to find several stages of DR and its progression. The continuous variables were expressed as mean and standard deviation and categorial variables as frequency and proportions. In this, we have discussed about various kind of statistical prediction models. Found the influencing factors in the progression of DR by using multiple logistic regression analysis, predicted the probability of a DM patient in the progression of DR and found the probability of DR among diabetes up to a given period of time and using by Markov Chain Analysis found the TPM and the absorbing state in a DM patient and to identify as having complete vision loss. I have concluded that the statistical models were explained and found the influenced factors and risk ratio to develop DR among DM patients has been computed, and transition of DR which predict the chance to develop DR in a DM patient and found the probability to develop DR over a period of time has also explained via procedure. Keywords:  diabetic mellitus, diabetic retinopathy, statistical models, risk ratio

This article is from Journal of the American Medical Informatics Association : JAMIA , volume 19 . Abstract Objective: The classification of complex or rare patterns in clinical and genomic data requires the availability of a large, labeled patient set. While methods that operate on large, centralized data sources have been extensively used, little attention has been paid to understanding whether models such as binary logistic regression (LR) can be developed in a distributed manner, allowing researchers to share models without necessarily sharing patient data. Material and methods: Instead of bringing data to a central repository for computation, we bring computation to the data. The Grid Binary LOgistic REgression (GLORE) model integrates decomposable partial elements or non-privacy sensitive prediction values to obtain model coefficients, the variance-covariance matrix, the goodness-of-fit test statistic, and the area under the receiver operating characteristic (ROC) curve. Results: We conducted experiments on both simulated and clinically relevant data, and compared the computational costs of GLORE with those of a traditional LR model estimated using the combined data. We showed that our results are the same as those of LR to a 10−15 precision. In addition, GLORE is computationally efficient. Limitation: In GLORE, the calculation of coefficient gradients must be synchronized at different sites, which involves some effort to ensure the integrity of communication. Ensuring that the predictors have the same format and meaning across the data sets is necessary. Conclusion: The results suggest that GLORE performs as well as LR and allows data to remain protected at their original sites.

The logistic specification has been used extensively in non-Bayesian statistics to model the dependence of discrete outcomes on the values of specified covariates. Because the likelihood function is globally weakly concave estimation by maximum likelihood is generally straightforward even in commonly arising applications with scores or hundreds of parameters. In contrast Bayesian inference has proven awkward, requiring normal approximations to the likelihood or specialized adaptations of existing Markov chain Monte Carlo and data augmentation methods. This paper approaches Bayesian inference in logistic models using recently developed generic sequential posterior simulaton (SPS) methods that require little more than the ability to evaluate the likelihood function. Compared with existing alternatives SPS is much simpler, and provides numerical standard errors and accurate approximations of marginal likelihoods as by-products. The SPS algorithm for Bayesian inference is amenable to massively parallel implementation, and when implemented using graphical processing units it is more efficient than existing alternatives. The paper demonstrates these points by means of several examples.

The logistic specification has been used extensively in non-Bayesian statistics to model the dependence of discrete outcomes on the values of specified covariates. Because the likelihood function is globally weakly concave estimation by maximum likelihood is generally straightforward even in commonly arising applications with scores or hundreds of parameters. In contrast Bayesian inference has proven awkward, requiring normal approximations to the likelihood or specialized adaptations of existing Markov chain Monte Carlo and data augmentation methods. This paper approaches Bayesian inference in logistic models using recently developed generic sequential posterior simulaton (SPS) methods that require little more than the ability to evaluate the likelihood function. Compared with existing alternatives SPS is much simpler, and provides numerical standard errors and accurate approximations of marginal likelihoods as by-products. The SPS algorithm for Bayesian inference is amenable to massively parallel implementation, and when implemented using graphical processing units it is more efficient than existing alternatives. The paper demonstrates these points by means of several examples.

The use of graphical methods for diagnostic purposes has an honorable tradition which is rooted in the pioneering work of Anscombe and Tukey and has been developed by Wilk, Gnanadesikan, and a host of others associated with Bell Laboratories. A paper by Landwehr, Pregibon, and Shoemaker (subsequently referred to as LPS) attempts to modify and extend graphical diagnostic displays that have been developed for ordinary regression to be of use for assessing logistic regression models for binary data. They propose displays for each of the three key components of regression diagnostics: goodness of fit, outliner detection, and model specification. Their is a pioneering effort and many useful ideas have emerged from it. Somewhat fuzzy analogies to linear regression are not sufficient to motivate the approaches adopted by LPS. Thus the authors of this paper have attempted to examine critically LPS's diagnostic displays to see if they could determine why in each instance the method works or fails. LPS suggest that the major obstacle in carrying linear regression diagnostics over to the logistic regression setting is the discreteness of binary data. While discreteness may well be a serious problem, additional ones are noted.

This article is from Statistics in Medicine , volume 32 . Abstract The change in c-statistic is frequently used to summarize the change in predictive accuracy when a novel risk factor is added to an existing logistic regression model. We explored the relationship between the absolute change in the c-statistic, Brier score, generalized R2, and the discrimination slope when a risk factor was added to an existing model in an extensive set of Monte Carlo simulations. The increase in model accuracy due to the inclusion of a novel marker was proportional to both the prevalence of the marker and to the odds ratio relating the marker to the outcome but inversely proportional to the accuracy of the logistic regression model with the marker omitted. We observed greater improvements in model accuracy when the novel risk factor or marker was uncorrelated with the existing predictor variable compared with when the risk factor has a positive correlation with the existing predictor variable. We illustrated these findings by using a study on mortality prediction in patients hospitalized with heart failure. In conclusion, the increase in predictive accuracy by adding a marker should be considered in the context of the accuracy of the initial model. Copyright © 2012 John Wiley & Sons, Ltd.

Includes bibliographical references (p. 35-36)

Logistic regression models with $n$ observations and $q$ linearly-independent covariates are shown to have Fisher information volumes which are bounded below by $\pi^q$ and above by ${n \choose q} \pi^q$. This is proved with a novel generalization of the classical theorems of Pythagoras and de Gua, which is of independent interest. The finding that the volume is always finite is new, and it implies that the volume can be directly interpreted as a measure of model complexity. The volume is shown to be a continuous function of the design matrix $X$ at generic $X$, but to be discontinuous in general. This means that models with sparse design matrices can be significantly less complex than nearby models, so the resulting model-selection criterion prefers sparse models. This is analogous to the way that $\ell^1$-regularisation tends to prefer sparse model fits, though in our case this behaviour arises spontaneously from general principles. Lastly, an unusual topological duality is shown to exist between the ideal boundaries of the natural and expectation parameter spaces of logistic regression models.

The use of logistic regression models to study the relationship between NFDRS indexes and historical fire data: statistical methodology

This paper develops a new family of estimators, MDPDEs, as a robust generalization of maximum likelihood estimator for the polytomous logistic regression model (PLRM) by using the DPD measure. Based on these estimators, the family of Wald-type test statistics for linear hypotheses is introduced and their robust properties are theoretically studied through the classical influence function analysis. Some numerical examples are presented to justify the requirement of a suitable robust statistical procedure of estimation in place of the MLE. Finally, a simulation study provides further confirmation of the validity of the theoretical results established in the paper.

Variable selection procedures are applicable to predictive model building process such as logistic regression, and generally for generalized linear modelling. The essence of variable selection is to select the best parsimonious adequate model among the available models for a data set, to avoid using redundant predictors in a model. In this study, variable selection procedures suitable for logistic regression model are considered namely: stepwise procedures, criterion-based procedures and cross-validation procedures. The three procedures of variable selection were exemplified on predictive logistic models using real life data sets on births and coronary heart disease (CHD) to determine the most suitable variable selection procedure for the logistic regression models. The logistic regression model for the birth data is to estimate the functional relationship between the binary response variable, type-of-birth and the predictors. For the coronary heart disease (CHD) data the interest is to explore the relationship between the risk factors, such as age, sex and cholesterol level of patients and the presence or absence of CHD in the study population. The stepwise procedures were computationally intensive. The criterion-based procedures and cross-validation procedures are investigated in this study, though, involve a wider search but in a preferable manner compared to the stepwise procedures that use restricted search through the space of potential models. It is therefore recommended to use criterion-based procedures when building a predictive logistic regression model for a data set with dichotomous response variable. 

Previous studies have shown that probabilistic forecasting may be a useful method for predicting persistent contrail formation. A probabilistic forecast to accurately predict contrail formation over the contiguous United States (CONUS) is created by using meteorological data based on hourly meteorological analyses from the Advanced Regional Prediction System (ARPS) and from the Rapid Update Cycle (RUC) as well as GOES water vapor channel measurements, combined with surface and satellite observations of contrails. Two groups of logistic models were created. The first group of models (SURFACE models) is based on surface-based contrail observations supplemented with satellite observations of contrail occurrence. The second group of models (OUTBREAK models) is derived from a selected subgroup of satellite-based observations of widespread persistent contrails. The mean accuracies for both the SURFACE and OUTBREAK models typically exceeded 75 percent when based on the RUC or ARPS analysis data, but decreased when the logistic models were derived from ARPS forecast data.

Previous studies have shown that probabilistic forecasting may be a useful method for predicting persistent contrail formation. A probabilistic forecast to accurately predict contrail formation over the contiguous United States (CONUS) is created by using meteorological data based on hourly meteorological analyses from the Advanced Regional Prediction System (ARPS) and from the Rapid Update Cycle (RUC) as well as GOES water vapor channel measurements, combined with surface and satellite observations of contrails. Two groups of logistic models were created. The first group of models (SURFACE models) is based on surface-based contrail observations supplemented with satellite observations of contrail occurrence. The second group of models (OUTBREAK models) is derived from a selected subgroup of satellite-based observations of widespread persistent contrails. The mean accuracies for both the SURFACE and OUTBREAK models typically exceeded 75 percent when based on the RUC or ARPS analysis data, but decreased when the logistic models were derived from ARPS forecast data.

Previous studies have shown that probabilistic forecasting may be a useful method for predicting persistent contrail formation. A probabilistic forecast to accurately predict contrail formation over the contiguous United States (CONUS) is created by using meteorological data based on hourly meteorological analyses from the Advanced Regional Prediction System (ARPS) and from the Rapid Update Cycle (RUC) as well as GOES water vapor channel measurements, combined with surface and satellite observations of contrails. Two groups of logistic models were created. The first group of models (SURFACE models) is based on surface-based contrail observations supplemented with satellite observations of contrail occurrence. The second group of models (OUTBREAK models) is derived from a selected subgroup of satellite-based observations of widespread persistent contrails. The mean accuracies for both the SURFACE and OUTBREAK models typically exceeded 75 percent when based on the RUC or ARPS analysis data, but decreased when the logistic models were derived from ARPS forecast data.

Thesis advisor, So Young Sohn

Thesis advisor, So Young Sohn

Since its establishment the Naval Space Surveillance Command (NAVSPASUR)in Dalhgren Virginia has been providing surveillance data (NAVSPASUR data sets) for thousands of space objects in a near earth orbit. To date, very little statistical analysis of these data sets in the form of a system performance evaluation has been conducted. The objective of this thesis is to provide NA VSPASUR with a statistical method to evaluate the system performance in terms of its capability of detecting space objects.. In this thesis six individual station models , as well as a system-wide model are estimated. Optimal probability levels for classifying predictions are additionally provided. The results being provided are obtained through the implementation of Logistic Regression analysis. The system- wide model estimated in this thesis, is superior in its prediction accuracy when compared to the previous mode! provided to NAVSPASUR in a September 1991, Naval Postgraduate School Master's Thesis. Finally an implementation program written in FORTRAN is given. This program provides a user friendly interface capability for predicting system performance in terms of its detection ability.