Statistical Theory Commons^™

A Simulation Study On Increasing Capture Periods In Bayesian Closed Population Capture-Recapture Models With Heterogeneity, Ross M. Gosky, Joel Sanqui

Journal of Modern Applied Statistical Methods

Capture-Recapture models are useful in estimating unknown population sizes. A common modeling challenge for closed population models involves modeling unequal animal catchability in each capture period, referred to as animal heterogeneity. Inference about population size N is dependent on the assumed distribution of animal capture probabilities in the population, and that different models can fit a data set equally well but provide contradictory inferences about N. Three common Bayesian Capture-Recapture heterogeneity models are studied with simulated data to study the prevalence of contradictory inferences is in different population sizes with relatively low capture probabilities, specifically at different numbers of …

An Exploration Of Link Functions Used In Ordinal Regression, Thomas J. Smith, David A. Walker, Cornelius M. Mckenna

Journal of Modern Applied Statistical Methods

The purpose of this study is to examine issues involved with choice of a link function in generalized linear models with ordinal outcomes, including distributional appropriateness, link specificity, and palindromic invariance are discussed and an exemplar analysis provided using the Pew Research Center 25th anniversary of the Web Omnibus Survey data. Simulated data are used to compare the relative palindromic invariance of four distinct indices of determination/discrimination, including a newly proposed index by Smith et al. (2017).

Personal Foul: How Head Trauma And The Insurance Industry Are Threatening Sports, Zachary Cooler

Senior Honors Theses

This thesis will investigate the growing problem of head trauma in contact sports like football, hockey, and soccer through medical studies, implications to the insurance industry, and ongoing litigation. The thesis will investigate medical studies that are finding more evidence to support the claim that contact sports players are more likely to receive head trauma symptoms such as memory loss, mood swings, and even Lou Gehrig’s disease in extreme cases. The thesis will also demonstrate that these medical symptoms and monetary losses from medical claims are convincing insurance companies to withdraw insurance coverage for sports leagues, which they are justifying …

Quasi-Likelihood Ratio Tests For Homoscedasticity In Linear Regression, Lili Yu, Varadan Sevilimedu, Robert Vogel, Hani Samawi

Journal of Modern Applied Statistical Methods

Two quasi-likelihood ratio tests are proposed for the homoscedasticity assumption in the linear regression models. They require few assumptions than the existing tests. The properties of the tests are investigated through simulation studies. An example is provided to illustrate the usefulness of the new proposed tests.

Investigating The Performance Of Propensity Score Approaches For Differential Item Functioning Analysis, Yan Liu, Chanmin Kim, Amrey D. Wu, Paul Gustafson, Edward Kroc, Bruno D. Zumbo

Journal of Modern Applied Statistical Methods

To evaluate the performance of propensity score approaches for differential item functioning analysis, this simulation study was conducted to assess bias, mean square error, Type I error, and power under different levels of effect size and a variety of model misspecification conditions, including different types and missing patterns of covariates.

A Glossary On Building Longitudinal, Population-Based Data Linkages To Explore Children’S Developmental Trajectories, Jennifer E. V. Lloyd, Jacqui Boonstra, Lisa Chen, Barry Forer, Ruth Hershler, Constance Milbrath, Brenda T. Poon, Neda Razaz, Pippa Rowcliffe, Kimberly Schonert-Reichl

Journal of Modern Applied Statistical Methods

Population-based, person-specific, longitudinal child and youth health and developmental data linkages involve connecting combinations of specially-collected data and administrative data for longitudinal population research purposes. This glossary provides definitions of key terms and concepts related to their theoretical basis, research infrastructure, research methodology, statistical analysis, and knowledge translation.

Robust Confidence Intervals For The Population Mean Alternatives To The Student-T Confidence Interval, Moustafa Omar Ahmed Abu-Shawiesh, Aamir Saghir

Journal of Modern Applied Statistical Methods

In this paper, three robust confidence intervals are proposed as alternatives to the Student‑t confidence interval. The performance of these intervals was compared through a simulation study shows that Q_n-t confidence interval performs the best and it is as good as Student’s‑t confidence interval. Real-life data was used for illustration and performing a comparison that support the findings obtained from the simulation study.

Using Spss To Analyze Complex Survey Data: A Primer, Danjie Zou, Jennifer E. V. Lloyd, Jennifer L. Baumbusch

Journal of Modern Applied Statistical Methods

An introduction to using SPSS to analyze complex survey data is given. Key features of complex survey design are described briefly, including stratification, clustering, multiple stages, and weights. Then, annotated SPSS syntax for complex survey data analysis is presented to demonstrate the step-by-step process using real complex samples data.

On The Authentic Notion, Relevance, And Solution Of The Jeffreys-Lindley Paradox In The Zettabyte Era, Miodrag M. Lovric

Journal of Modern Applied Statistical Methods

The Jeffreys-Lindley paradox is the most quoted divergence between the frequentist and Bayesian approaches to statistical inference. It is embedded in the very foundations of statistics and divides frequentist and Bayesian inference in an irreconcilable way. This paradox is the Gordian Knot of statistical inference and Data Science in the Zettabyte Era. If statistical science is ready for revolution confronted by the challenges of massive data sets analysis, the first step is to finally solve this anomaly. For more than sixty years, the Jeffreys-Lindley paradox has been under active discussion and debate. Many solutions have been proposed, none entirely satisfactory. …

Conflicts In Bayesian Statistics Between Inference Based On Credible Intervals And Bayes Factors, Miodrag M. Lovric

Journal of Modern Applied Statistical Methods

In frequentist statistics, point-null hypothesis testing based on significance tests and confidence intervals are harmonious procedures and lead to the same conclusion. This is not the case in the domain of the Bayesian framework. An inference made about the point-null hypothesis using Bayes factor may lead to an opposite conclusion if it is based on the Bayesian credible interval. Bayesian suggestions to test point-nulls using credible intervals are misleading and should be dismissed. A null hypothesized value may be outside a credible interval but supported by Bayes factor (a Type I conflict), or contrariwise, the null value may be inside …

A New Liu Type Of Estimator For The Restricted Sur Estimator, Kristofer Månsson, B. M. Golam Kibria, Ghazi Shukur

Journal of Modern Applied Statistical Methods

A new Liu type of estimator for the seemingly unrelated regression (SUR) models is proposed that may be used when estimating the parameters vector in the presence of multicollinearity if the it is suspected to belong to a linear subspace. The dispersion matrices and the mean squared error (MSE) are derived. The new estimator may have a lower MSE than the traditional estimators. It was shown using simulation techniques the new shrinkage estimator outperforms the commonly used estimators in the presence of multicollinearity.

Sampling The Porridge: A Comparison Of Ordered Variable Regression With F And R2 And Multiple Linear Regression With Corrected F And R2 In The Presence Of Multicollinearity, Grayson L. Baird, Stephen L. Bieber

Journal of Modern Applied Statistical Methods

Differences between the multiple linear regression model with Corrected R² and Corrected F and the ordered variable regression model with R² and F when intercorrelation is present are illustrated with simulated and real-world data.

A Study Verifying The Dimensioning Of A Multivariate Dichotomized Sample In Exploratory Factor Analysis, Rosilei S. Novak, Jair M. Marques

Journal of Modern Applied Statistical Methods

The sample size dichotomized was related to the measure of sampling adequacy, considering the explanations provided by factors and commonalities. Monte Carlo simulation generated multivariate normal samples and varying the number of observations, the factor analysis was applied in each sample dichotomized. Results were modeled by polynomial regression based on the sample sizing.

Parametric And Non-Parametric Tests For The Comparison Of Two Samples Which Both Include Paired And Unpaired Observations, Ben Derrick, Paul White, Deirdre Toher

Journal of Modern Applied Statistical Methods

Samples that include both independent and paired observations cause a dilemma for researchers that covers the full breadth of empirical research. Parametric approaches for the comparison of two samples using all available observations are considered, under normality and non-normality. These approaches are compared to naive and newly proposed non-parametric alternatives.

Small Area Estimation On Zero-Inflated Data Using Frequentist And Bayesian Approach, Kusman Sadik, Rahma Anisa, Euis Aqmaliyah

Journal of Modern Applied Statistical Methods

The most commonly used method of small area estimation (SAE) is the empirical best linear unbiased prediction method based on a linear mixed model. However, it is not appropriate in the case of the zero-inflated target variable with a mixture of zeros and continuously distributed positive values. Therefore, various model-based SAE methods for zero-inflated data are developed, such as the Frequentist approach and the Bayesian approach. Both approaches are compared with the survey regression (SR) method which ignores the presence of zero-inflation in the data. The results show that the two SAE approaches for zero-inflated data are capable to yield …

The Importance Of Type I Error Rates When Studying Bias In Monte Carlo Studies In Statistics, Michael Harwell

Journal of Modern Applied Statistical Methods

Two common outcomes of Monte Carlo studies in statistics are bias and Type I error rate. Several versions of bias statistics exist but all employ arbitrary cutoffs for deciding when bias is ignorable or non-ignorable. This article argues Type I error rates should be used when assessing bias.

Dynamic Conditional Correlation Garch: A Multivariate Time Series Novel Using A Bayesian Approach, Diego Nascimento, Cleber Xavier, Israel Felipe, Francisco Louzada Neto

Journal of Modern Applied Statistical Methods

The Dynamic Conditional Correlation GARCH (DCC-GARCH) mutation model is considered using a Monte Carlo approach via Markov chains in the estimation of parameters, time-dependence variation is visually demonstrated. Fifteen indices were analyzed from the main financial markets of developed and developing countries from different continents. The performances of indices are similar, with a joint evolution. Most index returns, especially SPX and NDX, evolve over time with a higher positive correlation.

Regression When There Are Two Covariates: Some Practical Reasons For Considering Quantile Grids, Rand Wilcox

Journal of Modern Applied Statistical Methods

When dealing with the association between some random variable and two covariates, extensive experience with smoothers indicates that often a linear model poorly reflects the nature of the association. A simple approach via quantile grids that reflects the nature of the association is given. The two main goals are to illustrate this approach can make a practical difference, and to describe R functions for applying it. Included are comments on dealing with more than two covariates.

Bivariate Analogs Of The Wilcoxon–Mann–Whitney Test And The Patel–Hoel Method For Interactions, Rand Wilcox

Journal of Modern Applied Statistical Methods

A fundamental way of characterizing how two independent compares compare is in terms of the probability that a randomly sampled observation from the first group is less than a randomly sampled observation from the second group. The paper suggests a bivariate analog and investigates methods for computing confidence intervals. An interaction for a two-by-two design is investigated as well.

Assessing The Accuracy Of Approximate Confidence Intervals Proposed For The Mean Of Poisson Distribution, Alireza Shirvani, Malek Fathizadeh

Journal of Modern Applied Statistical Methods

The Poisson distribution is applied as an appropriate standard model to analyze count data. Because this distribution is known as a discrete distribution, representation of accurate confidence intervals for its distribution mean is extremely difficult. Approximate confidence intervals were presented for the Poisson distribution mean. The purpose of this study is to simultaneously compare several confidence intervals presented, according to the average coverage probability and accurate confidence coefficient and the average confidence interval length criteria.

Analytical Closed-Form Solution For General Factor With Many Variables, Stan Lipovetsky, Vladimir Manewitsch

Journal of Modern Applied Statistical Methods

The factor analytic triad method of one-factor solution gives the explicit analytical form for a common latent factor built by three variables. The current work considers analytical presentation of a general latent factor constructed in a closed-form solution for multivariate case. The results can be supportive to theoretical description and practical application of latent variable modeling, especially for big data because the analytical closed-form solution is not prone to data dimensionality.

Regression Modeling And Prediction By Individual Observations Versus Frequency, Stan Lipovetsky

Journal of Modern Applied Statistical Methods

A regression model built by a dataset could sometimes demonstrate a low quality of fit and poor predictions of individual observations. However, using the frequencies of possible combinations of the predictors and the outcome, the same models with the same parameters may yield a high quality of fit and precise predictions for the frequencies of the outcome occurrence. Linear and logistical regressions are used to make an explicit exposition of the results of regression modeling and prediction.

Theory Of Principal Components For Applications In Exploratory Crime Analysis And Clustering, Daniel Silva

All Graduate Theses, Dissertations, and Other Capstone Projects

The purpose of this paper is to develop the theory of principal components analysis succinctly from the fundamentals of matrix algebra and multivariate statistics. Principal components analysis is sometimes used as a descriptive technique to explain the variance-covariance or correlation structure of a dataset. However, most often, it is used as a dimensionality reduction technique to visualize a high dimensional dataset in a lower dimensional space. Principal components analysis accomplishes this by using the first few principal components, provided that they account for a substantial proportion of variation in the original dataset. In the same way, the first few principal …

How Machine Learning And Probability Concepts Can Improve Nba Player Evaluation, Harrison Miller

CMC Senior Theses

In this paper I will be breaking down a scholarly article, written by Sameer K. Deshpande and Shane T. Jensen, that proposed a new method to evaluate NBA players. The NBA is the highest level professional basketball league in America and stands for the National Basketball Association. They proposed to build a model that would result in how NBA players impact their teams chances of winning a game, using machine learning and probability concepts. I preface that by diving into these concepts and their mathematical backgrounds. These concepts include building a linear model using ordinary least squares method, the bias …

Economic Design Of Acceptance Sampling Plans For Truncated Life Tests Using Three-Parameter Lindley Distribution, Amer Ibrahim Al-Omari, Enrico Ciavolino, Amjad D. Al-Nasser

Journal of Modern Applied Statistical Methods

A single acceptance sampling plan for the three-parameter Lindley distribution under a truncated life test is developed. For various consumer’s confidence levels, acceptance numbers, and values of the ratio of the experimental time to the specified average lifetime, the minimum sample size important to assert a certain average lifetime are calculated. The operating characteristic (OC) function values as well as the associated producer’s risks are also provided. A numerical example is presented to illustrate the suggested acceptance sampling plans.

The Estimation Of Missing Values In Rectangular Lattice Designs, Emmanuel Ogochukwu Ossai, Abimibola Victoria Oladugba

Journal of Modern Applied Statistical Methods

Algebraic expressions for estimating missing data when one or more observation(s) are missing in Rectangular lattice designs with repetition were derived using the method of minimizing the residual sum of squares. Results showed that the estimated value(s) were significantly approximate to that of the actual value(s).

Optimal Design For A Causal Structure, Zaher Kmail

Department of Statistics: Dissertations, Theses, and Student Research

Linear models and mixed models are important statistical tools. But in many natural phenomena, there is more than one endogenous variable involved and these variables are related in a sophisticated way. Structural Equation Modeling (SEM) is often used to model the complex relationships between the endogenous and exogenous variables. It was first implemented in research to estimate the strength and direction of direct and indirect effects among variables and to measure the relative magnitude of each causal factor.

Historically, traditional optimal design theory focuses on univariate linear, nonlinear, and mixed models. There is no current literature on the subject of …

Measure Of Departure From Marginal Average Point-Symmetry For Two-Way Contingency Tables, Kiyotaka Iki, Sadao Tomizawa

Journal of Modern Applied Statistical Methods

For the analysis of two-way contingency tables with ordered categories, Yamamoto, Tahata, Suzuki, and Tomizawa (2011) considered a measure to represent the degree of departure from marginal point-symmetry. The maximum value of the measure cannot distinguish two kinds of marginal complete asymmetry with respect to the midpoint. A measure is proposed which can distinguish two kinds of marginal asymmetry with respect to the midpoint. It also gives large-sample confidence interval for the proposed measure.

The Impact Of Equating On Detection Of Treatment Effects, Youn-Jeng Choi, Seohyun Kim, Allan S. Cohen, Zhenqiu Lu

Journal of Modern Applied Statistical Methods

Equating makes it possible to compare performances on different forms of a test. Three different equating methods (baseline selection, subgroup, and subscore equating) using common-item item response theory equating were examined for their impact on detection of treatment effects in multilevel models.

Upper Record Values From Extended Exponential Distribution, Devendra Kumar, Sanku Dey

Journal of Modern Applied Statistical Methods

Some recurrence relations are established for the single and product moments of upper record values for the extended exponential distribution by Nadarajah and Haghighi (2011) as an alternative to the gamma, Weibull, and the exponentiated exponential distributions. Recurrence relations for negative moments and quotient moments of upper record values are also obtained. Using relations of single moments and product moments, means, variances, and covariances of upper record values from samples of sizes up to 10 are tabulated for various values of the shape parameter and scale parameter. A characterization of this distribution based on conditional moments of record …