Estimating Benchmark Exposure for Air Particulate Matter Using Latent Class Models

We performed benchmark exposure (BME) calculations for particulate matter when multiple dichotomous outcome variables are involved using latent class modeling techniques and generated separate results for both the extra risk and additional risk. The use of latent class models in this study is advantageous because it combined several outcomes into just two classes (namely, a high‐risk class and a low‐risk class) and compared these two classes to obtain the BME levels. This novel approach addresses a key problem in risk estimation—namely, the multiple comparisons problem, where separate regression models are fitted for each outcome variable and the reference exposure will rely on the results of the best‐fitting model. Because of the complex nature of the estimation process, the bootstrap approach was used to estimate the reference exposure level, thereby reducing uncertainty in the obtained values. The methodology developed in this article was applied to environmental data by identifying unmeasured class membership (e.g., morbidity vs. no morbidity class) among infants in utero using observed characteristics that included low birth weight, preterm birth, and small for gestational age.     

Convergence of Known Distributions to Limiting Normal or Non-normal Distributions: An Elementary Ratio Technique

This article presents an elementary informal technique for deriving the convergence of known distributions to limiting normal or non-normal distributions. The presentation should be of interest to teachers and students of first year graduate level courses in probability and statistics.     

The Effects of Quality of Life on National Elections: A Multi-Country Analysis

This paper studies the effects of several Quality ofLife (QOL) indicators on the outcomes of nationalelections. We test the hypothesis that declines innational QOL will have a negative effect on the votingsupport for the governing party in the next election. For each election since 1960 in thirteen countries, weuse objective measures of QOL for the previous year toestimate the voting function by using astate-of-the-art technique called Sliced InverseRegression (Li, 1991). These objective measuresinclude GDP per capita, food availability, inflation,crime rates, divorce rate, and percent of females inthe labor force, among others. The estimated votingfunction is the best predictor of voters' behavior asa function of the changes in QOL.The results show that changes in economic variablesand food availability significantly affect electionoutcomes. In addition, changes in crime rates werefound to be nearly as important as economic variablesin influencing the election outcomes. This marks thefirst time that a non-economic indicator has beenshown to affect elections. In contrast, measures ofsatisfaction with family life, such as divorce, infantmortality, and percent females in the workforce, showno effect on voting behavior, probably because votersdo not hold their governments responsible for familyaffairs.     

Dispersive ordering—Some applications and examples

A basic concept for comparing spread among probability distributions is that of dispersive ordering. Let X and Y be two random variables with distribution functions F and G, respectively. Let F ⁻¹ and G ⁻¹ be their right continuous inverses (quantile functions). We say that Y is less dispersed than X (Y≤ _disp X) if G ⁻¹(β)−G ⁻¹(α)≤F ⁻¹(β)−F ⁻¹(α), for all 0<α≤β<1. This means that the difference between any two quantiles of G is smaller than the difference between the corresponding quantiles of F. A consequence of Y≤ _disp X is that |Y ₁−Y ₂| is stochastically smaller than |X ₁−X ₂| and this in turn implies var(Y)≤var(X) as well as E[|Y ₁−Y ₂|]≤E[|X ₁−X ₂|], where X ₁, X ₂ (Y ₁, Y ₂) are two independent copies of X(Y). In this review paper, we give several examples and applications of dispersive ordering in statistics. Examples include those related to order statistics, spacings, convolution of non-identically distributed random variables and epoch times of non-homogeneous Poisson processes. This work was supported in part by KOSEF through Statistical Research Center for Complex Systems at Seoul National University. Subhash Kochar is thankful to Dr. B. Khaledi for many helpful discussions.     

Constructing Near Optimal Schedules for the Flow-Shop Lot Streaming Problem with Sublot-Attached Setups

Lot streaming—the process of splitting a production lot into sublots—has been a common practice in flow-shop systems during the past decade. Nevertheless, a major limiting assumption has been made in the analysis of these systems in that the setup time is, at most, lot-attached but not sublot-attached. In this paper, we consider the single and multiple batch flow-shop lot-streaming problems with sublot-attached setup times. A fast, optimal solution algorithm for the single batch problem is presented. For the multiple batch problem, we propose a near optimal solution procedure which is optimal in two-machine flow-shops. Computational results are also presented for the multiple batch problem which indicate both the efficiency and effectiveness of this procedure.     

Measurement Equivalence Using Generalizability Theory: An Examination of Manufacturing Flexibility Dimensions

As the field of decision sciences in general and operations management in particular has matured from theory building to theory testing over the past two decades, it has witnessed an explosion in empirical research. Much of this work is anchored in survey‐based methodologies in which data are collected from the field in the form of scale items that are then analyzed to measure latent unobservable constructs. It is important to assess the invariance of scales across groups in order to reach valid, scientifically sound conclusions. Because studies have often been conducted in the field of decision sciences with small sample sizes, it further exacerbates the problem of reaching incorrect conclusions. Generalizability theory can more effectively test for measurement equivalence in the presence of small sample sizes than the confirmatory factor analysis (CFA) tests that have been conventionally used for assessing measurement equivalency across groups. Consequently, we introduce and explain the generalizability theory (G‐theory) in this article to examine measurement equivalence of 24 manufacturing flexibility dimension scales that have been published in prior literature and also compare and contrast G‐theory with CFA. We show that all the manufacturing flexibility scales tested in this study were invariant across the three industry SIC groups from which data were collected. We strongly recommend that G‐theory should always be used for determining measurement equivalence in empirical survey‐based studies. In addition, because using G‐theory alone does not always reveal the complete picture, CFA techniques for establishing measurement equivalence should also be invoked when sample sizes are large enough to do so. Implications of G‐theory for practice and its future use in operations management and decision sciences research are also presented.     

Analytic evaluation of the expectation and variance of different performance measures of a schedule on a single machine under processing time variability

In this paper, we present closed-form expressions, wherever possible, or devise algorithms otherwise, to determine the expectation and variance of a given schedule on a single machine. We consider a variety of completion time and due date-based objectives. The randomness in the scheduling process is due to variable processing times with known means and variances of jobs and, in some cases, a known underlying processing time distribution. The results that we present in this paper can enable evaluation of a schedule in terms of both the expectation and variance of a performance measure considered, and thereby, aid in obtaining a stable schedule. Additionally, the expressions and algorithms that are presented, can be incorporated in existing scheduling algorithms in order to determine expectation-variance efficient schedules.     

Some competitors of the mood test for the two-sample scale problem

Let X_l,…,X_n (Y_l,…,Y_m) be a random sample from an absolutely continuous distribution with distribution function F(G).A class of distribution-free tests based on U-statistics is proposed for testing the equality of F and G against the alternative that X's are more dispersed then Y's. Let 2 ? C ? n and 2 ? d ? m be two fixed integers. Let ?_c,d(X_il,…,X_ic ; Y_jl,…,X_jd)=1(-1)when max as well as min of {X_il,…,X_ic ; Y_jl,…,Y_jd } are some X_i's (Y_j's)and zero oterwise. Let S_c,d be the U-statistic corresponding to ?_c,d.In case of equal sample sizes, S22 is equivalent to Mood's Statistic.Large values of S_c,d are significant and these tests are quite efficient     

A test for exponentiatity against hnbue alternatives

Neyman's asymptotically most powerful test in the class of al1 similar tests for testing exponentiality against a parametric class of Makeham alternatives is shown to be consistent for the much wider class of harmonic new better than used in expectation distributions.