scholarly journals Categorical Functional Data Analysis. The cfda R Package

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3074
Author(s):  
Cristian Preda ◽  
Quentin Grimonprez ◽  
Vincent Vandewalle
Keyword(s):  
Functional Data ◽  
Multiple Correspondence Analysis ◽  
Real Data ◽  
Jump Process ◽  
R Package ◽  
Finite Basis ◽  
Data Set ◽  
Stochastic Jump ◽  
Finite Set ◽  
Infinite Set

Categorical functional data represented by paths of a stochastic jump process with continuous time and a finite set of states are considered. As an extension of the multiple correspondence analysis to an infinite set of variables, optimal encodings of states over time are approximated using an arbitrary finite basis of functions. This allows dimension reduction, optimal representation, and visualisation of data in lower dimensional spaces. The methodology is implemented in the cfda R package and is illustrated using a real data set in the clustering framework.

scholarly journals A Class of Local Linear Estimators with Functional Data

2019 ◽  
pp. 379-391 ◽  
Author(s):  
Sara Leulmi ◽  
Fatiha Messaci
Keyword(s):  
Nonparametric Estimation ◽  
Metric Space ◽  
Functional Data ◽  
Regression Function ◽  
Real Data ◽  
Random Variable ◽  
Data Set ◽  
Response Variable ◽  
Local Linear ◽  
Linear Estimators

We introduce a local linear nonparametric estimation for the generalized regression function of a scalar response variable given a random variable taking values in a semi metric space. We establish a rate of uniform consistency for the proposed estimators. Then, based on a real data set we illustrate the performance of a particular studied estimator with respect to other known estimators

scholarly journals SSP: An R package to estimate sampling effort in studies of ecological communities

2020 ◽  
Author(s):  
Edlin J. Guerra-Castro ◽  
Juan Carlos Cajas ◽  
Nuno Simões ◽  
Juan J Cruz-Motta ◽  
Maite Mascaró
Keyword(s):  
Simulated Data ◽  
Real Data ◽  
R Package ◽  
Sampling Effort ◽  
Ecological Communities ◽  
Ecological Data ◽  
Data Set ◽  
Pilot Studies ◽  
Ecological Features ◽  
Wide Range

ABSTRACTSSP (simulation-based sampling protocol) is an R package that uses simulation of ecological data and dissimilarity-based multivariate standard error (MultSE) as an estimator of precision to evaluate the adequacy of different sampling efforts for studies that will test hypothesis using permutational multivariate analysis of variance. The procedure consists in simulating several extensive data matrixes that mimic some of the relevant ecological features of the community of interest using a pilot data set. For each simulated data, several sampling efforts are repeatedly executed and MultSE calculated. The mean value, 0.025 and 0.975 quantiles of MultSE for each sampling effort across all simulated data are then estimated and standardized regarding the lowest sampling effort. The optimal sampling effort is identified as that in which the increase in sampling effort do not improve the precision beyond a threshold value (e.g. 2.5 %). The performance of SSP was validated using real data, and in all examples the simulated data mimicked well the real data, allowing to evaluate the relationship MultSE – n beyond the sampling size of the pilot studies. SSP can be used to estimate sample size in a wide range of situations, ranging from simple (e.g. single site) to more complex (e.g. several sites for different habitats) experimental designs. The latter constitutes an important advantage, since it offers new possibilities for complex sampling designs, as it has been advised for multi-scale studies in ecology.

Identifying and Classifying Aberrant Response Patterns Through Functional Data Analysis

2020 ◽  
Vol 45 (6) ◽  
pp. 719-749
Author(s):  
Eduardo Doval ◽  
Pedro Delicado
Keyword(s):  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Simulated Data ◽  
Real Data ◽  
Response Patterns ◽  
Fit Indices ◽  
Person Fit ◽  
Data Set ◽  
Aberrant Response Patterns

We propose new methods for identifying and classifying aberrant response patterns (ARPs) by means of functional data analysis. These methods take the person response function (PRF) of an individual and compare it with the pattern that would correspond to a generic individual of the same ability according to the item-person response surface. ARPs correspond to atypical difference functions. The ARP classification is done with functional data clustering applied to the PRFs identified as ARP. We apply these methods to two sets of simulated data (the first is used to illustrate the ARP identification methods and the second demonstrates classification of the response patterns flagged as ARP) and a real data set (a Grade 12 science assessment test, SAT, with 32 items answered by 600 examinees). For comparative purposes, ARPs are also identified with three nonparametric person-fit indices (Ht, Modified Caution Index, and ZU3). Our results indicate that the ARP detection ability of one of our proposed methods is comparable to that of person-fit indices. Moreover, the proposed classification methods enable ARP associated with either spuriously low or spuriously high scores to be distinguished.

scholarly journals cageminer: an R/Bioconductor package to prioritize candidate genes by integrating GWAS and gene coexpression networks

2021 ◽  
Author(s):  
Fabricio Almeida-Silva ◽  
Thiago M. Venancio
Keyword(s):  
Candidate Genes ◽  
Expression Profiles ◽  
Association Studies ◽  
Real Data ◽  
R Package ◽  
Genome Wide Association Studies ◽  
High Confidence ◽  
Data Set ◽  
Gene Coexpression ◽  
Coexpression Networks

Summary: Although genome-wide association studies (GWAS) identify variants associated with traits of interest, they often fail in identifying causative genes underlying a given phenotype. Integrating GWAS and gene coexpression networks can help prioritize high-confidence candidate genes, as the expression profiles of trait-associated genes can be used to mine novel candidates. Here, we present cageminer, the first R package to prioritize candidate genes through the integration of GWAS and coexpression networks. Genes are considered high-confidence candidates if they pass all three filtering criteria implemented in cageminer, namely physical proximity to SNPs, coexpression with known trait-associated genes, and significant changes in expression levels in conditions of interest. Prioritized candidates can also be scored and ranked to select targets for experimental validation. By applying cageminer to a real data set, we demonstrate that it can effectively prioritize candidates, leading to >99% reductions in candidate gene lists. Availability and implementation: The package is available at Bioconductor (http://bioconductor.org/packages/cageminer).

ROW AND COLUMN MATRICES IN MULTIPLE CORRESPONDENCE ANALYSIS WITH ORDERED CATEGORICAL AND DICHOTOMOUS VARIABLES

2016 ◽  
Vol 78 (2) ◽  
Author(s):  
Thanoon Y. Thanoon ◽  
Robiah Adnan
Keyword(s):  
Correspondence Analysis ◽  
Multiple Correspondence Analysis ◽  
Real Data ◽  
The Other ◽  
Factor Scores ◽  
Data Set ◽  
Factor Loadings ◽  
Dichotomous Data ◽  
Dichotomous Variables ◽  
Ordered Categorical

In multiple correspondence analysis, whenever the number of variables exceeds the number of observations, row matrix should be used, but if the number of variables is less than the number of observations column matrix is the suitable procedure to follow. One of the following matrices (rows, columns) leads to loss of information that can be found by the other method, therefore, this paper developed a proposal to overcome this problem, which is: to find a shortcut method allowing the use of the results of one matrix to obtain the results of the other matrix. Taking advantage of all information available, the phenomenon was studied. Some of these results are: Eigenvectors, factor loadings and factor scores based on ordered categorical and dichotomous data. This method is illustrated by using a real data set. Results were obtained by using Minitab program. As a result, it is possible to shortcut transformation between the results of row and column matrices depending on factor loadings and factor scores of the row and column matrices.

scholarly journals Sign, Wilcoxon and Mann-Whitney Tests for Functional Data: An Approach Based on Random Projections

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 44
Author(s):  
Rafael Meléndez ◽  
Ramón Giraldo ◽  
Víctor Leiva
Keyword(s):  
Functional Data ◽  
Real Data ◽  
Nonparametric Methods ◽  
Testing Hypothesis ◽  
Random Projections ◽  
Data Set ◽  
Standard Case ◽  
Regression Methods ◽  
Two Samples ◽  
Non Gaussian

Sign, Wilcoxon and Mann-Whitney tests are nonparametric methods in one or two-sample problems. The nonparametric methods are alternatives used for testing hypothesis when the standard methods based on the Gaussianity assumption are not suitable to be applied. Recently, the functional data analysis (FDA) has gained relevance in statistical modeling. In FDA, each observation is a curve or function which usually is a realization of a stochastic process. In the literature of FDA, several methods have been proposed for testing hypothesis with samples coming from Gaussian processes. However, when this assumption is not realistic, it is necessary to utilize other approaches. Clustering and regression methods, among others, for non-Gaussian functional data have been proposed recently. In this paper, we propose extensions of the sign, Wilcoxon and Mann-Whitney tests to the functional data context as methods for testing hypothesis when we have one or two samples of non-Gaussian functional data. We use random projections to transform the functional problem into a scalar one, and then we proceed as in the standard case. Based on a simulation study, we show that the proposed tests have a good performance. We illustrate the methodology by applying it to a real data set.

scholarly journals Causal mediation analysis in presence of multiple mediators uncausally related

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Allan Jérolon ◽  
Laura Baglietto ◽  
Etienne Birmelé ◽  
Flora Alarcon ◽  
Vittorio Perduca
Keyword(s):  
Mediation Analysis ◽  
Indirect Effects ◽  
Hormone Replacement ◽  
Real Data ◽  
R Package ◽  
Multiple Mediation ◽  
Data Set ◽  
Replacement Treatment ◽  
Causal Mediation Analysis ◽  
Causal Framework

AbstractMediation analysis aims at disentangling the effects of a treatment on an outcome through alternative causal mechanisms and has become a popular practice in biomedical and social science applications. The causal framework based on counterfactuals is currently the standard approach to mediation, with important methodological advances introduced in the literature in the last decade, especially for simple mediation, that is with one mediator at the time. Among a variety of alternative approaches, Imai et al. showed theoretical results and developed an R package to deal with simple mediation as well as with multiple mediation involving multiple mediators conditionally independent given the treatment and baseline covariates. This approach does not allow to consider the often encountered situation in which an unobserved common cause induces a spurious correlation between the mediators. In this context, which we refer to as mediation with uncausally related mediators, we show that, under appropriate hypothesis, the natural direct and joint indirect effects are non-parametrically identifiable. Moreover, we adopt the quasi-Bayesian algorithm developed by Imai et al. and propose a procedure based on the simulation of counterfactual distributions to estimate not only the direct and joint indirect effects but also the indirect effects through individual mediators. We study the properties of the proposed estimators through simulations. As an illustration, we apply our method on a real data set from a large cohort to assess the effect of hormone replacement treatment on breast cancer risk through three mediators, namely dense mammographic area, nondense area and body mass index.

scholarly journals Functional random forests for curve response

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Guifang Fu ◽  
Xiaotian Dai ◽  
Yeheng Liang
Keyword(s):  
Data Analysis ◽  
Random Forests ◽  
Functional Data ◽  
Leaf Shape ◽  
Real Data ◽  
R Package ◽  
Large Set ◽  
Prediction Errors ◽  
Model Free ◽  
Application Fields

AbstractThe rapid advancement of functional data in various application fields has increased the demand for advanced statistical approaches that can incorporate complex structures and nonlinear associations. In this article, we propose a novel functional random forests (FunFor) approach to model the functional data response that is densely and regularly measured, as an extension of the landmark work of Breiman, who introduced traditional random forests for a univariate response. The FunFor approach is able to predict curve responses for new observations and selects important variables from a large set of scalar predictors. The FunFor approach inherits the efficiency of the traditional random forest approach in detecting complex relationships, including nonlinear and high-order interactions. Additionally, it is a non-parametric approach without the imposition of parametric and distributional assumptions. Eight simulation settings and one real-data analysis consistently demonstrate the excellent performance of the FunFor approach in various scenarios. In particular, FunFor successfully ranks the true predictors as the most important variables, while achieving the most robust variable sections and the smallest prediction errors when comparing it with three other relevant approaches. Although motivated by a biological leaf shape data analysis, the proposed FunFor approach has great potential to be widely applied in various fields due to its minimal requirement on tuning parameters and its distribution-free and model-free nature. An R package named ’FunFor’, implementing the FunFor approach, is available at GitHub.

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

2019 ◽  
Vol XVI (2) ◽  
pp. 1-11
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Muhammad Akbar Ali Shah ◽  
Emrah Altun
Keyword(s):  
Real Data ◽  
Continuous Model ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Probability Weighted Moment ◽  
Record Statistics ◽  
Maximum Likelihood Criterion

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

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