Asymptotic Log-Linear Analysis: Some Cautions concerning Sparse Frequency Tables

2004 ◽  
Vol 94 (1) ◽  
pp. 19-32 ◽  
Author(s):  
Paul W. Mielke ◽  
Kenneth J. Berry ◽  
Janis E. Johnston
Keyword(s):  
Likelihood Ratio ◽  
Linear Models ◽  
Linear Analysis ◽  
Exact Probability ◽  
Permutation Methods ◽  
Chi Squared ◽  
Asymptotic Probability ◽  
Log Linear ◽  
Likelihood Ratio Statistics ◽  
Hypergeometric Distributions

Traditional asymptotic probability values resulting from log-linear analyses of sparse frequency tables are often much too large. Asymptotic probability values for chi-squared and likelihood-ratio statistics are compared to nonasymptotic and exact probability values for selected log-linear models. The asymptotic probability values are all too often substantially larger than the exact probability values for the analysis of sparse frequency tables. An exact nondirectional permutation method is presented to analyze combined independent multinomial distributions. Exact nondirectional permutation methods to analyze hypergeometric distributions associated with r-way frequency tables are confined to r = 2.

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 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.

Analysis of Mark–Recapture Data from Hatchery-Raised Salmon Using Log-Linear Models

1987 ◽  
Vol 44 (2) ◽  
pp. 316-326 ◽  
Author(s):  
Philip E. J. Green ◽  
P. D. M. Macdonald
Keyword(s):  
British Columbia ◽  
Oncorhynchus Tshawytscha ◽  
Linear Models ◽  
Coho Salmon ◽  
Pacific Salmon ◽  
Statistical Technique ◽  
Linear Analysis ◽  
Designed Experiment ◽  
Juvenile Pacific Salmon ◽  
Log Linear

Large numbers of hatchery-raised juvenile Pacific salmon are routinely marked with coded-wire tags before release from the hatchery. Log-linear models are an appropriate statistical technique to analyze the numbers of recaptures in different fisheries, and the numbers of tagged fish returning to the hatchery, in terms of such factors as brood year, treatment at the hatchery, timing of release, and size at release. Log-linear analysis of catches and hatchery returns of chinook salmon (Oncorhynchus tshawytscha) from Robertson Creek, British Columbia, indicates that all of these factors are important, but variation between brood years overrides all other factors. Within a brood year, the conditions that maximize the number of returns to the hatchery do not necessarily maximize the number of recaptures in the fishery. Log-linear analysis of hatchery returns from a designed experiment on a single brood year of coho salmon (O. kisutch) from Rosewall Creek, British Columbia, quantifies the effects of the various factors but will be of limited value until the causes of variations between brood years are better known.

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