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Related Concept Videos

Contingency Table01:29

Contingency Table

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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...
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Determination of Expected Frequency01:08

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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...
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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.
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Introduction to Test of Independence01:21

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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.
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Friedman Two-way Analysis of Variance by Ranks01:21

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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...
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Parametric Survival Analysis: Weibull and Exponential Methods01:14

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Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
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Bayesian modeling of temporal dependence in large sparse contingency tables.

Tsuyoshi Kunihama1, David B Dunson1

  • 1Department of Statistical Science, Duke University, Durham, NC 27708-0251, USA.

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|February 1, 2014
PubMed
Summary

This study introduces a Bayesian autoregressive tensor factorization to analyze trends in categorical data over time, addressing missing data and large sparse tables effectively.

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Dynamic modelMultivariate categorical dataNonparametric BayesPanel dataParafacProbabilistic tensor factorizationStick-breaking

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Area of Science:

  • Statistics
  • Social Sciences
  • Data Science

Background:

  • Analyzing trends in relationships among categorical variables over time is crucial for various applications.
  • Challenges include abundant missing data, changing variables, and large sparse contingency tables at each time point.

Purpose of the Study:

  • To develop a novel statistical approach for modeling time-varying categorical data.
  • To address the challenges of missing data and high dimensionality in longitudinal social surveys.

Main Methods:

  • A Bayesian autoregressive tensor factorization model is proposed.
  • The model utilizes probabilistic PARAFAC factorization of the joint probability mass function (pmf).
  • Autocorrelation across time points is incorporated, with efficient Markov Chain Monte Carlo (MCMC) methods developed for computation.

Main Results:

  • The proposed methods demonstrate effectiveness in simulation studies.
  • The approach is successfully applied to real-world social survey data.
  • The model successfully borrows information across time to handle large sparse contingency tables.

Conclusions:

  • The Bayesian autoregressive tensor factorization provides a robust framework for analyzing longitudinal categorical data.
  • This method offers a powerful tool for understanding dynamic social trends and complex relationships.
  • The developed computational techniques enable practical application to large-scale survey data.