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Polytomous Rasch Model
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. Background and overview The polytomous Rasch model was derived by , subsequent to derivations by and , through the resolution of relevant terms of a general form of Rasch's model into ''threshold'' and ''discrimination'' parameters. When the model was derived, Andrich focused on the use of Likert scales in psychometrics, both for illustrative purposes and to aid in the interpretation of the model. The model is sometimes referred to as the ''Rating Scale Model'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dichotomous
A dichotomy () is a partition of a set, partition of a whole (or a set) into two parts (subsets). In other words, this couple of parts must be * jointly exhaustive: everything must belong to one part or the other, and * mutually exclusive: nothing can belong simultaneously to both parts. If there is a concept A, and it is split into parts B and not-B, then the parts form a dichotomy: they are mutually exclusive, since no part of B is contained in not-B and vice versa, and they are jointly exhaustive, since they cover all of A, and together again give A. Such a partition is also frequently called a bipartition. The two parts thus formed are Complement (set theory), complements. In logic, the partitions are dual (category theory), opposites if there exists a proposition such that it holds over one and not the other. Treating continuous variables or multicategorical variables as binary variables is called discretization, dichotomization. The discretization error inherent in dichoto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Empirical
Empirical evidence is evidence obtained through sense experience or experimental procedure. It is of central importance to the sciences and plays a role in various other fields, like epistemology and law. There is no general agreement on how the terms ''evidence'' and ''empirical'' are to be defined. Often different fields work with quite different conceptions. In epistemology, evidence is what justifies beliefs or what determines whether holding a certain belief is rational. This is only possible if the evidence is possessed by the person, which has prompted various epistemologists to conceive evidence as private mental states like experiences or other beliefs. In philosophy of science, on the other hand, evidence is understood as that which '' confirms'' or ''disconfirms'' scientific hypotheses and arbitrates between competing theories. For this role, evidence must be public and uncontroversial, like observable physical objects or events and unlike private mental states, so ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Educational Psychology
Educational psychology is the branch of psychology concerned with the scientific study of human learning. The study of learning processes, from both cognitive psychology, cognitive and behavioral psychology, behavioral perspectives, allows researchers to understand individual differences in intelligence, cognitive development, Affect (psychology), affect, motivation, self-regulation, and self-concept, as well as their role in learning. The field of educational psychology relies heavily on quantitative methods, including testing and measurement, to enhance educational activities related to instructional design, classroom management, and assessment, which serve to facilitate learning processes in various educational settings across the lifespan.Snowman, Jack (1997). Educational Psychology: What Do We Teach, What Should We Teach?. "Educational Psychology", 9, 151-169 Educational psychology can in part be understood through its relationship with other disciplines. It is informed primar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Variable
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a Mathematics, mathematical formalization of a quantity or object which depends on randomness, random events. The term 'random variable' in its mathematical definition refers to neither randomness nor variability but instead is a mathematical function (mathematics), function in which * the Domain of a function, domain is the set of possible Outcome (probability), outcomes in a sample space (e.g. the set \ which are the possible upper sides of a flipped coin heads H or tails T as the result from tossing a coin); and * the Range of a function, range is a measurable space (e.g. corresponding to the domain above, the range might be the set \ if say heads H mapped to -1 and T mapped to 1). Typically, the range of a random variable is a subset of the Real number, real numbers. Informally, randomness typically represents some fundamental element of chance, such as in the roll of a dice, d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Likelihood
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference. If the likelihood function is differentiable, the derivative test for finding maxima can be applied. In some cases, the first-order conditions of the likelihood function can be solved analytically; for instance, the ordinary least squares estimator for a linear regression model maximizes the likelihood when the random errors are assumed to have normal distributions with the same variance. From the perspective of Bayesian inference, ML ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum (theory)
Continuum (: continua or continuums) theories or models explain variation as involving gradual quantitative transitions without abrupt changes or discontinuities. In contrast, categorical theories or models explain variation using qualitatively different states. In physics In physics, for example, the space-time continuum model describes space and time as part of the same continuum rather than as separate entities. A spectrum in physics, such as the electromagnetic spectrum, is often termed as either continuous (with energy at all wavelengths) or discrete (energy at only certain wavelengths). In contrast, quantum mechanics uses quanta, certain defined amounts (i.e. categorical amounts) which are distinguished from continuous amounts. In mathematics and philosophy A good introduction to the philosophical issues involved is John Lane Bell's essay in the ''Stanford Encyclopedia of Philosophy''. A significant divide is provided by the law of excluded middle. It determ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypothesis
A hypothesis (: hypotheses) is a proposed explanation for a phenomenon. A scientific hypothesis must be based on observations and make a testable and reproducible prediction about reality, in a process beginning with an educated guess or thought. If a hypothesis is repeatedly independently demonstrated by experiment to be true, it becomes a scientific theory. In colloquial usage, the words "hypothesis" and "theory" are often used interchangeably, but this is incorrect in the context of science. A working hypothesis is a provisionally-accepted hypothesis used for the purpose of pursuing further progress in research. Working hypotheses are frequently discarded, and often proposed with knowledge (and warning) that they are incomplete and thus false, with the intent of moving research in at least somewhat the right direction, especially when scientists are stuck on an issue and brainstorming ideas. A different meaning of the term ''hypothesis'' is used in formal l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parameter
A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc. ''Parameter'' has more specific meanings within various disciplines, including mathematics, computer programming, engineering, statistics, logic, linguistics, and electronic musical composition. In addition to its technical uses, there are also extended uses, especially in non-scientific contexts, where it is used to mean defining characteristics or boundaries, as in the phrases 'test parameters' or 'game play parameters'. Modelization When a system theory, system is modeled by equations, the values that describe the system are called ''parameters''. For example, in mechanics, the masses, the dimensions and shapes (for solid bodies), the densities and t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rasch Model
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 mathematical theory underlying Rasch models is a special case of item response theory. However, there are important differences in the interpretation of the model parameters and its philosophical implications that separate proponents of the Rasch model from the item response modeling tradition. A central aspect of this divide relates ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sufficient Statistics
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If then ", is necessary for , because the truth of is guaranteed by the truth of . (Equivalently, it is impossible to have without , or the falsity of ensures the falsity of .) Similarly, is sufficient for , because being true always implies that is true, but not being true does not always imply that is not true. In general, a necessary condition is one (possibly one of several conditions) that must be present in order for another condition to occur, while a sufficient condition is one that produces the said condition. The assertion that a statement is a "necessary ''and'' sufficient" condition of another means that the former statement is true if and only if the latter is true. That is, the two statements must be either simultaneously true, or simultaneously false. In ordinary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probabilistic
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th ed., (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', vol. 1, 3rd ed., (1968), Wiley, . This number is often expressed as a percentage (%), ranging from 0% to 100%. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These concepts have been given an axiomatic mathematical formaliza ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
