D-Optimal Split-plot Designs With Random Whole Plot Factor and Fixed Sub-plot Factor

This study examines design preference in Completely Randomized (CR) split-plot experiments involving random whole plot factor effect and fixed sub-plot factor effect. Many previous works on optimally designing split-plot experiments assumed only factors with fixed levels. However, the cases where interests are on random factors have received little attention. These problems have similarities with optimal design of experiments for fixed parameters of non-linear models because the solution rely on the unknown parameters.  Design Space (DS) containing exhaustive list of balanced designs for a fixed sample size were compared for optimality using the product of determinants of derived information matrices of the Maximum Likelihood (ML) estimators equivalent to random and fixed effect in the model. Different magnitudes of components of variance configurations where variances of factor effects are larger than variances of error term were empirically used for the comparisons. The results revealed that the D-optimal designs are those with whole plot factor levels greater than replicates within each level of whole plot.

On MSE-Optimal Circular Crossover Designs

In crossover designs, each subject receives a series of treatments, one after the other in p consecutive periods. There is concern that the measurement of a subject at a given period might be influenced not only by the direct effect of the current treatment but also by a carryover effect of the treatment applied in the preceding period. Sometimes, the periods of a crossover design are arranged in a circular structure. Before the first period of the experiment itself, there is a run-in period, in which each subject receives the treatment it will receive again in the last period. No measurements are taken during the run-in period. We consider the estimate for direct effects of treatments which is not corrected for carryover effects. If there are carryover effects, this uncorrected estimate will be biased. In that situation, the quality of the estimate can be measured by the mean square error, the sum of the squared bias and the variance. We determine MSE-optimal designs, that is, designs for which the mean square error is as small as possible. Since the optimal design will in general depend on the size of the carryover effects, we also determine the efficiency of some designs compared to the locally optimal design. It turns out that circular neighbour-balanced designs are highly efficient.

Pairwise Balanced Designs From Cyclic PBIB Designs

A pairwise balanced designs was constructed using cyclic partially balanced incomplete block designs with either (λ1 – λ2) = 1 or (λ2 – λ1) = 1. This method of construction of Pairwise balanced designs is further generalized to construct it using cyclic partially balanced incomplete block design when |(λ1 – λ2)| = p. The methods of construction of pairwise balanced designs was supported with examples. A table consisting parameters of Cyclic PBIB designs and its corresponding constructed pairwise balanced design is also included.

Reevaluating the SIBTEST Classification Heuristics for Dichotomous Differential Item Functioning

A simulation study was conducted to investigate the heuristics of the SIBTEST procedure and how it compares with ETS classification guidelines used with the Mantel–Haenszel procedure. Prior heuristics have been used for nearly 25 years, but they are based on a simulation study that was restricted due to computer limitations and that modeled item parameters from estimates of ACT and ASVAB tests from 1987 and 1984, respectively. Further, suggested heuristics for data fitting a two-parameter logistic model (2PL) have essentially went unused since their original presentation. This simulation study incorporates a wide range of data conditions to recommend heuristics for both 2PL and three-parameter logistic (3PL) data that correspond with ETS’s Mantel–Haenszel heuristics. Levels of agreement between the new SIBTEST heuristics and Mantel–Haenszel heuristics were similar for 2PL data and higher than prior SIBTEST heuristics for 3PL data. The new recommendations provide higher true-positive rates for 2PL data. Conversely, they displayed decreased true-positive rates for 3PL data. False-positive rates, overall, remained below the level of significance for the new heuristics. Unequal group sizes resulted in slightly larger false-positive rates than balanced designs for both prior and new SIBTEST heuristics, with rates less than alpha levels for equal ability distributions and unbalanced designs versus false-positive rates slightly higher than alpha with unequal ability distributions and unbalanced designs.

On the Relationship between ANOVA Main Effects and Average Treatment Effects

In unbalanced designs, there is a controversy about which ANOVA type of sums of squares should be used for testing main effects and whether main effects should be considered at all in the presence of interactions. Looking at this problem from a causal inference perspective, we show in which designs and under which conditions the ANOVA main effects correspond to average treatment effects as defined in the causal inference literature. We consider balanced, proportional and nonorthogonal designs, and models with and without interactions. In balanced designs, main effects obtained by type I, II, and III sums of squares all correspond to the average treatment effect. This is also true for proportional designs except for ANOVA type III which leads to bias if there are interactions. In nonorthogonal designs, ANOVA type I is always highly biased and ANOVA type II and III are biased if there are interactions. In a simulation study, we confirm our theoretical results and examine the severity of bias under different conditions.

Design and evaluation of mobile monitoring campaigns for air pollution exposure assessment in epidemiologic cohorts

Mobile monitoring makes it possible to estimate the long-term trends of less commonly measured pollutants through the collection of repeated short-term samples. While many different mobile monitoring approaches have been taken, few studies have looked at the importance of study design when the goal is application to epidemiologic cohort studies. Air pollution concentrations include random variability and systematic variability, and we hypothesize that mobile campaigns benefit from temporally balanced designs that randomly sample from all seasons of the year, days of the week, and hours of the day. We carried out a simulation study of fixed-site monitors to better understand the role of short-term mobile monitoring design on the prediction of long-term air pollution exposure surfaces. Specifically, we simulated three archetypal sampling designs using oxides of nitrogen (NOx) monitoring data from 69 California air quality system (AQS) sites: (1) a year-around, Balanced Design, (2) a Rush Hours Design, and (3) a Business Hours Design. We used Monte Carlo resampling to investigate the range of possible outcomes (i.e., the resulting annual average concentration prediction) from each design against the “truth”, the actual monitoring data. We found that the Balanced Design consistently yielded the most accurate annual averages; Rush Hours and Business Hours Designs generally resulted in comparatively more biased estimates and model predictions. Importantly, the superior performance of the Balanced Design was evident when predictions were evaluated against true concentrations but less detectable when predictions were evaluated against the measurements from the same sampling campaign since these were themselves biased. This result is important since mobile monitoring campaigns that use their own measurements to test the robustness of the results may underestimate the level of bias in their results. Appropriate study design is crucial for mobile monitoring campaigns aiming to assess accurate long-term exposure in epidemiologic cohorts. Campaigns should aim to implement balanced designs that sample during all seasons of the year, days of the week, and all or most hours of the day to produce generally unbiased, long-term averages. Furthermore, differential exposure misclassification could result from unbalanced designs, which may result in misleading health effect estimates in epidemiologic investigations.