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Thurstonian Model
A Thurstonian model is a stochastic transitivity model with latent variables for describing the mapping of some continuous scale onto discrete, possibly ordered categories of response. In the model, each of these categories of response corresponds to a latent variable whose value is drawn from a normal distribution, independently of the other response variables and with constant variance. Developments over the last two decades, however, have led to Thurstonian models that allow unequal variance and non zero covariance terms. Thurstonian models have been used as an alternative to generalized linear models in analysis of sensory discrimination tasks. They have also been used to model long-term memory in ranking tasks of ordered alternatives, such as the order of the amendments to the US Constitution. Their main advantage over other models ranking tasks is that they account for non-independence of alternatives. Ennis provides a comprehensive account of the derivation of Thurstonia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Transitivity
Stochastic transitivity models are stochastic versions of the transitivity property of binary relations studied in mathematics. Several models of stochastic transitivity exist and have been used to describe the probabilities involved in experiments of paired comparisons, specifically in scenarios where transitivity is expected, however, empirical observations of the binary relation is probabilistic. For example, players' skills in a sport might be expected to be transitive, i.e. "if player A is better than B and B is better than C, then player A must be better than C"; however, in any given match, a weaker player might still end up winning with a positive probability. Tightly matched players might have a higher chance of observing this inversion while players with large differences in their skills might only see these inversions happen seldom. Stochastic transitivity models formalize such relations between the probabilities (e.g. of an outcome of a match) and the underlying transiti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latent Variable Model
A latent variable model is a statistical model that relates a set of observable variables (also called ''manifest variables'' or ''indicators'') to a set of latent variables. Latent variable models are applied across a wide range of fields such as biology, computer science, and social science. Common use cases for latent variable models include applications in psychometrics (e.g., summarizing responses to a set of survey questions with a factor analysis model positing a smaller number of psychological attributes, such as the trait extraversion, that are presumed to cause the survey question responses), and natural language processing (e.g., a topic model summarizing a corpus of texts with a number of "topics"). It is assumed that the responses on the indicators or manifest variables are the result of an individual's position on the latent variable(s), and that the manifest variables have nothing in common after controlling for the latent variable ( local independence). Different ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Distribution
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f(x) = \frac e^\,. The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter \sigma^2 is the variance. The standard deviation of the distribution is (sigma). A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Linear Models
In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a ''link function'' and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. Generalized linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including linear regression, logistic regression and Poisson regression. They proposed an iteratively reweighted least squares method for maximum likelihood estimation (MLE) of the model parameters. MLE remains popular and is the default method on many statistical computing packages. Other approaches, including Bayesian regression and least squares fitting to variance stabilized responses, have been developed. Intuition Ordinary linear regression predicts the expected value of a given unknown quantity ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrimination Testing
Discrimination is the process of making unfair or prejudicial distinctions between people based on the groups, classes, or other categories to which they belong or are perceived to belong, such as race, gender, age, class, religion, or sexual orientation. Discrimination typically leads to groups being unfairly treated on the basis of perceived statuses based on ethnic, racial, gender or religious categories. It involves depriving members of one group of opportunities or privileges that are available to members of another group. Discriminatory traditions, policies, ideas, practices and laws exist in many countries and institutions in all parts of the world, including some, where such discrimination is generally decried. In some places, countervailing measures such as quotas have been used to redress the balance in favor of those who are believed to be current or past victims of discrimination. These attempts have often been met with controversy, and sometimes been called re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gibbs Sampling
In statistics, Gibbs sampling or a Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm for sampling from a specified multivariate distribution, multivariate probability distribution when direct sampling from the joint distribution is difficult, but sampling from the Conditional probability distribution, conditional distribution is more practical. This sequence can be used to approximate the joint distribution (e.g., to generate a histogram of the distribution); to approximate the marginal distribution of one of the variables, or some subset of the variables (for example, the unknown parameters or latent variables); or to compute an integral (such as the expected value of one of the variables). Typically, some of the variables correspond to observations whose values are known, and hence do not need to be sampled. Gibbs sampling is commonly used as a means of statistical inference, especially Bayesian inference. It is a randomized algorithm (i.e. an algorithm that makes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wishart Distribution
In statistics, the Wishart distribution is a generalization of the gamma distribution to multiple dimensions. It is named in honor of John Wishart (statistician), John Wishart, who first formulated the distribution in 1928. Other names include Wishart ensemble (in random matrix theory, probability distributions over matrices are usually called "ensembles"), or Wishart–Laguerre ensemble (since its eigenvalue distribution involve Laguerre polynomials), or LOE, LUE, LSE (in analogy with Random matrix#Gaussian ensembles, GOE, GUE, GSE). It is a family of probability distributions defined over symmetric, positive-definite random matrices (i.e. matrix (mathematics), matrix-valued random variables). These distributions are of great importance in the estimation of covariance matrices in multivariate statistics. In Bayesian inference, Bayesian statistics, the Wishart distribution is the conjugate prior of the matrix inverse, inverse covariance matrix, covariance-matrix of a multivariate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Louis Leon Thurstone
Louis Leon Thurstone (May 29, 1887 – September 29, 1955) was an American pioneer in the fields of psychometrics and psychophysics. He conceived the approach to measurement known as the law of comparative judgment, and is well known for his contributions to factor analysis. A ''Review of General Psychology'' survey, published in 2002, ranked Thurstone as the 88th most cited psychologist of the 20th century, tied with John Garcia, James J. Gibson, David Rumelhart, Margaret Floy Washburn, and Robert S. Woodworth. Early life and career Thurstone was born in Chicago, Illinois, to Swedish immigrant parents. His family returned to Stockholm, Sweden, when he was eight years old, before returning to the United States in 1901, settling in Jamestown, New York. Thurstone originally received a master's degree in mechanical engineering from Cornell University in 1912. Thurstone was offered a brief assistantship in the laboratory of Thomas Edison. In 1914, after two years as an instr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Law Of Comparative Judgment
The law of comparative judgment was conceived by L. L. Thurstone. In modern-day terminology, it is more aptly described as a model that is used to obtain measurements from any process of pairwise comparison. Examples of such processes are the comparisons of perceived intensity of physical stimuli, such as the weights of objects, and comparisons of the extremity of an attitude expressed within statements, such as statements about capital punishment. The measurements represent how we perceive entities, rather than measurements of actual physical properties. This kind of measurement is the focus of psychometrics and psychophysics. In somewhat more technical terms, the law of comparative judgment is a mathematical representation of a discriminal process, which is any process in which a comparison is made between pairs of a collection of entities with respect to magnitudes of an attribute, trait, attitude, and so on. The theoretical basis for the model is closely related to item respons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The Acoustical Society Of America
The ''Journal of the Acoustical Society of America'' (JASA) is a monthly peer-reviewed scientific journal covering all aspects of acoustics. It is published by the Acoustical Society of America. The editor-in-chief is James F. Lynch (Woods Hole Oceanographic Institution). ''JASA'' contains news items, book reviews, references to contemporary papers, reviews of acoustical patents, and standards news. According to the ''Journal Citation Reports'', the journal has a 2023 impact factor of 2.1. History In 1929, the newly formed Acoustical Society of America Publication Committee began investigating how to start a journal. The first issue of the ''Journal of the Acoustical Society of America'' (JASA) was published in October 1929 and contained 8 papers. The cover featured the 1929 logo designed by Wallace Waterfall. In May 1932, publication of JASA was transferred to the American Institute of Physics (AIP). In 1957 the publication frequency of the journal went from bimonthly to m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thurstone Scale
In psychology and sociology, the Thurstone scale was the first formal technique to measure an attitude. It was developed by Louis Leon Thurstone in 1928, originally as a means of measuring attitudes towards religion. Today it is used to measure attitudes towards a wide variety of issues. The technique uses a number of statements about a particular issue, and each statement is given a numerical value indicating how favorable or unfavorable it is judged to be. These numerical values are prepared ahead of time by the researcher and not shown to the test subjects. The subjects then check each of the statements with which they agree, and a mean score of those statements' values is computed, indicating their attitude. Thurstone scale Thurstone's method of pair comparisons can be considered a prototype of a normal distribution-based method for scaling-dominance matrices. Even though the theory behind this method is quite complex (Thurstone, 1927a), the algorithm itself is straightforward. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bradley–Terry Model
The Bradley–Terry model is a probability model for the outcome of pairwise comparisons between items, teams, or objects. Given a pair of items and drawn from some population, it estimates the probability that the pairwise comparison turns out true, as where is a positive real-valued score assigned to individual . The comparison can be read as " is preferred to ", " ranks higher than ", or " beats ", depending on the application. For example, might represent the skill of a team in a sports tournament and \Pr(i>j) the probability that wins a game against . Or might represent the quality or desirability of a commercial product and \Pr(i>j) the probability that a consumer will prefer product over product . The Bradley–Terry model can be used in the forward direction to predict outcomes, as described, but is more commonly used in reverse to infer the scores given an observed set of outcomes. In this type of application represents some measure of the strength or qualit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
