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In economics, polytomous choice is a setting (model) with more than two choices; contrast to dichotomous choice. The use of the term polychotomous is also in common usage in the prior research literature; however, polytomous is the more technically correct spelling. [1]
In psychometrics, item response theory (IRT) is a paradigm for the design, analysis, and scoring of tests, questionnaires, and similar instruments measuring abilities, attitudes, or other variables. It is a theory of testing based on the relationship between individuals' performances on a test item and the test takers' levels of performance on an overall measure of the ability that item was designed to measure. Several different statistical models are used to represent both item and test taker characteristics. Unlike simpler alternatives for creating scales and evaluating questionnaire responses, it does not assume that each item is equally difficult. This distinguishes IRT from, for instance, Likert scaling, in which "All items are assumed to be replications of each other or in other words items are considered to be parallel instruments". By contrast, item response theory treats the difficulty of each item as information to be incorporated in scaling items.
A Likert scale is a psychometric scale named after its inventor, American social psychologist Rensis Likert, which is commonly used in research questionnaires. It is the most widely used approach to scaling responses in survey research, such that the term is often used interchangeably with rating scale, although there are other types of rating scales.
In biology, an identification key, taxonomic key, or biological key is a printed or computer-aided device that aids the identification of biological entities, such as plants, animals, fossils, microorganisms, and pollen grains. Identification keys are also used in many other scientific and technical fields to identify various kinds of entities, such as diseases, soil types, minerals, or archaeological and anthropological artifacts.
In statistics, a categorical variable is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property. In computer science and some branches of mathematics, categorical variables are referred to as enumerations or enumerated types. Commonly, each of the possible values of a categorical variable is referred to as a level. The probability distribution associated with a random categorical variable is called a categorical distribution.
A questionnaire is a research instrument that consists of a set of questions for the purpose of gathering information from respondents through survey or statistical study. A research questionnaire is typically a mix of close-ended questions and open-ended questions. Open-ended, long-term questions offer the respondent the ability to elaborate on their thoughts. The Research questionnaire was developed by the Statistical Society of London in 1838.
The Rasch model, named after Georg Rasch, is a psychometric model for analyzing categorical data, such as answers to questions on a reading assessment or questionnaire responses, as a function of the trade-off between the respondent's abilities, attitudes, or personality traits, and the item difficulty. For example, they may be used to estimate a student's reading ability or the extremity of a person's attitude to capital punishment from responses on a questionnaire. In addition to psychometrics and educational research, the Rasch model and its extensions are used in other areas, including the health profession, agriculture, and market research.
The polytomous Rasch model is generalization of the dichotomous Rasch model. It is a measurement model that has potential application in any context in which the objective is to measure a trait or ability through a process in which responses to items are scored with successive integers. For example, the model is applicable to the use of Likert scales, rating scales, and to educational assessment items for which successively higher integer scores are intended to indicate increasing levels of competence or attainment.
Estimation of a Rasch model is used to estimate the parameters of the Rasch model. Various techniques are employed to estimate the parameters from matrices of response data. The most common approaches are types of maximum likelihood estimation, such as joint and conditional maximum likelihood estimation. Joint maximum likelihood (JML) equations are efficient, but inconsistent for a finite number of items, whereas conditional maximum likelihood (CML) equations give consistent and unbiased item estimates. Person estimates are generally thought to have bias associated with them, although weighted likelihood estimation methods for the estimation of person parameters reduce the bias.
In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than two possible discrete outcomes. That is, it is a model that is used to predict the probabilities of the different possible outcomes of a categorically distributed dependent variable, given a set of independent variables.
In economics, discrete choice models, or qualitative choice models, describe, explain, and predict choices between two or more discrete alternatives, such as entering or not entering the labor market, or choosing between modes of transport. Such choices contrast with standard consumption models in which the quantity of each good consumed is assumed to be a continuous variable. In the continuous case, calculus methods can be used to determine the optimum amount chosen, and demand can be modeled empirically using regression analysis. On the other hand, discrete choice analysis examines situations in which the potential outcomes are discrete, such that the optimum is not characterized by standard first-order conditions. Thus, instead of examining "how much" as in problems with continuous choice variables, discrete choice analysis examines "which one". However, discrete choice analysis can also be used to examine the chosen quantity when only a few distinct quantities must be chosen from, such as the number of vehicles a household chooses to own and the number of minutes of telecommunications service a customer decides to purchase. Techniques such as logistic regression and probit regression can be used for empirical analysis of discrete choice.
A rating scale is a set of categories designed to obtain information about a quantitative or a qualitative attribute. In the social sciences, particularly psychology, common examples are the Likert response scale and 0-10 rating scales, where a person selects the number that reflecting the perceived quality of a product.
A computerized classification test (CCT) refers to, as its name would suggest, a Performance Appraisal System that is administered by computer for the purpose of classifying examinees. The most common CCT is a mastery test where the test classifies examinees as "Pass" or "Fail," but the term also includes tests that classify examinees into more than two categories. While the term may generally be considered to refer to all computer-administered tests for classification, it is usually used to refer to tests that are interactively administered or of variable-length, similar to computerized adaptive testing (CAT). Like CAT, variable-length CCTs can accomplish the goal of the test with a fraction of the number of items used in a conventional fixed-form test.
In statistics, polychoric correlation is a technique for estimating the correlation between two hypothesised normally distributed continuous latent variables, from two observed ordinal variables. Tetrachoric correlation is a special case of the polychoric correlation applicable when both observed variables are dichotomous. These names derive from the polychoric and tetrachoric series which are used for estimation of these correlations.
In biology or medicine, a multi-access key is an identification key which overcomes the problem of the more traditional single-access keys of requiring a fixed sequence of identification steps. A multi-access key enables the user to freely choose the characteristics that are convenient to evaluate for the item to be identified.
In phylogenetics, a single-access key is an identification key where the sequence and structure of identification steps is fixed by the author of the key. At each point in the decision process, multiple alternatives are offered, each leading to a result or a further choice. The alternatives are commonly called "leads", and the set of leads at a given point a "couplet".
Instant-runoff voting (IRV), also known as ranked-choice voting (RCV), preferential voting (PV), or the alternative vote (AV), is a multi-round elimination rule where the loser of each round is determined by first-past-the-post voting. In academic contexts, the system is generally called instant-runoff voting to avoid conflating it with other methods of ranked voting in general.
Psychometric software refers to specialized programs used for the psychometric analysis of data obtained from tests, questionnaires, polls or inventories that measure latent psychoeducational variables. Although some psychometric analyses can be performed using general statistical software such as SPSS, most require specialized tools designed specifically for psychometric purposes.
Wayne Paul Maddison, is a professor and Canada Research Chair in Biodiversity at the departments of zoology and botany at the University of British Columbia, and the Director of the Spencer Entomological Collection at the Beaty Biodiversity Museum.
David Andrich is an Australian academic and assessment specialist. He has made substantial contributions to quantitative social science including seminal work on the Polytomous Rasch model for measurement, which is used in the social sciences, in health and other areas.
The Mokken scale is a psychometric method of data reduction. A Mokken scale is a unidimensional scale that consists of hierarchically-ordered items that measure the same underlying, latent concept. This method is named after the political scientist Rob Mokken who suggested it in 1971.
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