scholarly journals Asymptotic Results for Multinomial Models

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2173
Author(s):  
Isaac Akoto ◽  
João T. Mexia ◽  
Filipe J. Marques
Keyword(s):  
Linear Models ◽  
Confidence Regions ◽  
Asymptotic Results ◽  
Chi Square ◽  
Normal Distributions ◽  
Limit Distributions ◽  
Multinomial Models ◽  
Multidimensional Contingency Table ◽  
Log Linear ◽  
Key Parameter

In this work, we derived new asymptotic results for multinomial models. To obtain these results, we started by studying limit distributions in models with a compact parameter space. This restriction holds since the key parameter whose components are the probabilities of the possible outcomes have non-negative components that add up to 1. Based on these results, we obtained confidence ellipsoids and simultaneous confidence intervals for models with normal limit distributions. We then studied the covariance matrices of the limit normal distributions for the multinomial models. This was a transition between the previous general results and on the inference for multinomial models in which we considered the chi-square tests, confidence regions and non-linear statistics—namely log-linear models with two numerical applications to those models. Namely, our approach overcame the hierarchical restrictions assumed to analyse the multidimensional contingency table.

scholarly journals Risk factors for intradomiciliary infestation by the Chagas disease vector Triatoma dimidiatain Jutiapa, Guatemala

2009 ◽  
Vol 25 (suppl 1) ◽  
pp. S83-S92 ◽  
Author(s):  
Dulce Maria Bustamante ◽  
Carlota Monroy ◽  
Sandy Pineda ◽  
Antonieta Rodas ◽  
Xochitl Castro ◽  
...  
Keyword(s):  
Risk Factors ◽  
Socioeconomic Status ◽  
Chagas Disease ◽  
Linear Models ◽  
Control Strategies ◽  
Chi Square ◽  
Disease Vector ◽  
Log Linear ◽  
Chi Square Analysis

Seventeen variables were evaluated as possible risk factors for the intradomiciliary infestation with Triatoma dimidiata in 644 houses in Jutiapa, Guatemala. During 2004 the houses were assessed for vector presence and evaluated for hygiene, cluttering, material comfort, construction conditions and number of inhabitants, among other factors. Chi-square analysis detected significant associations between vector presence and eight variables related to domestic sanitary and construction conditions. Log-linear models showed that regardless of the age of the house, the odds of vector presence were 4.3 and 10 times lower in houses with a good socioeconomic status compared with poor and very poor houses respectively. Log-linear models also pointed to a greater chance of vector presence when walls lacked plastering (3.85 times) or walls had low quality-incomplete plastering (4.56 times), compared with walls that were completely plastered. Control strategies against T. dimidiata should include the introduction of better-quality but inexpensive plastering formulations and better sanitation practices should also be promoted among the population. Such control strategies should not only reduce or eliminate infestation, but also prevent vector reinfestation.

A Marketer'S Guide to Log-Linear Models for Qualitative Data Analysis

1980 ◽  
Vol 44 (3) ◽  
pp. 40-51 ◽  
Author(s):  
Wayne S. DeSarbo ◽  
David K. Hildebrand
Keyword(s):  
Data Analysis ◽  
Qualitative Data ◽  
Potential Problem ◽  
Linear Models ◽  
Model Fitting ◽  
Qualitative Data Analysis ◽  
Chi Square ◽  
Stepwise Procedures ◽  
Log Linear

This article presents a brief description of the development and use of log-linear models. Current research in areas of screening effects, partitioning chi-square statistics, stepwise procedures, and model fitting and selection is discussed. An analysis of inherent model ambiguities is provided, identifying potential problem areas for marketing applications.

scholarly journals Social-Psychological Determinants Of Anxiety Disorder (SAD) Among Youth (With Reference To Karachi University)

2014 ◽  
Vol 8 (1) ◽  
pp. 161-176
Author(s):  
Rana Saba Sultan ◽  
Ambreen Akber ◽  
Erum Zarrar
Keyword(s):  
Anxiety Disorder ◽  
Linear Models ◽  
Strong Relationship ◽  
Research Approach ◽  
Exploratory Research ◽  
Chi Square ◽  
Psychological Determinants ◽  
Chi Square Test ◽  
And Gender ◽  
Log Linear

The present study is “A study of Causes of Anxiety Disorder (SAD) among youth of Karachi University; deals with behavior patterns and expected to reflect on the type of society and its attitude towards SAD. The present research is an exploratory research. This study is based on the concept of level of sadness among youth of Karachi University. The mixed research approach quantitative and qualitative was adopted. The population of the study was Karachi University students; 120 students were selected through purposive sampling. Five hypotheses were formulated, from which three were accepted and two were rejected. Hence it is proved that there is a relationship between level of sadness with parents and gender, and this is also proved that there is a relationship between sadness and marital status and hence it is also proved that there is a relationship between level of troubled with appearance and gender, it is also found that there is a strong relationship between problem in decision making and cultural background and level of feeling of sadness and age. To test the hypotheses, statistical methods were applied to the data described in the contingency tables. The chi-square test was applied to test the existence of the relationship between two variables of hypothesis, and if the null hypothesis is rejected then the log linear models were also used to measure the degree of relationship. The hypotheses were then finally interpreted and the results were obtained.

Analysis of Coded Wire Tag Returns from Commercial Catches

1992 ◽  
Vol 49 (9) ◽  
pp. 1816-1825 ◽  
Author(s):  
R. M. Cormack ◽  
J. R. Skalski
Keyword(s):  
Least Squares ◽  
Linear Models ◽  
Coho Salmon ◽  
Weighted Least Squares ◽  
Oncorhynchus Kisutch ◽  
Normal Distributions ◽  
Constant Variance ◽  
Log Linear ◽  
Zero Counts ◽  
Sample Fraction

Three alternative but equivalent approaches to the analysis of coded wire tag (CWT) data using log-linear models are presented. All three use iteratively weighted least squares to estimate treatment effects in hatchery releases under the assumption that the variance of a count is proportional to its expected value. The commonly made assumption of normal distributions with constant variance for recovery rates is inefficient. Analysis of tag recovery at the most disaggregated level (i.e. the level at which the sample fraction f is measured) is found necessary for valid inferences. Failure to include zero counts in analyses of recovery data is also shown to induce or mask interactions among CWT recoveries. Recoveries of CWT from coho salmon (Oncorhynchus kisutch) are used to illustrate the method of analysis. Coordinated CWT releases to facilitate mixing of stocks is recommended in the design of hatchery studies.

When and why are log-linear models self-normalizing?

2015 ◽  
Author(s):  
Jacob Andreas ◽  
Dan Klein
Keyword(s):  
Linear Models ◽  
Log Linear

scholarly journals Testing for treatment effect in covariate-adaptive randomized trials with generalized linear models and omitted covariates

2021 ◽  
pp. 096228022110082
Author(s):  
Yang Li ◽  
Wei Ma ◽  
Yichen Qin ◽  
Feifang Hu
Keyword(s):  
Generalized Linear Models ◽  
Treatment Effect ◽  
Linear Models ◽  
Type I Error ◽  
Type I ◽  
Test Statistic ◽  
Asymptotic Results ◽  
Adaptive Randomization ◽  
Adjustment Method ◽  
Inflated Type

Concerns have been expressed over the validity of statistical inference under covariate-adaptive randomization despite the extensive use in clinical trials. In the literature, the inferential properties under covariate-adaptive randomization have been mainly studied for continuous responses; in particular, it is well known that the usual two-sample t-test for treatment effect is typically conservative. This phenomenon of invalid tests has also been found for generalized linear models without adjusting for the covariates and are sometimes more worrisome due to inflated Type I error. The purpose of this study is to examine the unadjusted test for treatment effect under generalized linear models and covariate-adaptive randomization. For a large class of covariate-adaptive randomization methods, we obtain the asymptotic distribution of the test statistic under the null hypothesis and derive the conditions under which the test is conservative, valid, or anti-conservative. Several commonly used generalized linear models, such as logistic regression and Poisson regression, are discussed in detail. An adjustment method is also proposed to achieve a valid size based on the asymptotic results. Numerical studies confirm the theoretical findings and demonstrate the effectiveness of the proposed adjustment method.

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