Statistics and Probability Commons^™

Higher Order Markov Structure-Based Logistic Model And Likelihood Inference For Ordinal Data, Soma Chowdhury Biswas, M. Ataharul Islam, Jamal Nazrul Islam

Journal of Modern Applied Statistical Methods

Azzalini (1994) proposed a first order Markov chain for binary data. Azzalini’s model is extended for ordinal data and introduces a second order model. Further, the test statistics are developed and the power of the test is determined. An application using real data is also presented.

Proxy Pattern-Mixture Analysis For A Binary Variable Subject To Nonresponse., Rebecca H. Andridge, Roderick J. Little

The University of Michigan Department of Biostatistics Working Paper Series

We consider assessment of the impact of nonresponse for a binary survey

variable Y subject to nonresponse, when there is a set of covariates

observed for nonrespondents and respondents. To reduce dimensionality and

for simplicity we reduce the covariates to a continuous proxy variable X

that has the highest correlation with Y, estimated from a probit

regression analysis of respondent data. We extend our previously proposed

proxy-pattern mixture analysis (PPMA) for continuous outcomes to the binary

outcome using a latent variable approach. The method does not assume data

are missing at random, and creates a framework for sensitivity analyses.

Maximum …

Cagan Type Rational Expectations Model On Time Scales With Their Applications To Economics, Funda Ekiz

Masters Theses & Specialist Projects

Rational expectations provide people or economic agents making future decision with available information and past experiences. The first approach to the idea of rational expectations was given approximately fifty years ago by John F. Muth. Many models in economics have been studied using the rational expectations idea. The most familiar one among them is the rational expectations version of the Cagans hyperination model where the expectation for tomorrow is formed using all the information available today. This model was reinterpreted by Thomas J. Sargent and Neil Wallace in 1973. After that time, many solution techniques were suggested to solve the …

Robustness, Power And Interpretability Of Pairwise Tests Of Discriminant Functions In Manova, Philip H. Ramsey, Patricia P. Ramsey, Priscila Hachimine, Nancy Andiloro

Journal of Modern Applied Statistical Methods

Limiting follow-up hypotheses to be tested can reduce problems relating to the control of Type I and Type II errors in multivariate analysis of variance (MANOVA). Such limitations can also improve the interpretability of results. The importance of sample size, shape of population distribution, within-group correlations and heterogeneity of variances are demonstrated. The protected greatest characteristic root (GCR) procedure is shown to work well for small, group size, N (≤ 10). The unprotected GCR is shown to work well for larger N.

A Comparison Of Factor Rotation Methods For Dichotomous Data, W. Holmes Finch

Journal of Modern Applied Statistical Methods

Exploratory factor analysis (EFA) is frequently used in the social sciences and is a common component in many validity studies. A core aspect of EFA is the determination of which observed indicator variables are associated with which latent factors through the use of factor loadings. Loadings are initially extracted using an algorithm, such as maximum likelihood or weighted least squares, and then transformed - or rotated - to make them more interpretable. There are a number of rotational techniques available to the researcher making use of EFA. Prior work has discussed the advantages of a number of these criteria from …

Indeterminacy Of Factor Score Estimates In Slightly Misspecified Confirmatory Factor Models, André Beauducel

Journal of Modern Applied Statistical Methods

Two methods to calculate a measure for the quality of factor score estimates have been proposed. These methods were compared by means of a simulation study. The method based on a covariance matrix reproduced from a model leads to smaller effects of sampling error.

Error Analysis On The Generalized Negative Binomial Distribution, Felix Famoye, Oluwakemi Aremu

Journal of Modern Applied Statistical Methods

The generalized negative binomial distribution characterized by three parameters, has been used to fit data from various fields of study. The distribution can model data for which the variance is larger or smaller than the mean, however, it becomes truncated under certain conditions. This truncation error is investigated via a detailed error analysis that determines the parameter space when the model can be used in place of the truncated generalized negative binomial distribution. The fitting of a generalized negative. K. M. Ramachandran is a

A Permutation Test For Compound Symmetry With Application To Gene Expression Data, Tracy L. Morris, Mark E. Payton, Stephanie A. Santorico

Journal of Modern Applied Statistical Methods

The development and application of a permutation test for compound symmetry is described. In a simulation study the permutation test appears to be a level-α test and is robust to non-normality. However, it exhibits poor power, particularly for small samples.

Ordinal Regression Analysis: Predicting Mathematics Proficiency Using The Continuation Ratio Model, Xing Liu, Ann A. O'Connell, Hari Koirala

Journal of Modern Applied Statistical Methods

One commonly used model to analyze ordinal response data is the proportional odds (PO) model. However, if research interest is focused on a particular category and if an individual must pass through lower categories before achieving a higher level, the continuation ratio (CR) model is a more appropriate choice than the PO model. In addition, statistical software, such as Stata and SAS, may use different techniques to estimate the parameters. The CR model is used to illustrate the analysis of ordinal data in education using Stata and SAS and compares the results of fitting the CR model between these two …

Estimation And Hypothesis Testing In Lav Regression With Autocorrelated Errors: Is Correction For Autocorrelation Helpful?, Terry E. Dielman

Journal of Modern Applied Statistical Methods

Using the Prais-Winsten correction and adding a lagged variable provides improved estimates (smaller MSE) in least absolute value (LAV) regression when moderate to high levels of autocorrelation are present. When comparing empirical levels of significance for hypothesis tests, adding a lagged variable outperforms other approaches but has a relative high empirical level of significance.

Control Balanced Designs Involving Sequences Of Treatments, Cini Varghese, Seema Jaggi

Journal of Modern Applied Statistical Methods

Designs involving sequences of treatments for test vs. control comparisons are suitable for research in which each experimental unit receives treatments over time in order to compare several test treatments to one (or more) control treatment(s). These designs can be advantageously used in screening experiments and bioequivalence trials. Three series of such designs are constructed in incomplete sequences wherein the first class of designs is variance balanced while the other two classes of designs are partially variance balanced for test versus test comparisons of both direct and residual effects of treatments.

Probabilistic Inferences For The Sample Pearson Product Moment Correlation, Jeffrey R. Harring, John A. Wasko

Journal of Modern Applied Statistical Methods

Fisher’s correlation transformation is commonly used to draw inferences regarding the reliability of tests comprised of dichotomous or polytomous items. It is illustrated theoretically and empirically that omitting test length and difficulty results in inflated Type I error. An empirically unbiased correction is introduced within the transformation that is applicable under any test conditions.

Non-Homogenous Poisson Process For Evaluating Stage I & Ii Ductal Breast Cancer Treatment, Chris P. Tsokos, Yong Xu

Journal of Modern Applied Statistical Methods

Non-Homogenous Poisson Process (NHPP), also known as the Power Law process (PLP) or the Weibull Process, is used to evaluate the effectiveness of a given treatment for Stage I & II ductal breast cancer patients. The behavior of the shape parameter of the intensity function is examined to evaluate the response of a given treatment with respect to its effectiveness for a cancer subject.

On Maximum Likelihood Estimators Of The Parameters Of A Modified Weibull Distribution Using Extreme Ranked Set Sampling, Amer Ibrahim Al-Omari, Said Ali Al-Hadhrami

Journal of Modern Applied Statistical Methods

Extreme ranked set sampling (ERSS) is considered to estimate the three parameters and population mean of the modified Weibull distribution (MWD). The maximum likelihood estimator (MLE) is investigated and compared to the corresponding one based on simple random sampling (SRS). It is found that, the MLE based on ERSS is more efficient than MLE using SRS for estimating the three parameters of the MWD. The ERSS estimator of the population mean of the MWD is also found to be more efficient than the SRS based on the same number of measured units.

Identifying Outliers In Fuzzy Time Series, S. Suresh, K. Senthamarai Kannan

Journal of Modern Applied Statistical Methods

Time series analysis is often associated with the discovery of patterns and prediction of features. Forecasting accuracy can be improved by removing identified outliers in the data set using the Cook’s distance and Studentized residual test. In this paper a modified fuzzy time series method is proposed based on transition probability vector membership function. It is experimentally shown that the proposed method minimizes the average forecasting error compared with other known existing methods.

Modeling Repairable System Failures With Interval Failure Data And Time Dependent Covariate, Jayanthi Arasan, Samira Ehsani

Journal of Modern Applied Statistical Methods

An application of a repairable system model for interval failure data with a time dependent covariate is examined. The performance of several models based on the NHPP when applied to real data on ball bearing failures is also explored. The best model for the data was selected based on results of the likelihood ratio test. The bootstrapping technique was applied to obtain the variance estimate for the estimated expected number of failures. Results demonstrate that the proposed model works well and is easy to implement, in addition the bootstrap variance estimate provides a simple substitute for the traditional estimate.

Salary Equity Studies: An Analysis Of Using The Blinder-Oaxaca Decomposition To Estimate Differences In Faculty Salaries By Gender, Sally A. Lesik, Carolyn R. Fallahi

Journal of Modern Applied Statistical Methods

Parameter estimates for equity studies tested for stability are described. Bootstrap simulation can test whether parameter estimates remain stable given changes in the sample data; fractional polynomials can be used to access functional form specification; and variance inflation factors can be used to test for multicollinearity.

Higher Order C(T, P, S) Crossover Designs, James F. Reed Iii

Journal of Modern Applied Statistical Methods

A crossover study is a repeated measures design in which each subject is randomly assigned to a sequence of treatments, including at least two treatments. The most damning characteristic of a crossover study is the potential of a carryover effect of one treatment to the next period. To solve the first-order crossover problem characteristic in the classic AB|BA design, the design must be extended. One alternative uses additional treatment sequences in two periods; a second option is to add a third period and repeat one of the treatments. Assuming a traditional model that specifies a first-order carryover effect, this study …

Assessing The Impact Of Non-Differential Genotyping Errors On Rare Variant Tests Of Association, Scott Powers, Shyam Gopalakrishnan, Nathan L. Tintle

Faculty Work Comprehensive List

Background/Aims: We aim to quantify the effect of non-differential genotyping errors on the power of rare variant tests and identify those situations when genotyping errors are most harmful. Methods: We simulated genotype and phenotype data for a range of sample sizes, minor allele frequencies, disease relative risks and numbers of rare variants. Genotype errors were then simulated using five different error models covering a wide range of error rates. Results: Even at very low error rates, misclassifying a common homozygote as a heterozygote translates into a substantial loss of power, a result that is exacerbated even further as the minor …

Habitat Use And Abundance Patterns Of Sandhill Cranes In The Central Platte River Valley, Nebraska, 2003–2010, Todd Joseph Buckley

School of Natural Resources: Dissertations, Theses, and Student Research

The Central Platte River Valley (CPRV) in Nebraska is an important spring stopover area for the midcontinent population of sandhill cranes. Alterations to crop rotation and loss habitat in the CPRV pose a risk to the population. Personnel drove designated routes in the CPRV from 2003–2010 to record the presence of cranes in agricultural fields and estimate abundance. I developed and evaluated models to predict habitat use and flock sizes. Alfalfa was predicted to receive the highest use followed by corn, soybeans, winter wheat, grassland, and shrubland. Use of all habitats and flock size increased as field area increased. Flock …