Étude du biais dans le modèle log-linéaire d'estimation régionale

2004 ◽  
Vol 31 (2) ◽  
pp. 361-368 ◽  
Author(s):  
Claude Girard ◽  
Taha B.M.J Ouarda ◽  
Bernard Bobée
Keyword(s):  
Linear Relationship ◽  
Key Words ◽  
Linear Model ◽  
Linear Models ◽  
Target Variable ◽  
Independent Variables ◽  
Regional Estimation ◽  
Log Linear

Log-linear models are frequently used in hydrology, especially for the regional estimation of flood volumes based on the physiographic data of a set of basins. A log-linear model describes a linear relationship between the log of a dependant variable and independent variables which are functions of parameters, of which the value remains to be determined. It is determined by using a set of basins with known values of dependant and independent variables. The model is then used to obtain a prediction for the dependant variable logarithm of a basin of interest, based on the known values of independent variables in the model. This prediction is unbiased with relation to the log of the target variable. However, the exponential value of this prediction is biased with relation to the target variable. This paper addresses the measures to correct the bias in the prediction, which is introduced by exponentiation; the impacts on the variance of the ensuing predictions is also discussed. Key words: bias, transformation, log-linear model.[Journal translation]

scholarly journals A Cascaded Unsupervised Model for PoS Tagging

2021 ◽  
Vol 20 (1) ◽  
pp. 1-23
Author(s):  
Necva Bölücü ◽  
Burcu Can
Keyword(s):  
Linear Model ◽  
Language Processing ◽  
Bayesian Model ◽  
Linear Models ◽  
Syntactic Category ◽  
Semantic Parsing ◽  
Pos Tagging ◽  
Part Of Speech ◽  
Sentence Level ◽  
Log Linear

Part of speech (PoS) tagging is one of the fundamental syntactic tasks in Natural Language Processing, as it assigns a syntactic category to each word within a given sentence or context (such as noun, verb, adjective, etc.). Those syntactic categories could be used to further analyze the sentence-level syntax (e.g., dependency parsing) and thereby extract the meaning of the sentence (e.g., semantic parsing). Various methods have been proposed for learning PoS tags in an unsupervised setting without using any annotated corpora. One of the widely used methods for the tagging problem is log-linear models. Initialization of the parameters in a log-linear model is very crucial for the inference. Different initialization techniques have been used so far. In this work, we present a log-linear model for PoS tagging that uses another fully unsupervised Bayesian model to initialize the parameters of the model in a cascaded framework. Therefore, we transfer some knowledge between two different unsupervised models to leverage the PoS tagging results, where a log-linear model benefits from a Bayesian model’s expertise. We present results for Turkish as a morphologically rich language and for English as a comparably morphologically poor language in a fully unsupervised framework. The results show that our framework outperforms other unsupervised models proposed for PoS tagging.

scholarly journals The Application of Log-Linear Model to Selected Poison Patients

2020 ◽  
pp. 1-7
Author(s):  
Fatin N.S.A. ◽  
Norlida M.N. ◽  
Siti Z.M.J.
Keyword(s):  
Linear Model ◽  
Linear Models ◽  
Demographic Data ◽  
Contingency Tables ◽  
Categorical Variables ◽  
State Variables ◽  
Exposure Route ◽  
Higher Dimensional ◽  
Route Of Exposure ◽  
Log Linear

Log-linear model is a technique used to analyze the cross-classification categorical data or the contingency table. It is used to obtain the parsimony models that describe the interaction between the categorical variables in contingency tables. Log-linear models are commonly used in evaluating higher dimensional contingency tables that involves more than two categorical variables. This study focuses on analyzing data of poisoned patients from 2012 to 2014 using log-linear model. There are two model analyzed; model for demographic data of patients and model of poisoning information. For the first model, the variables involved are gender, age, race and state. Variables for the second model are circumstance of exposure, type of exposure, location of exposure, route of exposure and types of poison. Both log-linear models are developed to investigate the association between variables in the model. As a result of this study, the best model for demographic data and poisoning information are the model with three-ways interaction. For the best model of demographic data, there is an association between gender, age and race, race, gender and state as well as age, race and state. Meanwhile, the best model for poisoning information reveals that there is relationship between circumstance of exposure, route of exposure and type of poison, location of exposure, route of exposure and type of poison, circumstance of exposure, type of exposure and route of exposure, circumstance of exposure, location of exposure and route of exposure, circumstance of exposure, type of exposure and type of poison and also type of exposure, location of exposure and type of poison. Keywords: log-linear; demographic; gender; age; race; state; circumstance of exposure; type of exposure; location of exposure; route of exposure; types of poison

Changes in the distribution of Poplar Box (Eucalyptus populnea) on major soil groups: An application of the log-linear model.

1981 ◽  
Vol 3 (1) ◽  
pp. 33 ◽  
Author(s):  
RB Cunningham ◽  
AA Webb ◽  
A Mortlock
Keyword(s):  
Statistical Analysis ◽  
Linear Model ◽  
Generalized Linear Models ◽  
Gradient Analysis ◽  
Linear Models ◽  
Geographic Location ◽  
Significance Tests ◽  
Log Linear ◽  
Eucalyptus Populnea ◽  
Soil Groups

The association of poplar box (Eucalyptus populnea) with five main soil groups is examined. A statistical analysis, using a log- linear model, indicated that the relative frequencies of poplar box sites occumng on major soil groups changed with geographic location. The change in distribution is shown to relate to climate, as indicated by summer and winter moisture indices and the diff- erence between them. This study illustrates the use of log-linear models in ecology; such models, and more generally, Generalized Linear Models, in providing significance tests, have advantages over the non-statistical methods of gradient analysis.

A Forum for Researchers: Is the (Psychological) World Flat?

1974 ◽  
Vol 5 (1) ◽  
pp. 57-59
Author(s):  
Christopher Columbus
Keyword(s):  
Education Research ◽  
Mathematics Education ◽  
Linear Model ◽  
Linear Models ◽  
Mathematics Education Research ◽  
Independent Variables ◽  
Model Fits

The purpose of this note is to question the almost exclusive use of linear models in mathematics education research and to urge thoughtful exploration of alternate models when a linear model fits the data of a study poorly. (Here “linear model” refers to a model linear in one or more continuous independent variables, not to a model linear in the parameters to be estimated.)

Log-Linear, Logit-Linear Models: A Didactic

1981 ◽  
Vol 6 (1) ◽  
pp. 75-102 ◽  
Author(s):  
Frank B. Baker
Keyword(s):  
Linear Model ◽  
Educational Research ◽  
Qualitative Data ◽  
Linear Models ◽  
Contingency Tables ◽  
Basic Logic ◽  
Data Analyses ◽  
Potential Applications ◽  
Log Linear ◽  
Model Technique

The recently developed log-linear model technique for the analysis of contingency tables has many potential applications within educational research. This paper describes the two major models, log-linear and logit-linear, that are employed under this approach. The basic logic of each is developed and illustrative data analyses presented. In addition, the underlying communality of the two schemes is shown. The intent was to provide the reader with perspective that will facilitate understanding the approach and its application to the analysis of qualitative data.

scholarly journals Restricted graphical log-linear models

2015 ◽  
Vol 44 (4) ◽  
pp. 17-33 ◽  
Author(s):  
Ricardo Ramírez-Aldana ◽  
Guillermina Eslava-Gómez
Keyword(s):  
Linear Model ◽  
Linear Models ◽  
Graphical Representation ◽  
Order Interaction ◽  
First Order ◽  
New Type ◽  
Log Linear ◽  
Main Effects

We introduce a new type of graphical log-linear model called restricted graphical log-linear model. This model is obtained by imposing equality restrictions on subsets of main effects and of first-order interactions. These restrictions are obtained through partitions of the variable and first-order interaction sets. The vertices or variables in the same class have the same main effects in all their categories and the first-order interactions in the same class are equal. We study its properties and derive its associated likelihood equations and give some applications. A graphical representation is possible through a coloured graph.

scholarly journals On the correspondence of deviances and maximum-likelihood and interval estimates from log-linear to logistic regression modelling

2020 ◽  
Vol 7 (1) ◽  
pp. 191483
Author(s):  
W. Jing ◽  
M. Papathomas
Keyword(s):  
New York ◽  
Logistic Regression ◽  
Maximum Likelihood ◽  
Linear Model ◽  
Contingency Table ◽  
Linear Models ◽  
Maximum Likelihood Estimates ◽  
Categorical Variables ◽  
Model Parameters ◽  
Log Linear

Consider a set of categorical variables P where at least one, denoted by Y , is binary. The log-linear model that describes the contingency table counts implies a logistic regression model, with outcome Y . Extending results from Christensen (1997, Log-linear models and logistic regression , 2nd edn. New York, NY, Springer), we prove that the maximum-likelihood estimates (MLE) of the logistic regression parameters equals the MLE for the corresponding log-linear model parameters, also considering the case where contingency table factors are not present in the corresponding logistic regression and some of the contingency table cells are collapsed together. We prove that, asymptotically, standard errors are also equal. These results demonstrate the extent to which inferences from the log-linear framework translate to inferences within the logistic regression framework, on the magnitude of main effects and interactions. Finally, we prove that the deviance of the log-linear model is equal to the deviance of the corresponding logistic regression, provided that no cell observations are collapsed together when one or more factors in P ∖ { Y } become obsolete. We illustrate the derived results with the analysis of a real dataset.

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

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