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Articles 841 - 870 of 1133
Full-Text Articles in Statistical Theory
Optimal Lp-Metric For Minimizing Powered Deviations In Regression, Stan Lipovetsky
Optimal Lp-Metric For Minimizing Powered Deviations In Regression, Stan Lipovetsky
Journal of Modern Applied Statistical Methods
Minimizations by least squares or by least absolute deviations are well known criteria in regression modeling. In this work the criterion of generalized mean by powered deviations is suggested. If the parameter of the generalized mean equals one or two, the fitting corresponds to the least absolute or the least squared deviations, respectively. Varying the power parameter yields an optimum value for the objective with a minimum possible residual error. Estimation of a most favorable value of the generalized mean parameter shows that it almost does not depend on data. The optimal power always occurs to be close to 1.7, …
A Comparison Of Two Rank Tests For Repeated Measure Designs, Tian Tian, Rand R. Wilcox
A Comparison Of Two Rank Tests For Repeated Measure Designs, Tian Tian, Rand R. Wilcox
Journal of Modern Applied Statistical Methods
This article compares the small-sample properties of the Agresti-Pendergast and the ATS rank-based method, as described in Brunner, Domh, and Langer (2002), for comparing J dependent groups. The results indicate that the Type I error of the Agresti-Pendergast method is more conservative when J = 2 , but under most conditions, the ATS method performs best in terms of both Type I errors and power.
Jmasm27: An Algorithm For Implementing Gibbs Sampling For 2pno Irt Models (Fortran), Yanyan Sheng, Todd C. Headrick
Jmasm27: An Algorithm For Implementing Gibbs Sampling For 2pno Irt Models (Fortran), Yanyan Sheng, Todd C. Headrick
Journal of Modern Applied Statistical Methods
A Fortran 77 subroutine is provided for implementing the Gibbs sampling procedure to a normal ogive IRT model for binary item response data with the choice of uniform and normal prior distributions for item parameters. The subroutine requires the user to have access to the IMSL library. The source code is available at http://www.siu.edu/~epse1/sheng/Fortran/, along with a stand alone executable file.
Mathmatics In Volume I Of Scripta Universitatis, Shlomo S. Sawilowsky
Mathmatics In Volume I Of Scripta Universitatis, Shlomo S. Sawilowsky
Journal of Modern Applied Statistical Methods
Immanuel Velikovsky’s journal, Scripta Universitatis, edited by Albert Einstein and first published in 1923, played a significant role in the establishment of the library, and hence, Hebrew University in Jerusalem. The inaugural issue contained an article by the French mathematician Jacques Hadamard. Excerpts from Velikovsky’s diary pertaining to the rationale for the creation of the journal, and the interest in Jewish scholars such as Hadamard, are translated here.
Practical Unit-Root Analysis Using Information Criteria: Simulation Evidence, Kosei Fukuda
Practical Unit-Root Analysis Using Information Criteria: Simulation Evidence, Kosei Fukuda
Journal of Modern Applied Statistical Methods
The information-criterion-based model selection method for detecting a unit root is proposed. The simulation results suggest that the performances of the proposed method are usually comparable to and sometimes better than those of the conventional unit-root tests. The advantages of the proposed method in practical applications are also discussed.
Tests For Treatment Group Equality When Data Are Nonnormal And Heteroscedastic, Robert A. Cribbie, Rand R. Wilcox, Carmen Bewell, H. J. Keselman
Tests For Treatment Group Equality When Data Are Nonnormal And Heteroscedastic, Robert A. Cribbie, Rand R. Wilcox, Carmen Bewell, H. J. Keselman
Journal of Modern Applied Statistical Methods
Several tests for group mean equality have been suggested for analyzing nonnormal and heteroscedastic data. A Monte Carlo study compared the Welch tests on ranked data and heterogeneous, nonparametric statistics with previously recommended procedures. Type I error rates for the Welch tests on ranks and the heterogeneous, nonparametric statistics were well controlled with a slight power advantage for the Welch tests on ranks.
A Fano-Huffman Based Statistical Coding Method, Aladdin Shamilov, Senay Asma
A Fano-Huffman Based Statistical Coding Method, Aladdin Shamilov, Senay Asma
Journal of Modern Applied Statistical Methods
Statistical coding techniques have been used for lossless statistical data compression, applying methods such as Ordinary, Shannon, Fano, Enhanced Fano, Huffman and Shannon-Fano-Elias coding methods. A new and improved coding method is presented, the Fano-Huffman Based Statistical Coding Method. It holds the advantages of both the Fano and Huffman coding methods. It is more easily applicable than the Huffman coding methods and it is more optimal than Fano coding method. The optimality with respect to the other methods is realized on the basis of English, German, Turkish, French, Russian and Spanish.
Modeling Longitudinal Ordinal Response Variables For Educational Data, Ann A. O'Connell, Heather Levitt Doucette
Modeling Longitudinal Ordinal Response Variables For Educational Data, Ann A. O'Connell, Heather Levitt Doucette
Journal of Modern Applied Statistical Methods
This article presents applications for the analysis of multilevel ordinal response data through the proportional odds model. Data are drawn from the public-use Early Childhood Longitudinal Study. Results showed that gender, number of family risk characteristics, and age at kindergarten entry were associated with initial reading proficiency (0 to 5 scale). The number of family risks and age were associated with time-slopes. Three issues are highlighted: building multilevel ordinal models, interpretation of multilevel effects; and determination of predicted probabilities based on results of the multilevel proportional odds models.
Bimodality Revisited, Thomas R. Knapp
Bimodality Revisited, Thomas R. Knapp
Journal of Modern Applied Statistical Methods
Degree of bimodality is an important feature of a frequency distribution, because it could suggest heterogeneity, such as polarization or two underlying distributions combined into one. The literature contains several measures of bimodality. This article attempts to summarize most of those measures, with their attendant advantages and disadvantages.
Type I Error Rates Of The Kenward-Roger Adjusted Degree Of Freedom F-Test For A Split-Plot Design With Missing Values, Miguel A. Padilla, James Algina
Type I Error Rates Of The Kenward-Roger Adjusted Degree Of Freedom F-Test For A Split-Plot Design With Missing Values, Miguel A. Padilla, James Algina
Journal of Modern Applied Statistical Methods
The Type I error rate of the Kenward-Roger (KR) test, implemented by PROC MIXED in SAS, was assessed through a simulation study for a one between- and one within-subjects factor split-plot design with ignorable missing values and covariance heterogeneity. The KR test controlled the Type I error well under all of the simulation factors, with all estimated Type I error rates between .040 and .075. The best control was for testing the between-subjects main effect (error rates between .041 and .057) and the worst control was for the between-by-within interaction (.040 to .075). The simulated factors had very small effects …
Comparison Of The T Vs. Wilcoxon Signed-Rank Test For Likert Scale Data And Small Samples, Gary E. Meek, Ceyhun Ozgur, Kenneth Dunning
Comparison Of The T Vs. Wilcoxon Signed-Rank Test For Likert Scale Data And Small Samples, Gary E. Meek, Ceyhun Ozgur, Kenneth Dunning
Journal of Modern Applied Statistical Methods
The one sample t-test is compared with the Wilcoxon Signed-Rank test for identical data sets representing various Likert scales. An empirical approach is used with simulated data. Comparisons are based on observed error rates for 27,850 data sets. Recommendations are provided.
Approximate Bayesian Confidence Intervals For The Mean Of An Exponential Distribution Versus Fisher Matrix Bounds Models, Vincent A. R. Camara
Approximate Bayesian Confidence Intervals For The Mean Of An Exponential Distribution Versus Fisher Matrix Bounds Models, Vincent A. R. Camara
Journal of Modern Applied Statistical Methods
The aim of this article is to obtain and compare confidence intervals for the mean of an exponential distribution. Considering respectively the square error and the Higgins-Tsokos loss functions, approximate Bayesian confidence intervals for parameters of exponential population are derived. Using exponential data, the obtained approximate Bayesian confidence intervals will then be compared to the ones obtained with Fisher Matrix bounds method. It is shown that the proposed approximate Bayesian approach relies only on the observations. The Fisher Matrix bounds method, that uses the z-table, does not always yield the best confidence intervals, and the proposed approach often performs better.
Beta-Weibull Distribution: Some Properties And Applications To Censored Data, Carl Lee, Felix Famoye, Olugbenga Olumolade
Beta-Weibull Distribution: Some Properties And Applications To Censored Data, Carl Lee, Felix Famoye, Olugbenga Olumolade
Journal of Modern Applied Statistical Methods
Some properties of a four-parameter beta-Weibull distribution are discussed. The beta-Weibull distribution is shown to have bathtub, unimodal, increasing, and decreasing hazard functions. The distribution is applied to censored data sets on bus-motor failures and a censored data set on head-and-neck-cancer clinical trial. A simulation is conducted to compare the beta-Weibull distribution with the exponentiated Weibull distribution.
Confidence Intervals For An Effect Size When Variances Are Not Equal, James Algina, H. J. Keselman, Randall D. Penfield
Confidence Intervals For An Effect Size When Variances Are Not Equal, James Algina, H. J. Keselman, Randall D. Penfield
Journal of Modern Applied Statistical Methods
Confidence intervals must be robust in having nominal and actual probability coverage in close agreement. This article examined two ways of computing an effect size in a two-group problem: (a) the classic approach which divides the mean difference by a single standard deviation and (b) a variant of a method which replaces least squares values with robust trimmed means and a Winsorized variance. Confidence intervals were determined with theoretical and bootstrap critical values. Only the method that used robust estimators and a bootstrap critical value provided generally accurate probability coverage under conditions of nonnormality and variance heterogeneity in balanced as …
Limitations Of The Analysis Of Variance, Phillip I. Good, Clifford E. Lunneborg
Limitations Of The Analysis Of Variance, Phillip I. Good, Clifford E. Lunneborg
Journal of Modern Applied Statistical Methods
Conditions under which the analysis of variance will yield inexact p-values or would be inferior in power to a permutation test are investigated. The findings for the one-way design are consistent with and extend those of Miller (1980).
Ancova: A Robust Omnibus Test Based On Selected Design Points, Rand R. Wilcox
Ancova: A Robust Omnibus Test Based On Selected Design Points, Rand R. Wilcox
Journal of Modern Applied Statistical Methods
Many robust analogs of the classic analysis of covariance method have been proposed. One approach, when comparing two independent groups, uses selected design points and then compares the groups at each design point using some robust method for comparing measures of location. So, if K design points are of interest, K tests are performed. There are rather obvious ways of performing, instead, an omnibus test that for all K points, no differences between the groups exist. One of the main results here is that several variations of these methods can perform very poorly in simulations. An alternative approach, based in …
Penalized Splines For Longitudinal Data With An Application In Aids Studies, Hua Liang, Yuanhui Xiao
Penalized Splines For Longitudinal Data With An Application In Aids Studies, Hua Liang, Yuanhui Xiao
Journal of Modern Applied Statistical Methods
A penalized spline approximation is proposed in considering nonparametric regression for longitudinal data. Standard linear mixed-effects modeling can be applied for the estimation. It is relatively simple, efficiently computed, and robust to the smooth parameters selection, which are often encountered when local polynomial and smoothing spline techniques are used to analyze longitudinal data set. The method is extended to time-varying coefficient mixed-effects models. The proposed methods are applied to data from an AIDS clinical study. Biological interpretations and clinical implications are discussed. Simulation studies are done to illustrate the proposed methods.
Choosing Smoothing Parameters For Exponential Smoothing: Minimizing Sums Of Squared Versus Sums Of Absolute Errors, Terry E. Dielman
Choosing Smoothing Parameters For Exponential Smoothing: Minimizing Sums Of Squared Versus Sums Of Absolute Errors, Terry E. Dielman
Journal of Modern Applied Statistical Methods
When choosing smoothing parameters in exponential smoothing, the choice can be made by either minimizing the sum of squared one-step-ahead forecast errors or minimizing the sum of the absolute onestep- ahead forecast errors. In this article, the resulting forecast accuracy is used to compare these two options.
The Efficiency Of Ols In The Presence Of Auto-Correlated Disturbances In Regression Models, Samir Safi, Alexander White
The Efficiency Of Ols In The Presence Of Auto-Correlated Disturbances In Regression Models, Samir Safi, Alexander White
Journal of Modern Applied Statistical Methods
The ordinary least squares (OLS) estimates in the regression model are efficient when the disturbances have mean zero, constant variance, and are uncorrelated. In problems concerning time series, it is often the case that the disturbances are correlated. Using computer simulations, the robustness of various estimators are considered, including estimated generalized least squares. It was found that if the disturbance structure is autoregressive and the dependent variable is nonstochastic and linear or quadratic, the OLS performs nearly as well as its competitors. For other forms of the dependent variable, rules of thumb are presented to guide practitioners in the choice …
Understanding Eurasian Convergence: Application Of Kohonen Self-Organizing Maps, Joel I. Deichmann, Abdolreza Eshghi, Dominique Haughton, Selin Sayek, Nicholas Teebagy, Heikki Topi
Understanding Eurasian Convergence: Application Of Kohonen Self-Organizing Maps, Joel I. Deichmann, Abdolreza Eshghi, Dominique Haughton, Selin Sayek, Nicholas Teebagy, Heikki Topi
Journal of Modern Applied Statistical Methods
Kohonen self-organizing maps (SOMs) are employed to examine economic and social convergence of Eurasian countries based on a set of twenty-eight socio-economic measures. A core of European Union states is identified that provides a benchmark against which convergence of post-socialist transition economies may be judged. The Central European Visegrád countries and Baltics show the greatest economic convergence to Western Europe, while other states form clusters that lag behind. Initial conditions on the social dimension can either facilitate or constrain economic convergence, as discovered in Central Europe vis-à-vis the Central Asian Republics. Disquiet in the convergence literature is resolved by providing …
Analysis Of Type-Ii Progressively Hybrid Censored Competing Risks Data, Debasis Kundu, Avijit Joarder
Analysis Of Type-Ii Progressively Hybrid Censored Competing Risks Data, Debasis Kundu, Avijit Joarder
Journal of Modern Applied Statistical Methods
A Type-II progressively hybrid censoring scheme for competing risks data is introduced, where the experiment terminates at a pre-specified time. The likelihood inference of the unknown parameters is derived under the assumptions that the lifetime distributions of the different causes are independent and exponentially distributed. The maximum likelihood estimators of the unknown parameters are obtained in exact forms. Asymptotic confidence intervals and two bootstrap confidence intervals are also proposed. Bayes estimates and credible intervals of the unknown parameters are obtained under the assumption of gamma priors on the unknown parameters. Different methods have been compared using Monte Carlo simulations. One …
Jmasm23: Cluster Analysis In Epidemiological Data (Matlab), Andrés M. Alonso
Jmasm23: Cluster Analysis In Epidemiological Data (Matlab), Andrés M. Alonso
Journal of Modern Applied Statistical Methods
Matlab functions for testing the existence of time, space and time-space clusters of disease occurrences are presented. The classical scan test, the Ederer, Myers and Mantel’s test, the Ohno, Aoki and Aoki’s test, and the Knox’s test are considered.
Properties Of Bound Estimators On Treatment Effect Heterogeneity For Binary Outcomes, Edward J. Mascha, Jeffrey M. Albert
Properties Of Bound Estimators On Treatment Effect Heterogeneity For Binary Outcomes, Edward J. Mascha, Jeffrey M. Albert
Journal of Modern Applied Statistical Methods
Variability in individual causal effects, treatment effect heterogeneity (TEH), is important to the interpretation of clinical trial results, regardless of the marginal treatment effect. Unfortunately, it is usually ignored. In the setting of two-arm randomized studies with binary outcomes, there are estimators for bounds on the probability of control success and treatment failure for an individual, or the treatment risk. Here, those bounds were refined and the sampling properties were assessed using simulations of correlated multinomial data via the Dirichlet multinomial. Results indicated low bias and mean squared error. Moderate to high intraclass correlation (ICC) and large numbers of clusters …
Two New Unbiased Point Estimates Of A Population Variance, Matthew E. Elam
Two New Unbiased Point Estimates Of A Population Variance, Matthew E. Elam
Journal of Modern Applied Statistical Methods
Two new unbiased point estimates of an unknown population variance are introduced. They are compared to three known estimates using the mean-square error (MSE). A computer program, which is available for download at http://program.20m.com, is developed for performing calculations for the estimates.
Multiple Comparison Procedures, Trimmed Means And Transformed Statistics, Rhonda K. Kowalchuk, H. J. Keselman, Rand R. Wilcox, James Algina, James Algina, James Algina
Multiple Comparison Procedures, Trimmed Means And Transformed Statistics, Rhonda K. Kowalchuk, H. J. Keselman, Rand R. Wilcox, James Algina, James Algina, James Algina
Journal of Modern Applied Statistical Methods
A modification to testing pairwise comparisons that may provide better control of Type I errors in the presence of non-normality is to use a preliminary test for symmetry which determines whether data should be trimmed symmetrically or asymmetrically. Several pairwise MCPs were investigated, employing a test of symmetry with a number of heteroscedastic test statistics that used trimmed means and Winsorized variances. Results showed improved Type I error control than competing robust statistics.
Confidence Intervals On Subsets May Be Misleading, Juliet Popper Shaffer
Confidence Intervals On Subsets May Be Misleading, Juliet Popper Shaffer
Journal of Modern Applied Statistical Methods
No abstract provided.
The Effect On Type I Error And Power Of Various Methods Of Resolving Ties For Six Distribution-Free Tests Of Location, Bruce R. Fay
The Effect On Type I Error And Power Of Various Methods Of Resolving Ties For Six Distribution-Free Tests Of Location, Bruce R. Fay
Journal of Modern Applied Statistical Methods
The impact on Type I error robustness and power for nine different methods of resolving ties was assessed for six distribution-free statistics with four empirical data sets using Monte Carlo techniques. These statistics share an underlying assumption of population continuity such that samples are assumed to have no equal data values (no zero difference–scores, no tied ranks). The best results across all tests and combinations of simulation parameters were obtained by randomly resolving ties, although there were exceptions. The method of dropping ties and reducing the sample size performed poorly.
Nonparametric Bayesian Multiple Comparisons For Dependence Parameter In Bivariate Exponential Populations, M. Masoom Ali, J. S. Cho, Munni Begum
Nonparametric Bayesian Multiple Comparisons For Dependence Parameter In Bivariate Exponential Populations, M. Masoom Ali, J. S. Cho, Munni Begum
Journal of Modern Applied Statistical Methods
A nonparametric Bayesian multiple comparisons problem (MCP) for dependence parameters in I bivariate exponential populations is studied. A simple method for pairwise comparisons of these parameters is also suggested. The methodology by Gopalan and Berry (1998) is extended using Dirichlet process priors, applied in the form of baseline prior and likelihood combination to provide the comparisons. Computation of the posterior probabilities of all possible hypotheses are carried out through a Markov Chain Monte Carlo, Gibbs sampling, due to the intractability of analytic evaluation. The process of MCP for the dependent parameters of bivariate exponential populations is illustrated with a numerical …
Entropy Criterion In Logistic Regression And Shapley Value Of Predictors, Stan Lipovetsky
Entropy Criterion In Logistic Regression And Shapley Value Of Predictors, Stan Lipovetsky
Journal of Modern Applied Statistical Methods
Entropy criterion is used for constructing a binary response regression model with a logistic link. This approach yields a logistic model with coefficients proportional to the coefficients of linear regression. Based on this property, the Shapley value estimation of predictors’ contribution is applied for obtaining robust coefficients of the linear aggregate adjusted to the logistic model. This procedure produces a logistic regression with interpretable coefficients robust to multicollinearity. Numerical results demonstrate theoretical and practical advantages of the entropy-logistic regression.
Comparison Of Some Simple Estimators Of The Lognormal Parameters Based On Censored Samples, Baklizi Ayman, Mohammed Al-Haj Ebrahem
Comparison Of Some Simple Estimators Of The Lognormal Parameters Based On Censored Samples, Baklizi Ayman, Mohammed Al-Haj Ebrahem
Journal of Modern Applied Statistical Methods
Point estimation of the parameters of the lognormal distribution with censored data is considered. The often employed maximum likelihood estimator does not exist in closed form and iterative methods that require very good starting points are needed. In this article, some techniques of finding closed form estimators to this situation are presented and extended. An extensive simulation study is carried out to investigate and compare the performance of these techniques. The results show that some of them are highly efficient as compared with the maximum likelihood estimator.