Continuous Response Variables Research Articles

Fast and Scalable Feature Selection for Gene Expression Data Using Hilbert-Schmidt Independence Criterion.

In computational biology, selecting a small subset of informative genes from microarray data continues to be a challenge due to the presence of thousands of genes. This paper aims at quantifying the dependence between gene expression data and the response variables and to identifying a subset of the most informative genes using a fast and scalable multivariate algorithm. A novel algorithm for feature selection from gene expression data was developed. The algorithm was based on the Hilbert-Schmidt independence criterion (HSIC), and was partly motivated by singular value decomposition (SVD). The algorithm is computationally fast and scalable to large datasets. Moreover, it can be applied to problems with any type of response variables including, biclass, multiclass, and continuous response variables. The performance of the proposed algorithm in terms of accuracy, stability of the selected genes, speed, and scalability was evaluated using both synthetic and real-world datasets. The simulation results demonstrated that the proposed algorithm effectively and efficiently extracted stable genes with high predictive capability, in particular for datasets with multiclass response variables. The proposed method does not require the whole microarray dataset to be stored in memory, and thus can easily be scaled to large datasets. This capability is an important attribute in big data analytics, where data can be large and massively distributed.

Effects of dietary urea concentration and zilpaterol hydrochloride on performance and carcass characteristics of finishing steers.

Cattle receiving zilpaterol hydrochloride () may recycle less N and require a greater supply of RDP. This study evaluated effects of ZH on performance and carcass characteristics of steers fed diets with increasing dietary RDP concentrations supplied as urea. Steers (429 animals; BW = 423 ± 4.5 kg) were sorted into 3 blocks according to BW and assigned to 1 of 6 treatments (6 pens per treatment) in a randomized complete block design. Treatments were a 2 × 3 factorial arrangement of either no ZH or ZH (75 mg ZH per steer daily) supplemented to finishing diets containing 0, 0.5, or 1.0% urea of dietary DM. Pen weights were recorded before treatment initiation; urea was fed for 27 d, and ZH treatments were fed for 24 d with a 3-d withdrawal period. Pen weights were recorded before transporting steers to a commercial abattoir. Continuous response variables were analyzed using the MIXED procedure and categorical data were analyzed using the GLIMMIX procedure of SAS. No ZH × dietary urea interactions ( ≥ 0.14) occurred for all performance and carcass response variables. Feeding ZH for the last 27 d (included a 3-d withdrawal period) of the finishing period increased ( < 0.01) ADG, decreased ( < 0.01) DMI, and increased ( < 0.01) G:F compared with no ZH. In addition, ZH increased HCW ( < 0.01), dressing percentage ( < 0.01), LM area ( < 0.01), and decreased ( = 0.01) yield grade. Increasing dietary urea linearly decreased ( = 0.01) ADG and DMI. A tendency for a linear decrease ( = 0.10) in HCW, and a tendency for a quadratic increase ( = 0.07) in marbling score were observed as urea increased in the diet. Results indicate that cattle supplemented with ZH do not require additional RDP in the diet, and that performance and carcass characteristics were negatively affected when urea was increased in the diet.

Pharmacogenetic Analysis of Functional Glutamate System Gene Variants and Clinical Response to Clozapine

Altered glutamate neurotransmission is implicated in the etiology of schizophrenia (SCZ) and the pharmacogenetics of response to clozapine (CLZ), which is the drug of choice for treatment-resistant SCZ. Response to antipsychotic therapy is highly variable, although twin studies suggest a genetic component. We investigated the association of 10 glutamate system gene variants with CLZ response using standard genotyping procedures. GRM2 (rs4067 and rs2518461), SLC1A2 (rs4354668, rs4534557, and rs2901534), SLC6A9 (rs12037805, rs1978195, and rs16831558), GRIA1 (rs2195450), and GAD1 (rs3749034) were typed in 163 European SCZ/schizoaffective disorder patients deemed resistant or intolerant to previous pharmacotherapy. Response was assessed following 6 months of CLZ monotherapy using change in Brief Psychiatric Rating Scale (BPRS) scores. Categorical and continuous response variables were analyzed using χ² tests and analysis of covariance, respectively. We report no significant associations following correction for multiple testing. Prior to correction, nominally significant associations were observed for SLC6A9, SLC1A2, GRM2, and GRIA1. Most notably, CC homozygotes of rs16831558 located in the glycine transporter 1 gene (SLC6A9) exhibited an allele dose-dependent improvement in positive symptoms compared to T allele carriers (p_uncorrected = 0.008, p_corrected = 0.08). To clarify the role of SLC6A9 in clinical response to antipsychotic medication, and CLZ in particular, this finding warrants further investigation in larger well-characterized samples.

Beta Regression Model for Predicting the Development of Pink Rot in Potato Tubers During Storage.

Pink rot is an important disease of potato with worldwide distribution. Severe yield and quality losses have been reported at harvest and in postharvest storage. Under conditions favoring disease development, pink rot severity can continue to increase from the field to storage and from storage to transit, causing further losses. Prediction of pink rot disease development in storage has great potential for growers to intervene at an earlier stage of disease development to minimize economic losses. Pink rot disease is estimated as percent rot confined on the interval (0 or 1, corresponding to 0% as no disease and 100% as maximum disease). In this study, beta regression is considered over the traditional ordinary least squares regression (linear regression) for fitting continuous response variables bounded on the unit interval (0,1). This method is considered a good alternative to data transformation and analysis by linear regression. The percentages of incidence of pink rot in tubers at harvest, yield, and days after harvest were used as study covariates to predict pink rot development from 32 to 78 days postharvest. Results demonstrate that the interaction between percentage of pink rot at harvest and yield is a significant predictor (P < 0.0001) of the beta regression model. A linear regression model was also designed to compare the results with the proposed beta regression model. Linear predictors observed in diagnostic plots with linear regression model was found to not be constant and an adjusted R2 (0.49) was obtained. The pseudo R2 (0.56) and constant variance for this study suggests that the beta regression function is adequate for predicting the development of pink rot during storage. The use of the beta prediction model could help growers decide whether to apply a fungicide to tubers going into storage or to market their crop before significant storage losses are incurred.

Learning a Hybrid Architecture for Sequence Regression and Annotation

When learning a hidden Markov model (HMM), sequential observations can often be complemented by real-valued summary response variables generated from the path of hidden states. Such settings arise in numerous domains, including many applications in biology, like motif discovery and genome annotation. In this paper, we present a flexible framework for jointly modeling both latent sequence features and the functional mapping that relates the summary response variables to the hidden state sequence. The algorithm is compatible with a rich set of mapping functions. Results show that the availability of additional continuous response variables can simultaneously improve the annotation of the sequential observations and yield good prediction performance in both synthetic data and real-world datasets.

Generalized Concept of Relative Risk and Wider Applications of the Proportional Hazards Model and the Kaplan–Meier Estimator

The concepts of relative risk and hazard ratio are generalized for ordinary ordinal and continuous response variables, respectively. Under the generalized concepts, the Cox proportional hazards model with the Breslow's and Efron's methods can be regarded as generalizations of the Mantel–Haenszel estimator for dealing with broader types of covariates and responses. When ordinal responses can be regarded as discretized observations of a hypothetical continuous variable, the estimated relative risks from the Cox model reflect the associations between the responses and covariates. Examples are given to illustrate the generalized concepts and wider applications of the Cox model and the Kaplan–Meier estimator.

Utilization of Reproducing Kernel Hilbert Spaces in Dynamic Discrete Choice Models: An Application to the High-speed Railway Timetabling Problem

This paper introduces a generalized nested logit model that results from combining discrete and continuous response variables. Reproducing Kernel Hilbert Spaces are used to define the (dynamic) systematic utilities, allowing correlations between alternatives close together on the continuous spectrum, and reconciliation mechanisms between both types of response variables are established. The seminal motivation of this model is the passenger-centric train timetabling problem. For this reason, the discussion in this paper focuses on a high-speed railway (HSR) demand-forecasting model.The model proposes a maximum likelihood approach to estimating the parameters, and a Monte Carlo simulation study is conducted to test the proposed methodology.

Likelihood analysis for a class of beta mixed models

Beta regression is a suitable choice for modelling continuous response variables taking values on the unit interval. Data structures such as hierarchical, repeated measures and longitudinal typically induce extra variability and/or dependence and can be accounted for by the inclusion of random effects. In this sense, Statistical inference typically requires numerical methods, possibly combined with sampling algorithms. A class of Beta mixed models is adopted for the analysis of two real problems with grouped data structures. We focus on likelihood inference and describe the implemented algorithms. The first is a study on the life quality index of industry workers with data collected according to an hierarchical sampling scheme. The second is a study assessing the impact of hydroelectric power plants upon measures of water quality indexes up, downstream and at the reservoirs of the dammed rivers, with a nested and longitudinal data structure. Results from different algorithms are reported for comparison including from data-cloning, an alternative to numerical approximations which also allows assessing identifiability. Confidence intervals based on profiled likelihoods are compared with those obtained by asymptotic quadratic approximations, showing relevant differences for parameters related to the random effects. In both cases, the scientific hypothesis of interest was investigated by comparing alternative models, leading to relevant interpretations of the results within each context.

A Change Point Method for Monitoring Generalized Linear Profiles in Phase I

The Phase I applications of the statistical profile monitoring have recently been extended to the case when the response variable is binary. We are motivated to undertake the current research in an attempt to try to provide a unified framework for the Phase I control in the context of statistical profile monitoring that can be used to tackle a large class of response variables, such as continuous, count, or categorical response variables. The unified framework is essentially based on applying the change point model to the class of generalized linear models. The proposed Phase I control chart is assessed and compared with the existing charts under binomial and Poisson profiles. Some diagnostic procedures are also discussed. A real data set obtained from a test lab concerning the dispersion of carbon black filler in a rubber mix is used to demonstrate how the proposed chart can be used in practical applications. Some future research directions are also discussed. Copyright © 2014 John Wiley &amp; Sons, Ltd.

Multiview Supervised Dictionary Learning in Speech Emotion Recognition

Recently, a supervised dictionary learning (SDL) approach based on the Hilbert-Schmidt independence criterion (HSIC) has been proposed that learns the dictionary and the corresponding sparse coefficients in a space where the dependency between the data and the corresponding labels is maximized. In this paper, two multiview dictionary learning techniques are proposed based on this HSIC-based SDL. While one of these two techniques learns one dictionary and the corresponding coefficients in the space of fused features in all views, the other learns one dictionary in each view and subsequently fuses the sparse coefficients in the spaces of learned dictionaries. The effectiveness of the proposed multiview learning techniques in using the complementary information of single views is demonstrated in the application of speech emotion recognition (SER). The fully-continuous sub-challenge (FCSC) of the AVEC 2012 dataset is used in two different views: baseline and spectral energy distribution (SED) feature sets. Four dimensional affects, i.e., arousal, expectation, power, and valence are predicted using the proposed multiview methods as the continuous response variables. The results are compared with the single views, AVEC 2012 baseline system, and also other supervised and unsupervised multiview learning approaches in the literature. Using correlation coefficient as the performance measure in predicting the continuous dimensional affects, it is shown that the proposed approach achieves the highest performance among the rivals. The relative performance of the two proposed multiview techniques and their relationship are also discussed. Particularly, it is shown that by providing an additional constraint on the dictionary of one of these approaches, it becomes the same as the other.

A review of recent variable selection methods in industrial and chemometrics applications

The massive amount of data collected from industrial processes has challenged researchers and practitioners, turning variable selection into a research topic of interest both in academia and in industry. The use of redundant, irrelevant, and noisy variables tends to compromise the performance of many statistical tools, leading to unreliable inferences and costly data collection. In this paper, we present a literature review on recent variable selection methods and applications in manufacturing and in the chemometrics field. These methods are deployed into two major categories: variable selection for prediction of continuous response variables and for prediction of a categorical variable (also referred to as classification). Future research directions are also outlined.

Covariate-adjusted confidence interval for the intraclass correlation coefficient

A crucial step in designing a new study is to estimate the required sample size. For a design involving cluster sampling, the appropriate sample size depends on the so-called design effect, which is a function of the average cluster size and the intracluster correlation coefficient (ICC). It is well-known that under the framework of hierarchical and generalized linear models, a reduction in residual error may be achieved by including risk factors as covariates. In this paper we show that the covariate design, indicating whether the covariates are measured at the cluster level or at the within-cluster subject level affects the estimation of the ICC, and hence the design effect. Therefore, the distinction between these two types of covariates should be made at the design stage. In this paper we use the nested-bootstrap method to assess the accuracy of the estimated ICC for continuous and binary response variables under different covariate structures. The codes of two SAS macros are made available by the authors for interested readers to facilitate the construction of confidence intervals for the ICC. Moreover, using Monte Carlo simulations we evaluate the relative efficiency of the estimators and evaluate the accuracy of the coverage probabilities of a 95% confidence interval on the population ICC. The methodology is illustrated using a published data set of blood pressure measurements taken on family members.

Multiple-Shrinkage Multinomial Probit Models with Applications to Simulating Geographies in Public Use Data

Multinomial outcomes with many levels can be challenging to model. Information typically accrues slowly with increasing sample size, yet the parameter space expands rapidly with additional covariates. Shrinking all regression parameters towards zero, as often done in models of continuous or binary response variables, is unsatisfactory, since setting parameters equal to zero in multinomial models does not necessarily imply "no effect." We propose an approach to modeling multinomial outcomes with many levels based on a Bayesian multinomial probit (MNP) model and a multiple shrinkage prior distribution for the regression parameters. The prior distribution encourages the MNP regression parameters to shrink toward a number of learned locations, thereby substantially reducing the dimension of the parameter space. Using simulated data, we compare the predictive performance of this model against two other recently-proposed methods for big multinomial models. The results suggest that the fully Bayesian, multiple shrinkage approach can outperform these other methods. We apply the multiple shrinkage MNP to simulating replacement values for areal identifiers, e.g., census tract indicators, in order to protect data confidentiality in public use datasets.

Distance-based approach in univariate longitudinal data analysis

In this paper, we propose a methodology to analyze longitudinal data through distances between pairs of observations (or individuals) with regard to the explanatory variables used to fit continuous response variables. Restricted maximum-likelihood and generalized least squares are used to estimate the parameters in the model. We applied this new approach to study the effect of gender and exposure on the deviant behavior variable with respect to tolerance for a group of youths studied over a period of 5 years. Were performed simulations where we compared our distance-based method with classic longitudinal analysis with both AR(1) and compound symmetry correlation structures. We compared them under Akaike and Bayesian information criterions, and the relative efficiency of the generalized variance of the errors of each model. We found small gains in the proposed model fit with regard to the classical methodology, particularly in small samples, regardless of variance, correlation, autocorrelation structure and number of time measurements.

Two-step spline estimating equations for generalized additive partially linear models with large cluster sizes

We propose a two-step estimating procedure for generalized additive partially linear models with clustered data using estimating equations. Our proposed method applies to the case that the number of observations per cluster is allowed to increase with the number of independent subjects. We establish oracle properties for the two-step estimator of each function component such that it performs as well as the univariate function estimator by assuming that the parametric vector and all other function components are known. Asymptotic distributions and consistency properties of the estimators are obtained. Finite-sample experiments with both simulated continuous and binary response variables confirm the asymptotic results. We illustrate the methods with an application to a U.S. unemployment data set.

A strategy for selecting among alternative models for continuous longitudinal data

Linear mixed models (LMMs) can be used to analyze continuous longitudinal response variables of research studies. Specific aims are then addressed through tests of fixed effects comparing means. However, generated fixed effects results can vary according to the choice of the covariance structure, and so strategies for selecting a model should be utilized first to identify an appropriate covariance structure. We describe alternative LMMs for analyzing continuous longitudinal data and discuss a strategy for using model selection criteria to choose among those models. This is accomplished through the analysis of an exemplar data set considering a wide variety of alternative models for the means, variances, and correlations.

Sample Size Adaptation in Fixed-Dose Combination Drug Trial

Statistical testing in clinical trials can be complex when the statistical distribution of the test statistic involves a nuisance parameter. Some type of nuisance parameters such as standard deviation of a continuous response variable can be handled without too much difficulty. Other type of nuisance parameters, specifically associated with the main parameter under testing, can be difficult to handle. Without knowledge of the possible value of such a nuisance parameter, the maximum type I error associated with testing the main parameter may occur at an extreme value of the nuisance parameter. A well known example is the intersection-union test for comparing a combination drug with its two component drugs where the nuisance parameter is the mean difference between the two components. Knowledge of the possible range of value of this mean difference may help enhance the clinical trial design. For instance, if the interim internal data suggest that this mean difference falls into a possible range of value, then the sample size may be reallocated after the interim look to possibly improve the efficiency of statistical testing. This research sheds some light into possible power advantage from such a sample size reallocation at the interim look.

Hierarchical Bayesian modeling of heterogeneous cluster‐ and subject‐level associations between continuous and binary outcomes in dairy production

The augmentation of categorical outcomes with underlying Gaussian variables in bivariate generalized mixed effects models has facilitated the joint modeling of continuous and binary response variables. These models typically assume that random effects and residual effects (co)variances are homogeneous across all clusters and subjects, respectively. Motivated by conflicting evidence about the association between performance outcomes in dairy production systems, we consider the situation where these (co)variance parameters may themselves be functions of systematic and/or random effects. We present a hierarchical Bayesian extension of bivariate generalized linear models whereby functions of the (co)variance matrices are specified as linear combinations of fixed and random effects following a square-root-free Cholesky reparameterization that ensures necessary positive semidefinite constraints. We test the proposed model by simulation and apply it to the analysis of a dairy cattle data set in which the random herd-level and residual cow-level effects (co)variances between a continuous production trait and binary reproduction trait are modeled as functions of fixed management effects and random cluster effects.

Estimating forest attribute parameters for small areas using nearest neighbors techniques

Nearest neighbors techniques have become extremely popular, particularly for use with forest inventory data. With these techniques, a population unit prediction is calculated as a linear combination of observations for a selected number of population units in a sample that are most similar, or nearest, in a space of ancillary variables to the population unit requiring the prediction. Nearest neighbors techniques are appealing for multiple reasons: they can be used with categorical response variables for which the objective is classification and with continuous response variables for which the objective is prediction; they can be used for both univariate and multivariate prediction; they are non-parametric in the sense that no assumptions regarding the distributions of response or predictor variables are necessary; they are synthetic in the sense that they can readily use information external to the geographic area for which an estimate is sought; they are useful for map construction, small area estimation, and inference; and they can be used with a wide variety of data sets. Recent advances and emerging issues in nearest neighbors techniques are reviewed for four topic areas: (1) distance metrics, (2) optimization, (3) diagnostic tools, and (4) inference. The focus of the study is estimation of mean forest stem volume per unit area for small areas using a combination of forest inventory observations and Landsat Thematic Mapper (TM) imagery. However, the concepts and techniques are generally applicable for all nearest neighbors problems.

Analyzing angle crashes at unsignalized intersections using machine learning techniques

A recently developed machine learning technique, multivariate adaptive regression splines (MARS), is introduced in this study to predict vehicles’ angle crashes. MARS has a promising prediction power, and does not suffer from interpretation complexity. Negative Binomial (NB) and MARS models were fitted and compared using extensive data collected on unsignalized intersections in Florida. Two models were estimated for angle crash frequency at 3- and 4-legged unsignalized intersections. Treating crash frequency as a continuous response variable for fitting a MARS model was also examined by considering the natural logarithm of the crash frequency. Finally, combining MARS with another machine learning technique (random forest) was explored and discussed. The fitted NB angle crash models showed several significant factors that contribute to angle crash occurrence at unsignalized intersections such as, traffic volume on the major road, the upstream distance to the nearest signalized intersection, the distance between successive unsignalized intersections, median type on the major approach, percentage of trucks on the major approach, size of the intersection and the geographic location within the state. Based on the mean square prediction error (MSPE) assessment criterion, MARS outperformed the corresponding NB models. Also, using MARS for predicting continuous response variables yielded more favorable results than predicting discrete response variables. The generated MARS models showed the most promising results after screening the covariates using random forest. Based on the results of this study, MARS is recommended as an efficient technique for predicting crashes at unsignalized intersections (angle crashes in this study).