scholarly journals Clustering in linear mixed models with approximate Dirichlet process mixtures using EM algorithm

2013 ◽  
Vol 13 (1) ◽  
pp. 41-67 ◽  
Author(s):  
Felix Heinzl ◽  
Gerhard Tutz
PLoS ONE ◽  
2020 ◽  
Vol 15 (11) ◽  
pp. e0242073
Author(s):  
Xinyan Zhang ◽  
Boyi Guo ◽  
Nengjun Yi

Motivation The human microbiome is variable and dynamic in nature. Longitudinal studies could explain the mechanisms in maintaining the microbiome in health or causing dysbiosis in disease. However, it remains challenging to properly analyze the longitudinal microbiome data from either 16S rRNA or metagenome shotgun sequencing studies, output as proportions or counts. Most microbiome data are sparse, requiring statistical models to handle zero-inflation. Moreover, longitudinal design induces correlation among the samples and thus further complicates the analysis and interpretation of the microbiome data. Results In this article, we propose zero-inflated Gaussian mixed models (ZIGMMs) to analyze longitudinal microbiome data. ZIGMMs is a robust and flexible method which can be applicable for longitudinal microbiome proportion data or count data generated with either 16S rRNA or shotgun sequencing technologies. It can include various types of fixed effects and random effects and account for various within-subject correlation structures, and can effectively handle zero-inflation. We developed an efficient Expectation-Maximization (EM) algorithm to fit the ZIGMMs by taking advantage of the standard procedure for fitting linear mixed models. We demonstrate the computational efficiency of our EM algorithm by comparing with two other zero-inflated methods. We show that ZIGMMs outperform the previously used linear mixed models (LMMs), negative binomial mixed models (NBMMs) and zero-inflated Beta regression mixed model (ZIBR) in detecting associated effects in longitudinal microbiome data through extensive simulations. We also apply our method to two public longitudinal microbiome datasets and compare with LMMs and NBMMs in detecting dynamic effects of associated taxa.


2017 ◽  
Vol 59 (4) ◽  
pp. 433-448 ◽  
Author(s):  
S. M. Diffey ◽  
A. B. Smith ◽  
A. H. Welsh ◽  
B. R. Cullis

2021 ◽  
Vol 13 (6) ◽  
pp. 3274
Author(s):  
Suzanne Maas ◽  
Paraskevas Nikolaou ◽  
Maria Attard ◽  
Loukas Dimitriou

Bicycle sharing systems (BSSs) have been implemented in cities worldwide in an attempt to promote cycling. Despite exhibiting characteristics considered to be barriers to cycling, such as hot summers, hilliness and car-oriented infrastructure, Southern European island cities and tourist destinations Limassol (Cyprus), Las Palmas de Gran Canaria (Canary Islands, Spain) and the Valletta conurbation (Malta) are all experiencing the implementation of BSSs and policies to promote cycling. In this study, a year of trip data and secondary datasets are used to analyze dock-based BSS usage in the three case-study cities. How land use, socio-economic, network and temporal factors influence BSS use at station locations, both as an origin and as a destination, was examined using bivariate correlation analysis and through the development of linear mixed models for each case study. Bivariate correlations showed significant positive associations with the number of cafes and restaurants, vicinity to the beach or promenade and the percentage of foreign population at the BSS station locations in all cities. A positive relation with cycling infrastructure was evident in Limassol and Las Palmas de Gran Canaria, but not in Malta, as no cycling infrastructure is present in the island’s conurbation, where the BSS is primarily operational. Elevation had a negative association with BSS use in all three cities. In Limassol and Malta, where seasonality in weather patterns is strongest, a negative effect of rainfall and a positive effect of higher temperature were observed. Although there was a positive association between BSS use and the number of visiting tourists in Limassol and Malta, this is predominantly explained through the multi-collinearity with weather factors rather than by intensive use of the BSS by tourists. The linear mixed models showed more fine-grained results and explained differences in BSS use at stations, including differences for station use as an origin and as a destination. The insights from the correlation analysis and linear mixed models can be used to inform policies promoting cycling and BSS use and support sustainable mobility policies in the case-study cities and cities with similar characteristics.


2019 ◽  
Vol 38 (30) ◽  
pp. 5603-5622 ◽  
Author(s):  
Bernard G. Francq ◽  
Dan Lin ◽  
Walter Hoyer

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