Statistical Theory Commons^™

On A Test Of Independence Via Quantiles That Is Sensitive To Curvature, Rand R. Wilcox

Journal of Modern Applied Statistical Methods

Let (Y_i ,X_i ) , i =1,..., n , be a random sample from some p+1 variate distribution where X_i 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

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

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

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

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

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

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

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

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

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

Journal of Modern Applied Statistical Methods

The new Log-Linear Test (T_L) is proposed to identify when the Poisson model fails for a collection of count random variables. T_L is shown to have better rejection rate with small sample size and essentially the same power compared to a classical Fisher-Bohning’s Statistic T_F for standard alternatives to Poisson.

Measuring Overall Heterogeneity In Meta-Analyses: Application To Csf Biomarker Studies In Alzheimer’S Disease, Chengjie Xiong, Feng Gao, Yan Yan, Jingqin Luo, Yunju Sung, Gang Shi

Journal of Modern Applied Statistical Methods

The interpretations of statistical inferences from meta-analyses depend on the degree of heterogeneity in the meta-analyses. Several new indices of heterogeneity in meta-analyses are proposed, and assessed the variation/difference of these indices through a large simulation study. The proposed methods are applied to biomakers of Alzheimer’s disease.

When Sensitivity Is A Function Of Age And Time Spent In The Preclinical State In Periodic Cancer Screening, Dongfeng Wu, Ricolindo L. Cariño, Xiaoqin Wu

Journal of Modern Applied Statistical Methods

Probability models are extended for periodic cancer screening trials to model sensitivity when it is changing with an individual’s age and time spent in the preclinical state. Wu et al. (2005) showed that sensitivity is monotone increasing with age, but intuitively, sensitivity is also a function of the time one has spent in the preclinical stage. This allows us to infer sensitivity at a late stage, just before symptoms manifest. We developed the probability model and applied Bayesian inference to the HIP study group data. The methodology we developed is also applicable to other kinds of chronic diseases.

Log-Linear Model To Assess Socioeconomic And Environmental Factors With Childhood Diarrhea Using Hospital Based Surveillance, Krishnan Rajendran, Thandavarayan Ramamurthy, Sujit Kumar Bhattacharya

Journal of Modern Applied Statistical Methods

Categorical outcomes with environment factors analyzed by log linear model are frequent in the environmental epidemiological literature. Epidemiological and socio-economical factors were obtained on 1,119 children below the age of 5 from Infectious Diseases Hospital (IDH) at the Kolkata, India. Significant associations of diarrhea were observed in the rural areas with family income, father’s occupation as a daily labor, literacy of parents, non-cemented floor and wall constructed of mud, and type of storage (wide mouthed earthen pot). The results of the study with specific Log linear model confirm environmental factors were important implications for childhood diarrhea in the rural community. …

Robust General Linear Models And Graphics Via A User Interface (Web Rglm), Kimberly Crimin, Asheber Abebe, Joseph W. Mckean

Journal of Modern Applied Statistical Methods

Rank-based procedures provide superior estimation and testing techniques when the data deviate from normality or contain gross outliers. However, these robust techniques are rarely incorporated in a nonparametric statistics or methods courses due to the lack of computational tools. One reason for this is the existence of certain unavoidable complexities in the numerical methods due to the absence of a closedform solution for the rank estimation problem. This article introduces a user interface, Web RGLM, which may be used to perform rank-based analyses of linear models across the World Wide Web. These models include simple location problems to complicated ANOVA …

Effect On Recreation Benefit Estimates From Correcting For On-Site Sampling Biases And Heterogeneous Trip Overdispersion In Count Data Recreation Demand Models (Stata), Roberto Martínez-Espiñeira, Joseph M. Hilbe

Journal of Modern Applied Statistical Methods

Correction procedures (STATA commands NBSTRAT and GNBSTRAT) are applied to simultaneously account for zero-truncation, endogenous stratification, and overdispersion, and also consider heterogeneity in the overdispersion parameter. Their effect is shown on welfare estimates from previous studies, confirming that the routines perform the appropriate correction and only when endogenous stratification is expected.

Computing Multivariate Process Capability Indices (Excel), Michele Scagliarini, Raffaele Vermiglio

Journal of Modern Applied Statistical Methods

In manufacturing industry there is growing interest in measures of process capability under multivariate setting. Although there are many statistical packages to assess univariate capability, a current problem with the multivariate measures of capability is the shortage of user friendly software. In this article a Visual Basic program has been developed to realize an Excel spreadsheet that may be used to compute two multivariate measures of capability. The aim of this article is to provide a useful tool for practitioners dealing with multivariate capability assessment problems. The features of the program include easy data entry and clear report format.

Logit Estimation Using Warner’S Randomized Response Model, Zawar Hussain, Javid Shabbir

Journal of Modern Applied Statistical Methods

A modified hidden logit estimation procedure is presented based on Warner (1965) randomized response model. Monte Carlo simulations explore the behavior of this estimator and compare its performance with the ordinary logits estimator. Warner’s model is more protective and less jeopardizing.

Estimation Of Covariance Matrix In Signal Processing When The Noise Covariance Matrix Is Arbitrary, Madhusudan Bhandary

Journal of Modern Applied Statistical Methods

An estimator of the covariance matrix in signal processing is derived when the noise covariance matrix is arbitrary based on the method of maximum likelihood estimation. The estimator is a continuous function of the eigenvalues and eigenvectors of the matrix Σ̂₁^1/2S^∗Σ̂₁^1/2, where S^∗ is the sample covariance matrix of observations consisting of both noise and signals and Σ̂₁ is the estimator of covariance matrix based on observations consisting of noise only. Strong consistency and asymptotic normality of the estimator are briefly discussed.

On The Length Of Nhl Shootouts, W. J. Hurley

Journal of Modern Applied Statistical Methods

When NHL teams are tied after 60 minutes of regulation time and 5 minutes of sudden-death overtime, they go to a shootout to determine who gets the overtime point. Teams alternate shots until a winner is determined. The probability of observing shootouts of various lengths is calculated.

Properties Of Monotonic Effects On Directed Acyclic Graphs, Tyler J. Vanderweele, James M. Robins

COBRA Preprint Series

Various relationships are shown hold between monotonic effects and weak monotonic effects and the monotonicity of certain conditional expectations. Counterexamples are provided to show that the results do not hold under less restrictive conditions. Monotonic effects are furthermore used to relate signed edges on a causal directed acyclic graph to qualitative effect modification. The theory is applied to an example concerning the direct effect of smoking on cardiovascular disease controlling for hypercholesterolemia. Monotonicity assumptions are used to construct a test for whether there is a variable that confounds the relationship between the mediator, hypercholesterolemia, and the outcome, cardiovascular disease.

Uncertainty Assessment Of Aircraft Maintenance Times By Using Evidence Theory And Expert Judgment Elicitation, Huseyin Kudak

Engineering Management & Systems Engineering Theses & Dissertations

The goal of this study is to demonstrate the use of the Dempster-Shafer Theory of evidence as a decision aid to predict aircraft maintenance times during wartime operations using expert judgment elicitation. Increased precision in time estimation enables the jet engine aircraft maintenance facility commander to make more accurate decisions for the Air Force's wartime tactical operations allowing the commander to gain a decisive advantage. A questionnaire was designed to elicit judgments from experts in the Aircraft Maintenance Facility (AMF) to investigate maintenance times of the major failure modes (Ignition, Fuel, and Electrical). Results of the expert judgment elicitation were …

The Construction And Analysis Of Adaptive Group Sequential Designs, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In order to answer scientific questions of interest one often carries out an ordered sequence of experiments generating the appropriate data over time. The design of each experiment involves making various decisions such as 1) What variables to measure on the randomly sampled experimental unit?, 2) How regularly to monitor the unit, and for how long?, 3) How to randomly assign a treatment or drug-dose to the unit?, among others. That is, the design of each experiment involves selecting a so called treatment mechanism/monitoring mechanism/ missingness/censoring mechanism, where these mechanisms represent a formally defined conditional distribution of one of these …

Empirical Null And False Discovery Rate Inference For Exponential Families, Armin Schwartzman

Harvard University Biostatistics Working Paper Series

No abstract provided.

Marginal Structural Models For Partial Exposure Regimes, Stijn Vansteelandt, Karl Mertens, Carl Suetens, Els Goetghebeur

Harvard University Biostatistics Working Paper Series

Intensive care unit (ICU) patients are ell known to be highly susceptible for nosocomial (i.e. hospital-acquired) infections due to their poor health and many invasive therapeutic treatments. The effects of acquiring such infections in ICU on mortality are however ill understood. Our goal is to quantify these effects using data from the National Surveillance Study of Nosocomial Infections in Intensive Care

Units (Belgium). This is a challenging problem because of the presence of time-dependent confounders (such as exposure to mechanical ventilation)which lie on the causal path from infection to mortality. Standard statistical analyses may be severely misleading in such settings …

Covariate Adjustment For The Intention-To-Treat Parameter With Empirical Efficiency Maximization, Daniel B. Rubin, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In randomized experiments, the intention-to-treat parameter is defined as the difference in expected outcomes between groups assigned to treatment and control arms. There is a large literature focusing on how (possibly misspecified) working models can sometimes exploit baseline covariate measurements to gain precision, although covariate adjustment is not strictly necessary. In Rubin and van der Laan (2008), we proposed the technique of empirical efficiency maximization for improving estimation by forming nonstandard fits of such working models. Considering a more realistic randomization scheme than in our original article, we suggest a new class of working models for utilizing covariate information, show …

A Bayesian Approach To Effect Estimation Accounting For Adjustment Uncertainty, Chi Wang, Giovanni Parmigiani, Ciprian Crainiceanu, Francesca Dominici

Johns Hopkins University, Dept. of Biostatistics Working Papers

Adjustment for confounding factors is a common goal in the analysis of both observational and controlled studies. The choice of which confounding factors should be included in the model used to estimate an effect of interest is both critical and uncertain. For this reason it is important to develop methods that estimate an effect, while accounting not only for confounders, but also for the uncertainty about which confounders should be included. In a recent article, Crainiceanu et al. (2008) have identified limitations and potential biases of Bayesian Model Averaging (BMA) (Raftery et al., 1997; Hoeting et al., 1999)when applied to …

Estimation Of Controlled Direct Effects, Sylvie Goetgeluk, Stijn Vansteelandt, Els Goetghebeur

Harvard University Biostatistics Working Paper Series

No abstract provided.

Using Regression Models To Analyze Randomized Trials: Asymptotically Valid Hypothesis Tests Despite Incorrectly Specified Models, Michael Rosenblum, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Regression models are often used to test for cause-effect relationships from data collected in randomized trials or experiments. This practice has deservedly come under heavy scrutiny, since commonly used models such as linear and logistic regression will often not capture the actual relationships between variables, and incorrectly specified models potentially lead to incorrect conclusions. In this paper, we focus on hypothesis test of whether the treatment given in a randomized trial has any effect on the mean of the primary outcome, within strata of baseline variables such as age, sex, and health status. Our primary concern is ensuring that such …

Geostatistical Inference Under Preferential Sampling, Peter J. Diggle, Raquel Menezes, Ting-Li Su

Johns Hopkins University, Dept. of Biostatistics Working Papers

Geostatistics involves the fitting of spatially continuous models to spatially discrete data (Chil`es and Delfiner, 1999). Preferential sampling arises when the process that determines the data-locations and the process being modelled are stochastically dependent. Conventional geostatistical methods assume, if only implicitly, that sampling is non-preferential. However, these methods are often used in situations where sampling is likely to be preferential. For example, in mineral exploration samples may be concentrated in areas thought likely to yield high-grade ore. We give a general expression for the likelihood function of preferentially sampled geostatistical data and describe how this can be evaluated approximately using …