In studies that produce data with spatial structure, it is common that covariates of interest vary spatially in addition to the error. Because of this, the error and covariate are often correlated. When this occurs, it is difficult to distinguish the covariate effect from residual spatial variation. In an i.i.d. normal error setting, it is well known that this type of correlation produces biased coefficient estimates, but predictions remain unbiased. In a spatial setting, recent studies have shown that coefficient estimates remain biased, but spatial prediction has not been addressed. The purpose of this paper is to provide a more detailed study of coefficient estimation from spatial models when covariate and error are correlated and then begin a formal study regarding spatial prediction. This is carried out by investigating properties of the generalized least squares estimator and the best linear unbiased predictor when a spatial random effect and a covariate are jointly modelled. Under this setup, we demonstrate that the mean squared prediction error is possibly reduced when covariate and error are correlated.

Appropriate control interventions are necessary to show the treatment effect of dry needling. Different control procedures, such as dry needling of the contralateral side, and sham treatments, such as random and superficial needle insertion, have been utilized in trials. However, those methods might elicit a physiological response and are subsequently not ideal for use as a control. This descriptive study illustrates the construction of low-cost sham dry needles and evaluates their validity. Forty-two healthy asymptomatic subjects received either sham or real dry needling intervention to their right gluteal muscles and reported if they felt that the needle pierced the skin. They also graded the severity and qualified (sharp or dull) the pain associated with the intervention. The results showed that most of the subjects in both groups believed the needle penetrated the skin. The quantity of pain associated with the treatment was similar in both groups, but the quality assigned was different. The authors conclude that sham dry needling can be accomplished and used as a valid control treatment in dry needling research using these low-cost sham needles.

While it is generally recognized that the relative importance of different skills is not constant across different positions on a basketball team, quantification of the differences has not been well studied. 1163 box scores from games in the National Basketball Association during the 1996-97 season were used to study the relationship of skill performance by position and game outcome as measured by point differentials. A hierarchical Bayesian model was fit with individual players viewed as a draw from a population of players playing a particular position: point guard, shooting guard, small forward, power forward, center, and bench. Posterior distributions for parameters describing position characteristics were examined to discover the relative importance of various skills as quantified in box scores across the positions. Results were consistent with expectations, although defensive rebounds from both point and shooting guards were found to be quite important.

When modeling geostatistical or areal data, spatial structure is commonly accommodated via a covariance function for the former and a neighborhood structure for the latter. In both cases the resulting spatial structure is a consequence of implicit spatial grouping in that observations near in space are assumed to behave similarly. It would be desirable to develop spatial methods that explicitly model the partitioning of spatial locations providing more control over resulting spatial structures and being able to better balance global vs local spatial dependence. To this end, we extend product partition models to a spatial setting so that the partitioning of locations into spatially dependent clusters is explicitly modeled. We explore the spatial structures that result from employing a spatial product partition model and demonstrate its flexibility in accommodating many types of spatial dependencies. We illustrate the method's utility through simulation studies and an education application. Computational techniques with additional simulations and examples are provided in a Supplementary Material file available online.

Context Chronic ankle instability (CAI) is characterized by multiple sensorimotor deficits, affecting strength, postural control, motion, and movement. Identifying specific deficits is the key to developing appropriate interventions for this patient population; however, multiple movement strategies within this population may limit the ability to identify specific movement deficits. Objective To identify specific movement strategies in a large sample of participants with CAI and to characterize each strategy relative to a sample of uninjured control participants. Design Descriptive laboratory study. Setting Biomechanics laboratory. Patients or Other Participants A total of 200 individuals with CAI (104 men, 96 women; age = 22.3 ± 2.2 years, height = 174.2 ± 9.5 cm, mass = 72.0 ± 14.0 kg) were selected according to the inclusion criteria established by the International Ankle Consortium and were fit into clusters based on movement strategy. A total of 100 healthy individuals serving as controls (54 men, 46 women; age = 22.2 ± 3.0 years, height = 173.2 ± 9.2 cm, mass = 70.7 ± 13.4 kg) were compared with each cluster. Main Outcome Measure(s) Lower extremity joint biomechanics and ground reaction forces were collected during a maximal vertical jump landing, followed immediately by a side cut. Data were reduced to functional output or curves, kinematic data from the frontal and sagittal planes were reduced to a single representative curve for each plane, and representative curves were clustered using a Bayesian clustering technique. Estimated functions for each dependent variable were compared with estimated functions from the control group to describe each cluster. Results Six distinct clusters were identified from the frontal-plane and sagittal-plane data. Differences in joint angles, joint moments, and ground reaction forces between clusters and the control group were also identified. Conclusions The participants with CAI demonstrated 6 distinct movement strategies, indicating that CAI could be characterized by multiple distinct movement alterations. Clinicians should carefully evaluate patients with CAI for sensorimotor deficits and quality of movement to determine the appropriate interventions for treatment.