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Statistics is a field of inquiry that studies the collection, analysis, interpretation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities; it is also used and misused for making informed decisions in all areas of business and government.
The likelihood function represents the probability of random variable realizations conditional on particular values of the statistical parameters. Thus, when evaluated on a given sample, the likelihood function indicates which parameter values are more likely than others, in the sense that they would have made the observed data more probable. Consequently, the likelihood is often written as instead of , to emphasize that it is to be understood as a function of the parameters instead of the random variable .
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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.
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In robust statistics, robust regression seeks to overcome some limitations of traditional regression analysis. A regression analysis models the relationship between one or more independent variables and a dependent variable. Standard types of regression, such as ordinary least squares, have favourable properties if their underlying assumptions are true, but can give misleading results otherwise. Robust regression methods are designed to limit the effect that violations of assumptions by the underlying data-generating process have on regression estimates.
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Friedrich Maria Urban was a psychologist from the Austro-Hungarian Empire, known for the introduction of probability weightings used in experimental psychology.
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References
- 1 2 3 4 Aitkin, Murray (23 May 2015). "Curriculum Vitae" (PDF). Retrieved 19 July 2021.
{{cite web}}: CS1 maint: url-status (link) - 1 2 Agresti, Alan; Bartolucci, Francesco; Mira, Antonietta (8 February 2021). "Reflections on Murray Aitkin's contributions to nonparametric mixture models and Bayes factors". Statistical Modelling: 1471082X20981312. doi: 10.1177/1471082X20981312 . ISSN 1471-082X.
- ↑ Bock, R. Darrell; Aitkin, Murray (1 December 1981). "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm". Psychometrika. 46 (4): 443–459. doi:10.1007/BF02293801. ISSN 1860-0980.
- ↑ "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm". scholar.google.co.uk. Retrieved 19 July 2021.
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