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Related Concept Videos

Ranks01:02

Ranks

Unlike parametric methods, nonparametric statistics are ideal for nominal and ordinal data, requiring fewer assumptions about the population's nature or distribution. This makes nonparametric methods easier to apply and interpret, as they do not depend on parameters like mean or standard deviation. One common approach in nonparametric analysis is to sort data according to a specific criterion. For instance, we might arrange weather data from hottest to coldest days in a month or rank cities...
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...
Ordinal Level of Measurement00:55

Ordinal Level of Measurement

The way a set of data is measured is called its level of measurement. Correct statistical procedures depend on a researcher being familiar with levels of measurement. For analysis, data are classified into four levels of measurement—nominal, ordinal, interval, and ratio.
Data measured using an ordinal scale are similar to nominal scale data, but there is one major difference. The ordinal scale data can be ordered. An example of ordinal scale data is a list of the top five national parks in the...
Serial Position Effect01:03

Serial Position Effect

The serial position effect is a cognitive phenomenon where individuals are more likely to recall the first and last items in a list compared to those in the middle. This effect is divided into the primacy effect and the recency effect. The primacy effect is observed when the initial items in a list are remembered better. This occurs because these items are rehearsed more frequently or receive more elaborative processing, allowing them to be encoded into long-term memory more effectively. For...
Kendall's Tau Test01:16

Kendall's Tau Test

Kendall's tau test, also known as the Kendall rank coefficient test, is a nonparametric method for assessing association between two variables. This test is particularly useful for identifying significant correlations when the distributions of the sample and population are unknown. Developed in 1938 by the British statistician Sir Maurice George Kendall, the tau coefficient (denoted as τ) serves as a rank correlation coefficient, with values ranging from -1 to +1.
A τ value of +1 indicates that...
Percentile01:18

Percentile

A percentile indicates the relative standing of a data value when data are sorted into numerical order from smallest to largest. It represents the percentages of data values that are less than or equal to the pth percentile. For example, 15% of data values are less than or equal to the 15th percentile. Low percentiles always correspond to lower data values. High percentiles always correspond to higher data values.Percentiles divide ordered data into hundredths. To score in the...

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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

A grouped ranking model for item preference parameter.

Hideitsu Hino1, Yu Fujimoto, Noboru Murata

  • 1School of Science and Engineering, Waseda University, Shinjuku, Tokyo 169-8555, Japan. hideitsu.hino@toki.waseda.jp

Neural Computation
|June 24, 2010
PubMed
Summary
This summary is machine-generated.

This study generalizes the Plackett-Luce model for grouped ranking data, like movie ratings. An Expectation-Maximization algorithm approximates preferences, demonstrating effectiveness with real-world data analysis.

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • Determining item preference from rating data is crucial.
  • Existing probability models, like the Plackett-Luce model, parameterize item preferences.
  • The Plackett-Luce model traditionally handles individual rankings.

Purpose of the Study:

  • To generalize the Plackett-Luce model for grouped ranking observations (e.g., movie, restaurant ratings).
  • To develop a feasible approximation and employ the Expectation-Maximization (EM) algorithm for parameter estimation.
  • To extend the model to a mixture model and propose novel applications.

Main Methods:

  • Generalization of the Plackett-Luce model for grouped ranking data.
  • Derivation of a feasible likelihood approximation.
  • Application of the Expectation-Maximization (EM) algorithm for parameter estimation.
  • Extension to a mixture model framework.

Main Results:

  • A generalized Plackett-Luce model effectively handles grouped ranking data.
  • The EM algorithm successfully estimates model parameters via approximate likelihood maximization.
  • The mixture model extension offers enhanced flexibility for preference modeling.
  • Numerical experiments confirm the model's effectiveness on real-world datasets.

Conclusions:

  • The proposed generalized Plackett-Luce model provides a robust method for analyzing grouped ranking data.
  • The developed EM-based approach offers a computationally feasible solution for preference inference.
  • The mixture model and proposed applications highlight the model's versatility and potential impact in various domains.