An alternative approach to variable selection for prediction

A procedure for selecting a subset of predictor variables in regression analysis is suggested. The procedure is so designed that it leads to the selection of a subset of variables having an adequate degree of informativeness with a directly specified confidence coefficient. Some examples are considered to illustrate the application of the procedure.     

Prevalence of Low Physical Activity and its Relation to Social Environment in Deprived Areas in the London Borough of Redbridge

Achieving adequate levels of physical activity (PA) is important to maintain health and prevent chronic disease. The costs of inadequate physical activity to the NHS have been estimated at over a billion pounds annually. While socio-demographic characteristics such as age, sex and ethnicity have been reported to be associated with different levels of PA, there is evidence that people??s social environments may also be important in encouraging a physically active lifestyle. The objective of this paper is to describe associations between the social environment and physical activity among the poorer communities in an outer London Borough, when other socio-demographic factors are controlled for. A household survey was carried out in six poorer neighbourhoods in Redbridge in 2008 as part of a wider health needs assessment. The questionnaire included questions allowing estimation of levels of physical activity as well as extent of social environment [social network score (SNS) and social support score (SSS)]. A random sample of households was taken and a total of 799 completed responses from over 16 year old were obtained. The association between physical activity and the social environment controlling for socio-demographic characteristics was estimated using a logistic nested model. Higher SNS was significantly associated with younger age, Black ethnicity, higher education level, higher household income and higher levels of PA in bivariate analyses. Higher SSS was positively associated with Indian ethnicity, higher household income and area of residence. In multivariate analyses higher levels of PA were significantly associated with wider social networks and stronger social support, educational level and marital status. Despite its limitations, our findings confirm that the relationship between low physical activity and weak social networks and low social support, observed in general population studies, also occurs in deprived communities in London. The relationship merits further exploration given the limited evidence on the effectiveness of interventions to promote physical activity.     

Feature selection and machine learning with mass spectrometry data for distinguishing cancer and non-cancer samples

This is a comparative study of various clustering and classification algorithms as applied to differentiate cancer and non-cancer protein samples using mass spectrometry data. Our study demonstrates the usefulness of a feature selection step prior to applying a machine learning tool. A natural and common choice of a feature selection tool is the collection of marginal p-values obtained from t-tests for testing the intensity differences at each m/z ratio in the cancer versus non-cancer samples. We study the effect of selecting a cutoff in terms of the overall Type 1 error rate control on the performance of the clustering and classification algorithms using the significant features. For the classification problem, we also considered m/z selection using the importance measures computed by the Random Forest algorithm of Breiman. Using a data set of proteomic analysis of serum from ovarian cancer patients and serum from cancer-free individuals in the Food and Drug Administration and National Cancer Institute Clinical Proteomics Database, we undertake a comparative study of the net effect of the machine learning algorithm–feature selection tool–cutoff criteria combination on the performance as measured by an appropriate error rate measure.     

Bayesian factor models in characterizing molecular adaptation

Assessing the selective influence of amino acid properties is important in understanding evolution at the molecular level. A collection of methods and models has been developed in recent years to determine if amino acid sites in a given DNA sequence alignment display substitutions that are altering or conserving a prespecified set of amino acid properties. Residues showing an elevated number of substitutions that favorably alter a physicochemical property are considered targets of positive natural selection. Such approaches usually perform independent analyses for each amino acid property under consideration, without taking into account the fact that some of the properties may be highly correlated. We propose a Bayesian hierarchical regression model with latent factor structure that allows us to determine which sites display substitutions that conserve or radically change a set of amino acid properties, while accounting for the correlation structure that may be present across such properties. We illustrate our approach by analyzing simulated data sets and an alignment of lysin sperm DNA.     

Determinants of Income Generation and Financial Performance Through Self-Help Groups

ABSTRACT

This study examines the efficacy of a microcredit-linked self-help group (SHG) program in identifying the problems faced by group members such as income generation and financial performance. To examine this, 120 members in each of three selected blocks in Birbhum District in West Bengal, India, were invited to participate. A multiple regression equation focused on identifying the contributing factors toward explaining SHG income. Results indicated that income generation for all the blocks together was significantly influenced by factors like loan amount, amount of saving, years of existence of SHG, education level of the group leader, and availability of the training facility. However, SHG-wise efficiency scores varied across the blocks that might be related to different sociocultural dimensions. Implications of the analytical findings for future research are discussed at the end of the article.     

Pseudo-empirical Bayes estimation of small area means under a nested error linear regression model with functional measurement errors

Small area estimation is studied under a nested error linear regression model with area level covariate subject to measurement error. Ghosh and Sinha (2007) obtained a pseudo-Bayes (PB) predictor of a small area mean and a corresponding pseudo-empirical Bayes (PEB) predictor, using the sample means of the observed covariate values to estimate the true covariate values. In this paper, we first derive an efficient PB predictor by using all the available data to estimate true covariate values. We then obtain a corresponding PEB predictor and show that it is asymptotically “optimal”. In addition, we employ a jackknife method to estimate the mean squared prediction error (MSPE) of the PEB predictor. Finally, we report the results of a simulation study on the performance of our PEB predictor and associated jackknife MSPE estimator. Our results show that the proposed PEB predictor can lead to significant gain in efficiency over the previously proposed PEB predictor. Area level models are also studied.     

Bayesian Estimators for Small Area Models when Auxiliary Information is Measured with Error

Small area estimators in linear models are typically expressed as a convex combination of direct estimators and synthetic estimators from a suitable model. When auxiliary information used in the model is measured with error, a new estimator, accounting for the measurement error in the covariates, has been proposed in the literature. Recently, for area‐level model, Ybarra & Lohr (Biometrika, 95, 2008, 919) suggested a suitable modification to the estimates of small area means based on Fay & Herriot (J. Am. Stat. Assoc., 74, 1979, 269) model where some of the covariates are measured with error. They used a frequentist approach based on the method of moments. Adopting a Bayesian approach, we propose to rewrite the measurement error model as a hierarchical model; we use improper non‐informative priors on the model parameters and show, under a mild condition, that the joint posterior distribution is proper and the marginal posterior distributions of the model parameters have finite variances. We conduct a simulation study exploring different scenarios. The Bayesian predictors we propose show smaller empirical mean squared errors than the frequentist predictors of Ybarra & Lohr (Biometrika, 95, 2008, 919), and they seem also to be more stable in terms of variability and bias. We apply the proposed methodology to two real examples.     

The Natsal-SF Measure of Sexual Function: Comparison of Three Scoring Methods

The Natsal-SF is a psychometrically validated measure of sexual function for use in community health surveys, derived from 17 questions reflecting three components of sexual function. Scoring requires knowledge of complex statistical modeling and, given the methodological complexities, we assessed the validity of two simplified scoring methods calculated using the factor loadings produced when originally modeling the Natsal-SF items. Method 1 uses these factor loadings to three decimal places, while method 2 assigns whole numbers to each item based on the factor loadings. Scores from these simplified methods are compared to the original score using correlation coefficients, by comparing the distributions and the scores of each method in a linear regression model with key variables. We found scores from the simplified methods both correlate highly with the original score, and the distributions of scores closely match. The simplified methods result in different regression coefficients for gender and relationship context but estimate the coefficients of all other variables similarly to the original method. While the Natsal-SF should ideally be scored using latent variable modeling, the simplified methods perform well so can be used in similar contexts, increasing the utility of the Natsal-SF and enabling future studies to measure sexual function more comprehensively.