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 likelihood .... 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 ... be any 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
Likelihood eikos , versimilis captures the idea that something is likely to happen. As a formal concept, it has appeared in jurisprudence , commerce and scholasticism long before it was given a rigorous mathematical foundation. ref cite 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 measure of how likely an event is, as can be expressed in terms of, for example, 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 from a set of statistic s. References references disambig statistics stub ... 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 ...? The likelihoodfunction is the same in both cases it is proportional to math p 3 1 p 9 math . According ... on the design of the experiment, not on the likelihood in the sense of the likelihoodfunction ... condensed 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 ... more details
In statistics , a marginal likelihoodfunction , or integrated likelihood , is a likelihoodfunction in which some parameter variables have been marginalisation probability marginalised . It may also be referred to as evidence , but this usage is somewhat idiosyncratic. Given a parameter , , where is the parameter of interest, it is often desirable to consider the likelihoodfunction only in terms of . If there exists a probability distribution for , sometimes referred to as the nuisance parameter , in terms of , then it may be possible to marginalise or integrate out math mathcal L psi x p x psi int Lambda p 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. In general, some kind of numerical integration method is needed, either a general method such as Gaussian integration or a Monte Carlo method , or a method specialized to statistical problems such as the Laplace approximation , Gibbs sampling or the EM algorithm . Applications Bayesian model comparison In Bayesian model comparison , the marginalized variables are parameters for a particular type of model, and the remaining variable is the identity of the model itself. In this case, the marginalized 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 M is math p x M int p x theta, M , p theta M , d theta math This quantity is important because the posterior odds ratio for a model M sub 1 sub against another model M sub 2 sub involves a ratio of marginal likelihoods, the so called Bayes factor math frac p M 1 x p M 2 x frac p M 1 p M 2 , frac p x M 1 p x M 2 math which can be stated schematically as posterior odds ratio odds prior odds ... Charles S. Bos. A comparison of marginal likelihood computation methods . In W. H rdle and B. Ronz ... more details
data the greatest probability i.e., parameters that maximize the likelihoodfunction . Maximum ... this distribution function will be called the likelihood math mathcal L theta , ,x 1, ldots,x n ... with the logarithm of the likelihoodfunction, called the log likelihood math ln mathcal L theta ... is the same regardless of whether we maximize the likelihood or the log likelihoodfunction, since log ... estimate exists meaning that the log likelihoodfunction increases without attaining the supremum ... parameters . Properties Maximum likelihood is the extremum estimator obtained by maximizing, as a function ... holds, the limiting likelihoodfunction has unique global maximum at sub 0 sub . li ..., 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 is less than the maximum by at least ... are The first and second derivatives of the log likelihoodfunction must be defined. The Fisher information ... the technicalities Since the log likelihoodfunction is differentiable, and sub 0 sub lies in the interior ... to 49 but different values of p the probability of success , the likelihoodfunction defined below ... any value 0 p 1. The likelihoodfunction to be maximised is math L p f D mathrm H 49 mid p binom 80 ... en.svg thumb 200px likelihoodfunction for proportion value of a binomial process n 10 One way ... function exists, the likelihoodfunction is defined as above, under Principles , using this density ... likelihood , a variation using a likelihoodfunction calculated from a transformed set of data ... function , a description on what likelihood functions are. Mean squared error , a measure of how ... function using R http www.netstorm.be home mle A selection of likelihood functions in R http ...More footnotes date September 2009 In statistics, maximum likelihood estimation MLE is a statistical ... more details
Likelihood ratio may refer to 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
wiktionary functionFunction may refer to Diatonic function , a term in music theory 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. A formal event such as a party or meeting See also Function hall Functional disambiguation Functionality in polymer chemistry see Structural unit Functionalism disambiguation Functor disambiguation bs Funkcija vor bg 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 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
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
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
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
likelihoodfunctionlikelihood recorded. The test statistic usually denoted D Citation needed date ... 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 ... 1 , math where math L theta x math is the likelihoodfunction . Note that some references may use ... math The likelihoodfunction is math L theta x f x theta math with math f x theta math being the pdf ... refers to the Supremum function. A likelihood ratio test is any test with critical region or rejection ... likelihood ratio tests focus on two issues Citation needed date April 2009 the supremum function ... based on the likelihoodfunction . Bayesian inference embodies the likelihood principle ie that all the information from the sample data is expressed through the likelihoodfunction , which using ...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 ... 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 significantly better ... or references to describe sup For example if model 1 has 1 free parameter and a log likelihood of &minus ... 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 Dodge, Y. 2003 The Oxford Dictionary of Statistical Terms , OUP, ISBN 0199206139 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 journal last Bartlett first M.S. authorlink M. S. Bartlett year 1937 title Properties of sufficiency and statistical tests journal Proceedings of the Royal Society of London , Series A volume 160 pages 268&ndash 282 doi 10.1098 rspa.1937.0109 issue 901 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 journal last Patterson first H.D. last2 Thompson first2 R. year 1971 title Recovery of inter block information when block sizes are unequal journal ... by Harville. ref cite journal last Harville first David A. year 1977 title Maximum Likelihood ... 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
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
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
Wikify date June 2009 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 ... are used to derive a Success Likelihood Index SLI , a form of preference index, which is calibrated ... attribute utility decomposition which scales the relative success likelihood in performing a range ... on the relevant scale, these are multiplied to produce a Success Likelihood Index SLI figure for each ... by enquiring, with the experts, the likelihood of success between pairs of tasks while considering ..., this stage should be carried out in an iterative manner. 7. Calculation of the SLI The Success Likelihood ... calculated require to be transformed to HEPs as they are only relative measures of the likelihood ... APJ . 10. Use of SLIM SARAH for Cost Effectiveness Analyses As SLIM evaluates HEPs as a function ... to calculate the Success Likelihood Index SLI for the task under assessment. class wikitable border ... as to the likelihood by which the various errors may occur. The SLIs determine the order in which ... 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 www.storagereview.com guide dataPRML.html Storage Review 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 that 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 these conditions, a person s unique cognitive responses to the message determine the persuasive ... Likelihood Model To design a way to test the Elaboration Likelihood Model, it is crucial to determine ... Likelihood Model . In turn, a strong argument under similar circumstances will return favorable .... To scientifically study either route of the Elaboration Likelihood Model, the arguments themselves ... Likelihood Model In addition to these factors, the ELM also makes several unique proposals ... of the Elaboration Likelihood Model to HIV Prevention A study performed in 1999 analyzed the effects ... in a way that will reach all types of individuals. In this study, the Elaboration Likelihood Model .... E., & Wegener, D. T. 1999 . The Elaboration Likelihood Model Current Status and Controversies. In S. Chaiken ... Press. Category 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 &omega function may mean Pearson&ndash Cunningham function Lambert W function Wright Omega function mathdab ... 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
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