Dirichlet-multinomial Regression Model Research Articles

A Model of Dynamic Flows: Explaining Turkey’s Interprovincial Migration

The flow of resources across nodes over time (e.g., migration, financial transfers, peer-to-peer interactions) is a common phenomenon in sociology. Standard statistical methods are inadequate to model such interdependent flows. We propose a hierarchical Dirichlet-multinomial regression model and a Bayesian estimation method. We apply the model to analyze 25,632,876 migration instances that took place between Turkey’s 81 provinces from 2009 to 2018. We then discuss the methodological and substantive implications of our results. Methodologically, we demonstrate the predictive advantage of our model compared to its most common alternative in migration research, the gravity model. We also discuss our model in the context of other approaches, mostly developed in the social networks literature. Substantively, we find that population, economic prosperity, the spatial and political distance between the origin and destination, the strength of the AKP (Justice and Development Party) in a province, and the network characteristics of the provinces are important predictors of migration, whereas the proportion of ethnic minority Kurds in a province has no positive association with in- and out-migration.

The rhizosphere microbiome and host plant glucosinolates exhibit feedback cycles in Brassica rapa.

The rhizosphere microbiome influences many aspects of plant fitness, including production of secondary compounds and defence against insect herbivores. Plants also modulate the composition of the microbial community in the rhizosphere via secretion of root exudates. We tested both the effect of the rhizosphere microbiome on plant traits, and host plant effects on rhizosphere microbes using recombinant inbred lines (RILs) of Brassica rapa that differ in production of glucosinolates (GLS), secondary metabolites that contribute to defence against insect herbivores. First, we investigated the effect of genetic variation in GLS production on the composition of the rhizosphere microbiome. Using a Bayesian Dirichlet-multinomial regression model (DMBVS), we identified both negative and positive associations between bacteria from six genera and the concentration of five GLS compounds produced in plant roots. Additionally, we tested the effects of microbial inoculation (an intact vs. disrupted soil microbiome) on GLS production and insect damage in these RILs. We found a significant microbial treatment × genotype interaction, in which total GLS was higher in the intact relative to the disrupted microbiome treatment in some RILs. However, despite differences in GLS production between microbial treatments, we observed no difference in insect damage between treatments. Together, these results provide evidence for a full feedback cycle of plant-microbe interactions mediated by GLS; that is, GLS compounds produced by the host plant "feed-down" to influence rhizosphere microbial community and rhizosphere microbes "feed-up" to influence GLS production.

New patterns in the locational choice of immigrants in Spain

ABSTRACTDuring recent years, Spain has experienced an important revolution in its migration flows. With the 2008–2013 Spanish financial crisis, the model of economic growth that attracted a large number of foreign people disappeared, and the entry of immigrants for reasons other than economic issues gained relevance. Linked with this phenomenon are the new patterns of locational choice across provinces and the variation in the nature of immigrants. In this paper, we examine the differential patterns and drivers of immigration across Spanish regions before and after the financial crisis. Special attention is paid to the question of how the characteristics of individual migrants influence their locational preferences. To answer this question, we use the Dirichlet multinomial regression model. The results obtained show a sharp change in the locational patterns of Spanish immigrants after the economic recession, confirming that traditional economic incentives are less relevant, while non-economic factors linked with a better lifestyle gain importance. They also reveal that, regardless of the economic conditions, network effects are strong. Finally, and what is probably more important for us, our estimates support the hypothesis that the locational preferences rely on the interaction between the immigrants’ characteristics and the underlying locational features.

Modeling Information Content Via Dirichlet-Multinomial Regression Analysis

ABSTRACTShannon entropy is being increasingly used in biomedical research as an index of complexity and information content in sequences of symbols, e.g. languages, amino acid sequences, DNA methylation patterns and animal vocalizations. Yet, distributional properties of information entropy as a random variable have seldom been the object of study, leading to researchers mainly using linear models or simulation-based analytical approach to assess differences in information content, when entropy is measured repeatedly in different experimental conditions. Here a method to perform inference on entropy in such conditions is proposed. Building on results coming from studies in the field of Bayesian entropy estimation, a symmetric Dirichlet-multinomial regression model, able to deal efficiently with the issue of mean entropy estimation, is formulated. Through a simulation study the model is shown to outperform linear modeling in a vast range of scenarios and to have promising statistical properties. As a practical example, the method is applied to a data set coming from a real experiment on animal communication.

An integrative Bayesian Dirichlet-multinomial regression model for the analysis of taxonomic abundances in microbiome data

BackgroundThe Human Microbiome has been variously associated with the immune-regulatory mechanisms involved in the prevention or development of many non-infectious human diseases such as autoimmunity, allergy and cancer. Integrative approaches which aim at associating the composition of the human microbiome with other available information, such as clinical covariates and environmental predictors, are paramount to develop a more complete understanding of the role of microbiome in disease development.ResultsIn this manuscript, we propose a Bayesian Dirichlet-Multinomial regression model which uses spike-and-slab priors for the selection of significant associations between a set of available covariates and taxa from a microbiome abundance table. The approach allows straightforward incorporation of the covariates through a log-linear regression parametrization of the parameters of the Dirichlet-Multinomial likelihood. Inference is conducted through a Markov Chain Monte Carlo algorithm, and selection of the significant covariates is based upon the assessment of posterior probabilities of inclusions and the thresholding of the Bayesian false discovery rate. We design a simulation study to evaluate the performance of the proposed method, and then apply our model on a publicly available dataset obtained from the Human Microbiome Project which associates taxa abundances with KEGG orthology pathways. The method is implemented in specifically developed R code, which has been made publicly available.ConclusionsOur method compares favorably in simulations to several recently proposed approaches for similarly structured data, in terms of increased accuracy and reduced false positive as well as false negative rates. In the application to the data from the Human Microbiome Project, a close evaluation of the biological significance of our findings confirms existing associations in the literature.

Variable selection for sparse Dirichlet-multinomial regression with an application to microbiome data analysis

With the development of next generation sequencing technology, researchers have now been able to study the microbiome composition using direct sequencing, whose output are bacterial taxa counts for each microbiome sample. One goal of microbiome study is to associate the microbiome composition with environmental covariates. We propose to model the taxa counts using a Dirichlet-multinomial (DM) regression model in order to account for overdispersion of observed counts. The DM regression model can be used for testing the association between taxa composition and covariates using the likelihood ratio test. However, when the number of the covariates is large, multiple testing can lead to loss of power. To deal with the high dimensionality of the problem, we develop a penalized likelihood approach to estimate the regression parameters and to select the variables by imposing a sparse group [Formula: see text] penalty to encourage both group-level and within-group sparsity. Such a variable selection procedure can lead to selection of the relevant covariates and their associated bacterial taxa. An efficient block-coordinate descent algorithm is developed to solve the optimization problem. We present extensive simulations to demonstrate that the sparse DM regression can result in better identification of the microbiome-associated covariates than models that ignore overdispersion or only consider the proportions. We demonstrate the power of our method in an analysis of a data set evaluating the effects of nutrient intake on human gut microbiome composition. Our results have clearly shown that the nutrient intake is strongly associated with the human gut microbiome.