The Role of Conditional Likelihoods in Latent Variable Modeling

In psychometrics, the canonical use of conditional likelihoods is for the Rasch model in measurement. Whilst not disputing the utility of conditional likelihoods in measurement, we examine a broader class of problems in psychometrics that can be addressed via conditional likelihoods. Specifically, we consider cluster-level endogeneity where the standard assumption that observed explanatory variables are independent from latent variables is violated. Here, “cluster” refers to the entity characterized by latent variables or random effects, such as individuals in measurement models or schools in multilevel models and “unit” refers to the elementary entity such as an item in measurement. Cluster-level endogeneity problems can arise in a number of settings, including unobserved confounding of causal effects, measurement error, retrospective sampling, informative cluster sizes, missing data, and heteroskedasticity. Severely inconsistent estimation can result if these challenges are ignored.

An Empirical Validation of the Regression Point Displacement Design Using Within-Study Comparison Logic: Emerging Possibilities and Cautions

Background The regression point displacement (RPD) design is a quasi-experiment (QE) that aims to control many threats to internal validity. Though it has existed for several decades, RPD has only recently begun to answer applied research questions in lieu of stronger QEs. Objectives Our primary objective was to implement within-study comparison (WSC) logic to create RPD replicates and to determine conditions under which RPD might provide estimates comparable to those found in validating experiments. Research Design We utilize three randomized controlled trials (two cluster-level, one individual-level), artificially decomposing or creating cluster structures, to create multiple RPDs. We compare results in each RPD treatment group to a fixed set of control groups to gauge the congruence of these repeated RPD realizations with results found in these three RCTs. Results RPD’s performance was uneven. Using multiple criteria, we found that RPDs successfully predicted the direction of the RCT’s intervention effect but inconsistently fell within the .10 SD threshold. A scant 13% of RPD results were statistically significant at either the .05 or .01 alpha-level. RPD results were within the 95% confidence interval of RCTs around half the time, and false negative rates were substantially higher than false positive rates. Conclusions RPD consistently underestimates treatment effects in validating RCTs. We analyze reasons for this insensitivity and offer practical suggestions to improve the chances RPD will correctly identify favorable results. We note that the synthetic, “decomposition of cluster RCTs,” WSC design represents a prototype for evaluating other QEs.

Location, Area, Curvature and Temporal Trends of Coral Sea Tropical Cyclone Tracks, Over 50 Years

Tropical Cyclones (TCs) with genesis in the Coral Sea, often near the east coast of Australia, present significant hazards to coastal regions in their surroundings. There has, therefore, been significant recent efforts to extract information from records of their historical tracks in order to help predict their future behaviour in the light of a changing climate. In this study, the Australian Bureau of Meteorology (BOM) database of TC tracks over the last fifty years were grouped based on K-means clustering of the maximum wind-weighted centroids. Track shape variance and track curvature (sinuosity) were assessed. Three well defined clusters of TC tracks were identified, and the results showed predominant directions of TC movement by cluster. Track sinuosity was shown to increase from east to west. Only one cluster showed a statistically significant trend (decreasing) in TC frequency. The concept of TC power dissipation index (PDI) was introduced, revealing that two of the clusters have diverging trends for PDI post 2004. The location of cyclone maximum intensity (LMI) was trended, and only one cluster showed a statistically significant trend (towards the equator) for LMI. All these findings demonstrated a clear variance in risk between the clusters and suggests that this method of cluster analysis is a useful and productive complementary tool when establishing future impacts of TCs - the method identifies divergent TC characteristics and trends at a finer scale (cluster) level which then aids in assigning specific and differing TC risk mitigation strategies to different areas of the Australian east coast.

The GW/BSE Method in Magnetic Fields

The GW approximation and the Bethe–Salpeter equation have been implemented into the Turbomole program package for computations of molecular systems in a strong, finite magnetic field. Complex-valued London orbitals are used as basis functions to ensure gauge-invariant computational results. The implementation has been benchmarked against triplet excitation energies of 36 small to medium-sized molecules against reference values obtained at the approximate coupled-cluster level (CC2 approximation). Finally, a spectacular change of colour from orange to green of the tetracene molecule is induced by applying magnetic fields between 0 and 9,000 T perpendicular to the molecular plane.

A simulation study for evaluating the performance of clustering measures in multilevel logistic regression

Background Multilevel logistic regression models are widely used in health sciences research to account for clustering in multilevel data when estimating effects on subject binary outcomes of individual-level and cluster-level covariates. Several measures for quantifying between-cluster heterogeneity have been proposed. This study compared the performance of between-cluster variance based heterogeneity measures (the Intra-class Correlation Coefficient (ICC) and the Median Odds Ratio (MOR)), and cluster-level covariate based heterogeneity measures (the 80% Interval Odds Ratio (IOR-80) and the Sorting Out Index (SOI)). Methods We used several simulation datasets of a two-level logistic regression model to assess the performance of the four clustering measures for a multilevel logistic regression model. We also empirically compared the four measures of cluster variation with an analysis of childhood anemia to investigate the importance of unexplained heterogeneity between communities and community geographic type (rural vs urban) effect in Malawi. Results Our findings showed that the estimates of SOI and ICC were generally unbiased with at least 10 clusters and a cluster size of at least 20. On the other hand, estimates of MOR and IOR-80 were less accurate with 50 or fewer clusters regardless of the cluster size. The performance of the four clustering measures improved with increased clusters and cluster size at all cluster variances. In the analysis of childhood anemia, the estimate of the between-community variance was 0.455, and the effect of community geographic type (rural vs urban) had an odds ratio (OR)=1.21 (95% CI: 0.97, 1.52). The resulting estimates of ICC, MOR, IOR-80 and SOI were 0.122 (indicative of low homogeneity of childhood anemia in the same community); 1.898 (indicative of large unexplained heterogeneity); 0.345-3.978 and 56.7% (implying that the between community heterogeneity was more significant in explaining the variations in childhood anemia than the estimated effect of community geographic type (rural vs urban)), respectively. Conclusion At least 300 clusters with sizes of at least 50 would be adequate to estimate the strength of clustering in multilevel logistic regression with negligible bias. We recommend using the SOI to assess unexplained heterogeneity between clusters when the interest also involves the effect of cluster-level covariates, otherwise, the usual intra-cluster correlation coefficient would suffice in multilevel logistic regression analyses.

Gray Matter Differentiation Between Two Subordinate Personality Traits of Extraversion: Enthusiasm and Assertiveness

Enthusiasm and assertiveness are two subordinate personality traits of extraversion. These traits reflect different aspects of extroversion and have distinct implications on mental health. Whereas enthusiasm predicts satisfaction in life and positive relationships, assertiveness predicts psychological distress and reduced social support. The neural basis of these subordinate traits is not well understood. To investigate brain regions where enthusiasm and assertiveness have diverging relationship with morphology, enthusiasm and assertiveness were regressed to gray matter volume (GMV) across the whole brain in a sample of 301 healthy individuals. A significant interaction was found between enthusiasm and assertiveness in the left angular gyrus (t(296) = 4.18, family wise error corrected, FWE p = .001 (cluster-level); Cluster size = 880 voxels). Larger GMV in this area was associated with more enthusiasm and less assertiveness. Our study emphasizes the value of separating extraversion into its subordinate traits when investigating associations to neuroanatomy.

Leveling up: improving power in fMRI by moving beyond cluster-level inference

Inference in neuroimaging commonly occurs at the level of "clusters" of neighboring voxels or connections, thought to reflect functionally specific brain areas. Yet increasingly large studies reveal effects that are shared throughout the brain, suggesting that reported clusters may only reflect the "tip of the iceberg" of underlying effects. Here, we empirically compare power of traditional levels of inference (edge and cluster) with broader levels of inference (network and whole-brain) by resampling functional connectivity data from the Human Connectome Project (n=40, 80, 120). Only network- and whole brain-level inference attained or surpassed "adequate" power (β =80%) to detect an average effect, with almost double the power for network- compared with cluster-level procedures at more typical sample sizes. Likewise, effects tended to be widespread, and more widespread pooling resulted in stronger magnitude effects. Power also substantially increased when controlling FDR rather than FWER. Importantly, there may be similar implications for task-based activation analyses where effects are also increasingly understood to be widespread. However, increased power with broader levels of inference may diminish the specificity to localize effects, especially for non-task contexts. These findings underscore the benefit of shifting the scale of inference to better capture the underlying signal, which may unlock opportunities for discovery in human neuroimaging.

Simple compared to covariate-constrained randomization methods in balancing baseline characteristics: a case study of randomly allocating 72 hemodialysis centers in a cluster trial

Background and aim Some parallel-group cluster-randomized trials use covariate-constrained rather than simple randomization. This is done to increase the chance of balancing the groups on cluster- and patient-level baseline characteristics. This study assessed how well two covariate-constrained randomization methods balanced baseline characteristics compared with simple randomization. Methods We conducted a mock 3-year cluster-randomized trial, with no active intervention, that started April 1, 2014, and ended March 31, 2017. We included a total of 11,832 patients from 72 hemodialysis centers (clusters) in Ontario, Canada. We randomly allocated the 72 clusters into two groups in a 1:1 ratio on a single date using individual- and cluster-level data available until April 1, 2013. Initially, we generated 1000 allocation schemes using simple randomization. Then, as an alternative, we performed covariate-constrained randomization based on historical data from these centers. In one analysis, we restricted on a set of 11 individual-level prognostic variables; in the other, we restricted on principal components generated using 29 baseline historical variables. We created 300,000 different allocations for the covariate-constrained randomizations, and we restricted our analysis to the 30,000 best allocations based on the smallest sum of the penalized standardized differences. We then randomly sampled 1000 schemes from the 30,000 best allocations. We summarized our results with each randomization approach as the median (25th and 75th percentile) number of balanced baseline characteristics. There were 156 baseline characteristics, and a variable was balanced when the between-group standardized difference was ≤ 10%. Results The three randomization techniques had at least 125 of 156 balanced baseline characteristics in 90% of sampled allocations. The median number of balanced baseline characteristics using simple randomization was 147 (142, 150). The corresponding value for covariate-constrained randomization using 11 prognostic characteristics was 149 (146, 151), while for principal components, the value was 150 (147, 151). Conclusion In this setting with 72 clusters, constraining the randomization using historical information achieved better balance on baseline characteristics compared with simple randomization; however, the magnitude of benefit was modest.