Log-Linear Models with Dependent Spatial Data

1983 ◽  
Vol 15 (6) ◽  
pp. 801-813 ◽  
Author(s):  
B Fingleton
Keyword(s):  
Spatial Data ◽  
Statistical Models ◽  
Linear Models ◽  
Square Lattice ◽  
Categorical Variables ◽  
Systematic Sampling ◽  
Pairwise Correlations ◽  
Independent Observations ◽  
Intersection Points ◽  
Log Linear

Log-linear models are an appropriate means of determining the magnitude and direction of interactions between categorical variables that in common with other statistical models assume independent observations. Spatial data are often dependent rather than independent and thus the analysis of spatial data by log-linear models may erroneously detect interactions between variables that are spurious and are the consequence of pairwise correlations between observations. A procedure is described in this paper to accommodate these effects that requires only very minimal assumptions about the nature of the autocorrelation process given systematic sampling at intersection points on a square lattice.

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

Life after Chi-Squared: An Introduction to Log-Linear Analysis

1998 ◽  
Vol 43 (8) ◽  
pp. 837-842 ◽  
Author(s):  
David L Streiner ◽  
Elizabeth Lin
Keyword(s):  
Linear Models ◽  
Linear Analysis ◽  
Categorical Variables ◽  
Factors Associated ◽  
Several Variables ◽  
Chi Squared ◽  
Log Linear

Chi-squared tests are used to examine the relationships among categorical variables. However, they are difficult to use and interpret when more than 2 variables are involved. In such cases, it is better to use a related statistic, called log-linear analysis. This article is an introduction to log-linear models, illustrating how they can be used to tease apart relationships among several variables in looking at the factors associated with photonumerophobia.

scholarly journals Modelling Tabular Data with an Ordered Outcome

1996 ◽  
Vol 1 (3) ◽  
pp. 1-10
Author(s):  
Vernon Gayle
Keyword(s):  
Model Building ◽  
Linear Models ◽  
Statistical Modelling ◽  
Categorical Variables ◽  
Sociological Research ◽  
Ratio Model ◽  
Ordered Categories ◽  
Continuation Ratio ◽  
Recent Developments ◽  
Log Linear

A large amount of data that is considered within sociological studies consists of categorical variables that lend themselves to tabular analysis. In the sociological analysis of data regarding social class and educational attainment, for example, the variables of interest can often plausibly be considered as having a substantively interesting order. Standard log-linear models do not take ordinality into account, thereby potentially they may disregard useful information. Analyzing tables where the response variable has ordered categories through model building has been problematic in software packages such as GLIM (Aitken et al., 1989). Recent developments in statistical modelling have offered new possibilities and this paper explores one option, namely the continuation ratio model which was initially reported by Fienberg and Mason (1979). The fitting of this model to data in tabular form is possible in GLIM although not especially trivial and by and large this approach has not been employed in sociological research. In this paper I outline the continuation ratio model and comment upon how it can be fitted to data by sociologists using the GLIM software. In addition I present a short description of the relative merits of such an approach. Presenting this paper in an electronic format facilitates the possibility of replicating the analysis. The data is appended to the paper in the appropriate format along with a copy of the GLIM transcript. A dumped GLIM4 file is also attached.

scholarly journals Heatmaps for Patterns of Association in log-Linear Models

2020 ◽  
Vol 6 ◽  
pp. 237802311989921
Author(s):  
Mauricio Bucca
Keyword(s):  
Social Mobility ◽  
Linear Models ◽  
Categorical Variables ◽  
Visualization Technique ◽  
Odds Ratios ◽  
Detailed Characterization ◽  
Log Odds ◽  
Sociological Work ◽  
Log Linear

Log-linear models offer a detailed characterization of the association between categorical variables, but the breadth of their outputs is difficult to grasp because of the large number of parameters these models entail. Revisiting seminal findings and data from sociological work on social mobility, the author illustrates the use of heatmaps as a visualization technique to convey the complex patterns of association captured by log-linear models. In particular, turning log odds ratios derived from a model’s predicted counts into heatmaps makes it possible to summarize large amounts of information and facilitates comparison across models’ outcomes.

scholarly journals Modelling Synergy using Manifest Categorical Variables

1998 ◽  
Vol 22 (3) ◽  
pp. 537-557 ◽  
Author(s):  
Alexander von Eye ◽  
Christof Schuster ◽  
William M. Rogers
Keyword(s):  
Social Sciences ◽  
Linear Models ◽  
Contraceptive Use ◽  
Natural Sciences ◽  
Alternative Methods ◽  
Categorical Variables ◽  
The Social ◽  
Log Linear ◽  
The Relationship

This paper discusses methods to model the concept of synergy at the level of manifest categorical variables. First, a classification of concepts of synergy is presented. A dditive and nonadditive concepts of synergy are distinguished. Most prominent among the nonadditive concepts is superadditive synergy. Examples are given from the natural sciences and the social sciences. M delling focuses on the relationship between the agents involved in a synergetic process. These relationships are expressed in form of contrasts, expressed in effect coding vectors in design matrices for nonstandard log-linear models. A method by Schuster is used to transform design matrices such that parameters reflect the proposed relationships. A n example reanalyses data presented by Bishop, Fienberg, and Holland (1975) that describe the development of thromboembolisms in women who differ in their patterns of contraceptive use and smoking. Alternative methods of analysis are com pared. Implications for developmental research are discussed.

Analysis of Two-Way Contingency Tables : Log-Linear Models and Dual Scaling

1987 ◽  
Vol 26 (03) ◽  
pp. 104-108
Author(s):  
M. A. A. Moussa
Keyword(s):  
Linear Models ◽  
Contingency Tables ◽  
Real Data ◽  
Categorical Variables ◽  
Bayes Estimators ◽  
Dual Scaling ◽  
Independence Model ◽  
Optimal Weights ◽  
Log Linear ◽  
Female Nurses

SummaryThe paper focuses upon the measurement of association in two-way contingency tables, using the log-linear models and dual scaling approaches. The former comprises [1] the use of pseudo-Bayes estimators to remove zeros, [2] fitting the resulting smoothed array to all possible configurations of log-linear models, [3] fitting the quasi-independence model to detect anomalous cells that caused deviation from the null-independence model. The latter includes [1] estimation of the optimal weights that maximize the canonical correlation between the two categorical variables by an optimization iterative method, [2] testing the discriminability of the estimated scoring scheme. The two approaches were applied to a set of real data for the study of the association between maternal age at marriage and types of reproductive wastage in a sampling survey conducted in the population of female nurses in Kuwait.

scholarly journals Modelling association between two Multiple Response Categorical Variables (MRCV) using generalized log-linear models: the case of urban agriculture in Mutare City

2021 ◽  
Vol 1 (2) ◽  
pp. 117-132
Author(s):  
Absai Chakaipa ◽  
◽  
Vitalis Basera ◽  
Phamella Dube ◽  
◽  
...  
Keyword(s):  
Urban Agriculture ◽  
Linear Models ◽  
Positive Association ◽  
Categorical Variables ◽  
Multiple Response ◽  
Agricultural Activities ◽  
Pearson Residuals ◽  
Strong Negative Association ◽  
Farm Produce ◽  
Log Linear

Purpose: This research aimed to apply log-linear modelling to model association between multiple response categorical variables (MRCV) on urban agriculture and enhance data analysis of the paper by Basera, Chakaipa, & Dube (2020) impetus of urban agriculture on open spaces of Mutare City. Research methodology: The research data was obtained from households and farmers in Mutare City - urban and peri-urban (inclusive of plots in Weirmouth Park and Fern Valley area in December 2020. A total of one hundred and fifteen (115) household farmers were surveyed. Results: Simultaneous Pairwise Marginal Independence (SPMI) tests revealed the presence of associations. Log-linear tests revealed a perfect fit based on small standardized Pearson residuals and a strong positive association based on observed and model-predicted odds ratios on-field agricultural activities and use of herbicides. Log-linear and further application of heterogeneity tests revealed partial and near no perfect fit in other pairs of MRCVs with a strong negative association between municipality vacant places and field agricultural activities. Limitations: The research could not carry out log-linear model associations of three or more MRCVs because files exceeded 2GB in memory on both MI.test () function for SPMI tests and genloglin regressions. Contribution: The study contributes to urban agriculture planning especially in enactment of urban agriculture laws, agriculture one stop shop business centers housing farm input supply shops, farm produce shops, and determining fit support that can be rendered to urban farmers. Keywords: Multiple Response Categorical Variables (MRCV), Association, Urban agriculture

scholarly journals Ordinal Log-Linear Models for Contingency Tables

2016 ◽  
Vol 16 (1) ◽  
pp. 264-273
Author(s):  
Justyna Brzezińska
Keyword(s):  
Contingency Table ◽  
Linear Models ◽  
Contingency Tables ◽  
Linear Analysis ◽  
Categorical Variables ◽  
Ordinal Variables ◽  
Advantages And Disadvantages ◽  
Effect Model ◽  
Log Linear ◽  
Model Algorithm

Abstract A log-linear analysis is a method providing a comprehensive scheme to describe the association for categorical variables in a contingency table. The log-linear model specifies how the expected counts depend on the levels of the categorical variables for these cells and provide detailed information on the associations. The aim of this paper is to present theoretical, as well as empirical, aspects of ordinal log-linear models used for contingency tables with ordinal variables. We introduce log-linear models for ordinal variables: linear-by-linear association, row effect model, column effect model and RC Goodman’s model. Algorithm, advantages and disadvantages will be discussed in the paper. An empirical analysis will be conducted with the use of R.

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