In statistics , a likelihoodfunction often simply the likelihood is a function of the statistical parameter ... of the parameter, given a fixed outcome. In the latter case the function is called the likelihoodfunction .... Definition For the definition of the likelihoodfunction, one has to distinguish between discrete ... mathcal L theta x p theta x P theta X x , , math considered as a function of , is called the likelihood ... x f theta x , , math considered as a function of , is called the likelihoodfunction of , given .... The actual value of a likelihoodfunction bears no meaning. Its use lies in comparing one value with another ... L math . More precisely, then, a likelihoodfunction is any representative from an equivalence ... defined support to be the natural logarithm of the likelihood ratio, and the support function as the natural logarithm of the likelihoodfunction the same as the log likelihood see below . ref Edwards ... of the natural logarithm of the likelihoodfunction, called the log likelihood , than in terms of the likelihood ... is a log likelihood rather than the original likelihoodfunction. For example, some likelihood .... In such a situation, the likelihoodfunction factors into a product of individual likelihood functions ... function. As an example, consider the gamma distribution , whose likelihoodfunction is math mathcal ... the maximum likelihood estimate of &beta for a single observed value x . This function looks rather .... Likelihoodfunction of a parameterized model Among many applications, we consider here one of broad ... theta , math where is the parameter, the likelihoodfunction is math theta mapsto f x mid theta , math ... density function, and when viewed as a function of with x fixed, it is a likelihoodfunction ... the likelihoodfunction above may be justified in a simple way. Suppose that, instead of an exact observation ... point in interval j . Then, recalling that the likelihoodfunction is defined up to a multiplicative constant, it is just as valid to say that the likelihoodfunction is approximately math ... more details
one source date February 2012 Likelihood eikos , versimilis captures the idea that something is likely to happen or to have happened. As a formal concept, it has appeared in jurisprudence , commerce and scholasticism long before it was given a rigorous mathematical foundation. ref citation author James Franklin title The Science of Conjecture Evidence and Probability before Pascal publisher The Johns Hopkins University Press year 2001 ISBN 0 8018 7109 3 ref Likelihoodfunction Main LikelihoodfunctionLikelihood is a function of how likely an event is, which is weaker than probability or odds in favor . In statistics , a likelihoodfunction is a function of the statistical parameter parameters of a statistical model , defined as follows the likelihood of a set of parameter values given some observed outcomes is equal to the probability of those observed outcomes given those parameter values. Likelihood functions play a key role in statistical inference , especially methods of estimating a parameter using a statistic s a function of the data . References references statistics stub Category Statistical terminology ... more details
Likelihood ratio may refer to The ratio of two likelihoodfunction s Likelihood ratio test , a statistical test for comparing two models. Likelihood ratios in diagnostic testing , ratios based on sensitivity and specificity, used to assess diagnostic tests. Bayes factor , ratio of likelihoods used to update prior probabilities to posterior in Bayes theorem and Bayesian inference . disambig ... more details
In statistics , quasi likelihood estimation is one way of allowing for overdispersion , that is, greater variability in the data than would be expected from the statistical model used. It is most often used with models for count data or grouped binary data, i.e. data that otherwise be modelled using the Poisson or binomial distribution. The term quasi likelihoodfunction was introduced by Robert Wedderburn statistician Robert Wedderburn in 1974 ref cite journal first R.W.M. last Wedderburn title Quasi likelihood functions, generalized linear models, and the Gauss Newton method journal Biometrika year 1974 volume 61 issue 3 pages 439 447 doi 10.1093 biomet 61.3.439 mr 0375592 ref to describe a function which has similar properties to the log likelihoodfunction , except that a quasi likelihoodfunction is not the log likelihood corresponding to any actual probability distribution . Quasi likelihood models can be fitted using a straightforward extension of the algorithms used to fit generalized linear models . Instead of specifying a probability distribution for the data, only a relationship between the mean and the variance is specified in the form of a variance function giving the variance as a function of the mean. Generally, this function is allowed to include a multiplicative factor known as the overdispersion parameter or scale parameter that is estimated from the data. Most commonly, the variance function is of a form such that fixing the overdispersion parameter at unity results in the variance mean relationship of an actual probability distribution such as the binomial or Poisson. For formulae, see the Generalized linear model Binomial data binomial data example and Generalized ... data. Quasi likelihood methods have the advantage of relative computational simplicity, speed ... linear models . Quasi likelihood has no role in Bayesian statistics , as this is based on a fully ... Press date 2001, 2007 DEFAULTSORT Quasi Likelihood Category Statistical inference Category Statistical ... more details
In statistics , the likelihood principle is a controversial principle of statistical inference which asserts that all of the information in a Sampling statistics sample is contained in the likelihoodfunction . A likelihoodfunction arises from a conditional probability distribution considered as a function ..., again with probability of success on each trial. Then the observation that X 3 induces the likelihoodfunction math L theta X 3 begin pmatrix 12 3 end pmatrix theta 3 1 theta 9 220 theta 3 1 theta 9 math and the observation that Y 12 induces the likelihoodfunction math L theta Y 12 begin pmatrix ... of the complexity of different hypotheses. Combining the likelihood principle with the law of likelihood yields the consequence that the parameter value which maximizes the likelihoodfunction is the value ... on the design of the experiment, not on the likelihood in the sense of the likelihoodfunction ... here. Note that the likelihoodfunction depends only on what actually happened, and not on what ..., consider a model which gives the probability density function of observable random variable X as a function of a parameter . Then for a specific value x of X , the function L x P X x is a likelihoodfunction of it gives a measure of how likely any particular value of is, if we know that X has the value x . Two likelihood functions are equivalent if one is a scalar multiple of the other. The likelihood principle states that all information from the data relevant to inferences about the value of is found in the equivalence class. The strong likelihood principle applies this same criterion ... is a scalar multiple of the other. The likelihood principle therefore says the inferences drawn about ... is the same in both cases. The law of likelihood A related concept is the law of likelihood ... likelihood method of maximum likelihood . Historical remarks The likelihood principle was first ... of Ronald A. Fisher R.A. Fisher in the 1920s. The law of likelihood was identified by that name ... more details
data the greatest probability i.e., parameters that maximize the likelihoodfunction . Maximum likelihood ... will be the function s variable and allowed to vary freely this function will be called the likelihood ... In practice it is often more convenient to work with the logarithm of the likelihoodfunction, called ... function, since log is a monotone transformation . For many models, a maximum likelihood estimator ... problems, no maximum likelihood estimate exists meaning that the log likelihoodfunction increases ... estimator to be consistent. When this condition holds, the limiting likelihoodfunction has ... can be replaced by some other conditions, such as both Concave function concavity of the log likelihoodfunction and compactness of some nonempty upper level set s of the log likelihoodfunction, or existence of a compact neighborhood N of sub 0 sub such that outside of N the log likelihoodfunction ... , there exists no maximum for the likelihoodfunction For any estimate of theta, there exists a greater ... which ensure this behavior are The first and second derivatives of the log likelihoodfunction must ... N 0, ,I 1 . math Proof, skipping the technicalities Since the log likelihoodfunction is differentiable ... of success , the likelihoodfunction defined below takes one of three values math begin align ... that there was only one coin but its p could have been any value 0 p 1. The likelihoodfunction ... is over all possible values 0 p 1. Image MLfunctionbinomial en.svg thumb 200px likelihoodfunction ... continuous strictly increasing function over the range mathematics range of the likelihood, the values ... right math In this and other cases where a joint density function exists, the likelihoodfunction ... function calculated from a transformed set of data. Quasi maximum likelihood estimator, an MLE ..., its relationship to covariance matrix of ML estimates Likelihoodfunction , a description on what ... ajayshah KB R documents mle mle.html Implementing MLE for your own likelihoodfunction using R http ... more details
In statistics , a marginal likelihoodfunction , or integrated likelihood , is a likelihoodfunction in which some parameter variables have been marginalisation probability marginalised . In the context of Bayesian statistics , it may also be referred to as the evidence or model evidence . Given a set of independent identically distributed data points math mathbb X x 1, ldots,x n , math where math x i sim p x i theta math according to some probability distribution parameterized by , where itself is a random variable described by a distribution, i.e. math theta sim p theta alpha , math the marginal likelihood in general asks what the probability math p mathbb X alpha math is, where has been marginal distribution marginalized out integrated out math p mathbb X alpha int theta p mathbb X theta , p theta alpha operatorname d theta math The above definition is phrased in the context of Bayesian statistics . In classical frequentist statistics frequentist statistics, the concept of marginal likelihood occurs instead in the context of a joint parameter , , where is the actual parameter of interest, and is a non interesting nuisance parameter . If there exists a probability distribution for , it is often desirable to consider the likelihoodfunction only in terms of , by marginalizing out math mathcal L psi mathbb X p mathbb X psi int Lambda p mathbb X psi, lambda , p lambda psi operatorname d lambda math Unfortunately, marginal likelihoods are generally difficult to compute. Exact solutions are known for a small class of distributions, particularly when the marginalized out parameter is the conjugate prior of the distribution of the data. In other cases, some ... likelihood is the probability of the data given the model type, not assuming any particular model parameters. Writing for the model parameters, the marginal likelihood for the model ... of marginal likelihood computation methods . In W. H rdle and B. Ronz, editors, COMPSTAT 2002 ... more details
with respect to the goals of the analysis. As long as the quasi likelihoodfunction that is maximized is not overly simplified, the QMLE or composite likelihood estimate is consistent estimator consistent ...Expert subject statistics date May 2009 A quasi maximum likelihood estimate QMLE, also known as a pseudo likelihood estimate or a composite likelihood estimate is an estimate of a parameter &theta in a statistical model that is formed by maximizing a function that is related to the logarithm of the likelihoodfunction , but is not equal to it ref cite journal last Lindsay first Bruce G. year 1988 journal Contemporary Mathematics title Composite Likelihood Methods volume 80 pages 221&ndash 239 ref ref name SLP cite book last MacKinnon first James year 2004 title Econometric Theory and Methods publisher Oxford University Press location New York, New York isbn 0 19 512372 7 ref . In contrast, the maximum likelihood estimate maximizes the actual log likelihoodfunction for the data and model. The function that is maximized to form a QMLE is often a simplified form of the actual log likelihoodfunction. A common way to form such a simplified function is to use the log likelihoodfunction of a specification misspecified model that treats certain data values as being independent, even when in actuality ... the maximum likelihood estimate, but may only be slightly less efficient if the quasi likelihood is constructed so as to minimize the loss of information relative to the actual likelihood ref cite journal last Cox first D.R. coauthors Reid, Nancy title A note on pseudo likelihood constructed from ... 91.3.729 ref . Standard approaches to statistical inference that are used with maximum likelihood ... 92 issue 3 pages 519&ndash 528 doi 10.1093 biomet 92.3.519 title A note on composite likelihood inference and model selection ref , can be generalized to the quasi maximum likelihood setting. See also Quasi likelihood References references Category Estimation theory econometrics stub statistics stub ... more details
model, is separately fitted to the data and the log likelihoodfunctionlikelihood recorded. The test ... ,L theta mid x theta in theta 0, theta 1 , math where math L theta x math is the likelihoodfunction ... in Theta 0 complement end align math The likelihoodfunction is math L theta x f x theta math ... Here, the math sup math notation refers to the Supremum function. A likelihood ratio test is any ... as log likelihood ratios or approximations thereof. Interpretation Being a function of the data math ... date April 2009 the supremum function in the calculation of the likelihood ratio, saying that this takes ...Distinguish2 the use of likelihood ratios in diagnostic testing Citations missing date September 2009 Expert subject Statistics date November 2008 In statistics , a likelihood ratio test is a statistical ... case of the other the alternative hypothesis alternative model . The test is based on the likelihood ratio, which expresses how many times more likely the data are under one model than the other. This likelihood ... of the alternative model. When the logarithm of the likelihood ratio is used, the statistic is known as a log likelihood ratio statistic , and the probability distribution of this test statistic ... of the likelihood ratio test can be justified by the Neyman Pearson lemma , which demonstrates that such a test ... D & 2 ln left frac text likelihood for null model text likelihood for alternative model right & 2 ln text likelihood for null model 2 ln text likelihood for alternative model end align math The model with more parameters will always fit at least as well have a greater log likelihood . Whether it fits ... parameter and a log likelihood of &minus 8024 and the alternative model has 3 degrees of freedom ... p values are computed. Background The likelihood ratio, often denoted by math Lambda math the capital Greek alphabet Greek letter lambda , is the ratio of the likelihoodfunction varying the parameters over two different sets in the numerator and denominator. A likelihood ratio test is a statistical ... more details
The query likelihood model is a language model used in Information Retrieval . A language model is constructed for each document in the collection. It is then possible to rank each document by the probability of specific documents given a query. This is interpreted as being the Likelihoodfunctionlikelihood of a document being relevant given a query. Calculating the likelihood Using Bayes theorem Bayes rule , the probability of a document, given a query can be written as follows math P d q frac P q d P d P q math Since the probability of the query P q is the same for all documents, this can be ignored. Further, it is typical to assume that the probability of documents is uniform. Thus, P d is also ignored. math P d q P q d math Documents are then ranked by the probability that a query is observed as a random sample from the document model. The multinomial unigram language model is commonly used to achieve this. We have math P q M d K q prod t in V P t M d tf t,d math ,where the multinomial coefficient is math K q L d tf t1,d tf t2,d ...tf tM,d math for query math q . ref Christopher D. Manning, Prabhakar Raghavan, Hinrich Sch tze An Introduction to Information Retrieval, page 242. Cambridge University Press, 2009 ref References references Category Information retrieval ... more details
wiktionary functionFunction may refer to Diatonic function , a term in music theory Function E 40 song , a 2012 song by American rapper E 40 featuring YG rapper YG , iAmSu & Problem Function biology , explaining why a feature survived selection Function computer science , or subroutine, a portion of code within a larger program, performs a specific task Function engineering , related to the selected property of a system Function language , in linguistics, a way of achieving an aim using language Function mathematics , an abstract entity that associates an input to a corresponding output according to some rule Function model , a structured representation of the functions, activities or processes Function object , or functor or functionoid, a concept of object oriented programming Function Drinks , a beverage company based in Redondo Beach, California. An organised event such as a party or meeting See also Functionalism disambiguation Function hall Functional disambiguation Functionality in polymer chemistry see Structural unit Functor disambiguation bg bs Funkcija vor ca Funci desambiguaci cs Funkce da Funktion de Funktion et Funktsioon es Funci n eo Funkcio eu Funtzio argipena fr Fonction ko id Fungsi it Funzione lt Funkcija lmo Funziun nl Functie ja no Funksjon nn Funksjon pl Funkcja ujednoznacznienie pt Fun o desambigua o ro Func ie dezambiguizare ru simple Function sk Funkcia sl Funkcija razlo itev sr sh Funkcija razvrstavanje sv Funktion olika betydelser th uk zh ... more details
context date December 2010 Maximum likelihood sequence estimation MLSE is a mathematical algorithm to extract useful data out of a noisy data stream. Theory For an optimized detector for digital signals the priority is not to reconstruct the transmitter signal, but it should do a best estimation of the transmitted data with the least possible number of errors. The receiver emulates the distorted channel. All possible transmitted data streams are fed into this distorted channel model. The receiver compares the time response with the actual received signal and determines the most likely signal. In cases that are most computationally straightforward, root mean square deviation can be used as the decision criterion ref G. Bosco, P. Poggiolini, and M. Visintin, Performance Analysis of MLSE Receivers Based on the Square Root Metric, J. Lightwave Technol. 26, 2098&ndash 2109 2008 ref for the lowest ... the observations r t to create a good estimate of x t . Maximum likelihood sequence estimation is formally the application of maximum likelihood to this problem. That is, the estimate of x t is defined ... the conditional joint probability density function of the observed series r t given that the underlying ... than maximum likelihood sequence estimation and requires a known distribution in Bayesian inference ... x r denotes the conditional joint probability density function of the underlying series x t given that the observed ... normal distribution , the problem of maximum likelihood sequence estimation can be reduced to that of a least ... Cite book title Wireless Communications author Andrea Goldsmith chapter Maximum Likelihood Sequence ... v35n2a04.pdf Performance evaluation of maximum likelihood sequence estimation receivers in lightwave ..., D., Mahlab, U., and Levy, A. 2008 Channel estimators for maximum likelihood sequence estimation ... External links Cite web title Maximum Likelihood Sequence Estimation of Nonlinear Channels in High ... The Telecommunications Research Center Vienna date 2001 04 16 DEFAULTSORT Maximum Likelihood Sequence ... more details
In mathematics, S function may refer to sigmoid function Schur polynomials In physics, it may refer to Action physics action functional mathdab Short pages monitor This long comment was added to the page to prevent it from being listed on Special Shortpages. It and the accompanying monitoring template were generated via Template Long comment. Please do not remove the monitor template without removing the comment as well. ... more details
In statistics , the restricted or residual , or reduced maximum likelihood REML approach is a particular form of maximum likelihood estimation which does not base estimates on a maximum likelihood fit of all the information, but instead uses a likelihoodfunction calculated from a transformed set of data, so that nuisance parameter s have no effect. ref name Dodge cite book last1 Dodge first1 Yadolah authorlink Yadolah Dodge title The Oxford Dictionary of Statistical Terms publisher Oxford University Press location Oxford Oxfordshire year 2006 pages isbn 0 19 920613 9 see REML ref In the case of variance component estimation, the original data set is replaced by a set of contrast statistics contrasts calculated from the data, and the likelihoodfunction is calculated from the probability distribution of these contrasts, according to the model for the complete data set. In particular, REML is used as a method for fitting linear mixed model s. In contrast to the earlier maximum likelihood estimation, REML can produce unbiased estimates of variance and covariance parameters. ref Baker, Bob. http homepage.usask.ca rjb609 stats4.html Estimating variances and covariances broken, original link available at the Wayback Machine http web.archive.org web 20080630063659 http homepage.usask.ca rjb609 stats4.html ref The idea underlying REML estimation was put forward by M. S. Bartlett in 1937. ref name Dodge ref cite doi 10.1098 rspa.1937.0109 ref The first description of the approach applied to estimating components of variance in unbalanced data was by Desmond Patterson and Robin Thompson statistician Robin Thompson ref name Dodge ref cite doi 10.1093 biomet 58.3.545 ref of the University of Edinburgh , although they did not use the term REML. A review of the early literature was given by Harville. ref cite doi 10.2307 2286796 ref REML estimation is available in a number of general purpose statistical software packages, including Genstat the REML directive , SAS software SAS the MIXED ... more details
Image VEST Core4 LowLevel.png thumbnail 320px right VEST 4 T function followed by a transposition layer In cryptography , a T function is a bijection bijective mapping that updates every bit of the state computer science state in a way that can be described as math x i x i f x 0, cdots, x i 1 math , or in simple words an update function in which each bit of the state is updated by a linear combination of the same bit and a function of a subset of its less significant bits. If every single less significant bit is included in the update of every bit in the state, such a T function is called triangular . Thanks to their bijectivity no collisions, therefore no entropy loss regardless of the used Boolean function s and regardless of the selection of inputs as long as they all come from one side of the output bit , T functions are now widely used in cryptography to construct block cipher s, stream cipher s, PRNG s and cryptographic hash function hash functions . T functions were first proposed in 2002 by Alexander Klimov A. Klimov and Adi Shamir A. Shamir in their paper A New Class of Invertible Mappings . Ciphers such as TSC 1 , TSC 3 , TSC 4 , ABC stream cipher ABC , Mir 1 and VEST are built with different types of T functions. Because arithmetic operation s such as addition , subtraction and multiplication are also T functions triangular T functions , software efficient word based T functions can be constructed by combining bitwise logic with arithmetic operations. Another important property of T functions based on arithmetic operations is predictability of their period mathematics period , which is highly attractive to cryptographers. Although triangular T functions are naturally vulnerable to guess and determine attacks, well chosen bitwise transposition mathematics transposition ... bit. Subsequent transposition of the output bits and iteration of the T function also do not affect ... and losing the T function bias of depending only on the less significant bits of the state. References ... more details
technology worker s effort, for instance and math y math its output, the likelihood of which is described by a probability density function math f y e . math Then the monotone likelihood ratio ... math g math . As usual for monotonic relationships, the likelihood ratio s monotonicity comes in handy in statistics, particularly when using Maximum likelihood maximum likelihood estimation . Also, distribution ... has the Monotone Likelihood Ratio Property MLRP . A family of density functions math f theta ... math is said to have a monotone likelihood ratio MLR in the statistic math T X math if for any math ... is a non decreasing function of math T X math . Then we say the family of distributions has ... likelihood ratio property in math T X math , the family has monotone decreasing hazard rate ... distributions DEFAULTSORT Monotone Likelihood Ratio Property Category Theory of probability distributions ... more details
Success Likelihood Index Method SLIM is a technique used in the field of Human reliability Assessment HRA , for the purposes of evaluating the probability of a human error occurring throughout the completion of a specific task. From such analyses measures can then be taken to reduce the likelihood of errors occurring within a system and therefore lead to an improvement in the overall levels of safety. There exist three primary reasons for conducting an HRA error identification, error quantification and error reduction. As there exist a number of techniques used for such purposes, they can be split into one of two classifications first generation techniques and second generation techniques. First generation techniques work on the basis of the simple dichotomy of fits doesn t fit in the matching of the error situation in context with related error identification and quantification and second generation techniques are more theory based in their assessment and quantification of errors. HRA techniques have been utilised in a range of industries including healthcare , engineering , nuclear ... a Success Likelihood Index SLI , a form of preference index, which is calibrated against existing ... which scales the relative success likelihood in performing a range of tasks, given the PSFs ..., these are multiplied to produce a Success Likelihood Index SLI figure for each task. To improve the validity ..., the likelihood of success between pairs of tasks while considering two previously identified ... be carried out in an iterative manner. 7. Calculation of the SLI The Success Likelihood Index for each ... require to be transformed to HEPs as they are only relative measures of the likelihood of success .... Use of SLIM SARAH for Cost Effectiveness Analyses As SLIM evaluates HEPs as a function of the PSFs ... the Success Likelihood Index SLI for the task under assessment. class wikitable border 1 Weighting ... these SLI figures are not yet in the form of probabilities they are only indications as to the likelihood ... more details
Distinguish Likelihood ratio test In evidence based medicine , likelihood ratios are used for assessing ... state exists. Calculation Two versions of the likelihood ratio exist, one for positive and one for negative test results. Respectively, they are known as the likelihood ratio positive LR and likelihood ratio negative LR . The likelihood ratio positive is calculated as math LR frac text sensitivity ... are those that test positive T but do not have the disease D&minus . The likelihood ratio negative ... not have the disease testing negative. The pretest odds of a particular diagnosis, multiplied by the likelihood ... that odds can be calculated from, and then converted to, probability . Application to medicine A likelihood ratio of greater than 1 indicates the test result is associated with the disease. A likelihood ... the likelihood ratios lie close to 1 have little practical significance as the post test probability ... purposes, and not screening purposes. When the positive likelihood ratio is greater than 5 or the negative likelihood ratio is less than 0.2 i.e. 1 5 then they can be applied to the pre test ... Simplifying likelihood ratios journal J Gen Intern Med volume 17 issue 8 pages 646 9 year 2002 ... the clinician to better interpret the results of the diagnostic test and helps to predict the likelihood ... as either sensitivity tests sensitivity and specificity tests specificity , a likelihood ratio, or an inexact graphic of the likelihood ratio, found no difference between the three modes in interpretation ... doi ref Example A medical example is the likelihood that a given test result would be expected in a patient with a certain disorder compared to the likelihood that same result would occur in a patient ... ratios cite web url http www.poems.msu.edu InfoMastery Diagnosis likelihood ratios.htm title Likelihood ratios work accessdate 2009 04 04 ref A worked example is shown below. SensSpecPPVNPV Estimation of pre and post test probability See Pre and post test probability The likelihood ratio ... more details
In computer data storage , Partial Response Maximum Likelihood PRML is a method for converting the weak analog signal from the head of a magnetic disk or tape drive into a digital signal . PRML attempts to correctly interpret even small changes in the analog signal, whereas peak detection relies on fixed thresholds. Because PRML can correctly decode a weaker signal it allows higher density recording. For example, PRML would read the magnetic flux density pattern 70, 60, 55, 60, 70 where 60 is the baseline signal as binary 101 , and the same for 45, 40, 30, 40, 45 baseline of 40 whereas peak detector would decode everything above, say, 50 as high, and below 50 as low, so the first pattern would read 111 and the second as 000 . See also Maximum likelihood Viterbi algorithm External links http pcguide.com ref hdd geom dataPRML c.html The PC Guide PRML http www.guzik.com solutions chapter9.asp Online Chapter Introduction to PRML from Alex Taratorin s book Characterization of Magnetic Recording Systems A Practical Approach FOLDOC Category Computer storage devices de Partial Response Maximum Likelihood fr PRML ... more details
No footnotes date April 2009 The elaboration likelihood model ELM of persuasion ref name Petty & Cacioppo, 1986 Petty, R. E., & Cacioppo, J. T. 1986 . Communication and Persuasion Central and Peripheral Routes to Attitude Change . New York Springer Verlag. ref is a model of how attitudes are formed and changed that was developed by R. E. Petty and J. T. Cacioppo in the early 1980s see also attitude change . Central to this model is the elaboration continuum , which ranges from low elaboration low thought to high elaboration high thought . The ELM distinguishes between two routes to persuasion the central route, where a subject considers an idea logically, and the peripheral route, in which the audience uses preexisting ideas and superficial qualities to be persuaded. Central route Central route processes require a great deal of thought, and therefore are likely to predominate under conditions that promote high elaboration. Central route processes involve careful scrutiny of a persuasive communication e.g., a speech, an advertisement, etc. to determine the merits of the arguments. Under ..., and ability strongly increase the likelihood that a message will be ingrained in the minds of listeners ... ref Testing the Elaboration Likelihood Model To design a way to test the Elaboration Likelihood ... the central route of the Elaboration Likelihood Model . In turn, a strong argument under similar ..., complexity, and familiarity. To scientifically study either route of the Elaboration Likelihood ... if the folks are turned off. ref name Petty & Cacioppo, 1986 Conclusions of the Elaboration Likelihood ... Likelihood Model to HIV Prevention A study performed in 1999 analyzed the effects of different persuasion ... all types of individuals. In this study, the Elaboration Likelihood Model was being tested .... T. 1999 . The Elaboration Likelihood Model Current Status and Controversies. In S. Chaiken & Y. Trope ... Attitude change de Elaboration Likelihood Model nl Elaboration likelihood model zh ... more details
The term score function may refer to Scoring rule , in decision theory, a measure of one s performance when making decisions under uncertainty Score statistics , the derivative of the log likelihoodfunction with respect to the parameter disambig ... more details
A discrepancy function is a mathematical function which describes how closely a Structural equation modeling structural model conforms to observed data. Larger values of the discrepancy function indicate a poor fit of the model to data. In general, the parameter estimates for a given model are chosen so as to make the discrepancy function for that model as small as possible. ref name multiple cite web url http spin.magnet.fsu.edu local stat book glosd.html title Department of Chemistry and Biochemistry at Florida State University accessdate September 10, 2006 ref Ref gone 404 There are several basic types of discrepancy functions, including maximum likelihood ML , generalized least squares GLS , and ordinary least squares OLS , which are considered the classical discrepancy functions. ref cite web title Discrepancy Functions Used in SEM url http www2.gsu.edu mkteer discrep.html accessdate 2008 08 18 ref Discrepancy functions all meet the following basic criteria They are non negative, i.e., always greater than or equal to zero. They are zero only if the fit is perfect, i.e., if the model and parameter estimates perfectly reproduce the observed data. The discrepancy function is a continuous function of the elements of S , the sample covariance matrix, and , the reproduced estimate of S obtained by using the parameter estimates and the structural model. In order for maximum likelihood to meet the first criterion, it is used in a revised form as the Deviance statistics deviance . See also Discrepancy theory Low discrepancy sequence Constructions of low discrepancy sequences References references Category Structural equation models stat stub ... more details
In mathematics, omega function or function may refer to Pearson Cunningham function Lambert W function Wright Omega function Mathematical disambiguation ... more details
Barnes G function , related to the Gamma function Meijer G function , a generalization of the hypergeometric function Siegel G function , a class of functions in transcendence theory mathdab ... more details
In mathematics, by sigma function one can mean one of the following The Divisor function sum of divisors function sub a sub n , an arithmetic function Weierstrass sigma function , related to elliptic functions Kronecker s sigma function Rado s sigma function, see busy beaver See also sigmoid function . mathdab de Teilersumme fr Fonction sigma ... more details
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