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90 relations: Asymptote, Bayesian probability, Bayesian statistics, Bernoulli distribution, Binomial distribution, Canonical form, Categorical distribution, Closed-form expression, Comparison of general and generalized linear models, Correlation and dependence, Count data, Cumulative distribution function, Dependent and independent variables, Domain of a function, Eta, Expected value, Exponential dispersion model, Exponential distribution, Exponential family, Fisher information, Gamma distribution, Gauss–Markov theorem, General linear model, Generalized additive model, Generalized estimating equation, Generalized linear array model, Generalized linear mixed model, Gibbs sampling, GLIM (software), Greek alphabet, Hessian matrix, Heteroscedasticity-consistent standard errors, Injective function, Inverse Gaussian distribution, Iterative method, Iteratively reweighted least squares, John Nelder, Journal of the Royal Statistical Society, Laplace's method, Least squares, Likelihood function, Linear combination, Linear probability model, Linear regression, Log-linear model, Logarithm, Logistic regression, Logit, Longitudinal study, Markov chain Monte Carlo, ..., Maximum likelihood estimation, Mixed model, Multilevel model, Multinomial distribution, Multinomial logistic regression, Multinomial probit, Multiplicative inverse, Natural exponential family, Natural logarithm, Newton's method, Normal distribution, Observed information, Odds ratio, Ordered logit, Ordered probit, Overdispersion, Poisson distribution, Poisson regression, Posterior probability, Prior probability, Probability density function, Probability distribution, Probability mass function, Probit model, Quasi-likelihood, Quasi-variance, Random effects model, Random variable, Range (mathematics), Robert Wedderburn (statistician), Score (statistics), Scoring algorithm, Smoothing, Statistics, Sufficient statistic, Tweedie distribution, Uncorrelated random variables, Variance function, Variance-stabilizing transformation, Vector generalized linear model. Expand index (40 more) »
Asymptote
In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity.
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Bayesian probability
Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief.
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Bayesian statistics
Bayesian statistics, named for Thomas Bayes (1701–1761), is a theory in the field of statistics in which the evidence about the true state of the world is expressed in terms of degrees of belief known as Bayesian probabilities.
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Bernoulli distribution
In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution of a random variable which takes the value 1 with probability p and the value 0 with probability q.
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Binomial distribution
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own boolean-valued outcome: a random variable containing a single bit of information: success/yes/true/one (with probability p) or failure/no/false/zero (with probability q.
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Canonical form
In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression.
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Categorical distribution
In probability theory and statistics, a categorical distribution (also called a generalized Bernoulli distribution, multinoulli distribution) is a discrete probability distribution that describes the possible results of a random variable that can take on one of K possible categories, with the probability of each category separately specified.
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Closed-form expression
In mathematics, a closed-form expression is a mathematical expression that can be evaluated in a finite number of operations.
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Comparison of general and generalized linear models
No description.
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Correlation and dependence
In statistics, dependence or association is any statistical relationship, whether causal or not, between two random variables or bivariate data.
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Count data
In statistics, count data is a statistical data type, a type of data in which the observations can take only the non-negative integer values, and where these integers arise from counting rather than ranking.
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Cumulative distribution function
In probability theory and statistics, the cumulative distribution function (CDF, also cumulative density function) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. In the case of a continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables.
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Dependent and independent variables
In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables.
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Domain of a function
In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.
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Eta
Eta (uppercase, lowercase; ἦτα ē̂ta or ήτα ita) is the seventh letter of the Greek alphabet.
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Expected value
In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents.
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Exponential dispersion model
In probability and statistics, the class of exponential dispersion models (EDM) is a set of probability distributions that represents a generalisation of the natural exponential family.
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Exponential distribution
No description.
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Exponential family
In probability and statistics, an exponential family is a set of probability distributions of a certain form, specified below.
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Fisher information
In mathematical statistics, the Fisher information (sometimes simply called information) is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of the score, or the expected value of the observed information.
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Gamma distribution
In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions.
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Gauss–Markov theorem
In statistics, the Gauss–Markov theorem, named after Carl Friedrich Gauss and Andrey Markov, states that in a linear regression model in which the errors have expectation zero and are uncorrelated and have equal variances, the best linear unbiased estimator (BLUE) of the coefficients is given by the ordinary least squares (OLS) estimator, provided it exists.
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General linear model
The general linear model or multivariate regression model is a statistical linear model.
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Generalized additive model
In statistics, a generalized additive model (GAM) is a generalized linear model in which the linear predictor depends linearly on unknown smooth functions of some predictor variables, and interest focuses on inference about these smooth functions.
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Generalized estimating equation
In statistics, a generalized estimating equation (GEE) is used to estimate the parameters of a generalized linear model with a possible unknown correlation between outcomes.
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Generalized linear array model
In statistics, the generalized linear array model (GLAM) is used for analyzing data sets with array structures.
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Generalized linear mixed model
In statistics, a generalized linear mixed model (GLMM) is an extension to the generalized linear model (GLM) in which the linear predictor contains random effects in addition to the usual fixed effects.
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Gibbs sampling
In statistics, Gibbs sampling or a Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm for obtaining a sequence of observations which are approximated from a specified multivariate probability distribution, when direct sampling is difficult.
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GLIM (software)
GLIM (an acronym for Generalized Linear Interactive Modelling) is a statistical software program for fitting generalized linear models (GLMs).
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Greek alphabet
The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BC.
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Hessian matrix
In mathematics, the Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field.
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Heteroscedasticity-consistent standard errors
The topic of heteroscedasticity-consistent (HC) standard errors arises in statistics and econometrics in the context of linear regression as well as time series analysis.
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Injective function
In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain.
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Inverse Gaussian distribution
In probability theory, the inverse Gaussian distribution (also known as the Wald distribution) is a two-parameter family of continuous probability distributions with support on (0,∞).
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Iterative method
In computational mathematics, an iterative method is a mathematical procedure that uses an initial guess to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones.
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Iteratively reweighted least squares
The method of iteratively reweighted least squares (IRLS) is used to solve certain optimization problems with objective functions of the form: by an iterative method in which each step involves solving a weighted least squares problem of the form:C.
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John Nelder
John Ashworth Nelder (8 October 1924 – 7 August 2010) was a British statistician known for his contributions to experimental design, analysis of variance, computational statistics, and statistical theory.
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Journal of the Royal Statistical Society
The Journal of the Royal Statistical Society is a peer-reviewed scientific journal of statistics.
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Laplace's method
In mathematics, Laplace's method, named after Pierre-Simon Laplace, is a technique used to approximate integrals of the form where ƒ(x) is some twice-differentiable function, M is a large number, and the endpoints a and b could possibly be infinite.
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Least squares
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns.
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Likelihood function
In frequentist inference, a likelihood function (often simply the likelihood) is a function of the parameters of a statistical model, given specific observed data.
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Linear combination
In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).
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Linear probability model
In statistics, a linear probability model is a special case of a binomial regression model.
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Linear regression
In statistics, linear regression is a linear approach to modelling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent variables).
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Log-linear model
A log-linear model is a mathematical model that takes the form of a function whose logarithm equals a linear combination of the parameters of the model, which makes it possible to apply (possibly multivariate) linear regression.
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Logarithm
In mathematics, the logarithm is the inverse function to exponentiation.
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Logistic regression
In statistics, the logistic model (or logit model) is a statistical model that is usually taken to apply to a binary dependent variable.
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Logit
The logit function is the inverse of the sigmoidal "logistic" function or logistic transform used in mathematics, especially in statistics.
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Longitudinal study
A longitudinal study (or longitudinal survey, or panel study) is a research design that involves repeated observations of the same variables (e.g., people) over short or long periods of time (i.e., uses longitudinal data).
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Markov chain Monte Carlo
In statistics, Markov chain Monte Carlo (MCMC) methods comprise a class of algorithms for sampling from a probability distribution.
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Maximum likelihood estimation
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of a statistical model, given observations.
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Mixed model
A mixed model is a statistical model containing both fixed effects and random effects.
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Multilevel model
Multilevel models (also known as hierarchical linear models, nested data models, mixed models, random coefficient, random-effects models, random parameter models, or split-plot designs) are statistical models of parameters that vary at more than one level.
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Multinomial distribution
In probability theory, the multinomial distribution is a generalization of the binomial distribution.
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Multinomial logistic regression
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.
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Multinomial probit
In statistics and econometrics, the multinomial probit model is a generalization of the probit model used when there are several possible categories that the dependent variable can fall into.
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Multiplicative inverse
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1.
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Natural exponential family
In probability and statistics, a natural exponential family (NEF) is a class of probability distributions that is a special case of an exponential family (EF).
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Natural logarithm
The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.
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Newton's method
In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.
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Normal distribution
In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.
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Observed information
In statistics, the observed information, or observed Fisher information, is the negative of the second derivative (the Hessian matrix) of the "log-likelihood" (the logarithm of the likelihood function).
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Odds ratio
In statistics, the odds ratio (OR) is one of three main ways to quantify how strongly the presence or absence of property A is associated with the presence or absence of property B in a given population.
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Ordered logit
In statistics, the ordered logit model (also ordered logistic regression or proportional odds model), is an ordinal regression model—that is, a regression model for ordinal dependent variables—first considered by Peter McCullagh.
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Ordered probit
In statistics, ordered probit is a generalization of the widely used probit analysis to the case of more than two outcomes of an ordinal dependent variable (a dependent variable for which the potential values have a natural ordering, as in poor, fair, good, excellent).
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Overdispersion
In statistics, overdispersion is the presence of greater variability (statistical dispersion) in a data set than would be expected based on a given statistical model.
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Poisson distribution
In probability theory and statistics, the Poisson distribution (in English often rendered), named after French mathematician Siméon Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently of the time since the last event.
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Poisson regression
In statistics, Poisson regression is a generalized linear model form of regression analysis used to model count data and contingency tables.
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Posterior probability
In Bayesian statistics, the posterior probability of a random event or an uncertain proposition is the conditional probability that is assigned after the relevant evidence or background is taken into account.
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Prior probability
In Bayesian statistical inference, a prior probability distribution, often simply called the prior, of an uncertain quantity is the probability distribution that would express one's beliefs about this quantity before some evidence is taken into account.
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Probability density function
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function, whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.
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Probability distribution
In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.
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Probability mass function
In probability and statistics, a probability mass function (pmf) is a function that gives the probability that a discrete random variable is exactly equal to some value.
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Probit model
In statistics, a probit model is a type of regression where the dependent variable can take only two values, for example married or not married.
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Quasi-likelihood
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.
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Quasi-variance
Quasi-variance (qv) estimates are a statistical approach to overcome the reference category problem when estimating the effects of a categorical explanatory variable within a statistical model.
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Random effects model
In statistics, a random effects model, also called a variance components model, is a statistical model where the model parameters are random variables.
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Random variable
In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is a variable whose possible values are outcomes of a random phenomenon.
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Range (mathematics)
In mathematics, and more specifically in naive set theory, the range of a function refers to either the codomain or the image of the function, depending upon usage.
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Robert Wedderburn (statistician)
Robert William Maclagan Wedderburn (1947–1975) was a Scottish statistician who worked at the Rothamsted Experimental Station.
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Score (statistics)
In statistics, the score, score function, efficient score or informant indicates how sensitive a likelihood function \mathcal L(\theta; X) is to its parameter \theta.
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Scoring algorithm
Scoring algorithm, also known as Fisher's scoring, is a form of Newton's method used in statistics to solve maximum likelihood equations numerically, named after Ronald Fisher.
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Smoothing
In statistics and image processing, to smooth a data set is to create an approximating function that attempts to capture important patterns in the data, while leaving out noise or other fine-scale structures/rapid phenomena.
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Statistics
Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.
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Sufficient statistic
In statistics, a statistic is sufficient with respect to a statistical model and its associated unknown parameter if "no other statistic that can be calculated from the same sample provides any additional information as to the value of the parameter".
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Tweedie distribution
In probability and statistics, the Tweedie distributions are a family of probability distributions which include the purely continuous normal and gamma distributions, the purely discrete scaled Poisson distribution, and the class of mixed compound Poisson–gamma distributions which have positive mass at zero, but are otherwise continuous.
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Uncorrelated random variables
In probability theory and statistics, two real-valued random variables, X,Y, are said to be uncorrelated if their covariance, E(XY) − E(X)E(Y), is zero.
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Variance function
In statistics, the variance function is a smooth function which depicts the variance of a random quantity as a function of its mean.
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Variance-stabilizing transformation
In applied statistics, a variance-stabilizing transformation is a data transformation that is specifically chosen either to simplify considerations in graphical exploratory data analysis or to allow the application of simple regression-based or analysis of variance techniques.
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Vector generalized linear model
In statistics, the class of vector generalized linear models (VGLMs) was proposed to enlarge the scope of models catered for by generalized linear models (GLMs).
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References
[1] https://en.wikipedia.org/wiki/Generalized_linear_model
