scholarly journals Convergence Theorems in Multinomial Saturated and Logistic Models

2020 ◽  
Vol 43 (2) ◽  
pp. 211-231
Author(s):  
Erick Orozco-Acosta ◽  
Humberto LLinás-Solano ◽  
Javier Fonseca-Rodríguez
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Theory ◽  
Theoretical Study ◽  
Logistic Models ◽  
Convergence Theorems ◽  
Response Variable ◽  
Multinomial Models ◽  
Statistical Program ◽  
Using Data ◽  
Information Matrices

In  this  paper,  we  develop  a  theoretical study about the  logistic  and saturated multinomial models when the response  variable takes  one of R ≥ 2 levels.  Several  theorems on the  existence  and  calculations of the  maximum likelihood  (ML)  estimates of the  parameters of both  models  are  presented and  demonstrated. Furthermore, properties are identified and,  based  on an asymptotic  theory,  convergence theorems are  tested for  score  vectors  and information matrices of both  models.  Finally, an application of this  theory is presented and  assessed  using data from the  R statistical program.

scholarly journals Genome-wide association study of psychiatric and substance use comorbidity in Mexican individuals

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
José Jaime Martínez-Magaña ◽  
Alma Delia Genis-Mendoza ◽  
Jorge Ameth Villatoro Velázquez ◽  
Marycarmen Bustos-Gamiño ◽  
Isela Esther Juárez-Rojop ◽  
...  
Keyword(s):  
Substance Use ◽  
Association Study ◽  
Genome Wide Association Study ◽  
Logistic Models ◽  
Genome Wide Association ◽  
Risk Scores ◽  
Multinomial Models ◽  
Gamma Receptor ◽  
Genome Wide ◽  
A Genome

AbstractThe combination of substance use and psychiatric disorders is one of the most common comorbidities. The objective of this study was to perform a genome-wide association study of this comorbidity (Com), substance use alone (Subs), and psychiatric symptomatology alone (Psych) in the Mexican population. The study included 3914 individuals of Mexican descent. Genotyping was carried out using the PsychArray microarray and genome-wide correlations were calculated. Genome-wide associations were analyzed using multiple logistic models, polygenic risk scores (PRSs) were evaluated using multinomial models, and vertical pleiotropy was evaluated by generalized summary-data-based Mendelian randomization. Brain DNA methylation quantitative loci (brain meQTL) were also evaluated in the prefrontal cortex. Genome-wide correlation and vertical pleiotropy were found between all traits. No genome-wide association signals were found, but 64 single-nucleotide polymorphism (SNPs) reached nominal associations (p < 5.00e−05). The SNPs associated with each trait were independent, and the individuals with high PRSs had a higher prevalence of tobacco and alcohol use. In the multinomial models all of the PRSs (Subs-PRS, Com-PRS, and Psych-PRS) were associated with all of the traits. Brain meQTL of the Subs-associated SNPs had an effect on the genes enriched in insulin signaling pathway, and that of the Psych-associated SNPs had an effect on the Fc gamma receptor phagocytosis pathway.

Disproportionately Overrepresented: Women in Local Elected Offices

2018 ◽  
Vol 50 (3) ◽  
pp. 165-176 ◽  
Author(s):  
Ethan M. Bernick ◽  
Brianne Heidbreder
Keyword(s):  
United States ◽  
Maximum Likelihood ◽  
Gender Norms ◽  
The United States ◽  
Census Bureau ◽  
National Association ◽  
County Level ◽  
Political Factors ◽  
Using Data ◽  
The U.S

This research examines the position of county clerk, where women are numerically disproportionately over-represented. Using data collected from the National Association of Counties and the U.S. Census Bureau, the models estimate the correlation between the county clerk’s sex and county-level demographic, social, and political factors with maximum likelihood logit estimates. This research suggests that while women are better represented in the office of county clerk across the United States, when compared to other elective offices, this representation may be because this office is not seen as attractive to men and its responsibilities fit within the construct of traditional gender norms.

scholarly journals Methods for Stratified Cluster Sampling with Informative Stratification

2007 ◽  
Vol 2007 ◽  
pp. 1-12
Author(s):  
Alastair Scott ◽  
Chris Wild
Keyword(s):  
Maximum Likelihood ◽  
Regression Models ◽  
Population Distribution ◽  
Estimating Equation ◽  
Cluster Sampling ◽  
Likelihood Methods ◽  
Weighted Estimating Equation ◽  
The Family ◽  
Maximum Likelihood Methods ◽  
Using Data

We look at fitting regression models using data from stratified cluster samples when the strata may depend in some way on the observed responses within clusters. One important subclass of examples is that of family studies in genetic epidemiology, where the probability of selecting a family into the study depends on the incidence of disease within the family. We develop the survey-weighted estimating equation approach for this problem, with particular emphasis on the estimation of superpopulation parameters. Full maximum likelihood for this class of problems involves modelling the population distribution of the covariates which is simply not feasible when there are a large number of potential covariates. We discuss efficient semiparametric maximum likelihood methods in which the covariate distribution is left completely unspecified. We further discuss the relative efficiencies of these two approaches.

scholarly journals Epidemiology of recreational football in Brazil: prevalence and association with risk factors for chronic diseases and self-rated health in adults

2013 ◽  
Vol 19 (1) ◽  
pp. 224-230 ◽  
Author(s):  
Alex Antonio Florindo ◽  
José Cazuza de Farias Júnior ◽  
Jonathan Charles Kingdon Wells ◽  
Pedro Curi Hallal
Keyword(s):  
Descriptive Analysis ◽  
Logistic Models ◽  
Cross Sectional Study ◽  
Football Players ◽  
Cross Sectional ◽  
Health And Wellbeing ◽  
Self Rated Health ◽  
The Social ◽  
Using Data ◽  
Weekly Frequency

The aim of this study was to describe the social and health characteristics of adults who practice football for recreation in adult living in Brazil. This was a cross-sectional study using data from the VIGITEL Surveillance System. In 2006, 54,369 interviews were carried out with adults. Individuals were classified in three groups: inactive in leisure-time; recreational football participants: one/ two times per week or three or more times per week. We ran descriptive analysis and binary logistic models. Recreation footballers in Brazil are mostly young men of low schooling levels. The southeastern region had the greatest proportion of practitioners in Brazil. Most footballers practiced once or two times per week (75.9%), for 60 minutes or more per day (87.7%), and used public locations (94.2%). Football players had less obesity and poor self-rated health compared with inactive. Football practice seems to provide health and wellbeing benefits, independent of the weekly frequency.

scholarly journals Comparative effectiveness of dimethyl fumarate in Multiple Sclerosis

2021 ◽  
Author(s):  
Pauline Bosco-Levy ◽  
Marc Debouverie ◽  
Bruno Brochet ◽  
Céline Louapre ◽  
Elisabeth Maillard ◽  
...  
Keyword(s):  
Multiple Sclerosis ◽  
Negative Binomial ◽  
Real Life ◽  
Logistic Models ◽  
Negative Binomial Regression ◽  
Dimethyl Fumarate ◽  
Population Based ◽  
Disability Progression ◽  
Real Life Setting ◽  
Using Data

Abstract Objectives: To assess the effectiveness of dimethyl fumarate (DMF) on annual rate of relapse (ARR) and disability progression in multiple sclerosis (MS) compared to injectable immunomodulators (IMM), teriflunomide (TERI) and fingolimob (FTY), in real life setting. Methods: A population-based cohort study was conducted using data of the French nationwide claims database, SNDS. All patients initiating IMM, TERI, FTY or DMF between July 1, 2015 and December 12, 2017, with 4.5 years of database history and 1 to 3.5 years of follow-up were included in this study. DMF patients were 1:1 matched to IMM, TERI or FTY using a high dimensional Propensity Score. Negative binomial regression and a regression logistic models were used to estimate the relative risk (RR ± [95% CI]) of ARR and the Odds Ratio (OR ± [95% CI]) of disability progression, respectively. Results: Overall, 9 304 subjects were identified: 29.0% initiated DMF, 33.2% TERI, 5.6% FTY and 32.2% an IMM. The matched cohorts consisted of 1779 DMF- IMM, patients, 1679 DMF-TERI patients, and 376 DMF-FTY patients. DMF significantly reduced ARR compared to IMM (RR 0.72 [0.61 - 0.86]) and TERI (0.81 [0.68 - 0.96]). The risk of the progression of MS specific disability was not significantly different for any matched cohorts.Interpretation: DMF is associated with lower risk of relapse for patients with RRMS than other first-line RRMS agents (TERI and IIM).

scholarly journals Selecting Amongst Multinomial Models: An Apologia for Normalized Maximum Likelihood

2019 ◽  
Author(s):  
David Kellen ◽  
Karl Christoph Klauer
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Minimum Description Length ◽  
Seminal Paper ◽  
Multinomial Data ◽  
Functional Flexibility ◽  
Multinomial Models ◽  
Tremendous Progress ◽  
Normalized Maximum Likelihood ◽  
Important Addition

The modeling of multinomial data has seen tremendous progress since Riefer and Batchelder’s (1988) seminal paper. One recurring challenge, however, concerns theavailability of relative performance measures that strike an ideal balance between goodness of fit and functional flexibility. One approach to the problem of model selection is Normalized Maximum Likelihood (NML), a solution derived from the Minimum Description Length principle. In the present work we provide an R implementation of a Gibbs sampler that can be used to compute NML for models of joint multinomial data. We discuss the application of NML in different examples, compare NML with Bayes Factors, and show how it constitutes an important addition to researchers’ toolboxes.

scholarly journals Multivariate Skew-Power-Normal Distributions: Properties and Associated Inference

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1509
Author(s):  
Guillermo Martínez-Flórez ◽  
Artur J. Lemonte ◽  
Hugo S. Salinas
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Multivariate Distributions ◽  
Likelihood Approach ◽  
Information Matrices ◽  
Univariate Distribution

The univariate power-normal distribution is quite useful for modeling many types of real data. On the other hand, multivariate extensions of this univariate distribution are not common in the statistic literature, mainly skewed multivariate extensions that can be bimodal, for example. In this paper, based on the univariate power-normal distribution, we extend the univariate power-normal distribution to the multivariate setup. Structural properties of the new multivariate distributions are established. We consider the maximum likelihood method to estimate the unknown parameters, and the observed and expected Fisher information matrices are also derived. Monte Carlo simulation results indicate that the maximum likelihood approach is quite effective to estimate the model parameters. An empirical application of the proposed multivariate distribution to real data is provided for illustrative purposes.

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