119 research outputs found

    Model Selection for Exposure-Mediator Interaction

    Full text link
    In mediation analysis, the exposure often influences the mediating effect, i.e., there is an interaction between exposure and mediator on the dependent variable. When the mediator is high-dimensional, it is necessary to identify non-zero mediators (M) and exposure-by-mediator (X-by-M) interactions. Although several high-dimensional mediation methods can naturally handle X-by-M interactions, research is scarce in preserving the underlying hierarchical structure between the main effects and the interactions. To fill the knowledge gap, we develop the XMInt procedure to select M and X-by-M interactions in the high-dimensional mediators setting while preserving the hierarchical structure. Our proposed method employs a sequential regularization-based forward-selection approach to identify the mediators and their hierarchically preserved interaction with exposure. Our numerical experiments showed promising selection results. Further, we applied our method to ADNI morphological data and examined the role of cortical thickness and subcortical volumes on the effect of amyloid-beta accumulation on cognitive performance, which could be helpful in understanding the brain compensation mechanism.Comment: 15 pages, 3 figure

    Independent component analysis on spectral domain

    Get PDF
    Independent component analysis (ICA) is an effective data-driven method for blind source separation. It has been successfully applied to separate source signals of interest from their mixtures. Most existing ICA procedures are carried out by relying solely on the estimation of the marginal density functions, either parametrically or nonparametrically. In many applications, correlation structures within each source also play an important role besides the marginal distributions. One important example is functional magnetic resonance imaging (fMRI) analysis where the brain-function-related signals are temporally correlated. In this thesis, we propose two novel ICA algorithms that fully exploit the correlation structures within the source signals through spectral density estimation. Our methodology development is two-fold: 1) ICA for auto-correlated sources via parametric spectral density estimation (cICA-YW); 2) ICA for sources with mixed spectra via nonparametric spectral density estimation and atom detection (cICA-LSP). The cICA-YW focuses on the sources with autocorrelation and is implemented using spectral density functions from frequently used time series models such as autoregressive moving average (ARMA) processes. The time series parameters and the mixing matrix are estimated via maximizing the Whittle likelihood function. We illustrate the performance of the proposed method through extensive simulation studies and a real fMRI application. The numerical results indicate that our approach outperforms several popular methods including the most widely used fastICA algorithm. We also establish the sampling properties of the proposed method. For the cICA-LSP, we consider the case of sources with possibly mixed spectra, where ARMA estimates are often unstable. Specifically, we propose to estimate the spectral density functions and the line spectra of the source signals using cubic splines and indicator functions, respectively. The mixed spectra and the mixing matrix are estimated via maximizing the Whittle likelihood function. We illustrate the performance of the proposed method through extensive simulation studies.Doctor of Philosoph

    Nonparametric Independent Component Analysis for the Sources with Mixed Spectra

    Full text link
    Independent component analysis (ICA) is a blind source separation method to recover source signals of interest from their mixtures. Most existing ICA procedures assume independent sampling. Second-order-statistics-based source separation methods have been developed based on parametric time series models for the mixtures from the autocorrelated sources. However, the second-order-statistics-based methods cannot separate the sources accurately when the sources have temporal autocorrelations with mixed spectra. To address this issue, we propose a new ICA method by estimating spectral density functions and line spectra of the source signals using cubic splines and indicator functions, respectively. The mixed spectra and the mixing matrix are estimated by maximizing the Whittle likelihood function. We illustrate the performance of the proposed method through simulation experiments and an EEG data application. The numerical results indicate that our approach outperforms existing ICA methods, including SOBI algorithms. In addition, we investigate the asymptotic behavior of the proposed method.Comment: 27 pages, 10 figure

    Selective Association between Cortical Thickness and Reference Abilities in Normal Aging

    Get PDF
    A previous study of reference abilities and cortical thickness reported that association between reference abilities and cortical thickness summarized over large ROIs suppressed was suppressed after controlling for mean cortical thickness and global cognition. In this manuscript, we showed that preserving detailed spatial patterns of cortical thickness can identify reference-ability-specific association besides the association explained by global cognition and mean cortical thickness. We identified associations between cortical thickness and 3 cognitive reference abilities after controlling for mean thickness, global cognition, and linear chronological age: (1) memory, (2) perceptual speed, and (3) vocabulary. Global cognition was correlated with mean overall thickness but also was found to have a regionally specific pattern of associations. Nonlinear associations between cortical thickness and cognition were not observed, neither were nonlinear age effects. Age-by-thickness interactions were also absent. This implies that all thickness-cognition relations and age associations are independent of age and that consequently no age range is inherently special, since brain-behavioral findings are invariant across the whole age range
    corecore