Performance of traditional f tests in repeated measures designs under covariance heterogeneity

This study investigates the performance of two traditional F tests, one for main effects and the other for interaction in repeated measures designs under several conditions of covariance heterogeneity. Overall, the test for interaction is more vulnerable than the one for main effects. Distortion in the level of significance is less serious for the case of equal group size.     

Continuity of f-projections and applications to the iterative proportional fitting procedure*

This paper proves continuity of f-projections and the continuous dependence of the limit matrix of the iterative proportional fitting procedure (IPF procedure) on the given matrix as well as the given marginals under certain regularity constraints. For finite spaces, the concept of f-projections of finite measures on a compact and convex set is introduced and continuity of f-projections is proven. This result is applied to the IPF procedure. Given a nonnegative matrix as well as row and column marginals the IPF procedure generates a sequence of matrices, called the IPF sequence, by alternately fitting rows and columns to match their respective marginals. The procedure is equivalent to cyclic f-projections. If the IPF sequence converges, the application of the continuity of f-projections yields the continuous dependence of the limit matrix on the given matrix. By generalized convex programming and under some constraints, it is shown that the limit matrix of the IPF sequence continuously depends not only on the given matrix but also on the marginals.     

Regression for non-Euclidean data using distance matrices

Regression methods for common data types such as measured, count and categorical variables are well understood but increasingly statisticians need ways to model relationships between variable types such as shapes, curves, trees, correlation matrices and images that do not fit into the standard framework. Data types that lie in metric spaces but not in vector spaces are difficult to use within the usual regression setting, either as the response and/or a predictor. We represent the information in these variables using distance matrices which requires only the specification of a distance function. A low-dimensional representation of such distance matrices can be obtained using methods such as multidimensional scaling. Once these variables have been represented as scores, an internal model linking the predictors and the responses can be developed using standard methods. We call scoring as the transformation from a new observation to a score, whereas backscoring is a method to represent a score as an observation in the data space. Both methods are essential for prediction and explanation. We illustrate the methodology for shape data, unregistered curve data and correlation matrices using motion capture data from an experiment to study the motion of children with cleft lip.     

Weighted Stochastic Restricted Estimation in Linear Measurement Error Models

This article discusses the consistent estimation of the parameters in a linear measurement error model when stochastic linear restrictions on regression coefficients are available. We propose some methodologies to obtain the consistent estimation when either the covariance matrix of the measurement errors or the reliability matrix of independent variables is known. Their finite- and large-sample properties are derived with not necessarily normal errors. A Monte Carlo simulation is carried out to study the the finite properties of the estimators.     

Finding environmentally important industry clusters: Multiway cut approach using nonnegative matrix factorization

This paper proposes an optimal combinatorial method for finding groups of industries with relatively large CO₂ emissions through industrial relations. Using an economic input–output table, we estimated a non-symmetric matrix describing how much CO₂ is emitted in producing the commodity of industry i, which was purchased to produce commodity of industry j, to meet the final demand for a specific commodity. A symmetric strength of relations matrix describing the CO₂ emissions associated with the industrial relations was further estimated using the non-symmetric matrix. The strength of relations matrix can be viewed as a representation of the supply-chain network of the final commodity. In this study, we estimated the strength of relations matrix associated with the final demand for automobiles and applied the multiway cut approach using nonnegative matrix factorization to the matrix in order to find environmentally important industry clusters in the Japanese automobile supply chain. According to our empirical results, the optimal number of industry clusters is 19, and 4 industry clusters are playing a key role in CO₂ emission reduction.     

On the simple step-stress model for two-parameter exponential distribution

In this paper, we consider the simple step-stress model for a two-parameter exponential distribution, when both the parameters are unknown and the data are Type-II censored. It is assumed that under two different stress levels, the scale parameter only changes but the location parameter remains unchanged. It is observed that the maximum likelihood estimators do not always exist. We obtain the maximum likelihood estimates of the unknown parameters whenever they exist. We provide the exact conditional distributions of the maximum likelihood estimators of the scale parameters. Since the construction of the exact confidence intervals is very difficult from the conditional distributions, we propose to use the observed Fisher Information matrix for this purpose. We have suggested to use the bootstrap method for constructing confidence intervals. Bayes estimates and associated credible intervals are obtained using the importance sampling technique. Extensive simulations are performed to compare the performances of the different confidence and credible intervals in terms of their coverage percentages and average lengths. The performances of the bootstrap confidence intervals are quite satisfactory even for small sample sizes.     

A simplified proof of a theorem on the difference of the moore–penrose inverses of two positive semi–difinte matrices

Simplified proofs are given of a standard result that establishes positive semi–definiteness of the difference of the inverses of two non–singular matrices, and of the extension of this result by Milliken and Akdeniz (1977) to the difference of the Moore–Penrose inverse of two singular matrices.     

Production scheduling in SMT electronic boards assembly

This paper tackles the problem of scheduling in the assembly of SMT electronic boards. In particular, it focuses on a new scheduling method developed within the framework of an industry-university joint research project. The scheduling system aims at minimizing the makespan; this goal is achieved by reducing setup times and idle times of the machines. As an example, the outcome of a test carried out on a production mix made up of 10 board types is presented and analyzed in a summarized form.     

Exploring types of interference between work and non-work: using a diary study approach

Studies of work and family issues have used predominately between-subject cross-sectional designs. While some researchers have called for more longitudinal studies, others have suggested that a more strategic way forward for the field is the use of daily diary studies (Frone, Russell, & Cooper, 1992). This study explores different types of interference between work and non-work domains, using a diary study methodology. This study consisted of a two-week diary study among 12 Irish employees. Analysis involved a two-step procedure involving both content analysis and interpretative phenomenological analysis (IPA). Results indicated that while individuals reported strain-based and time-based interference, evidence was also found of interference concerning persistent and intrusive thoughts. Despite some limitations to the study, this paper demonstrates that diary studies represent an opportunity for researchers to explore work and non-work experiences in a sensitive and ecologically valid way.