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Related Concept Videos

Contingency Table01:29

Contingency Table

A contingency table provides a way of portraying data that can facilitate calculating probabilities. It is a method of displaying a frequency distribution as a table with rows and columns to show how two variables may be dependent (contingent) upon each other; The table helps determine conditional probabilities quite quickly and can help systematically organize, analyze and quantify data. The table displays sample values concerning two variables that may be dependent or contingent on one...
Introduction to Test of Independence01:21

Introduction to Test of Independence

In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their individual probabilities. Tests of independence are chi-square tests involving the use of a contingency table of observed (data) values.
The test statistic for a test of independence is similar to that of a goodness-of-fit test:
Survival Tree01:19

Survival Tree

Survival trees are a non-parametric method used in survival analysis to model the relationship between a set of covariates and the time until an event of interest occurs, often referred to as the "time-to-event" or "survival time." This method is particularly useful when dealing with censored data, where the event has not occurred for some individuals by the end of the study period, or when the exact time of the event is unknown.
 Building a Survival Tree
Constructing a survival tree begins...
Determination of Expected Frequency01:08

Determination of Expected Frequency

Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of the dataset. But how does one determine the expected frequency of the dataset? One of the important assumptions is that the two variables are independent, which means the variables do not influence each other. For independent variables, the statistical probability of any event involving both variables is calculated by multiplying the individual...
Friedman Two-way Analysis of Variance by Ranks01:21

Friedman Two-way Analysis of Variance by Ranks

Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures from...
One-Way ANOVA: Unequal Sample Sizes01:15

One-Way ANOVA: Unequal Sample Sizes

One-way ANOVA can be performed on three or more samples of unequal sizes. However, calculations get complicated when sample sizes are not always the same. So, while performing ANOVA with unequal samples size, the following equation is used:

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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Decomposition and model selection for large contingency tables.

Corinne Dahinden1, Markus Kalisch, Peter Bühlmann

  • 1Seminar für Statistik, ETH Zürich, CH-8092 Zürich, Switzerland.

Biometrical Journal. Biometrische Zeitschrift
|March 10, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces a novel decomposition method to efficiently analyze large contingency tables, addressing computational challenges in log-linear models for high-dimensional biological data. The approach breaks down complex problems into smaller, manageable parts for feasible analysis.

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Area of Science:

  • Statistics
  • Computational Biology
  • Bioinformatics

Background:

  • Large contingency tables are common in biology, particularly for analyzing interactions among multiple biomarkers.
  • Log-linear models are used to study these interactions, but face computational burdens with many variables.
  • High-dimensional tables present challenges like a large number of cells and sampling zeros, hindering maximum likelihood estimation.

Purpose of the Study:

  • To develop a computationally feasible method for analyzing log-linear interaction models with many categorical variables.
  • To overcome the computational complexity and issues with maximum likelihood estimation in high-dimensional contingency tables.
  • To provide a practical approach for analyzing complex biological data, such as multi-biomarker expression levels.

Main Methods:

  • A decomposition approach is proposed, dividing the large problem into several lower-dimensional subproblems.
  • These subproblems are then solved and combined to achieve a global solution.
  • The methodology is designed to be computationally feasible even with many variables or levels.

Main Results:

  • The decomposition method offers a computationally efficient solution for log-linear models with high-dimensional contingency tables.
  • The approach effectively handles the challenges posed by a large number of cells and sampling zeros.
  • Demonstrated feasibility through simulated data and application to a cancer research problem.

Conclusions:

  • The proposed decomposition approach provides a computationally feasible and effective solution for analyzing large contingency tables in high-dimensional settings.
  • This method enables the study of complex interactions in biological data, such as biomarker expression, overcoming previous computational limitations.
  • The technique is applicable to various fields dealing with large categorical data, including biomedical research.