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Articles 751 - 780 of 1133
Full-Text Articles in Statistical Theory
Size-Biased Generalized Negative Binomial Distribution, Khurshid Ahmad Mir
Size-Biased Generalized Negative Binomial Distribution, Khurshid Ahmad Mir
Journal of Modern Applied Statistical Methods
A size biased generalized negative binomial distribution (SBGNBD) is defined and a recurrence relationship for the moments of SBGNBD is established. The Bayes’ estimator for a parametric function of one parameter when two other parameters of a known size-biased generalized negative binomial distribution is derived. Prior information on one parameter is given by a beta distribution and the parameters in the prior distribution are assigned by computer using Monte Carlo and R-software.
Non-Parametric Quantile Selection For Extreme Distributions, Wan Zawiah Wan Zin, Abdul Aziz Jemain
Non-Parametric Quantile Selection For Extreme Distributions, Wan Zawiah Wan Zin, Abdul Aziz Jemain
Journal of Modern Applied Statistical Methods
The objective is to select the best non-parametric quantile estimation method for extreme distributions. This serves as a starting point for further research in quantile application such as in parameter estimation using LQ-moments method. Thirteen methods of non-parametric quantile estimation were applied on six types of extreme distributions and their efficiencies compared. Monte Carlo methods were used to generate the results, which showed that the method of Weighted Kernel estimator of Type 1 was more efficient than the other methods in many cases.
Analyzing Incomplete Categorical Data: Revisiting Maximum Likelihood Estimation (Mle) Procedure, Hoo Ling Ping, M. Ataharul Islam
Analyzing Incomplete Categorical Data: Revisiting Maximum Likelihood Estimation (Mle) Procedure, Hoo Ling Ping, M. Ataharul Islam
Journal of Modern Applied Statistical Methods
Incomplete data poses formidable difficulties in the application of statistical techniques and requires special procedures to handle. The most common ways to solve this problem are by ignoring, truncating, censoring or collapsing those data, but these may lead to inappropriate conclusions because those data might contain important information. Most of the research for estimating cell probabilities involving incomplete categorical data is based on the EM algorithm. A likelihood approach is employed for estimating cell probabilities for missing values and makes comparisons between maximum likelihood estimation (MLE) and the EM algorithm. The MLE can provide almost the same estimates as that …
Adaptive Estimation Of Heteroscedastic Linear Regression Model Using Probability Weighted Moments, Faqir Muhammad, Muhammad Aslam, G.R. Pasha
Adaptive Estimation Of Heteroscedastic Linear Regression Model Using Probability Weighted Moments, Faqir Muhammad, Muhammad Aslam, G.R. Pasha
Journal of Modern Applied Statistical Methods
An adaptive estimator is presented by using probability weighted moments as weights rather than conventional estimates of variances for unknown heteroscedastic errors while estimating a heteroscedastic linear regression model. Empirical studies of the data generated by simulations for normal, uniform, and logistically distributed error terms support our proposed estimator to be quite efficient, especially for small samples.
Construction Of Insurance Scoring System Using Regression Models, Noriszura Ismail, Abdul Aziz Jemain
Construction Of Insurance Scoring System Using Regression Models, Noriszura Ismail, Abdul Aziz Jemain
Journal of Modern Applied Statistical Methods
This study suggests the regression models of Lognormal, Normal and Gamma for constructing insurance scoring system. The main advantage of a scoring system is that it can be used by insurers to differentiate between high and low risks insureds, thus allowing the profitability of insureds to be predicted.
Type I Error Rates Of The Kenward-Roger F-Test For A Split-Plot Design With Missing Values And Non-Normal Data, Miguel A. Padilla, Youngkyoung Min, Guili Zhang
Type I Error Rates Of The Kenward-Roger F-Test For A Split-Plot Design With Missing Values And Non-Normal Data, Miguel A. Padilla, Youngkyoung Min, Guili Zhang
Journal of Modern Applied Statistical Methods
The Type I error of the Kenward-Roger (KR) F-test was assessed through a simulation study for a between- by within-subjects split-plot design with non-normal ignorable missing data. The KR-test for the between- and within-subjects main effect was robust under all simulation variables investigated and when the data were missing completely at random (MCAR). This continued to hold for the between-subjects main effect when data were missing at random (MAR). For the interaction, the KR F-test performed fairly well at controlling Type I under MCAR and the simulation variables investigated. However, under MAR, the KR F-test for the …
Constructing Confidence Intervals For Spearman’S Rank Correlation With Ordinal Data: A Simulation Study Comparing Analytic And Bootstrap Methods, John Ruscio
Journal of Modern Applied Statistical Methods
Research shows good probability coverage using analytic confidence intervals (CIs) for Spearman’s rho with continuous data, but poorer coverage with ordinal data. A simulation study examining the latter case replicated prior results and revealed that coverage of bootstrap CIs was usually as good or better than coverage of analytic CIs.
An Optimum Allocation With A Family Of Estimators Using Auxiliary Information In Sample Survey, Gajendra K. Vishwakarma, Housila P. Singh
An Optimum Allocation With A Family Of Estimators Using Auxiliary Information In Sample Survey, Gajendra K. Vishwakarma, Housila P. Singh
Journal of Modern Applied Statistical Methods
The problem of obtaining optimum allocation using auxiliary information in stratified random sampling. An optimum allocation with a family of estimators is obtained and its efficiency is compared with that of Neyman allocation based on Srivastava (1971) class of estimators and the optimum allocation suggested by Zaidi et al., (1989). It is shown that the proposed allocation is better in the sense having smaller variance compared to other optimum allocation.
On Some Properties Of Quasi-Negative-Binomial Distribution And Its Applications, Anwar Hassan, Sheikh Bilal
On Some Properties Of Quasi-Negative-Binomial Distribution And Its Applications, Anwar Hassan, Sheikh Bilal
Journal of Modern Applied Statistical Methods
The quasi-negative-binomial distribution was applied to queuing theory for determining the distribution of total number of customers served before the queue vanishes under certain assumptions. Some structural properties (probability generating function, convolution, mode and recurrence relation) for the moments of quasi-negative-binomial distribution are discussed. The distribution’s characterization and its relation with other distributions were investigated. A computer program was developed using R to obtain ML estimates and the distribution was fitted to some observed sets of data to test its goodness of fit.
Confidence Intervals Based On Robust Estimators, Meral Cetin, Serpil Aktas
Confidence Intervals Based On Robust Estimators, Meral Cetin, Serpil Aktas
Journal of Modern Applied Statistical Methods
Classical estimation of confidence intervals based on the sample mean and variance is sensitive to outliers. Robust methods were proposed for reducing the influence of outliers. The Minimum Volume Ellipsoid estimator (MVE), having a high breakdown point, is one of the robust estimators for location and scale parameters. The robust confidence interval for location parameter is constructed based on the MVE, and compared with the proposed robust confidence interval estimation methods. The performance of the robust confidence interval based on MVE is illustrated with a simulation study. The lengths of 100(1-α)% confidence intervals were investigated.
Using Connectionist Models To Evaluate Examinees’ Response Patterns To Achievement Tests, Mark J. Gierl, Ying Cui, Steve Hunka
Using Connectionist Models To Evaluate Examinees’ Response Patterns To Achievement Tests, Mark J. Gierl, Ying Cui, Steve Hunka
Journal of Modern Applied Statistical Methods
The attribute hierarchy method (AHM) applied to assessment engineering is described. It is a psychometric method for classifying examinees’ test item responses into a set of attribute mastery patterns associated with different components in a cognitive model of task performance. Attribute probabilities, computed using a neural network, can be estimated for each examinee thereby providing specific information about the examinee’s attribute-mastery level. The pattern recognition approach described in this study relies on an explicit cognitive model to produce the expected response patterns. The expected response patterns serve as the input to the neural network. The model also yields the cognitive …
Coverage Performance Of The Non-Central F-Based And Percentile Bootstrap Confidence Intervals For Root Mean Square Standardized Effect Size In One-Way Fixed-Effects Anova, Guili Zhang, James Algina
Coverage Performance Of The Non-Central F-Based And Percentile Bootstrap Confidence Intervals For Root Mean Square Standardized Effect Size In One-Way Fixed-Effects Anova, Guili Zhang, James Algina
Journal of Modern Applied Statistical Methods
The coverage performance of the confidence intervals (CIs) for the Root Mean Square Standardized Effect Size (RMSSE) was investigated in a balanced, one-way, fixed-effects, between-subjects ANOVA design. The noncentral F distribution-based and the percentile bootstrap CI construction methods were compared. The results indicated that the coverage probabilities of the CIs for RMSSE were not adequate.
An Evaluation Of Standard, Alternative, And Robust Slope Test Strategies, Tim Moses, Alan Klockars
An Evaluation Of Standard, Alternative, And Robust Slope Test Strategies, Tim Moses, Alan Klockars
Journal of Modern Applied Statistical Methods
The robustness and power of nine strategies for testing the differences between two groups’ regression slopes under nonnormality and residual variance heterogeneity are compared. The results showed that three most robust slope test strategies were the combination of the trimmed and Winsorized slopes with the James second order test, the combination of Theil-Sen with James, and Theil-Sen with percentile bootstrapping. The slope tests based on Theil-Sen slopes were more powerful than those based on trimmed and Winsorized slopes.
Second-Order Latent Growth Models With Shifting Indicators, Gregory R. Hancock, Michelle M. Buehl
Second-Order Latent Growth Models With Shifting Indicators, Gregory R. Hancock, Michelle M. Buehl
Journal of Modern Applied Statistical Methods
Second-order latent growth models assess longitudinal change in a latent construct, typically employing identical manifest variables as indicators across time. However, the same indicators may be unavailable and/or inappropriate for all time points. This article details methods for second-order growth models in which constructs’ indicators shift over time.
Selection Of Non-Regular Fractional Factorial Designs When Some Two-Factor Interactions Are Important, Weiming Ke, Rui Yao
Selection Of Non-Regular Fractional Factorial Designs When Some Two-Factor Interactions Are Important, Weiming Ke, Rui Yao
Journal of Modern Applied Statistical Methods
A new method is proposed for selecting the optimal non-regular fractional factorial designs in the situation when some two-factor interactions are potentially important. Searching for the best designs according to this method is discussed and some results for the Plackett-Burman design of 12 runs are presented.
A Weighted Moving Average Process For Forecasting, Shou Hsing Shih, Chris P. Tsokos
A Weighted Moving Average Process For Forecasting, Shou Hsing Shih, Chris P. Tsokos
Journal of Modern Applied Statistical Methods
The object of the present study is to propose a forecasting model for a nonstationary stochastic realization. The subject model is based on modifying a given time series into a new k-time moving average time series to begin the development of the model. The study is based on the autoregressive integrated moving average process along with its analytical constrains. The analytical procedure of the proposed model is given. A stock XYZ selected from the Fortune 500 list of companies and its daily closing price constitute the time series. Both the classical and proposed forecasting models were developed and a comparison …
Comparing Different Methods For Multiple Testing In Reaction Time Data, Massimiliano Pastore, Massimo Nucci, Giovanni Galfano
Comparing Different Methods For Multiple Testing In Reaction Time Data, Massimiliano Pastore, Massimo Nucci, Giovanni Galfano
Journal of Modern Applied Statistical Methods
Reaction times were simulated for examining the power of six methods for multiple testing, as a function of sample size and departures from normality. Power estimates were low for all methods for non-normal distributions. With normal distributions, even for small sample sizes, satisfactory power estimates were observed, especially for FDR-based procedures.
Two-Stage Short-Run (X, Mr) Control Charts, Matthew E. Elam, Kenneth E. Case
Two-Stage Short-Run (X, Mr) Control Charts, Matthew E. Elam, Kenneth E. Case
Journal of Modern Applied Statistical Methods
This article is the first in a series of two articles that applies two-stage short-run control charting to (X, MR) charts. Theory is developed and then used to derive the control chart factor equations. In the sequel, the control chart factor calculations are computerized and an example is presented.
Confidence Intervals For The Squared Multiple Semipartial Correlation Coefficient, James Algina, H. J. Keselman, Randall D. Penfield
Confidence Intervals For The Squared Multiple Semipartial Correlation Coefficient, James Algina, H. J. Keselman, Randall D. Penfield
Journal of Modern Applied Statistical Methods
The squared multiple semipartial correlation coefficient is the increase in the squared multiple correlation coefficient that occurs when two or more predictors are added to a multiple regression model. Coverage probability was investigated for two variations of each of three methods for setting confidence intervals for the population squared multiple semipartial correlation coefficient. Results indicated that the procedure that provides coverage probability in the [.925, .975] interval for a 95% confidence interval depends primarily on the number of added predictors. Guidelines for selecting a procedure are presented.
On A Test Of Independence Via Quantiles That Is Sensitive To Curvature, Rand R. Wilcox
On A Test Of Independence Via Quantiles That Is Sensitive To Curvature, Rand R. Wilcox
Journal of Modern Applied Statistical Methods
Let (Yi ,Xi ) , i =1,..., n , be a random sample from some p+1 variate distribution where Xi is a vector having length p. Many methods for testing the hypothesis that Y is independent of X are relatively insensitive to a broad class of departures from independence. Power improvements focus on the median of Y or some other quantile and test the hypothesis that the regression surface is a horizontal plane versus some unknown form. A wild bootstrap method (Stute et al. 1998) can be used based on quantiles, but with small or moderate sample …
A Monte Carlo Power Analysis Of Traditional Repeated Measures And Hierarchical Multivariate Linear Models In Longitudinal Data Analysis, Hua Fang, Gordon P. Brooks, Maria L. Rizzo, Kimberly A. Espy, Robert S. Barcikowski
A Monte Carlo Power Analysis Of Traditional Repeated Measures And Hierarchical Multivariate Linear Models In Longitudinal Data Analysis, Hua Fang, Gordon P. Brooks, Maria L. Rizzo, Kimberly A. Espy, Robert S. Barcikowski
Journal of Modern Applied Statistical Methods
The power properties of traditional repeated measures and hierarchical linear models have not been clearly determined in the balanced design for longitudinal studies in the current literature. A Monte Carlo power analysis of traditional repeated measures and hierarchical multivariate linear models are presented under three variance-covariance structures. Results suggest that traditional repeated measures have higher power than hierarchical linear models for main effects, but lower power for interaction effects. Significant power differences are also exhibited when power is compared across different covariance structures. Results also supplement more comprehensive empirical indexes for estimating model precision via bootstrap estimates and the approximate …
Estimating How Many Observations Are Needed To Obtain A Required Level Of Reliability, David A. Walker
Estimating How Many Observations Are Needed To Obtain A Required Level Of Reliability, David A. Walker
Journal of Modern Applied Statistical Methods
This article provides a detailed table containing estimations of how many observations are needed to obtain an increased reliability coefficient for situations such as observational data collection in the classroom. A SPSS program is provided for users to analyze situations where an initial reliability value is obtained and the user wants to determine how many more observations are needed to reach a required level of reliability.
Tests For Independence In Two-Way Contingency Tables With Small Samples, Stephen Sharp
Tests For Independence In Two-Way Contingency Tables With Small Samples, Stephen Sharp
Journal of Modern Applied Statistical Methods
When testing the null hypothesis of independence in a two-way contingency table, the likelihood ratio test statistic is approximately distributed as Chi-squared d for large sample sizes (N) but may not be for small samples. This paper presents expressions which match the mean of the statistic to Chi-squared d as far as N−1 and N−2, derives a method of estimating the expressions from observed data and evaluates them using Monte Carlo simulations. It is concluded that using appropriate dividing factors, rejection rates after matching are more accurate than for either the unadjusted likelihood ratio statistic …
Utility Of Weights For Weighted Kappa As A Measure Of Interrater Agreement On Ordinal Scale, Moonseong Heo
Utility Of Weights For Weighted Kappa As A Measure Of Interrater Agreement On Ordinal Scale, Moonseong Heo
Journal of Modern Applied Statistical Methods
Kappa statistics, unweighted or weighted, are widely used for assessing interrater agreement. The weights of the weighted kappa statistics in particular are defined in terms of absolute and squared distances in ratings between raters. It is proposed that those weights can be used for assessment of interrater agreements. A closed form expectations and variances of the agreement statistics referred to as AI1 and AI2, functions of absolute and squared distances in ratings between two raters, respectively, are obtained. AI1 and AI2 are compared with the weighted and unweighted kappa statistics in …
Robustness Of Some Estimators Of Linear Model With Autocorrelated Error Terms When Stochastic Regressors Are Normally Distributed, Kayode Ayinde, J. O. Olaomi
Robustness Of Some Estimators Of Linear Model With Autocorrelated Error Terms When Stochastic Regressors Are Normally Distributed, Kayode Ayinde, J. O. Olaomi
Journal of Modern Applied Statistical Methods
Performances of estimators of the linear model under different level of autocorrelation (ρ) are known to be affected by different specifications of regressors. The robustness of some methods of parameter estimation of linear model to autocorrelation are examined when stochastic regressors are normally distributed. Monte Carlo experiments were conducted at both low and high replications. Comparison and preference of estimator(s) are based on their performances via bias, absolute bias, variance and more importantly the mean squared error of the estimated parameters of the model. Results show that the performances of the estimators improve with increased replication. In estimating …
Jacques Salomon Hadamard And The Use Of Symbols In Teaching Differential Calculus, Daniel S. Drucker, Claude Schochet, John Cuzzocrea, Shlomo Sawilowsky
Jacques Salomon Hadamard And The Use Of Symbols In Teaching Differential Calculus, Daniel S. Drucker, Claude Schochet, John Cuzzocrea, Shlomo Sawilowsky
Journal of Modern Applied Statistical Methods
Scripta Universitatis, edited by Albert Einstein and first published in 1923, played a significant role in the establishment of Hebrew University in Jerusalem. Articles appeared on the left half of the journal in the author’s chosen language and they were translated into Hebrew on the right half. The inaugural issue contained an article by the French mathematician Jacques Hadamard (8 December 1865 – 17 October 1963). Y. Wolfson of Kharkov translated it into Hebrew. An English translation is presented here, along with scans of the original first pages that were published in French and Hebrew. Documents pertaining to the …
On Measuring The Relative Importance Of Explanatory Variables In A Logistic Regression , D. Roland Thomas, Pengcheng Zhu, Bruno D. Zumbo, Shantanu Dutta
On Measuring The Relative Importance Of Explanatory Variables In A Logistic Regression , D. Roland Thomas, Pengcheng Zhu, Bruno D. Zumbo, Shantanu Dutta
Journal of Modern Applied Statistical Methods
A search is described for valid methods of assessing the importance of explanatory variables in logistic regression, motivated by earlier work on the relationship between corporate governance variables and the issuance of restricted voting shares (RSF). The methods explored are adaptations of Pratt’s (1987) approach for measuring variable importance in simple linear regression, which is based on a special partition of R2. Pseudo-R2 measures for logistic regression are briefly reviewed, and two measures are selected which can be partitioned in a manner analogous to that used by Pratt. One of these is ultimately selected for the variable …
Using Exploratory Factor Analysis For Locating Invariant Referents In Factor Invariance Studies, W. Holmes Finch, Brian F. French
Using Exploratory Factor Analysis For Locating Invariant Referents In Factor Invariance Studies, W. Holmes Finch, Brian F. French
Journal of Modern Applied Statistical Methods
Model identification in multi-group confirmatory factor analysis (MCFA) requires an equality constraint of referent variables across groups. Invariance assumption violations make it difficult to locate parameters that actually differ. Suggested procedures for locating invariant referents are cumbersome, complex, and provide imperfect results. Exploratory factor analysis (EFA) may be an alternative because of its ease of use, yet empirical evaluation of its effectiveness is lacking. EFAs accuracy for distinguishing invariant from non-invariant referents was examined.
Probability Of Coverage And Interval Length For Two-Group Techniques Assessing The Median And Trimmed Mean, S. Jonathan Mends-Cole
Probability Of Coverage And Interval Length For Two-Group Techniques Assessing The Median And Trimmed Mean, S. Jonathan Mends-Cole
Journal of Modern Applied Statistical Methods
The purpose of the present study was to assess the probability of coverage and interval length of selected statistical techniques that have a higher finite sample breakdown point than the mean and appropriate levels of probability of coverage when using Bradley’s (1978) criterion. The techniques were examined using real education and psychology datasets (Sawilowsky & Fahoome, 2003, Sawilowsky & Blair, 1992). Welch’s test exhibited appropriate coverage for the smooth symmetric, mass at zero, digit preference, and extreme bimodal distributions. Yuen’s technique performed well under an extreme bimodal distribution. Results concerning the Maritz-Jarrett and the McKean-Schrader techniques are also presented.
Test For Spatio-Temporal Counts Being Poisson, Haiyan Chen, Howard H. Stratton
Test For Spatio-Temporal Counts Being Poisson, Haiyan Chen, Howard H. Stratton
Journal of Modern Applied Statistical Methods
The new Log-Linear Test (TL) is proposed to identify when the Poisson model fails for a collection of count random variables. TL is shown to have better rejection rate with small sample size and essentially the same power compared to a classical Fisher-Bohning’s Statistic TF for standard alternatives to Poisson.