Physical Sciences and Mathematics Commons^™

A Bayesian Beta-Mixture Model For Nonparametric Irt (Bbm-Irt), Ethan A. Arenson, George Karabatsos

Journal of Modern Applied Statistical Methods

Item response models typically assume that the item characteristic (step) curves follow a logistic or normal cumulative distribution function, which are strictly monotone functions of person test ability. Such assumptions can be overly-restrictive for real item response data. A simple and more flexible Bayesian nonparametric IRT model for dichotomous items is introduced, which constructs monotone item characteristic (step) curves by a finite mixture of beta distributions, which can support the entire space of monotone curves to any desired degree of accuracy. An adaptive random-walk Metropolis-Hastings algorithm is proposed to estimate the posterior distribution of the model parameters. The Bayesian IRT …

Robust Estimation And Inference On Current Status Data With Applications To Phase Iv Cancer Trial, Deo Kumar Srivastava, Liang Zhu, Melissa M. Hudson, Jianmin Pan, Shesh N. Rai

Journal of Modern Applied Statistical Methods

The use of piecewise exponential distributions was proposed by Rai et al. (2013) for analyzing cardiotoxicity data. Some parametric models are proposed, but the focus is on the Weibull distribution, which overcomes the limitation of piecewise exponential.

Shear Wave Tomography Beneath The United States Using A Joint Inversion Of Surface And Body Waves, E. M. Golos, H. Fang, H. Yao, H. Zhang, Scott Burdick, F. Vernon, A. Schaeffer, S. Lebedev, R. D. Van Der Hilst

Environmental Science and Geology Faculty Research Publications

Resolving both crustal and shallow-mantle heterogeneity, which is needed to study processes in and fluxes between crust and mantle, is still a challenge for seismic tomography. Body wave data can constrain deep features but often produce vertical smearing in the crust and upper mantle; in contrast, surface wave data can provide good vertical resolution of lithospheric structure but may lack lateral resolution and are less sensitive to the deeper Earth. These two data types are usually treated and inverted separately, and tomographic models therefore do not, in general, benefit from the complementary nature of sampling by body and surface waves. …

Robust Heteroscedasticity Consistent Covariance Matrix Estimator Based On Robust Mahalanobis Distance And Diagnostic Robust Generalized Potential Weighting Methods In Linear Regression, M. Habshah, Muhammad Sani, Jayanthi Arasan

Journal of Modern Applied Statistical Methods

The violation of the assumption of homoscedasticity and the presence of high leverage points (HLPs) are common in the use of regression models. The weighted least squares can provide the solution to heteroscedastic regression model if the heteroscedastic error structures are known. Based on Furno (1996), two robust weighting methods are proposed based on HLP detection measures (robust Mahalanobis distance based on minimum volume ellipsoid and diagnostic robust generalized potential based on index set equality (DRGP(ISE)) on robust heteroscedasticity consistent covariance matrix estimators. Results obtained from a simulation study and real data sets indicated the DRGP(ISE) method is superior.

Internal Consistency Reliability In Measurement: Aggregate And Multilevel Approaches, Georgios Sideridis, Abdullah Saddaawi, Khaleel Al-Harbi

Journal of Modern Applied Statistical Methods

The purpose of the present paper was to evaluate the internal consistency reliability of the General Teacher Test assuming clustered and non-clustered data using commercial software (Mplus). Participants were 2,000 testees who were selected using random sampling from a larger pool of examinees (more than 65k). The measure involved four factors, namely: (a) planning for learning, (b) promoting learning, (c) supporting learning, and (d) professional responsibilities and was hypothesized to comprise a unidimensional instrument assessing generalized skills and competencies. Intra-class correlation coefficients and variance ratio statistics suggested the need to incorporate a clustering variable (i.e., university) when evaluating the factor …

Fitting The Rasch Model Under The Logistic Regression Framework To Reduce Estimation Bias, Tianshu Pan

Journal of Modern Applied Statistical Methods

This article showed how and why the Rasch model can be fitted under the logistic regression framework. Then a penalized maximum likelihood (Firth 1993) for logistic regression models can also be used to reduce ML biases when fitting the Rasch model. These conclusions are supported by a simulation study.

Regressions Regularized By Correlations, Stan Lipovetsky

Journal of Modern Applied Statistical Methods

The regularization of multiple regression by proportionality to correlations of predictors with dependent variable is applied to the least squares objective and normal equations to relax the exact equalities and to get a robust solution. This technique produces models not prone to multicollinearity and is very useful in practical applications.

An Explanatory Study On The Non-Parametric Multivariate T2 Control Chart, Abdolrasoul Mostajeran, Nasrolah Iranpanah, Rassoul Noorossana

Journal of Modern Applied Statistical Methods

Most control charts require the assumption of normal distribution for observations. When distribution is not normal, one can use non-parametric control charts such as sign control chart. A deficiency of such control charts could be the loss of information due to replacing an observation with its sign or rank. Furthermore, because the chart statistics of T² are correlated, the T² chart is not a desire performance. Non-parametric bootstrap algorithm could help to calculate control chart parameters using the original observations while no assumption regarding the distribution is needed. In this paper, first, a bootstrap multivariate control chart is …

Optimum Stratification In Bivariate Auxiliary Variables Under Neyman Allocation, Faizan Danish, S.E.H. Rizvi

Journal of Modern Applied Statistical Methods

In several situations complete data set of the study variable is unknown that becomes a stumbling block in various stratification techniques in order to obtain stratification points on two way stratification method. In this paper a technique has been proposed under Neyman allocation when the stratification is done oj the two auxiliary variable having one estimation variable under consideration. Due to complexities created by minimal equations approximate optimum strata boundaries has been obtained. Empirical study has been done to illustrate the proposed method when the auxiliary variables have standard Cauchy and power distributions.

Discrete-Time Hybrid Control In Borel Spaces: Average Cost Optimality Criterion, Héctor Jasso-Fuentes, José-Luis Menaldi, Tomás Prieto-Rumeau, Maurice Robin

Mathematics Faculty Research Publications

This paper addresses an optimal hybrid control problem in discrete-time with Borel state and action spaces. By hybrid we mean that the evolution of the state of the system may undergo deep changes according to structural modifications of the dynamic. Such modifications occur either by the position of the state or by means of the controller's actions. The optimality criterion is of a long-run ratio-average (or ratio-ergodic) type. We provide the existence of optimal average policies for this hybrid control problem by analyzing an associated dynamic programming equation. We also show that this problem can be translated into a standard …

Estimation Of Zero-Inflated Population Mean: A Bootstrapping Approach, Khyam Paneru, R. Noah Padgett, Hanfeng Chen

Journal of Modern Applied Statistical Methods

A mixture model was adopted from the maximum pseudo-likelihood approach under complex sampling designs to estimate the mean of zero-inflated population. To overcome the complexity and assumptions of asymptotic distribution, the maximum pseudo-likelihood function was used, but a bootstrapping procedure was proposed as an alternative. Bootstrap confidence intervals consistently capture the true means of zero-inflated populations of the simulation studies.

Moment Generating Functions Of Complementary Exponential-Geometric Distribution Based On K-Th Lower Record Values, Devendra Kumar, Sanku Dey, Mansoor Rashid Malik, Fahad M. Al-Aboud

Journal of Modern Applied Statistical Methods

The complementary exponential-geometric (CEG) distribution is a useful model for analyzing lifetime data. For this distribution, some recurrence relations satisfied by marginal and joint moment generating functions of k-th lower record values were established. They enable the computation of the means, variances, and covariances of k-th lower record values for all sample sizes in a simple and efficient recursive manner. Means, variances, and covariances of lower record values were tabulated from samples of sizes up to 10 for various values of the parameters.

Optimal Model Selection For Truncated Data Among Non-Nested Competitive Models, Parisa Torkaman

Journal of Modern Applied Statistical Methods

Selecting a model for incomplete data is an important issue. Truncated data is an example of incomplete data, which sometimes occurs due to inherent limitations. The maximum likelihood estimator features and its asymptotic distribution are studied, and a test statistic among non-nested competitive model of incomplete data is presented, which can select an appropriate model close to the true model. This close-to-true model under the null hypothesis of the equivalency of two competitive models against alternative hypothesis is selected.

Letter To The Editor: Regarding A Possible Non-Null Interpretation Of The Michelson-Morley Experiment, Maurizio Consoli

Journal of Modern Applied Statistical Methods

The author writes in response to Sawilowsky in JMASM 2(2) and 4(1).

The Transmuted Exponentiated Additive Weibull Distribution: Properties And Applications, Zohdy M. Nofal, Ahmed Z. Afify, Haitham M. Yousof, Daniele Cristina Tita Granzotto, Francisco Louzada

Journal of Modern Applied Statistical Methods

A new generalization of the transmuted additive Weibull distribution is proposed by using the quadratic rank transmutation map, the so-called transmuted exponentiated additive Weibull distribution. It retains the characteristics of a good model. It is more flexible, being able to analyze more complex data; it includes twenty-seven sub-models as special cases and it is interpretable. Several mathematical properties of the new distribution as closed forms for ordinary and incomplete moments, quantiles, and moment generating function are presented, as well as the MLEs. The usefulness of the model is illustrated by using two real data sets.

Modeling Insurance Claims Using Flexible Skewed And Mixture Probability Distributions, Aaron J. Leinwander, Mohammad A. Aziz

Journal of Modern Applied Statistical Methods

The normal distribution comes as a first choice when fitting real data, but it may not be suitable if the assumed distribution deviates from normality. Flexible skewed distributions are capable of including skewness and taking into account multimodality. They may be applied to find appropriate distributions for describing the claim amounts in insurance. The objective is to model insurance claims using a set of flexible skewed and mixture probability distributions, and to test how well they fit the claims. Results indicate the skew-t distribution and alpha-skew Laplace distribution are able to describe unimodal claims accurately, whereas scale mixture of …

Single Missing Data Imputation In Pls-Based Structural Equation Modeling, Ned Kock

Journal of Modern Applied Statistical Methods

Missing data, a source of bias in structural equation modeling (SEM) employing the partial least squares method (PLS), are commonly handled with deletion methods such as listwise and pairwise deletion. Missing data imputation methods do not resort to deletion. Five single missing data imputation methods are considered employing the PLS Mode A algorithm of which two hierarchical methods are new. The results of a Monte Carlo experiment suggest that Multiple Regression Imputation yielded the least biased mean path coefficient estimates, followed by Arithmetic Mean Imputation. With respect to mean loading estimates, Arithmetic Mean Imputation yielded the least biased results, followed …

A New Lifetime Distribution For Series System: Model, Properties And Application, Adil Rashid, Zahooor Ahmad, T R. Jan

Journal of Modern Applied Statistical Methods

A new lifetime distribution for modeling system lifetime in series setting is proposed that embodies most of the compound lifetime distribution. The reliability analysis of parent and of sub-models has also been discussed. Various mathematical properties that include moment generating function, moments, and order statistics have been obtained. The newly-proposed distribution has a flexible density function; more importantly its hazard rate function can take up different shapes such as bathtub, upside down bathtub, increasing, and decreasing shapes. The unknown parameters of the proposed generalized family have been estimated through MLE technique. The strength and usefulness of the proposed family was …

An Inferential Method For Determining Which Of Two Independent Variables Is Most Important When There Is Curvature, Rand Wilcox

Journal of Modern Applied Statistical Methods

Consider three random variables Y, X₁ and X₂, where the typical value of Y, given X₁ and X₂, is given by some unknown function m(X₁, X₂). A goal is to determine which of the two independent variables is most important when both variables are included in the model. Let τ₁ denote the strength of the association associated with Y and X₁, when X₂ is included in the model, and let τ₂ be defined in an analogous manner. If it is assumed …

Sample Size For Non-Inferiority Tests For One Proportion: A Simulation Study, Özlem Güllü, Mustafa Agah Tekindal

Journal of Modern Applied Statistical Methods

The objective of non-inferiority trials is to demonstrate the efficiency of a novel treatment whether it is acceptably less or more efficient than a control or active (existing) treatment. They are employed in situations where, when compared to the active treatment, the novel treatment is to be advantageous with higher rates of reliability, compatibility, cost-efficiency, etc. Odds ratio is the most significant measure used in investigating the size of efficiency of treatments relative to one another. The purpose of the study is to calculate and evaluate the sample size under different scenarios based on three different test statistics in non-inferiority …

Handling Missing Data In Single-Case Studies, Chao-Ying Joanne Peng, Li-Ting Chen

Journal of Modern Applied Statistical Methods

Multiple imputation is illustrated for dealing with missing data in a published SCED study. Results were compared to those obtained from available data. Merits and issues of implementation are discussed. Recommendations are offered on primal/advanced readings, statistical software, and future research.

Discrete-Time Hybrid Control In Borel Spaces, Héctor Jasso-Fuentes, José-Luis Menaldi, Tomás Prieto-Rumeau

Mathematics Faculty Research Publications

A discrete-time hybrid control model with Borel state and action spaces is introduced. In this type of models, the dynamic of the system is composed by two sub-dynamics affecting the evolution of the state; one is of a standard-type that runs almost every time and another is of a special-type that is active under special circumstances. The controller is able to use two different type of actions, each of them is applied to each of the two sub-dynamics, and the activations of these sub-dynamics are possible according to an activation rule that can be handled by the controller. The aim …

Cyanobacteria Reduce Quagga Mussel (Dreissena Rostriformis Bugensis) Spawning And Fertilization Success, Anna G. Boegehold, Nicholas S. Johnson, Jeffrey L. Ram, Donna R. Kashian

Environmental Science and Geology Faculty Research Publications

Quagga mussels (Dreissena rostriformis bugensis) are highly fecund broadcast spawners invasive to freshwaters of North America and western Europe. We hypothesized that environmental cues from phytoplankton can trigger gamete release in quagga mussels. Nutritious algae may stimulate dreissenid spawning, but less palatable food, such as bloom-forming cyanobacteria, could be a hindrance. The objective of our study was to test whether exposure to cyanobacteria can inhibit quagga mussel spawning and fertilization. We assessed spawning in the presence of serotonin, a known spawning inducer, where adult quagga mussels placed in individual vials were exposed to 13 cyanobacteria cultures and purified algal toxin …

Evaluating The Efficacy Of Conditional Analysis Of Variance Under Heterogeneity And Non-Normality, Yan Wang, Thanh Pham, Diep Nguyen, Eun Sook Kim, Yi-Hsin Chen, Jeffrey Kromrey, Zhiyao Yi, Yue Yin

Journal of Modern Applied Statistical Methods

A simulation study was conducted to examine the efficacy of conditional analysis of variance (ANOVA) methods where the initial homogeneity of variance screening leads to the choice between the ANOVA F test and robust ANOVA methods. Type I error control and statistical power were investigated under various conditions.

Synthesis Of Volatile And Thermally Stable Aluminum Hydride Complexes And Their Use In Atomic Layer Deposition Of Metal Thin Films, Kyle Blakeney

Wayne State University Dissertations

The research discussed in this dissertation spans both synthetic inorganic and nanomaterials chemistry. Aluminum hydride complexes have been synthesized and characterized which are highly volatile and thermally stable and their potential as reducing agents for ALD of electropositive metal and metal-containing films was evaluated. A major discovery has been the deposition of aluminum metal films by thermal ALD using an aluminum dihydride complex supported by a simple amido-amine ligand (Chapters 2). Aluminum is the most electropositive element deposited by purely thermal ALD to date and represents a significant breakthrough for this field. This process may have important industrial applications and …

Applications Of Molecular And Quantum Mechanical Methods For Studying The Chemical Reactions Of Inorganic And Organic Systems, Yi-Jung Tu

Wayne State University Dissertations

Computational studies can assist chemists to interpret experimental observations and to predict the properties and behaviors of molecules. The work presented in this dissertation applies different computational methods to study the molecular properties and reaction paths for various inorganic and organic systems. The second and third chapters discuss the force field development using “Gaussian Electrostatic Model (GEM)” and its amenability for use in the AMOEBA force field. The forth and fifth chapters discuss the density functional theory (DFT) studies of photodissociation behaviors for inorganic molecules. The sixth chapter explores the oxidation mechanisms of ascorbic acid and its antioxidant properties in …

Hydroxylamines And Hydrazines As Surrogates Of Sp3 Carbons In Medicinal Chemistry, Sandeep Dhanju

Wayne State University Dissertations

Current compound libraries that are used in high-throughput screening (HTS) are populated by low molecular weight and relatively planar compounds with high sp2 character and little stereochemical complexity. Unfortunately, such planar compounds cover only a very small corner of chemical space. In order to increase the diversity, structurally complex molecules with high fractions of sp3-hybridized atoms should be included in compound libraries. However, generating a large number of architecturally complex molecules using the current organic synthesis toolbox is considered tedious due to the requirement of multi-step synthesis. Recognizing this need, several creative strategies, like diversity-oriented synthesis, have been developed with …

Applications Of Effective Field Theories To New Physics, Derek Edward Hazard

Wayne State University Dissertations

We apply an effective field theory approach and argue that lepton flavor violating (LFV) decays M → l1l2 of meson states M with different quantum numbers could be used to put constraints on the Wilson coefficients of effective operators describing LFV interactions at low energy scales. We note that the restricted kinematics of the two-body decay of quarkonium or a heavy quark meson allows us to select operators with particular quantum numbers, significantly reducing the reliance on the single operator dominance assumption that is prevalent in constraining parameters of the effective LFV Lagrangian. We shall also argue that studies of …

Kilovoltage Intensity Modulated Radiotherapy, Brian Loughery

Wayne State University Dissertations

Contrast enhanced kilovoltage radiotherapy could be a significant improvement over the standard of care in glioblastoma multiforme, but its potential benefit has been hindered by fears of insufficient dose falloff, high skin and skull dose, contrast delivery concerns, and high cost. This dissertation aims to address the validity of these fears.

Contrast delivery concerns are examined by assuming that sufficient dose can be safely delivered to the tumor. Iodine, gadolinium, and gold nanoparticle biological effect and delivery research is examined and the ideal contrast delivery methods are reported. Dose falloff and skull dose are then investigated through treatment planning and …

Hardy Space Theory And Endpoint Estimates For Multi-Parameter Singular Radon Transforms, Jiawei Shen

Wayne State University Dissertations

In [12], Christ, Nagel, Stein and Waigner studied the L p theories for the singular Radon Trans-

forms. Furthermore, B. Street in [68], and Stein and Street in [64–67] extended the theories of the

L p boundedness for multi-parameter singular integral operators, such as the Calderón Zygmund

operators and singular Radon transforms. In this dissertation, we will study the Hardy space H p

and its dual space associated with both the one-parameter and multi-parameter singular Radon

transforms, and consider the boundedness of the singular Radon transforms on such Hardy spaces

H p when 0 ≤ p ≤ 1.

Inspired by …