Performance of Confidence Intervals in Regression Models with Unbalanced One-Fold Nested Error Structures

Abstract

In this article we consider the problem of constructing confidence intervals for a linear regression model with unbalanced nested error structure. A popular approach is the likelihood-based method employed by PROC MIXED of SAS. In this article, we examine the ability of MIXED to produce confidence intervals that maintain the stated confidence coefficient. Our results suggest that intervals for the regression coefficients work well, but intervals for the variance component associated with the primary level cannot be recommended. Accordingly, we propose alternative methods for constructing confidence intervals on the primary level variance component. Computer simulation is used to compare the proposed methods. A numerical example and SAS code are provided to demonstrate the methods.     

A MODEL FOR BATCH ADVANCED AVAILABLE‐TO‐PROMISE

The available‐to‐promise (atp) function is becoming increasingly important in supply chain management since it directly links production resources with customer orders. In this paper, a mixed integer programming (mip) ATP model is presented. This model can provide an order‐promising and ‐fulfillment solution for a batch of orders that arrive within a predefined batching interval. A variety of constraints, such as raw material availability, production capacity, material compatibility, and customer preferences, are considered. Simulation experiments using the model investigate the sensitivity of supply chain performance to changes in certain parameters, such as batching interval size and customer order flexibility.     

Some Notes on Refereeing

Analysis of longitudinal data using a general linear mixed model requires the specification of a form for the covariance matrix of within-subject observations. Graphical diagnostics, such as the scatterplot matrix, can be of substantial help in making this specification. I introduce another graphical diagnostic, the Partial-Regression-on-Intervenors Scatterplot Matrix (PRISM), which complements the ordinary scatterplot matrix and which is more useful for identifying certain kinds of correlation structures. PRISMs corresponding to several commonly used correlation structures are displayed. The PRISM's usefulness in model specification is illustrated with an example of longitudinal data from a 100-kilometer road race.     

TECHNICAL NOTE: A SIMPLE MODEL FOR OPTIMIZING THE SINGLE MACHINE EARLY/TARDY PROBLEM WITH SEQUENCE-DEPENDENT SETUPS

A simple mixed integer programming model for the N job/single machine scheduling problem with possibly sequence-dependent setup times, differing earliness/tardiness cost penalties, and variable due dates is proposed and evaluated for computational efficiency. Results indicated that the computational effort required to reach optimality rose with the number of jobs to be scheduled and with decreased variance in due dates. Though computational effort was significant for the largest problems solved, the model remained viable for optimizing research scale problems.     

Accounting for variability in individual hierarchical clinical trial data

Meta-analytical approaches have been extensively used to analyze medical data. In most cases, the data come from different studies or independent trials with similar characteristics. However, these methods can be applied in a broader sense. In this paper, we show how existing meta-analytic techniques can also be used as well when dealing with parameters estimated from individual hierarchical data. Specifically, we propose to apply statistical methods that account for the variances (and possibly covariances) of such measures. The estimated parameters together with their estimated variances can be incorporated into a general linear mixed model framework. We illustrate the methodology by using data from a first-in-man study and a simulated data set. The analysis was implemented with the SAS procedure MIXED and example code is offered.     

A BRANCH AND BOUND PROCEDURE FOR SETUP PROBLEMS IN FLEXIBLE MANUFACTURING SYSTEMS

We address a medium- to short-term production planning problem in a flexible manufacturing environment. First we present a single-machine, mixed integer programming model for part type selection and lot-sizing problems over a T-period planning horizon. Demand for part types changes dynamically through the periods. The objective is to meet the demand for part types during the periods they are demanded. Available machine time and tool magazine capacities are the system constraints in our models. We next extend on the single- machine model to include multiple machines. In addition to part type selection and lotsizing decisions, the extended model also addresses the machine-loading decision. We present exact branch and bound procedures based on linear programming relaxations for the two models. We also report the results of our computational experiments.