Statistical Theory Commons^™

Bayesian Analysis Under Progressively Censored Rayleigh Data, Gyan Prakash

Journal of Modern Applied Statistical Methods

The one-parameter Rayleigh model is considered as an underlying model for evaluating the properties of Bayes estimator under Progressive Type-II right censored data. The One‑Sample Bayes prediction bound length (OSBPBL) is also measured. Based on two different asymmetric loss functions a comparative study presented for Bayes estimation. A simulation study was used to evaluate their comparative properties.

Statistical Modeling Of Migration Attractiveness Of The Eu Member States, Tatiana Tikhomirova, Yulia Lebedeva

Journal of Modern Applied Statistical Methods

Identifying the relationship between the migration attractiveness of the European Union countries and their level of socio-economic development is investigated. An approach is proposed identify influences on migration socio-economic characteristics, by aggregating and reducing their diversity, and substantiating the cause-and-effect relationships of the studied phenomenon. A stable classification of countries scheme is developed according to the attractiveness of migration on aggregate factors, and then an econometric model of a binary choice using panel data for 2008-2010 was applying, quantifying the impact of aggregate designed factors on immigration and emigration.

The Distribution Of The Inverse Square Root Transformed Error Component Of The Multiplicative Time Series Model, Bright F. Ajibade, Chinwe R. Nwosu, J. I. Mbegdu

Journal of Modern Applied Statistical Methods

The probability density function, mean and variance of the inverse square-root transformed left-truncated N(1,σ²) error component e^*_t(=1/ √e_t) of the multiplicative time series model were established. A comparison of key-statistical properties of e^*_t and e_t confirmed normality with mean 1 but with Var(e^*_t) ≈1/4Var(e_t) when σ≤0.14. Hence σ≤0.14 is the required condition for successful transformation.

Approaches For Detection Of Unstable Processes: A Comparative Study, Yerriswamy Wooluru, D. R. Swamy, P. Nagesh

Journal of Modern Applied Statistical Methods

A process is stable only when parameters of the distribution of a process or product characteristic remain same over time. Only a stable process has the ability to perform in a predictable manner over time. Statistical analysis of process data usually assume that data are obtained from stable process. In the absence of control charts, the hypothesis of process stability is usually assessed by visual examination of the pattern in the run chart. In this paper appropriate statistical approaches have been adopted to detect instability in the process and compared their performance with the run chart of considerably shorter length …

A Robust Panel Unit Root Test In The Presence Of Cross Sectional Dependence, Nurul Sima Mohamad Shariff, Nor Aishah Hamzah

Journal of Modern Applied Statistical Methods

Problems arise in testing the stationarity of the panel in the presence of cross sectional dependence and outliers. The currently available panel unit root tests are very much affected by the presence of outliers. As such, this article introduces an alternative test which is robust to outliers and cross sectional dependence. The performance and robustness of the proposed test is discussed and comparisons are made to the existing tests via simulation studies.

A Study Of The Parametric And Nonparametric Linear-Circular Correlation Coefficient, Robin Tu

Statistics

Circular statistics are specialized statistical methods that deal specifically with directional data. Data that is angular require specialized techniques due to the modulo 2π (in radians) or modulo 360^◦ (in degrees) nature of angles.

Correlation, typically in terms of Pearson’s correlation coefficient, is a measure of association between two linear random variables x and y. In this paper, the specific circular technique of the parametric and nonparametric linear-circular correlation coefficient will be explored where correlation is no longer between two linear variables x and y, but between a linear random variable x and circular random variable θ.

A simulation …

Applying Penalized Binary Logistic Regression With Correlation Based Elastic Net For Variables Selection, Zakariya Yahya Algamal, Muhammad Hisyam Lee

Journal of Modern Applied Statistical Methods

Reduction of the high dimensional classification using penalized logistic regression is one of the challenges in applying binary logistic regression. The applied penalized method, correlation based elastic penalty (CBEP), was used to overcome the limitation of LASSO and elastic net in variable selection when there are perfect correlation among explanatory variables. The performance of the CBEP was demonstrated through its application in analyzing two well-known high dimensional binary classification data sets. The CBEP provided superior classification performance and variable selection compared with other existing penalized methods. It is a reliable penalized method in binary logistic regression.

Spss Programs For Addressing Two Forms Of Power For Multiple Regression Coefficients, Christopher Aberson

Journal of Modern Applied Statistical Methods

This paper presents power analysis tools for multiple regression. The first takes input of correlations between variables and sample size and outputs power for multiple predictors. The second addresses power to detect significant effects for all of the predictors in the model. Both employ user-friendly SPSS Custom Dialogs.

Are Per-Family Type I Error Rates Relevant In Social And Behavioral Science?, Andrew V. Frane

Journal of Modern Applied Statistical Methods

The familywise Type I error rate is a familiar concept in hypothesis testing, whereas the per‑family Type I error rate is rarely addressed. This article uses Monte Carlo simulations and graphics to make a case for the relevance of the per‑family Type I error rate in research practice and pedagogy.

Per Family Error Rates: A Response, James F. Troendle, Keshia-Lee Martin, Vance W. Berger

Journal of Modern Applied Statistical Methods

As the authors note, the familywise error rate (FWER) is used rather often, whereas the per-family error rate (PFER) is not. Is this as it should be? It would seem that no universal answer is possible, as context determines which is more appropriate in any given application. In the general scenario of testing the benefit of an intervention, one might ideally want an error rate that aligns with the decision for benefit. In most cases the FWER does this pretty well, while allowing one to identify those endpoints for which benefit exists. The PFER does not seem to have any …

Maximum Likelihood Estimation Of The Kumaraswamy Exponential Distribution With Applications, K. A. Adepoju, O. I. Chukwu

Journal of Modern Applied Statistical Methods

The Kumaraswamy exponential distribution, a generalization of the exponential, is developed as a model for problems in environmental studies, survival analysis and reliability. The estimation of parameters is approached by maximum likelihood and the observed information matrix is derived. The proposed models are applied to three real data sets.

Test For The Equality Of Partial Correlation Coefficients For Two Populations, Madhusudan Bhandary, Arjun K. Gupta

Journal of Modern Applied Statistical Methods

A likelihood ratio test for the equality of two partial correlation coefficients based on two independent multinormal samples has been derived. The large sample Z-test for the same problem has also been discussed. The power analysis of the two tests is obtained. It has been found that the approximate likelihood ratio (ALR) test showed consistently better results than Z -test in terms of power. The size of the ALR test is slightly more than the alpha level. The ALR test is recommended strongly for use in practice.

Comparison Of Model Fit Indices Used In Structural Equation Modeling Under Multivariate Normality, Sengul Cangur, Ilker Ercan

Journal of Modern Applied Statistical Methods

The purpose of this study is to investigate the impact of estimation techniques and sample sizes on model fit indices in structural equation models constructed according to the number of exogenous latent variables under multivariate normality. The performances of fit indices are compared by considering effects of related factors. The Ratio Chi-square Test Statistic to Degree of Freedom, Root Mean Square Error of Approximation, and Comparative Fit Index are the least affected indices by estimation technique and sample size under multivariate normality, especially with large sample size.

Method Of Estimation In The Presence Of Non-Response And Measurement Errors Simultaneously, Rajesh Singh Singh, Prayas Sharma

Journal of Modern Applied Statistical Methods

The problem of estimating the finite population mean of in simple random sampling in the presence of non-response and response error was considered. The estimators use auxiliary information to improve efficiency, assuming non–response and measurement error are present in both the study and auxiliary variables. A class of estimators was proposed and its properties studied in the simultaneous presence of non-response and response errors. It was shown that the proposed class of estimators is more efficient than the usual unbiased estimator, ratio and product estimators under non-response and response error together. A numerical study was carried out to compare its …

Pseudo-Random Number Generators For Vector Processors And Multicore Processors, Agner Fog

Journal of Modern Applied Statistical Methods

Large scale Monte Carlo applications need a good pseudo-random number generator capable of utilizing both the vector processing capabilities and multiprocessing capabilities of modern computers in order to get the maximum performance. The requirements for such a generator are discussed. New ways of avoiding overlapping subsequences by combining two generators are proposed. Some fundamental philosophical problems in proving independence of random streams are discussed. Remedies for hitherto ignored quantization errors are offered. An open source C++ implementation is provided for a generator that meets these needs.

Estimating The Accuracy Of Automated Classification Systems Using Only Expert Ratings That Are Less Accurate Than The System, Paul E. Lehner

Journal of Modern Applied Statistical Methods

A method is presented to estimate the accuracy of an automated classification system based only on expert ratings on test cases, where the system may be substantially more accurate than the raters. In this method an estimate of overall rater accuracy is derived from the level of inter-rater agreement, Bayesian updating based on estimated rater accuracy is applied to estimate a ground truth probability for each classification on each test case, and then overall system accuracy is estimated by comparing the relative frequency that the system agrees with the most probable classification at different probability levels. A simulation analysis provides …

Modeling Probability Of Causal And Random Impacts, Stan Lipovetsky, Igor Mandel

Journal of Modern Applied Statistical Methods

The method of the estimation of the probability of an event occurring under the influence of the causal and random effects is considered. Epistemological differences from the traditional approaches to causality are discussed, and a new model of the statistical estimation of the parameters of each effect is proposed. The simple and effective algorithms of the model parameters estimation are presented, and numerical simulations are performed. A practical marketing example is analyzed. The results support the validity of the estimation procedure and open the perspective for the application of the method for various decision making problems, where different causes can …

Estimation For The Parameters Of The Exponentiated Exponential Distribution Using A Median Ranked Set Sampling, Monjed H. Samuh, Areen Qtait

Journal of Modern Applied Statistical Methods

The method of maximum likelihood estimation based on Median Ranked Set Sampling (MRSS) was used to estimate the shape and scale parameters of the Exponentiated Exponential Distribution (EED). They were compared with the conventional estimators. The relative efficiency was used for comparison. The amount of information (in Fisher's sense) available from the MRSS about the parameters of the EED were be evaluated. Confidence intervals for the parameters were constructed using MRSS.

Estimating The Strength Of An Association Based On A Robust Smoother, Rand Wilcox

Journal of Modern Applied Statistical Methods

It is known that the more obvious parametric approaches to fitting a regression line to data are often not flexible enough to provide an adequate approximation of the true regression line. Many nonparametric regression estimators, often called smoothers, have been derived that are aimed at dealing with this problem. The paper deals with the issue of estimating the strength of an association based on the fit obtained by a robust smoother. A simple approach, already known, is to estimate explanatory power in a fairly obvious manner. This approach has been found to perform reasonably well when using the smoother LOESS. …

Per Family Or Familywise Type I Error Control: "Eether, Eyether, Neether, Nyther, Let's Call The Whole Thing Off!", H. J. Keselman

Journal of Modern Applied Statistical Methods

Frane (2015) pointed out the difference between per-family and familywise Type I error control and how different multiple comparison procedures control one method but not necessarily the other. He then went on to demonstrate in the context of a two group multivariate design containing different numbers of dependent variables and correlations between variables how the per-family rate inflates beyond the level of significance. In this article I reintroduce other newer better methods of Type I error control. These newer methods provide more power to detect effects than the per-family and familywise techniques of control yet maintain the overall rate of …

Comparison Of Bayesian Credible Intervals To Frequentist Confidence Intervals, Kathy Gray, Brittany Hampton, Tony Silveti-Falls, Allison Mcconnell, Casey Bausell

Journal of Modern Applied Statistical Methods

Frequentist confidence intervals were compared with Bayesian credible intervals under a variety of scenarios to determine when Bayesian credible intervals outperform frequentist confidence intervals. Results indicated that Bayesian interval estimation frequently produces results with precision greater than or equal to the frequentist method.

Special Education Distributions And Analysis, Valerie Felder, Shlomo S. Sawilowsky

Journal of Modern Applied Statistical Methods

Micceri (1989) examined the distributional characteristics of 440 large sample general education achievement and psychometric measures. All the distributions were found to be statistically significantly different from the normal distribution. In this study, 395 special education datasets were examined. Although there were some normally distributed datasets, most were not, and some were markedly different in shape from those found by Micceri (1989). Implications for statistical testing and making special education policy decisions were given.

Vol. 14, No. 1 (Full Issue), Jmasm Editors

Journal of Modern Applied Statistical Methods

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A Comparison Of Semi-Parametric And Nonparametric Methods For Estimating Mean Time To Event For Randomly Left Censored Data, Farzana Chowdhury, Jahida Gulshan, Syed Shahadat Hossain

Journal of Modern Applied Statistical Methods

The aim of this study was to make a comparison among existing estimation methods (Kaplan-Meier, Nelson-Aalen and Regression on Ordered Statistics (ROS)) for randomly left censored time to event data under selected distributions and for different level of censoring and sample sizes in order to determine the strength of these methods based on simulated data. Comparisons among the methods are made on the basis of unbiasedness and Monte Carlo Standard Error of the summary statistics (mean time to event) obtained by those methods under different conditions.

Best Practice Recommendations For Data Screening, Justin A. Desimone, Peter D. Harms, Alice J. Desimone

Department of Management: Faculty Publications

Survey respondents differ in their levels of attention and effort when responding to items. There are a number of methods researchers may use to identify respondents who fail to exert sufficient effort in order to increase the rigor of analysis and enhance the trustworthiness of study results. Screening techniques are organized into three general categories, which differ in impact on survey design and potential respondent awareness. Assumptions and considerations regarding appropriate use of screening techniques are discussed along with descriptions of each technique. The utility of each screening technique is a function of survey design and administration. Each technique has …

Retained-Components Factor Transformation: Factor Loadings And Factor Score Predictors In The Column Space Of Retained Components, André Beauducel, Frank Spohn

Journal of Modern Applied Statistical Methods

Factor loadings optimally account for the non-diagonal elements of the covariance matrix of observed variables. Principal component analysis leads to components accounting for a maximum of the variance of the observed variables. Retained-components factor transformation is proposed in order to combine the advantages of factor analysis and principal component analysis.

Pairwise Comparison In Repeated Measures, I.C.A. Oyeka, C. C. Nnanatu

Journal of Modern Applied Statistical Methods

Sometimes a random sample of subjects or patients may be exposed to a battery of diagnostic tests or medication over time and interest is on determining whether there is progressive remission of condition, disease or symptom. Also perhaps early in a program or experiment, subjects or candidates may be required to significantly improve in their performance rates at the current trial relative to an immediately preceding trial, otherwise they may have to withdraw from or drop out. The research interest would then be to determine some critical minimum marginal success rate to guide the management in decision making as well …

A Comparison Of Methods For Group Prediction With High Dimensional Data, Holmes Finch

Journal of Modern Applied Statistical Methods

High dimensional data is the situation in which the number of variables included in an analysis approaches or exceeds the sample size. In the context of group classification, researchers are typically interested in finding a model that can be used to correctly place an individual into their appropriate group; e.g. correctly diagnose individuals with depression. However, when the size of the training sample is small and the number of predictors used to differentiate the groups is larger, standard approaches such as discriminant analysis may not work well. In order to address this issue, statisticians have developed a number of tools …

Objective Priors For Estimation Of Extended Exponential Geometric Distribution, Pedro L. Ramos, Fernando A. Moala, Jorge A. Achcar

Journal of Modern Applied Statistical Methods

A Bayesian analysis was developed with different noninformative prior distributions such as Jeffreys, Maximal Data Information, and Reference. The aim was to investigate the effects of each prior distribution on the posterior estimates of the parameters of the extended exponential geometric distribution, based on simulated data and a real application.

Some General Guidelines For Choosing Missing Data Handling Methods In Educational Research, Jehanzeb R. Cheema

Journal of Modern Applied Statistical Methods

The effect of a number of factors, such as the choice of analytical method, the handling method for missing data, sample size, and proportion of missing data, were examined to evaluate the effect of missing data treatment on accuracy of estimation. A methodological approach involving simulated data was adopted. One outcome of the statistical analyses undertaken in this study is the formulation of easy-to-implement guidelines for educational researchers that allows one to choose one of the following factors when all others are given: sample size, proportion of missing data in the sample, method of analysis, and missing data handling method.