Pupillary response to complex interdependent tasks: A cognitive-load theory perspective.

Pupil dilation is known to indicate cognitive load. In this study, we looked at the average pupillary responses of a cohort of 29 undergraduate students during graphical problem solving. Three questions were asked, based on the same graphical input. The questions were interdependent and comprised multiple steps. We propose a novel way of analyzing pupillometry data for such tasks on the basis of eye fixations, a commonly used eyetracking parameter. We found that pupil diameter increased during the solution process. However, pupil diameter did not always reflect the expected cognitive load. This result was studied within a cognitive-load theory model. Higher-performing students showed evidence of germane load and schema creation, indicating use of the interdependent nature of the tasks to inform their problem-solving process. However, lower-performing students did not recognize the interdependent nature of the tasks and solved each problem independently, which was expressed in a markedly different pupillary response pattern. We discuss the import of our findings for instructional design.

Spatial regression with covariate measurement error: A semiparametric approach.

Spatial data have become increasingly common in epidemiology and public health research thanks to advances in GIS (Geographic Information Systems) technology. In health research, for example, it is common for epidemiologists to incorporate geographically indexed data into their studies. In practice, however, the spatially defined covariates are often measured with error. Naive estimators of regression coefficients are attenuated if measurement error is ignored. Moreover, the classical measurement error theory is inapplicable in the context of spatial modeling because of the presence of spatial correlation among the observations. We propose a semiparametric regression approach to obtain bias-corrected estimates of regression parameters and derive their large sample properties. We evaluate the performance of the proposed method through simulation studies and illustrate using data on Ischemic Heart Disease (IHD). Both simulation and practical application demonstrate that the proposed method can be effective in practice.

A penalized likelihood approach for investigating gene-drug interactions in pharmacogenetic studies.

Pharmacogenetics investigates the relationship between heritable genetic variation and the variation in how individuals respond to drug therapies. Often, gene-drug interactions play a primary role in this response, and identifying these effects can aid in the development of individualized treatment regimes. Haplotypes can hold key information in understanding the association between genetic variation and drug response. However, the standard approach for haplotype-based association analysis does not directly address the research questions dictated by individualized medicine. A complementary post-hoc analysis is required, and this post-hoc analysis is usually under powered after adjusting for multiple comparisons and may lead to seemingly contradictory conclusions. In this work, we propose a penalized likelihood approach that is able to overcome the drawbacks of the standard approach and yield the desired personalized output. We demonstrate the utility of our method by applying it to the Scottish Randomized Trial in Ovarian Cancer. We also conducted simulation studies and showed that the proposed penalized method has comparable or more power than the standard approach and maintains low Type I error rates for both binary and quantitative drug responses. The largest performance gains are seen when the haplotype frequency is low, the difference in effect sizes are small, or the true relationship among the drugs is more complex.

Incorporating covariates in skewed functional data models.

We introduce a class of covariate-adjusted skewed functional models (cSFM) designed for functional data exhibiting location-dependent marginal distributions. We propose a semi-parametric copula model for the pointwise marginal distributions, which are allowed to depend on covariates, and the functional dependence, which is assumed covariate invariant. The proposed cSFM framework provides a unifying platform for pointwise quantile estimation and trajectory prediction. We consider a computationally feasible procedure that handles densely as well as sparsely observed functional data. The methods are examined numerically using simulations and is applied to a new tractography study of multiple sclerosis. Furthermore, the methodology is implemented in the R package cSFM, which is publicly available on CRAN.

Interquantile Shrinkage and Variable Selection in Quantile Regression.

Examination of multiple conditional quantile functions provides a comprehensive view of the relationship between the response and covariates. In situations where quantile slope coefficients share some common features, estimation efficiency and model interpretability can be improved by utilizing such commonality across quantiles. Furthermore, elimination of irrelevant predictors will also aid in estimation and interpretation. These motivations lead to the development of two penalization methods, which can identify the interquantile commonality and nonzero quantile coefficients simultaneously. The developed methods are based on a fused penalty that encourages sparsity of both quantile coefficients and interquantile slope differences. The oracle properties of the proposed penalization methods are established. Through numerical investigations, it is demonstrated that the proposed methods lead to simpler model structure and higher estimation efficiency than the traditional quantile regression estimation.

Interquantile Shrinkage in Regression Models.

Conventional analysis using quantile regression typically focuses on fitting the regression model at different quantiles separately. However, in situations where the quantile coefficients share some common feature, joint modeling of multiple quantiles to accommodate the commonality often leads to more efficient estimation. One example of common features is that a predictor may have a constant effect over one region of quantile levels but varying effects in other regions. To automatically perform estimation and detection of the interquantile commonality, we develop two penalization methods. When the quantile slope coefficients indeed do not change across quantile levels, the proposed methods will shrink the slopes towards constant and thus improve the estimation efficiency. We establish the oracle properties of the two proposed penalization methods. Through numerical investigations, we demonstrate that the proposed methods lead to estimations with competitive or higher efficiency than the standard quantile regression estimation in finite samples. Supplemental materials for the article are available online.

A nonparametric spatial model for periodontal data with non-random missingness.

Periodontal disease progression is often quantified by clinical attachment level (CAL) defined as the distance down a tooth's root that is detached from the surrounding bone. Measured at 6 locations per tooth throughout the mouth (excluding the molars), it gives rise to a dependent data set-up. These data are often reduced to a one-number summary, such as the whole mouth average or the number of observations greater than a threshold, to be used as the response in a regression to identify important covariates related to the current state of a subject's periodontal health. Rather than a simple one-number summary, we set forward to analyze all available CAL data for each subject, exploiting the presence of spatial dependence, non-stationarity, and non-normality. Also, many subjects have a considerable proportion of missing teeth which cannot be considered missing at random because periodontal disease is the leading cause of adult tooth loss. Under a Bayesian paradigm, we propose a nonparametric flexible spatial (joint) model of observed CAL and the location of missing tooth via kernel convolution methods, incorporating the aforementioned features of CAL data under a unified framework. Application of this methodology to a data set recording the periodontal health of an African-American population, as well as simulation studies reveal the gain in model fit and inference, and provides a new perspective into unraveling covariate-response relationships in presence of complexities posed by these data.

Efficient Robust Regression via Two-Stage Generalized Empirical Likelihood.

Large- and finite-sample efficiency and resistance to outliers are the key goals of robust statistics. Although often not simultaneously attainable, we develop and study a linear regression estimator that comes close. Efficiency obtains from the estimator's close connection to generalized empirical likelihood, and its favorable robustness properties are obtained by constraining the associated sum of (weighted) squared residuals. We prove maximum attainable finite-sample replacement breakdown point, and full asymptotic efficiency for normal errors. Simulation evidence shows that compared to existing robust regression estimators, the new estimator has relatively high efficiency for small sample sizes, and comparable outlier resistance. The estimator is further illustrated and compared to existing methods via application to a real data set with purported outliers.

Consistent Group Identification and Variable Selection in Regression with Correlated Predictors.

Statistical procedures for variable selection have become integral elements in any analysis. Successful procedures are characterized by high predictive accuracy, yielding interpretable models while retaining computational efficiency. Penalized methods that perform coefficient shrinkage have been shown to be successful in many cases. Models with correlated predictors are particularly challenging to tackle. We propose a penalization procedure that performs variable selection while clustering groups of predictors automatically. The oracle properties of this procedure including consistency in group identification are also studied. The proposed method compares favorably with existing selection approaches in both prediction accuracy and model discovery, while retaining its computational efficiency. Supplemental material are available online.

Environmental, institutional, and demographic predictors of environmental literacy among middle school children.

Building environmental literacy (EL) in children and adolescents is critical to meeting current and emerging environmental challenges worldwide. Although environmental education (EE) efforts have begun to address this need, empirical research holistically evaluating drivers of EL is critical. This study begins to fill this gap with an examination of school-wide EE programs among middle schools in North Carolina, including the use of published EE curricula and time outdoors while controlling for teacher education level and experience, student attributes (age, gender, and ethnicity), and school attributes (socio-economic status, student-teacher ratio, and locale). Our sample included an EE group selected from schools with registered school-wide EE programs, and a control group randomly selected from NC middle schools that were not registered as EE schools. Students were given an EL survey at the beginning and end of the spring 2012 semester. Use of published EE curricula, time outdoors, and having teachers with advanced degrees and mid-level teaching experience (between 3 and 5 years) were positively related with EL whereas minority status (Hispanic and black) was negatively related with EL. Results suggest that school-wide EE programs were not associated with improved EL, but the use of published EE curricula paired with time outdoors represents a strategy that may improve all key components of student EL. Further, investments in teacher development and efforts to maintain enthusiasm for EE among teachers with more than 5 years of experience may help to boost student EL levels. Middle school represents a pivotal time for influencing EL, as improvement was slower among older students. Differences in EL levels based on gender suggest boys and girls may possess complementary skills sets when approaching environmental issues. Our findings suggest ethnicity related disparities in EL levels may be mitigated by time spent in nature, especially among black and Hispanic students.

Factor selection and structural identification in the interaction ANOVA model.

When faced with categorical predictors and a continuous response, the objective of an analysis often consists of two tasks: finding which factors are important and determining which levels of the factors differ significantly from one another. Often times, these tasks are done separately using Analysis of Variance (ANOVA) followed by a post hoc hypothesis testing procedure such as Tukey's Honestly Significant Difference test. When interactions between factors are included in the model the collapsing of levels of a factor becomes a more difficult problem. When testing for differences between two levels of a factor, claiming no difference would refer not only to equality of main effects, but also to equality of each interaction involving those levels. This structure between the main effects and interactions in a model is similar to the idea of heredity used in regression models. This article introduces a new method for accomplishing both of the common analysis tasks simultaneously in an interaction model while also adhering to the heredity-type constraint on the model. An appropriate penalization is constructed that encourages levels of factors to collapse and entire factors to be set to zero. It is shown that the procedure has the oracle property implying that asymptotically it performs as well as if the exact structure were known beforehand. We also discuss the application to estimating interactions in the unreplicated case. Simulation studies show the procedure outperforms post hoc hypothesis testing procedures as well as similar methods that do not include a structural constraint. The method is also illustrated using a real data example.

Consistent high-dimensional Bayesian variable selection via penalized credible regions.

For high-dimensional data, particularly when the number of predictors greatly exceeds the sample size, selection of relevant predictors for regression is a challenging problem. Methods such as sure screening, forward selection, or penalized regressions are commonly used. Bayesian variable selection methods place prior distributions on the parameters along with a prior over model space, or equivalently, a mixture prior on the parameters having mass at zero. Since exhaustive enumeration is not feasible, posterior model probabilities are often obtained via long MCMC runs. The chosen model can depend heavily on various choices for priors and also posterior thresholds. Alternatively, we propose a conjugate prior only on the full model parameters and use sparse solutions within posterior credible regions to perform selection. These posterior credible regions often have closed-form representations, and it is shown that these sparse solutions can be computed via existing algorithms. The approach is shown to outperform common methods in the high-dimensional setting, particularly under correlation. By searching for a sparse solution within a joint credible region, consistent model selection is established. Furthermore, it is shown that, under certain conditions, the use of marginal credible intervals can give consistent selection up to the case where the dimension grows exponentially in the sample size. The proposed approach successfully accomplishes variable selection in the high-dimensional setting, while avoiding pitfalls that plague typical Bayesian variable selection methods.

A Confidence Region Approach to Tuning for Variable Selection.

We develop an approach to tuning of penalized regression variable selection methods by calculating the sparsest estimator contained in a confidence region of a specified level. Because confidence intervals/regions are generally understood, tuning penalized regression methods in this way is intuitive and more easily understood by scientists and practitioners. More importantly, our work shows that tuning to a fixed confidence level often performs better than tuning via the common methods based on AIC, BIC, or cross-validation (CV) over a wide range of sample sizes and levels of sparsity. Additionally, we prove that by tuning with a sequence of confidence levels converging to one, asymptotic selection consistency is obtained; and with a simple two-stage procedure, an oracle property is achieved. The confidence region based tuning parameter is easily calculated using output from existing penalized regression computer packages.Our work also shows how to map any penalty parameter to a corresponding confidence coefficient. This mapping facilitates comparisons of tuning parameter selection methods such as AIC, BIC and CV, and reveals that the resulting tuning parameters correspond to confidence levels that are extremely low, and can vary greatly across data sets. Supplemental materials for the article are available online.

Surface Estimation, Variable Selection, and the Nonparametric Oracle Property.

Variable selection for multivariate nonparametric regression is an important, yet challenging, problem due, in part, to the infinite dimensionality of the function space. An ideal selection procedure should be automatic, stable, easy to use, and have desirable asymptotic properties. In particular, we define a selection procedure to be nonparametric oracle (np-oracle) if it consistently selects the correct subset of predictors and at the same time estimates the smooth surface at the optimal nonparametric rate, as the sample size goes to infinity. In this paper, we propose a model selection procedure for nonparametric models, and explore the conditions under which the new method enjoys the aforementioned properties. Developed in the framework of smoothing spline ANOVA, our estimator is obtained via solving a regularization problem with a novel adaptive penalty on the sum of functional component norms. Theoretical properties of the new estimator are established. Additionally, numerous simulated and real examples further demonstrate that the new approach substantially outperforms other existing methods in the finite sample setting.

Radiographic evaluation of feline appendicular degenerative joint disease vs. Macroscopic appearance of articular cartilage.

Degenerative joint disease (DJD) is common in domesticated cats. Our purpose was to describe how radiographic findings thought to indicate feline DJD relate to macroscopic cartilage degeneration in appendicular joints. Thirty adult cats euthanized for reasons unrelated to this study were evaluated. Orthogonal digital radiographs of the elbow, tarsus, stifle, and coxofemoral joints were evaluated for the presence of DJD. The same joints were dissected for visual inspection of changes indicative of DJD and macroscopic cartilage damage was graded using a Total Cartilage Damage Score. When considering all joints, there was statistically significant fair correlation between cartilage damage and the presence of osteophytes and joint-associated mineralizations, and the subjective radiographic DJD score. Most correlations were statistically significant when looking at the different joints individually, but only the correlation between the presence of osteophytes and the subjective radiographic DJD score with the presence of cartilage damage in the elbow and coxofemoral joints had a value above 0.4 (moderate correlation). The joints most likely to have cartilage damage without radiographic evidence of DJD are the stifle (71% of radiographically normal joints) followed by the coxofemoral joint (57%), elbow (57%), and tarsal joint (46%). Our data support radiographic findings not relating well to cartilage degeneration, and that other modalities should be evaluated to aid in making a diagnosis of feline DJD.

A spatial dirichlet process mixture model for clustering population genetics data.

Identifying homogeneous groups of individuals is an important problem in population genetics. Recently, several methods have been proposed that exploit spatial information to improve clustering algorithms. In this article, we develop a Bayesian clustering algorithm based on the Dirichlet process prior that uses both genetic and spatial information to classify individuals into homogeneous clusters for further study. We study the performance of our method using a simulation study and use our model to cluster wolverines in Western Montana using microsatellite data.

Sufficient dimension reduction via bayesian mixture modeling.

Dimension reduction is central to an analysis of data with many predictors. Sufficient dimension reduction aims to identify the smallest possible number of linear combinations of the predictors, called the sufficient predictors, that retain all of the information in the predictors about the response distribution. In this article, we propose a Bayesian solution for sufficient dimension reduction. We directly model the response density in terms of the sufficient predictors using a finite mixture model. This approach is computationally efficient and offers a unified framework to handle categorical predictors, missing predictors, and Bayesian variable selection. We illustrate the method using both a simulation study and an analysis of an HIV data set.

Item generation and design testing of a questionnaire to assess degenerative joint disease-associated pain in cats.

OBJECTIVE: To determine the items (question topics) for a subjective instrument to assess degenerative joint disease (DJD)-associated chronic pain in cats and determine the instrument design most appropriate for use by cat owners. ANIMALS: 100 randomly selected client-owned cats from 6 months to 20 years old. PROCEDURES: Cats were evaluated to determine degree of radiographic DJD and signs of pain throughout the skeletal system. Two groups were identified: high DJD pain and low DJD pain. Owner-answered questions about activity and signs of pain were compared between the 2 groups to define items relating to chronic DJD pain. Interviews with 45 cat owners were performed to generate items. Fifty-three cat owners who had not been involved in any other part of the study, 19 veterinarians, and 2 statisticians assessed 6 preliminary instrument designs. RESULTS: 22 cats were selected for each group; 19 important items were identified, resulting in 12 potential items for the instrument; and 3 additional items were identified from owner interviews. Owners and veterinarians selected a 5-point descriptive instrument design over 11-point or visual analogue scale formats. CONCLUSIONS AND CLINICAL RELEVANCE: Behaviors relating to activity were substantially different between healthy cats and cats with signs of DJD-associated pain. Fifteen items were identified as being potentially useful, and the preferred instrument design was identified. This information could be used to construct an owner-based questionnaire to assess feline DJD-associated pain. Once validated, such a questionnaire would assist in evaluating potential analgesic treatments for these patients.

Evaluating haplotype effects in case-control studies via penalized-likelihood approaches: prospective or retrospective analysis?

Penalized likelihood methods have become increasingly popular in recent years for evaluating haplotype-phenotype association in case-control studies. Although a retrospective likelihood is dictated by the sampling scheme, these penalized methods are typically built on prospective likelihoods due to their modeling simplicity and computational feasibility. It has been well documented that for unpenalized methods, prospective analyses of case-control data can be valid but less efficient than their retrospective counterparts when testing for association, and result in substantial bias when estimating the haplotype effects. For penalized methods, which combine effect estimation and testing in one step, the impact of using a prospective likelihood is not clear. In this work, we examine the consequences of ignoring the sampling scheme for haplotype-based penalized likelihood methods. Our results suggest that the impact of prospective analyses depends on (1) the underlying genetic mode and (2) the genetic model adopted in the analysis. When the correct genetic model is used, the difference between the two analyses is negligible for additive and slight for dominant haplotype effects. For recessive haplotype effects, the more appropriate retrospective likelihood clearly outperforms the prospective likelihood. If an additive model is incorrectly used, as the true underlying genetic mode is unknown a priori, both retrospective and prospective penalized methods suffer from a sizeable power loss and increase in bias. The impact of using the incorrect genetic model is much bigger on retrospective analyses than prospective analyses, and results in comparable performances for both methods. An application of these methods to the Genetic Analysis Workshop 15 rheumatoid arthritis data is provided.

Joint variable selection for fixed and random effects in linear mixed-effects models.

It is of great practical interest to simultaneously identify the important predictors that correspond to both the fixed and random effects components in a linear mixed-effects (LME) model. Typical approaches perform selection separately on each of the fixed and random effect components. However, changing the structure of one set of effects can lead to different choices of variables for the other set of effects. We propose simultaneous selection of the fixed and random factors in an LME model using a modified Cholesky decomposition. Our method is based on a penalized joint log likelihood with an adaptive penalty for the selection and estimation of both the fixed and random effects. It performs model selection by allowing fixed effects or standard deviations of random effects to be exactly zero. A constrained expectation-maximization algorithm is then used to obtain the final estimates. It is further shown that the proposed penalized estimator enjoys the Oracle property, in that, asymptotically it performs as well as if the true model was known beforehand. We demonstrate the performance of our method based on a simulation study and a real data example.