Binary Factor Analysis Research Articles

Transcription network analysis by a sparse binary factor analysis algorithm.

Transcription factor activities (TFAs), rather than expression levels, control gene expression and provide valuable information for investigating TF-gene regulations. The underlying bimodal or switch-like patterns of TFAs may play important roles in gene regulation. Network Component Analysis (NCA) is a popular method to deduce TFAs and TF-gene control strengths from microarray data. However, it does not directly examine the bimodality of TFAs and it needs TF-gene connection topology a priori known. In this paper, we modify NCA to model gene expression regulation by Binary Factor Analysis (BFA), which directly captures switch-like patterns of TFAs. Moreover, sparse technique is employed on the mixing matrix of BFA, and thus the proposed sparse BYY-BFA algorithm, developed under Bayesian Ying-Yang (BYY) learning framework, can not only uncover the latent TFA profile’s switch-like patterns, but also be capable of automatically shutting off the unnecessary connections. Simulation study demonstrates the effectiveness of BYY-BFA, and a preliminary application to Saccharomyces cerevisiae cell cycle data and Escherichia coli carbon source transition data shows that the reconstructed binary patterns of TFAs by BYY-BFA are consistent with the ups and downs of TFAs by NCA, and that BYY-BFA also works well when the network topology is unknown.

Limited information estimation in binary factor analysis: A review and extension

Based on the Bayes modal estimate of factor scores in binary latent variable models, this paper proposes two new limited information estimators for the factor analysis model with a logistic link function for binary data based on Bernoulli distributions up to the second and the third order with maximum likelihood estimation and Laplace approximations to required integrals. These estimators and two existing limited information weighted least squares estimators are studied empirically. The limited information estimators compare favorably to full information estimators based on marginal maximum likelihood, MCMC, and multinomial distribution with a Laplace approximation methodology. Among the various estimators, Maydeu-Olivares and Joe’s (2005) weighted least squares limited information estimators implemented with Laplace approximations for probabilities are shown in a simulation to have the best root mean square errors.

Transcription Network Analysis by A Sparse Binary Factor Analysis Algorithm

Summary Transcription factor activities (TFAs), rather than expression levels, control gene expres- sion and provide valuable information for investigating TF-gene regulations. The underly- ing bimodal or switch-like patterns of TFAs may play important roles in gene regulation. Network Component Analysis (NCA) is a popular method to deduce TFAs and TF-gene control strengths from microarray data. However, it does not directly examine the bimodal- ity of TFAs and it needs the TF-gene connection topology to be a priori known. In this paper, we modify NCA to model gene expression regulation by Binary Factor Analysis (BFA), which directly captures switch-like patterns of TFAs. Moreover, sparse technique is employed on the mixing matrix of BFA, and thus the proposed sparse BYY-BFA al- gorithm, developed under Bayesian Ying-Yang (BYY) learning framework, can not only uncover the latent TFA profile’s switch-like patterns, but also be capable of automatically shutting off the unnecessary connections. Simulation study demonstrates the effectiveness of BYY-BFA, and a preliminary application to Saccharomyces cerevisiae cell cycle data and Escherichia coli carbon source transition data shows that the reconstructed binary pat- terns of TFAs by BYY-BFA are consistent with the ups and downs of TFAs by NCA, and that BYY-BFA also works well when the network topology is unknown.

Application of H-likelihood to factor analysis models with binary response data

The estimation of binary responses in factor analysis models is often complicated, because the marginal likelihood involves an intractable integral. When the number of latent variables is large, the dimensionality of a required integral will be high, and thus numerical integration would not be an ideal estimation method. This paper proposes H-likelihood for the estimation of binary response factor analysis models, avoiding the intractable integral. Examples and simulation studies demonstrate the performance of the proposed method.

The Level of Service Inventory-Revised (Lsi-R) and Australian Offenders

The Level of Service Inventory—Revised (LSI-R) assesses the risk of reoffending and identifies criminogenic need characteristics of offenders. Despite the assessment’s popularity, its factor structure remains under-researched. Inconsistency in published research may be attributed to the misuse, and inappropriate statistical analyses, of the LSI-R subscale scores. The present study explored the factor structure of the LSI-R, at the item level, using a sample of Australian offenders. Binary exploratory factor analysis found a five-factor solution for male offenders and a four-factor solution for female offenders. Using these data to “recalibrate” the LSI-R, sensitivity and specificity comparisons of the original and modified LSI-R were undertaken. With specific attention to Indigenous status and types of sentence orders served, sensitivity and specificity improvements were observed. Findings are discussed in terms of the value of exploring latent constructs and validating assessment tools, as well as the potential impact on the management and rehabilitation of Australian offenders.

Codimensional matrix pairing perspective of BYY harmony learning: hierarchy of bilinear systems, joint decomposition of data-covariance, and applications of network biology

One paper in a preceding issue of this journal has introduced the Bayesian Ying-Yang (BYY) harmony learning from a perspective of problem solving, parameter learning, and model selection. In a complementary role, the paper provides further insights from another perspective that a co-dimensional matrix pair (shortly co-dim matrix pair) forms a building unit and a hierarchy of such building units sets up the BYY system. The BYY harmony learning is re-examined via exploring the nature of a co-dim matrix pair, which leads to improved learning performance with refined model selection criteria and a modified mechanism that coordinates automatic model selection and sparse learning. Besides updating typical algorithms of factor analysis (FA), binary FA (BFA), binary matrix factorization (BMF), and nonnegative matrix factorization (NMF) to share such a mechanism, we are also led to (a) a new parametrization that embeds a de-noise nature to Gaussian mixture and local FA (LFA); (b) an alternative formulation of graph Laplacian based linear manifold learning; (c) a codecomposition of data and covariance for learning regularization and data integration; and (d) a co-dim matrix pair based generalization of temporal FA and state space model. Moreover, with help of a co-dim matrix pair in Hadamard product, we are led to a semi-supervised formation for regression analysis and a semi-blind learning formation for temporal FA and state space model. Furthermore, we address that these advances provide with new tools for network biology studies, including learning transcriptional regulatory, Protein-Protein Interaction network alignment, and network integration.

An implicitization challenge for binary factor analysis

We use tropical geometry to compute the multidegree and Newton polytope of the hypersurface of a statistical model with two hidden and four observed binary random variables, solving an open question stated by Drton, Sturmfels and Sullivant in (Drton et al., 2009, Ch. VI, Problem 7.7). The model is obtained from the undirected graphical model of the complete bipartite graph K2,4 by marginalizing two of the six binary random variables. We present algorithms for computing the Newton polytope of its defining equation by parallel walks along the polytope and its normal fan. In this way we compute vertices of the polytope. Finally, we also compute and certify its facets by studying tangent cones of the polytope at the symmetry classes of vertices. The Newton polytope has 17214912 vertices in 44938 symmetry classes and 70646 facets in 246 symmetry classes.

Mobility Management Measures by Employers: Overview and Exploratory Analysis for Belgium

The renewed interest for sustainable transport in Europe is often labelled as mobility management. With this, major attention goes towards the role of employers in the commuting behaviour of their employees. Indeed, employers can encourage a more sustainable commuting by the promotion of alternative modes, like public transport, carpooling and/or cycling, by the designation of an Employee Transport Coordinator, through their location policy, and/or by adapting work schedules and the organisation of telework. An overview of these measures is followed by an analysis of the Belgian situation. The Belgian 2005 questionnaire Home-to-WorkTravel (HTWT) enables us to make an inventory of mobility management in Belgium. The database HTWT contains information on 7460 worksites. Besides having data on modal split, work regimes and accessibility problems, 38 different mobility management measures are checked in the questionnaire. Given that we assume a relationship between accessibility problems and sustainable commuting measures both are incorporated in one analysis. Binary exploratory factor analysis (EFA) is used to make a classification and to obtain a better insight in the structure of the variables. However, no strong link between accessibility problems on the one hand and sustainable commuting measures on the other hand could be detected. Despite the absence of this link, a classification of mobility management measures and accessibility problems has been made. This indicates that employers regularly choose to implement a set of related sustainable commuting measures.

A Note on the Relation Between Factor Analytic and Item Response Theory Models

The relations among several alternative parameterizations of the binary factor analysis model and the 2-parameter item response theory model are discussed. It is pointed out that different parameterizations of factor analysis model parameters can be transformed into item response model theory parameters, and general formulas are provided. Illustrative data analysis is provided to demonstrate the transformations.

A Comparative Investigation on Model Selection in Independent Factor Analysis

With uncorrelated Gaussian factors extended to mutually independent factors beyond Gaussian, the conventional factor analysis is extended to what is recently called independent factor analysis. Typically, it is called binary factor analysis (BFA) when the factors are binary and called non-Gaussian factor analysis (NFA) when the factors are from real non-Gaussian distributions. A crucial issue in both BFA and NFA is the determination of the number of factors. In the literature of statistics, there are a number of model selection criteria that can be used for this purpose. Also, the Bayesian Ying-Yang (BYY) harmony learning provides a new principle for this purpose. This paper further investigates BYY harmony learning in comparison with existing typical criteria, including Akaik’s information criterion (AIC), the consistent Akaike’s information criterion (CAIC), the Bayesian inference criterion (BIC), and the cross-validation (CV) criterion on selection of the number of factors. This comparative study is made via experiments on the data sets with different sample sizes, data space dimensions, noise variances, and hidden factors numbers. Experiments have shown that for both BFA and NFA, in most cases BIC outperforms AIC, CAIC, and CV while the BYY criterion is either comparable with or better than BIC. In consideration of the fact that the selection by these criteria has to be implemented at the second stage based on a set of candidate models which have to be obtained at the first stage of parameter learning, while BYY harmony learning can provide not only a new class of criteria implemented in a similar way but also a new family of algorithms that perform parameter learning at the first stage with automated model selection, BYY harmony learning is more preferred since computing costs can be saved significantly.

Bayesian factor analysis for multilevel binary observations

Multilevel covariance structure models have become increasingly popular in the psychometric literature in the past few years to account for population heterogeneity and complex study designs. We develop practical simulation based procedures for Bayesian inference of multilevel binary factor analysis models. We illustrate how Markov Chain Monte Carlo procedures such as Gibbs sampling and Metropolis-Hastings methods can be used to perform Bayesian inference, model checking and model comparison without the need for multidimensional numerical integration. We illustrate the proposed estimation methods using three simulation studies and an application involving student's achievement results in different areas of mathematics.