scholarly journals On Some Mixture Models for Over-dispersed Binary Data

2017 ◽  
Vol 6 (2) ◽  
pp. 134
Author(s):  
Bayo H. Lawal
Keyword(s):  
Mixture Models ◽  
Binary Data ◽  
Mixed Model ◽  
Gaussian Quadrature ◽  
Optimization Methods ◽  
Data Sets ◽  
Binomial Mixture ◽  
Adaptive Gaussian Quadrature ◽  
Quasi Newton ◽  
Proc Nlmixed

In this paper, we consider several binomial mixture models for fitting over-dispersed binary data. The models range from the binomial itself, to the beta-binomial (BB), the Kumaraswamy distributions I and II (KPI \& KPII) as well as the McDonald generalized beta-binomial mixed model (McGBB). The models are applied to five data sets that have received attention in various literature. Because of convergence issues, several optimization methods ranging from the Newton-Raphson to the quasi-Newton optimization algorithms were employed with SAS PROC NLMIXED using the Adaptive Gaussian Quadrature as the integral approximation method within PROC NLMIXED. Our results differ from those presented in Li, Huang and Zhao (2011) for the example data sets in that paper but agree with those presented in Manoj, Wijekoon and Yapa (2013). We also applied these models to the case where we have a $k$ vector of covariates $(x_1, x_2, \ldots, x_k)^{'}$. Our results here suggest that the McGBB performs better than the other models in the GLM framework. All computations in this paper employed PROC NLMIXED in SAS. We present in the appendix a sample of the SAS program employed for implementing the McGBB model for one of the examples.

scholarly journals Mixture models as a method for comparative sociality: social networks and demographic change in resident killer whales

2021 ◽  
Vol 75 (4) ◽  
Author(s):  
Samuel Ellis ◽  
Daniel W. Franks ◽  
Michael N. Weiss ◽  
Michael A. Cant ◽  
Paolo Domenici ◽  
...  
Keyword(s):  
Mixture Models ◽  
Demographic Change ◽  
Social Preferences ◽  
Social Bonds ◽  
Killer Whales ◽  
Animal Populations ◽  
Binomial Mixture ◽  
Opposite Sex ◽  
Social Associations ◽  
Social Association

Abstract In studies of social behaviour, social bonds are usually inferred from rates of interaction or association. This approach has revealed many important insights into the proximate formation and ultimate function of animal social structures. However, it remains challenging to compare social structure between systems or time-points because extrinsic factors, such as sampling methodology, can also influence the observed rate of association. As a consequence of these methodological challenges, it is difficult to analyse how patterns of social association change with demographic processes, such as the death of key social partners. Here we develop and illustrate the use of binomial mixture models to quantitatively compare patterns of social association between networks. We then use this method to investigate how patterns of social preferences in killer whales respond to demographic change. Resident killer whales are bisexually philopatric, and both sexes stay in close association with their mother in adulthood. We show that mothers and daughters show reduced social association after the birth of the daughter’s first offspring, but not after the birth of an offspring to the mother. We also show that whales whose mother is dead associate more with their opposite sex siblings and with their grandmother than whales whose mother is alive. Our work demonstrates the utility of using mixture models to compare social preferences between networks and between species. We also highlight other potential uses of this method such as to identify strong social bonds in animal populations. Significance statement Comparing patters of social associations between systems, or between the same systems at different times, is challenging due to the confounding effects of sampling and methodological differences. Here we present a method to allow social associations to be robustly classified and then compared between networks using binomial mixture models. We illustrate this method by showing how killer whales change their patterns of social association in response to the birth of calves and the death of their mother. We show that after the birth of her calf, females associate less with their mother. We also show that whales’ whose mother is dead associate more with their opposite sex siblings and grandmothers than whales’ whose mother is alive. This clearly demonstrates how this method can be used to examine fine scale temporal processes in animal social systems.

Nondegenerate Piecewise Linear Systems: A Finite Newton Algorithm and Applications in Machine Learning

2012 ◽  
Vol 24 (4) ◽  
pp. 1047-1084 ◽  
Author(s):  
Xiao-Tong Yuan ◽  
Shuicheng Yan
Keyword(s):  
Linear Systems ◽  
Optimization Problems ◽  
Piecewise Linear ◽  
Optimization Methods ◽  
Coefficient Matrix ◽  
Learning Problems ◽  
Support Vector ◽  
Data Sets ◽  
Piecewise Linear Systems ◽  
Vector Machines

We investigate Newton-type optimization methods for solving piecewise linear systems (PLSs) with nondegenerate coefficient matrix. Such systems arise, for example, from the numerical solution of linear complementarity problem, which is useful to model several learning and optimization problems. In this letter, we propose an effective damped Newton method, PLS-DN, to find the exact (up to machine precision) solution of nondegenerate PLSs. PLS-DN exhibits provable semiiterative property, that is, the algorithm converges globally to the exact solution in a finite number of iterations. The rate of convergence is shown to be at least linear before termination. We emphasize the applications of our method in modeling, from a novel perspective of PLSs, some statistical learning problems such as box-constrained least squares, elitist Lasso (Kowalski & Torreesani, 2008 ), and support vector machines (Cortes & Vapnik, 1995 ). Numerical results on synthetic and benchmark data sets are presented to demonstrate the effectiveness and efficiency of PLS-DN on these problems.

MODELING AVIAN ABUNDANCE FROM REPLICATED COUNTS USING BINOMIAL MIXTURE MODELS

2005 ◽  
Vol 15 (4) ◽  
pp. 1450-1461 ◽  
Author(s):  
Marc Kéry ◽  
J. Andrew Royle ◽  
Hans Schmid
Keyword(s):  
Mixture Models ◽  
Avian Abundance ◽  
Binomial Mixture

Migration‐based traveltime waveform inversion of 2-D simple structures: A synthetic example

Geophysics ◽  
2001 ◽  
Vol 66 (3) ◽  
pp. 845-860 ◽  
Author(s):  
François Clément ◽  
Guy Chavent ◽  
Susana Gómez
Keyword(s):  
Least Squares ◽  
Waveform Inversion ◽  
Domain Of Attraction ◽  
Optimization Methods ◽  
Data Sets ◽  
Seismic Reflection Data ◽  
Prestack Migration ◽  
Reflection Data ◽  
Full Wave ◽  
The Time Domain

Migration‐based traveltime (MBTT) formulation provides algorithms for automatically determining background velocities from full‐waveform surface seismic reflection data using local optimization methods. In particular, it addresses the difficulty of the nonconvexity of the least‐squares data misfit function. The method consists of parameterizing the reflectivity in the time domain through a migration step and providing a multiscale representation for the smooth background velocity. We present an implementation of the MBTT approach for a 2-D finite‐difference (FD) full‐wave acoustic model. Numerical analysis on a 2-D synthetic example shows the ability of the method to find much more reliable estimates of both long and short wavelengths of the velocity than the classical least‐squares approach, even when starting from very poor initial guesses. This enlargement of the domain of attraction for the global minima of the least‐squares misfit has a price: each evaluation of the new objective function requires, besides the usual FD full‐wave forward modeling, an additional full‐wave prestack migration. Hence, the FD implementation of the MBTT approach presented in this paper is expected to provide a useful tool for the inversion of data sets of moderate size.

Functional Delineation of Prefrontal Networks Underlying Working Memory in Schizophrenia: A Cross-data-set Examination

2021 ◽  
pp. 1-29
Author(s):  
Nicole Sanford ◽  
Todd S. Woodward
Keyword(s):  
Working Memory ◽  
Mixed Model ◽  
Data Sets ◽  
Generation Task ◽  
Data Set ◽  
Set Switching ◽  
Dorsolateral Prefrontal ◽  
Task Conditions ◽  
Experiment Analysis ◽  
Internal Attention

Abstract Background: Working memory (WM) impairment in schizophrenia substantially impacts functional outcome. Although the dorsolateral pFC has been implicated in such impairment, a more comprehensive examination of brain networks comprising pFC is warranted. The present research used a whole-brain, multi-experiment analysis to delineate task-related networks comprising pFC. Activity was examined in schizophrenia patients across a variety of cognitive demands. Methods: One hundred schizophrenia patients and 102 healthy controls completed one of four fMRI tasks: a Sternberg verbal WM task, a visuospatial WM task, a Stroop set-switching task, and a thought generation task (TGT). Task-related networks were identified using multi-experiment constrained PCA for fMRI. Effects of task conditions and group differences were examined using mixed-model ANOVA on the task-related time series. Correlations between task performance and network engagement were also performed. Results: Four spatially and temporally distinct networks with pFC activation emerged and were postulated to subserve (1) internal attention, (2) auditory–motor attention, (3) motor responses, and (4) task energizing. The “energizing” network—engaged during WM encoding and diminished in patients—exhibited consistent trend relationships with WM capacity across different data sets. The dorsolateral-prefrontal-cortex-dominated “internal attention” network exhibited some evidence of hypoactivity in patients, but was not correlated with WM performance. Conclusions: Multi-experiment analysis allowed delineation of task-related, pFC-anchored networks across different cognitive constructs. Given the results with respect to the early-responding “energizing” network, WM deficits in schizophrenia may arise from disruption in the “energization” process described by Donald Stuss' model of pFC functions.

scholarly journals Safe projections of binary data sets

2006 ◽  
Vol 42 (8-9) ◽  
pp. 617-638 ◽  
Author(s):  
Nikolaj Tatti
Keyword(s):  
Binary Data ◽  
Data Sets

scholarly journals Approaches to improve the robustness of the Comparison Model Method for the inverse problem of groundwater hydrology

2021 ◽  
Author(s):  
Alessandro Comunian ◽  
Mauro Giudici
Keyword(s):  
Geometric Mean ◽  
Optimization Methods ◽  
Forward Problem ◽  
Data Sets ◽  
Direct Inversion ◽  
Model Method ◽  
Comparison Model ◽  
Multiple Data ◽  
Hydraulic Gradients ◽  
Multiple Data Sets

<p>Indirect inversion approaches are widely used in Geosciences, and in particular also for the identification of the hydraulic properties of aquifers. Nevertheless, their application requires a substantial number of model evaluation (forward problem) runs, a task that for complex problems can be computationally intensive. Reducing this computational burden is an active research topic, and many solutions, including the use of hybrid optimization methods, the use of physical proxies or again machine-learning tools <span>allow to avoid</span> considering the full physics of the problem when running a numerical implementation of the forward problem.</p><p>Direct inversion approaches represent computationally frugal alternatives to indirect approaches, because in general they require a smaller number of runs of the forward problem. The classical drawbacks of these methods can be alleviated by some implementation approaches and in particular by using multiple sets of data, when available.</p><p>This work is an effort to improve the robustness of the Comparison Model Method (CMM), a direct inversion approach aimed at the identification of the hydraulic transmissivity of a confined aquifer. The robustness of the CMM is here ameliorated by (i) improving the parameterization required to handle small hydraulic gradients; (ii) investigating the role of different criteria aimed at merging multiple data-sets corresponding to different flow conditions.</p><p>On a synthetic case study, it is demonstrated that correcting a small percentage of the small hydraulic gradients (about 10%) allows to obtain reliable results, and that a criteria based on the geometric mean is adequate to merge the results coming from multiple data-sets. In addition, the use of multiple-data sets allows to noticeably improve the robustness of the CMM when the input data are affected by noise.</p><p>All the tests are performed by using open source and widely <span>used</span> tools like the USGS Modflow6 and its Python interface flopy to foster the application of the <span>CMM. The scripts and corresponding package</span>, named <em>cmmpy</em>, is available on the Python Package Index (PyPI) and on bitbucket at the following address: https://bitbucket.org/alecomunian/cmmpy.</p>

Approximate confidence intervals for the difference in proportions for partially observed binary data

2021 ◽  
pp. 096228022110605
Author(s):  
Ujjwal Das ◽  
Ranojoy Basu
Keyword(s):  
Binary Data ◽  
Type I Error ◽  
Missing At Random ◽  
Matched Pair ◽  
Data Sets ◽  
Type I ◽  
Real World Data ◽  
Partially Observed ◽  
The Difference ◽  
Interval Estimator

We consider partially observed binary matched-pair data. We assume that the incomplete subjects are missing at random. Within this missing framework, we propose an EM-algorithm based approach to construct an interval estimator of the proportion difference incorporating all the subjects. In conjunction with our proposed method, we also present two improvements to the interval estimator through some correction factors. The performances of the three competing methods are then evaluated through extensive simulation. Recommendation for the method is given based on the ability to preserve type-I error for various sample sizes. Finally, the methods are illustrated in two real-world data sets. An R-function is developed to implement the three proposed methods.

The Impact of Clinical Review Bias on Child Language Grammaticality

2019 ◽  
Vol 41 (4) ◽  
pp. 214-221
Author(s):  
Anny P. Castilla-Earls ◽  
Brittany Harvey ◽  
Katrina Fulcher-Rood ◽  
Christopher D. Barr
Keyword(s):  
Clinical Review ◽  
Language Impairment ◽  
Binary Data ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Child Language ◽  
Communication Disorders ◽  
The Impact ◽  
English Students ◽  
Language Sample

The purpose of this study was to examine the impact of clinical review bias on the coding of grammaticality in child language. Seventy-four native-English students studying communication disorders and sciences made judgments about the grammaticality of 250 utterances presented in five language samples. Each language sample included grammatical, ungrammatical, and ambiguous utterances. Participants were randomly assigned to a blind or nonblind group. The nonblind group was presented with diagnostic information, whereas the blind group was not. We employed a generalized linear mixed model to examine the binary data. Our results suggest that both blind and nonblind participants were accurate in judging grammatical and ungrammatical utterances. However, nonblind participants were slightly more likely to judge ambiguous utterances as ungrammatical when the language sample identified the child as having a language impairment, suggesting that there was an effect of clinical review bias in this study. This effect, although statistically significant, was small.

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