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Compositional data (CoDa) often appear in various fields such as biology, medicine, geology, chemistry, economics, ecology and sociology. Although existing Dirichlet and related models are frequently employed in CoDa analysis, sometimes they may provide unsatisfactory performances in modelling CoDa as shown in our first real data example. First, this paper develops a multivariate compositional inverse Gaussian (CIG) model as a new tool for analysing CoDa. By incorporating the stochastic representation (SR), the expectation–maximization (EM) algorithm (aided by a one-step gradient descent algorithm) can be established to solve the parameter estimation for the proposed distribution (model). Next, zero observations may be often encountered in the real CoDa analysis. Therefore, the second aim of this paper is to propose a new model (called as ZCIG model) through a novel mixture SR based on both the CIG random vector and a so-called zero-truncated product Bernoulli random vector to model CoDa with zeros. Corresponding statistical inference methods are also developed for both cases without/with covariates. Two real data sets are analysed to illustrate the proposed statistical methods by comparing the proposed CIG and ZCIG models with existing Dirichlet and logistic-normal models. [ABSTRACT FROM AUTHOR]

Missing observations in r × c contingency tables often occur in medical, bio-pharmaceutical and epidemiological researches. The most common method to analyze incomplete contingency tables simply removes the non-response counts from both variables or depends on an independence assumption, which may be improper and could result in unreliable conclusions because of the under-estimation of the uncertainty. In this article, we first derive the valid sampling distribution of the observed counts by taking three categories missing data into consideration under the assumption of missing at random and the assumption of the total number of observations being fixed. Next, based on the new sampling distribution, the Fisher scoring algorithm for calculating the maximum likelihood estimates of parameters is developed, and the small-sample bootstrap confidence interval method is also provided. In addition, we theoretically compare the proposed sampling distribution with two existing sampling distributions, and conduct some simulations to investigate the performance of the three different sampling distributions in statistical inferences. Finally, two real data sets are analyzed to illustrate the newly proposed sampling distribution and corresponding statistical methods. [ABSTRACT FROM AUTHOR]

Background: Emerging functional imaging studies suggest that schizophrenia is associated with aberrant spatiotemporal interaction which may result in aberrant global and local dynamic properties. Methods: We investigated the dynamic functional connectivity (FC) by using instantaneous phase method based on Hilbert transform to detect abnormal spatiotemporal interaction in schizophrenia. Based on resting-state functional magnetic resonance imaging, two independent datasets were included, with 114 subjects from COBRE [51 schizophrenia patients (SZ) and 63 healthy controls (HCs)] and 96 from OpenfMRI (36 SZ and 60 HCs). Phase differences and instantaneous coupling matrices were firstly calculated at all time points by extracting instantaneous parameters. Global [global synchrony and intertemporal closeness (ITC)] and local dynamic features [strength of FC (sFC) and variability of FC (vFC)] were compared between two groups. Support vector machine (SVM) was used to estimate the ability to discriminate two groups by using all aberrant features. Results: We found SZ had lower global synchrony and ITC than HCs on both datasets. Furthermore, SZ had a significant decrease in sFC but an increase in vFC, which were mainly located at prefrontal cortex, anterior cingulate cortex, temporal cortex and visual cortex or temporal cortex and hippocampus, forming significant dynamic subnetworks. SVM analysis revealed a high degree of balanced accuracy (85.75%) on the basis of all aberrant dynamic features. Conclusions: SZ has worse overall spatiotemporal stability and extensive FC subnetwork lesions compared to HCs, which to some extent elucidates the pathophysiological mechanism of schizophrenia, providing insight into time-variation properties of patients with other mental illnesses. [ABSTRACT FROM AUTHOR]

To model count data with excess zeros, ones and twos, for the first time we introduce a so-called zero-one-two-inflated Poisson (ZOTIP) distribution, including the zero-inflated Poisson (ZIP) and the zero-and-one-inflated Poisson (ZOIP) distributions as two special cases. We establish three equivalent stochastic representations for the ZOTIP random variable to develop important distributional properties of the ZOTIP distribution. The Fisher scoring and expectation–maximization (EM) algorithms are derived to obtain the maximum likelihood estimates of parameters of interest. Bootstrap confidence intervals are also provided. Testing hypotheses are considered, simulation studies are conducted, and two real data sets are used to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]