Statistics and Probability Commons^™

Extended Poisson Models For Count Data With Inflated Frequencies, Monika Arora

Mathematics & Statistics Theses & Dissertations

Count data often exhibits inflated counts for zero. There are numerous papers in the literature that show how to fit Poisson regression models that account for the zero inflation. However, in many situations the frequencies of zero and of some other value k tends to be higher than the Poisson model can fit appropriately. Recently, Sheth-Chandra (2011), Lin and Tsai (2012) introduced a mixture model to account for the inflated frequencies of zero and k. In this dissertation, we study basic properties of this mixture model and parameter estimation for grouped and ungrouped data. Using stochastic representation we show …

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.

Masked Instability: Within-Sector Financial Risk In The Presence Of Wealth Inequality, Youngna Choi

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

We investigate masked financial instability caused by wealth inequality. When an economic sector is decomposed into two subsectors that possess a severe wealth inequality, the sector in entirety can look financially stable while the two subsectors possess extreme financially instabilities of opposite nature, one from excessive equity, the other from lack thereof. The unstable subsector can result in further financial distress and even trigger a financial crisis. The market instability indicator, an early warning system derived from dynamical systems applied to agent-based models, is used to analyze the subsectoral financial instabilities. Detailed mathematical analysis is provided to explain what financial …

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 …

Applying Conditional Distributions To Individuals: Using Latent Variable Models, Feng Ji

Theses and Dissertations

This study proposes a new method to interpret individual results of psychological test batteries. The Mahalanobis distance is a commonly-used measure of how unusual an individual’s profile of scores is compared to a population of score profiles. In models in which there is a set of predictors and a set of dependent variables (e.g., cognitive abilities predicting academic abilities), it is useful to distinguish between a profile of dependent scores that is unusual because its profile of predictor scores is unusual and a profile of dependent scores that is unusual even after controlling for the predictors. The conditional Mahalanobis distance …

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.

Robust Computation In 2d Absolute Eit (A-Eit) Using D-Bar Methods With The “Exp” Approximation, Sarah J. Hamilton, J. L. Mueller, T. R. Santos

Mathematical and Statistical Science Faculty Research and Publications

Objective

Absolute images have important applications in medical Electrical Impedance Tomography (EIT) imaging, but the traditional minimization and statistical based computations are very sensitive to modeling errors and noise. In this paper, it is demonstrated that D-bar reconstruction methods for absolute EIT are robust to such errors.

Approach

The effects of errors in domain shape and electrode placement on absolute images computed with 2-D D-bar reconstruction algorithms are studied on experimental data.

Main Results

It is demonstrated with tank data from several EIT systems that these methods are quite robust to such modeling errors, and furthermore the artefacts arising from …

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.

Presence Of Antibiotic-Resistant Escherichia Coli In Wastewater Treatment Plant Effluents Utilized As Water Reuse For Irrigation, Asli Aslan, Zach A. Coles, Anunay Bhattacharya, Oghenekpaobor Oyibo

Biostatistics, Epidemiology & Environmental Health Sciences: Faculty Publications

Providing safe water through water reuse is becoming a global necessity. One concern with water reuse is the introduction of unregulated contaminants to the environment that cannot be easily removed by conventional wastewater treatment plants (WWTP). The occurrence of ampicillin, sulfamethoxazole, ciprofloxacin, and tetracycline-resistant Escherichia coli through the treatment stages of a WWTP (raw sewage, post-secondary, post-UV and post-chlorination) was investigated from January to May 2016. The highest concentrations of antibiotic resistant E. coli in the effluent were detected in April after rainfall. Ampicillin-resistant E. coli was the most common at the post UV and chlorination stages comprising 63% of …

Development Of A Slab-Based Monte Carlo Proton Dose Algorithm With A Robust Material-Dependent Nuclear Halo Model, John Wesley Chapman Jr

LSU Doctoral Dissertations

Pencil beam algorithms (PBAs) are often utilized for dose calculation in proton therapy treatment planning because they are fast and accurate under most conditions. However, as discussed in Chapman et al (2017), the accuracy of a PBA can be limited under certain conditions because of two major assumptions: (1) the central-axis semi-infinite slab approximation; and, (2) the lack of material dependence in the nuclear halo model. To address these limitations, we transported individual protons using a class II condensed history Monte Carlo and added a novel energy loss method that scaled the nuclear halo equation in water to arbitrary geometry. …

A Mapping Review Of Randomized Controlled Trials In The Spinal Cord Injury Research Literature, Amanda Mcintyre, Brooke Benton, Shannon Janzen, Jerome Iruthayarajah, Joshua Weiner, Janice J. Eng, Robert Teasell, Spinal Cord Injury Research Evidence Team

Epidemiology and Biostatistics Publications

Study design

Mapping Review.

Objective

The objective of this study was to map out and characterize the quantity and quality of all published spinal cord injury (SCI) randomized controlled trials (RCTs) with respect to number, sample size, and methodological quality between January 1970 and December 2016.

Setting

Not applicable.

Methods

A literature search of multiple research databases was conducted. Studies adhering to the following criteria were included: the research design was an RCT; written in English; participants were >18 years; and the sample was >50% SCI. Data were extracted pertaining to author(s), year of publication, country of origin, initial and …

A Comparison Of The Predictive Ability Of Logistic Regression And Time Series Analysis On Business Credit Data, Lauren Staples

Published and Grey Literature from PhD Candidates

The credit industry creates models to determine the risk of lending money to consumers as well as to commercial customers. These models are heavily regulated in the U.S. as well as in other countries. Model inputs must be explainable to customers as well as to regulators. Two such modeling approaches that are currently commonly used are logistic regression models and time series models. This paper steps through the preprocessing and model building of these two models on a large commercial data set and compares the predictive ability of these two methods. The two models achieved similar accuracy results: the logistic …

Recent Trends In The Frequency And Duration Of Global Floods, Nasser Najibi, Naresh Devineni

Publications and Research

Frequency and duration of floods are analyzed using the global flood database of the Dartmouth Flood Observatory (DFO) to explore evidence of trends during 1985–2015 at global and latitudinal scales. Three classes of flood duration (i.e., short: 1–7, moderate: 8–20, and long: 21 days and above) are also considered for this analysis. The nonparametric Mann–Kendall trend analysis is used to evaluate three hypotheses addressing potential monotonic trends in the frequency of flood, moments of duration, and frequency of specific flood duration types. We also evaluated if trends could be related to large-scale atmospheric teleconnections using a generalized linear model framework. …

Improving Shewhart Control Chart Performance In The Presence Of Measurement Error Using Multiple Measurements And Two-Stage Sampling, Kenneth W. Linna

Journal of International & Interdisciplinary Business Research (2014-2019)

The usual Shewhart control chart efficiently detects large shifts in the mean of a quality characteristic and has been extensively studied in the literature. Most proposed alternatives to the Shewhart chart aim to improve either the signal performance for smaller mean shifts or reduce the sampling effort required to detect a larger shift. Measurement error has been shown in the literature to result in reduced power to detect process shifts. The combination of multiple measurements and two-stage sampling is considered here as a strategy for both regaining power lost due to measurement error and specifically tuning the charts for shifts …

A Qualitative Study Examining The Benefits And Challenges Of Incorporating Patient-Reported Outcome Substance Use And Mental Health Questionnaires Into Clinical Practice To Improve Outcomes On The Hiv Care Continuum., Anne K Monroe, Sarah M Jabour, Sebastian Peña, Jeanne C Keruly, Richard D Moore, Geetanjali Chander, Kristin A Riekert

Epidemiology Faculty Publications

BACKGROUND: Inadequate identification and treatment of substance use (SU) and mental health (MH) disorders hinders retention in HIV care. The objective of this study was to elicit stakeholder input on integration of SU/MH screening using computer-assisted patient-reported outcomes (PROs) into clinical practice.

METHODS: We conducted semi-structured interviews with HIV-positive patients who self-reported SU/MH symptoms on a computer-assisted PROs (n = 19) and HIV primary care providers (n = 11) recruited from an urban academic HIV clinic. Interviews were audio-recorded and transcribed. We iteratively developed codes and organized key themes using editing style analysis.

RESULTS: Two themes emerged: (1) Honest Disclosure: …

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.

Robust Statistics, Bruce E. Blaine

Statistics Faculty/Staff Publications

In lieu of an abstract, here is the entry's first paragraph:

Robust statistics are procedures that maintain nominal Type I error rates and statistical power in the presence of violations of the assumptions that underpin parametric inferential statistics. Since George Box coined the term in 1953, research on robust statistics has centered on the assumption of normality, although the violation of other parametric assumptions (e.g., homogeneity of variance) has their own implications for the accuracy of parametric procedures. This entry looks at the importance of robust statistics in educational and social science research and explains the robustness argument. It then …

Winsorizing, Bruce E. Blaine

Statistics Faculty/Staff Publications

In lieu of an abstract, here is the entry's first paragraph:

Winsorizing is a procedure that moderates the influence of outliers on the mean and variance and thereby creates more robust estimators of location and variability. The procedure is named for biostatistician Charles P. Winsor. Parametric inferential procedures that rely on the mean and variance (e.g., t test) become more robust when they incorporate Winsorized estimators. Winsorizing is an important tool for educational and social science researchers for two reasons. First, significance tests based on the mean and variance are very common procedures for significance testing in the social sciences. …