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In probability theory, the multinomial distribution is a generalization of the binomial distribution. For example, it models the probability of counts...

Multinomial may refer to: Multinomial theorem, and the multinomial coefficient Multinomial distribution Multinomial logistic regression Multinomial test...

In mathematics, the multinomial theorem describes how to expand a power of a sum in terms of powers of the terms in that sum. It is the generalization...

In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more...

In probability theory and statistics, the Dirichlet-multinomial distribution is a family of discrete multivariate probability distributions on a finite...

proposed and evaluated as base estimators in random forests, in particular multinomial logistic regression and naive Bayes classifiers. In cases that the relationship...

With a multinomial event model, samples (feature vectors) represent the frequencies with which certain events have been generated by a multinomial ( p 1...

In statistics and econometrics, the multinomial probit model is a generalization of the probit model used when there are several possible categories that...

Multinomial test is the statistical test of the null hypothesis that the parameters of a multinomial distribution equal specified values; it is used for...

the other hand, the categorical distribution is a special case of the multinomial distribution, in that it gives the probabilities of potential outcomes...

many forms, including: Binary Logit, Binary Probit, Multinomial Logit, Conditional Logit, Multinomial Probit, Nested Logit, Generalized Extreme Value Models...

distribution is the conjugate prior of the categorical distribution and multinomial distribution. The infinite-dimensional generalization of the Dirichlet...

dog, lion, etc.), and the binary logistic regression generalized to multinomial logistic regression. If the multiple categories are ordered, one can...

(Y=m\mid Y\in \{1,m\}).\,} for m > 2. Different links g lead to multinomial logit or multinomial probit models. These are more general than the ordered response...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

⁠ x {\displaystyle x} ⁠. Binomial coefficients can be generalized to multinomial coefficients defined to be the number: ( n k 1 , k 2 , … , k r ) = n...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

In probability theory and statistics, the negative multinomial distribution is a generalization of the negative binomial distribution (NB(x0, p)) to more...

and later rediscovered by Euler, is a very simple application of the multinomial theorem, which states ( x 1 + x 2 + ⋯ + x m ) n = ∑ k 1 , k 2 , … , k...

trinomial coefficients, expansions, and distributions are subsets of the multinomial constructs with the same names. Because the tetrahedron is a three-dimensional...

generalization of the logistic function to multiple dimensions, and is used in multinomial logistic regression. The softmax function is often used as the last activation...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

{\displaystyle \{X=k\},} { Y i } {\displaystyle \{Y_{i}\}} follows a multinomial distribution, { Y i } ∣ ( X = k ) ∼ M u l t i n o m ( k , p i ) , {\displaystyle...

making no assumptions of the interval distances between options. Multinomial logit Multinomial probit McCullagh, Peter (1980). "Regression Models for Ordinal...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

and can be represented as a Beta PDF (Probability Density Function). A multinomial opinion applies to a state variable of multiple possible values, and...

In probability theory and statistics, the Dirichlet negative multinomial distribution is a multivariate distribution on the non-negative integers. It...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

{2+3-2}{2-1}}=3.} Kummer's theorem can be generalized to multinomial coefficients ( n m 1 , … , m k ) = n ! m 1 ! ⋯ m k ! {\displaystyle {\tbinom...

binomial, and instead require 3 or more categories, which leads to the multinomial distribution. Just as de Moivre and Laplace sought for and found the...

and in latent profile analysis and latent class analysis as from a multinomial distribution. The manifest variables in factor analysis and latent profile...

i n o m i a l ( N ; 1 / 6 , . . . , 1 / 6 ) {\displaystyle \mathrm {Multinomial} (N;1/6,...,1/6)} , and χ 2 := ∑ i = 1 6 ( O i − N / 6 ) 2 N / 6 {\textstyle...

determine which of the variants is more effective. Multivariate testing or multinomial testing is similar to A/B testing but may test more than two versions...

Gaussian binomial coefficient Multinomial generalizations Multinomial coefficient · Multinomial formula/theorem · Multinomial distribution · Pascal's pyramid...

estimation, simulation and diagnostic tools for multinomial discrete-choice models—ranging from basic multinomial logit to mixed logit, random-regret logit...

version of the Dirichlet-multinomial distribution as the binomial and beta distributions are univariate versions of the multinomial and Dirichlet distributions...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

multivariate statistics, particularly for his measure of similarity between two multinomial distributions, known as the Bhattacharyya coefficient, based on which...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

learning and statistical classification, multiclass classification or multinomial classification is the problem of classifying instances into one of three...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

i , j ∼ Multinomial ⁡ ( θ i ) . {\displaystyle z_{i,j}\sim \operatorname {Multinomial} (\theta _{i}).} (b) Choose a word w i , j ∼ Multinomial ⁡ ( φ z...

Gompertz function is obtained. In the latent variable formulation of the multinomial logit model — common in discrete choice theory — the errors of the latent...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

analysis on categorical outcomes is accomplished through multinomial logistic regression, multinomial probit or a related type of discrete choice model. Categorical...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

t-distribution. The negative multinomial distribution, a generalization of the negative binomial distribution. The Dirichlet negative multinomial distribution, a generalization...

yes/no/maybe in a survey); a generalization of the Bernoulli distribution Multinomial distribution, for the number of each type of categorical outcome, given...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

distribution (also known as the generalized Bernoulli distribution) and the multinomial distribution. If the discrete distribution has two or more categories...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

distribution#Random variate generation Laplace distribution#Random variate generation Multinomial distribution#Random variate distribution Pareto distribution#Random variate...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

that utilize standard hyperbolastic functions to model a dichotomous or multinomial outcome variable. The purpose of hyperbolastic regression is to predict...

implementation is easier. Sigmoid function Discrete choice on binary logit, multinomial logit, conditional logit, nested logit, mixed logit, exploded logit,...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

fixed and known. For example: binomial (with fixed number of trials) multinomial (with fixed number of trials) negative binomial (with fixed number of...

also known as the logistic normal distribution, which often refers to a multinomial logit version (e.g.). A variable might be modeled as logit-normal if...

representation of an integer Mahler's theorem Multinomial distribution Multinomial coefficient, Multinomial formula, Multinomial theorem Multiplicities of entries...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

others (link) Kern, John C. (2006). "Pig Data and Bayesian Inference on Multinomial Probabilities". Journal of Statistics Education. 14 (3). American Statistical...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

analysis Multinomial distribution Multinomial logistic regression Multinomial logit – see Multinomial logistic regression Multinomial probit Multinomial test...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

economic contexts. The Boltzmann distribution has the same form as the multinomial logit model. As a discrete choice model, this is very well known in economics...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

binomial coefficients. Pascal's rule can also be generalized to apply to multinomial coefficients. Pascal's rule has an intuitive combinatorial meaning, that...

score export to data functionality ✓ ✓ / AMOS X X Frequencies (Binomial, Multinomial, Contingency, Chi², log-linear regression) ✓ ✓ ✓ (✓) JAGS (Bayesian black-box...

Quadrature Method in Inference Problems Arising From the Generalized Multinomial Distribution. After working for a year as a visiting assistant professor...

x_{2},\ldots ,x_{d}\rangle } from a d {\displaystyle d} -dimensional multinomial distribution with N {\displaystyle N} trials, a "smoothed" version of...

affected by the change are automatically updated. The software includes a multinomial test to determine whether observed data differs from researchers' predictions...

three-parameter Student's t distribution, beta-binomial distribution and Dirichlet-multinomial distribution are all predictive distributions of exponential-family distributions...

and differentiation — this is an application of polynomial fitting. Multinomials in more than one independent variable, including surface fitting Curve...

(1993) attempted to model memory redintegration using a multinomial processing tree. In a multinomial processing tree, the cognitive processes and their outcomes...

m ) {\displaystyle {\tbinom {n}{k_{1},\cdots ,k_{m}}}} are known as multinomial coefficients, and can be computed by the formula ( n k 1 , k 2 , … ,...

restrictive assumption of mutually exclusive alternatives, which characterizes multinomial discrete choice methods. Ashford, J.R.; Sowden, R.R. (September 1970)...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

marketing research practice has shifted towards choice-based models using multinomial logit, mixed versions of this model, and other refinements. Bayesian...

1935. Generalized linear model Limited dependent variable Logit model Multinomial probit Multivariate probit models Ordered probit and ordered logit model...

Compounding a multinomial distribution with probability vector distributed according to a Dirichlet distribution yields a Dirichlet-multinomial distribution...

choice models developed by Charles Manski in 1975. Unlike the multinomial probit and multinomial logit estimators, it makes no assumptions about the distribution...

preferred brand of cereal, then probit or logit regression (or multinomial probit or multinomial logit) can be used. If both variables are ordinal, meaning...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

distribution, the multivariate stable distribution, the multinomial distribution, the negative multinomial distribution, the multivariate hypergeometric distribution...

Dirichlet distribution (probability theory) Dirichlet-multinomial distribution Dirichlet negative multinomial distribution Generalized Dirichlet distribution...

relationship to the multinomial distribution that the hypergeometric distribution has to the binomial distribution—the multinomial distribution is the...

the probability of each diploid–diploid combination, which follows a multinomial distribution with k = 3. For example, the probability of the mating combination...

Myanmar National League, Myanmar (Burma)'s national football league Multinomial logit, a generalized logistic regression model National Archives of Hungary...

Bretagnolle–Huber–Carol Inequality bounds the difference between a vector of multinomially distributed random variables and a vector of expected values. A simple...

than two categories, and an exact test is required, the multinomial test, based on the multinomial distribution, must be used instead of the binomial test...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

ethnobiological study in Kala Chitta hills of Pothwar region, Pakistan: multinomial logit specification". Journal of Ethnobiology and Ethnomedicine. 10:...

_{i=1}^{k}a_{i}^{{\bar {n}}_{i}}}{(\sum _{i}a_{i})^{\bar {n}}}}} where we use the multinomial coefficient. Conditional on the urn ending up with ( a i + n i ) {\displaystyle...

statistics Bayesian knowledge base Naive Bayes Gaussian Naive Bayes Multinomial Naive Bayes Averaged One-Dependence Estimators (AODE) Bayesian Belief...

Logistic regression – Statistical model for a binary dependent variable Multinomial logistic regression – Regression for more than two discrete outcomes...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

regression and probit regression for binary data. Multinomial logistic regression and multinomial probit regression for categorical data. Ordered logit...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

unable to generalise this binary choice into a multinomial choice framework (which required the multinomial logistic regression rather than probit link function)...

two non-normal distributions and illustrated this with the classical multinomial populations, this work despite being submitted for publication in 1941...

joint distribution of these variables after collapsing is a Dirichlet-multinomial distribution. The conditional distribution of a given categorical variable...

Discrete-Choice Modelling (1981) offered the first practical guide to estimating multinomial-logit models, while Stated Choice Methods (2000) systematised experimental...

k}={\frac {n!}{i!\,j!\,k!}}\,.} This formula is a special case of the multinomial formula for m = 3. The coefficients can be defined with a generalization...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

detailed example, refer to: Tetsuo Yai, Seiji Iwakura, Shigeru Morichi, Multinomial probit with structured covariance for route choice behavior, Transportation...

Britain (PDF). Oxford Internet Institute. p. 6. Flood, Joe (2008). "Multinomial Analysis for Housing Careers Survey". Paper to the European Network for...

distribution is the conjugate prior of the categorical distribution or multinomial distribution. W ( ) {\displaystyle {\mathcal {W}}()} is the Wishart distribution...

given n draws with replacement in an urn with black and white balls. multinomial distribution: there are balls of more than two colors. Each time a ball...

Gijswijt's upper bound. Jiang showed that by precisely examining the multinomial coefficients that come out of Ellenberg and Gijswijt's proof, one can...

structures in Great Britain Paviland These predictions were obtained using a multinomial logistic regression model based on a panel of 36 carefully selected SNPs...

variables. For categorical variables with more than two values there is the multinomial logit. For ordinal variables with more than two values, there are the...

function to multiple inputs is the softmax activation function, used in multinomial logistic regression. Another application of the logistic function is...

{red}{6}}xy^{5}+{\color {red}1}y^{6}\,} Polynomial factorization Factorization Multinomial theorem Discussion Review of Algebra: Expansion Archived 2014-12-10 at...

probability of each co-occurrence as a mixture of conditionally independent multinomial distributions: P ( w , d ) = ∑ c P ( d ) P ( c | d ) P ( w | c ) = P...

recognized as Pascal's triangle. Mathematics portal Logistic regression Multinomial distribution Negative binomial distribution Beta-binomial distribution...

(specific blood type, political party, word, etc.) categorical multinomial logit, multinomial probit ordinal ordering categories or integer or real number...

ordinal non-parametric No Pearson's χ 2 {\displaystyle \chi ^{2}} test Multinomial test nominal non-parametric univariate 1 Yes Location test McNemar's...

one bin. The number of ways to put objects into bins is given by the multinomial coefficient ( n k 1 , k 2 , … , k m ) = n ! k 1 ! k 2 ! ⋯ k m ! , {\displaystyle...

multivariate hypergeometric, multivariate negative hypergeometric, multinomial, or Dirichlet distribution, but not in general otherwise. Formally, the...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

Kuder–Richardson Formula 20 Linear discriminant analysis Multinomial distribution Multinomial logit Multinomial probit Multiple correspondence analysis Odds ratio...

the maximum size of an antichain of p-compositions is the largest p-multinomial coefficient ( n n 1   n 2   …   n p ) , {\displaystyle {\binom {n}{n_{1}\...

dimensions; for σ = 1 {\displaystyle \sigma =1} , its expansion using the multinomial theorem is: exp ⁡ ( − 1 2 ‖ x − x ′ ‖ 2 ) = exp ⁡ ( 2 2 x ⊤ x ′ − 1 2...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

obtain the following nice distributional result of yi yi ∨ ni, xi, ci ~ Multinomial (ni, p1 (xi, b0), ..., pT (xi, b0 )) (2) where p t ( x i , b 0 ) = m...

Text Classification" The R Journal "maxent: An R Package for Low-memory Multinomial Logistic Regression with Support for Semi-automated Text Classification"...

F_{N}(t_{2}),\dots ,F_{N}(t_{n})} is a multinomial distribution. Now, the central limit approximation for multinomial distributions shows that lim N N ( F...

(LDA)—assumes Gaussian conditional density models Naive Bayes classifier with multinomial or multivariate Bernoulli event models. The second set of methods includes...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

algorithms: Classification Bayesian classifiers Naive Bayes Naive Bayes Multinomial Decision trees classifiers Decision Stump Hoeffding Tree Hoeffding Option...

"Non-parametric modeling of rainfall in Manizales City (Colombia) using multinomial probability and imprecise probabilities. Modelación no paramétrica de...

categorical variables with more than two categories can be modeled with a multinomial regression. Counts of non-i.i.d. binary data can be modeled by more complicated...

testing were first discussed in Hoeffding's work on optimal tests for multinomial distributions. There have been many subsequent works on the topic in...

Dickson, Leonard E. (1919). "Chapter IX: Divisibility of factorials and multinomial coefficients". History of the Theory of Numbers. Vol. 1. Carnegie Institution...

an ideal A higher order derivative in Lagrange's notation Binomial or multinomial coefficient Commutator, an indicator to which a binary operation fails...

alternative name trinomial coefficients because of their relationship to the multinomial coefficients: ( n k ) 2 = ∑ 0 ≤ μ , ν ≤ n μ + 2 ν = n + k n ! μ ! ν ...

k_{m}}={\frac {n!}{k_{1}!\,k_{2}!\cdots k_{m}!}}} are the multinomial coefficients. This is akin to the multinomial formula from algebra. The proof of the general...

(specific blood type, political party, word, etc.) categorical multinomial logit, multinomial probit ordinal ordering categories or integer or real number...

charges, charges, and death sentences. In this case, the multinomial probit or multinomial logit technique is used. Contrariety Dichotomy Disjoint sets...

procedure is to just draw one item at a time (like getting n draws from a multinomial distribution with N elements, each with their own p i {\displaystyle...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

naïve Bayes classifier Discriminative: maximum entropy models such as Multinomial logistic regression Sequence models Recurrent neural network Hidden Markov...

{\alpha _{n}}{\beta _{n}}}={\frac {\alpha !}{\beta !(\alpha -\beta )!}}} Multinomial coefficient ( k α ) = k ! α 1 ! α 2 ! ⋯ α n ! = k ! α ! {\displaystyle...

G-test from the log-likelihood ratio test where the underlying model is a multinomial model. Suppose we had a sample O = ( O 1 , … , O m ) {\displaystyle O=(O_{1}...

continuous- discrete Rectified Gaussian Multivariate (joint) Discrete: Ewens Multinomial Dirichlet Negative Continuous: Dirichlet Generalized Multivariate Laplace...

models, and the like, to distinguish between certain variants and fit a multinomial logit model to, e.g., transport choices. A variable such as cost differs...

ethnobiological study in Kala Chitta hills of Pothwar region, Pakistan: multinomial logit specification". Journal of Ethnobiology and Ethnomedicine. 10 (1)...

complex and time-consuming process. Trinomial expansion Monomial Binomial Multinomial Simple expression Compound expression Sparse polynomial Quadratic expressions...

log-likelihood ratio test in the context of contingency tables and the multinomial distribution and to Pearson's χ2 test: mutual information can be considered...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

probability of a 2 × 2 table under the first study design is given by the multinomial distribution; where the total number of samples taken is the only statistical...

called a trinomial. A polynomial with two or more terms is also called a multinomial. A real polynomial is a polynomial with real coefficients. When it is...

this number the load on the bin. The problem can be modelled using a Multinomial distribution, and may involve asking a question such as: What is the...

a description of the clove, the starfruit and durian. Rumphius used multinomial names and his descriptions were largely missed by Linnaeus as he received...

discrete choice (including binary choice, ordered choice and unordered multinomial choice), censoring and truncation, sample selection, loglinear models...

much smaller than that. Relief was also described as generalizable to multinomial classification by decomposition into a number of binary problems. Kononenko...

discriminant analysis Maximum entropy classifier (aka logistic regression, multinomial logistic regression): Note that logistic regression is an algorithm for...

"multinomial PCA". When NMF is obtained by minimizing the Kullback–Leibler divergence, it is in fact equivalent to another instance of multinomial PCA...

logistic regression. Multiclass classification methods include multinomial probit and multinomial logit. When the classification function is not perfect, false...

successes, yes votes, etc.) given a fixed number of total occurrences Multinomial distribution, similar to the binomial distribution, but for counts of...

hidden to the classifier. An example is explained in Zemel et al. where a multinomial random variable is used as an intermediate representation. In the process...

\end{bmatrix}}_{q}z^{n}.\end{aligned}}} One may further define the q-multinomial coefficients [ n k 1 , … , k m ] q = [ n ] ! q [ k 1 ] ! q ⋯ [ k m ]...

as a mixture of unobserved topics. Furthermore, each topic defines a multinomial distribution over a set of terms. Thus, for each word of each document...

farmers' decisions on child labor and schooling in the cocoa sector: a multinomial logit analysis in Cˆote d'Ivoire" (PDF). Agricultural Economics. 35 (3):...

publisher (link) multgee: GEE solver for correlated nominal or ordinal multinomial responses using a local odds ratios parameterization, CRAN, 13 May 2021{{citation}}:...

minimax character of the sample distribution function and of the classical multinomial estimator". The Annals of Mathematical Statistics. 27 (3): 642–669. doi:10...

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: P (...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

454–461. Gerber, E. A. E., and Craig, B. A. (2021). A mixed effects multinomial logistic-normal model for forecasting baseball performance. Journal of...

Bhattacharyya (1946), entitled "On a Measure of Divergence between Two Multinomial Populations", which defined the Bhattacharyya angle. The term was popularized...

\choose m_{1},\ldots ,m_{k}}:={\frac {m!}{m_{1}!\cdots m_{k}!}}} is the multinomial coefficient. These two formulas follow directly from Pólya's enumeration...

encountered in machine learning, for example, as the cumulant of the multinomial/binomial family. In tropical analysis, this is the sum in the log semiring...

Accounting. 3 (3). Ostrovski, Vladimir (May 2017). "Testing equivalence of multinomial distributions". Statistics & Probability Letters. 124: 77–82. doi:10...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

There is evidence suggesting that different processes are involved in remembering something versus knowing whether it is familiar. It appears that "remembering"...

negative multinomial distribution if a generalized form of odds ratio is used instead of the categories' probabilities- if the negative multinomial parameter...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

Cramer, Jan Salomon; Ridder, Geert (1991). "Pooling states in the multinomial logit model". Journal of Econometrics. 47 (2): 267–272. doi:10...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

like max, min, sum, statistical distributions like uniform, normal and multinomial, and basic linear algebra subprogram (BLAS) operations like dot product...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

log-likelihood ratio test in the context of contingency tables and the multinomial distribution and to Pearson's χ2 test: mutual information can be considered...

(1981-12-01). "Some local limit theorems in the symmetric Dirichlet-Multinomial urn models". Annals of the Institute of Statistical Mathematics. 33 (1):...

conjoint structures. Karabatsos (2005) generalised this work with his multinomial Dirichlet framework, which enabled the probabilistic testing of many...

Milliken–Taylor theorem (Ramsey theory) Milliken's tree theorem (Ramsey theory) Multinomial theorem (algebra, combinatorics) Mycielski's theorem (graph theory) Nicomachus's...

extreme-value judgments, and the resulting data can be analyzed using multinomial logit, mixed logit, or related models commonly used in conjoint and discrete...

Poisson distribution, Bernoulli distribution, Monte Carlo method, and multinomial distribution. Using these, it can look for areas of higher and lower...

logistic sigmoid. The visible units of Restricted Boltzmann Machine can be multinomial, although the hidden units are Bernoulli.[clarification needed] In this...

derivative of an arbitrary number of factors, one has a similar formula with multinomial coefficients: ( ∏ i = 1 k f i ) ( n ) = ∑ j 1 + j 2 + ⋯ + j k = n ( n...

Paleolithic Bichon from Switzerland. These predictions were obtained using a multinomial logistic regression model based on a panel of 36 carefully selected SNPs...

k_{2},\ldots ,k_{m}}={\frac {n!}{k_{1}!\,k_{2}!\cdots k_{m}!}}} is the multinomial coefficient and k 1 , … , k n {\displaystyle k_{1},\dots ,k_{n}} contains...

variance of a multinomial distribution (Swanson 1976) (there called an "expanded binomial model"). M1 is the variance of the multinomial distribution and...

11770215. JSTOR 20628591. S2CID 141134485. Yamaguchi, Kazuo (May 2000). "Multinomial logit latent-class regression models: an analysis of the predictors of...

Moivre also generalised Newton's noteworthy binomial theorem into the multinomial theorem. The Royal Society became apprised of this method in 1697, and...

the Dirichlet-multinomial model should be done. Per every sample, based on the fragment lengths observed in that sample, a multinomial maximum likelihood...

binomial distribution Extended negative binomial distribution Negative multinomial distribution Binomial distribution Poisson distribution Compound Poisson...

exactly the same way as the Dirichlet distribution is conjugate to the multinomial distribution and categorical distribution. The Pearson type I distribution...

activation within each pooling region is picked randomly according to a multinomial distribution, given by the activities within the pooling region. This...

heuristic more precisely devised a multinomial processing tree model for the recognition heuristic. A multinomial processing tree model is a simple statistical...

obtained by collecting like terms, or alternatively, by applying the multinomial theorem. The special case f ( x ) = e x {\displaystyle f(x)=e^{x}} ,...

with vertices 1, 2, …, n of degrees d1, d2, …, dn respectively, is the multinomial coefficient ( n − 2 d 1 − 1 , d 2 − 1 , … , d n − 1 ) . {\displaystyle...

}}x_{2}^{j_{2}}\cdots x_{n-k+1}^{j_{n-k+1}},} where we have used the multinomial coefficient. The ordinary Bell polynomials can be expressed in the terms...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

means that substitution models can be viewed as implying a specific multinomial distribution for site pattern frequencies. If we consider a multiple...

Brussaard, Lijbert (2003). "Food preference of wireworms analyzed with multinomial logit models". Journal of Insect Behavior. 16 (5): 647–665. Bibcode:2003JIBeh...

estimation of haplotypes. Some of the earliest approaches used a simple multinomial model in which each possible haplotype consistent with the sample was...

PMID 28584021. Nowicka M, Robinson MD (6 December 2016). "DRIMSeq: a Dirichlet-multinomial framework for multivariate count outcomes in genomics". F1000Research...

Y_{i}=nP_{n}(A_{i})} form a multinomial distribution with event probabilities P ( A i ) {\displaystyle P(A_{i})} The covariance matrix of this multinomial distribution...

model theory and the use of sense-making to understand event outcomes. A multinomial processing tree (MPT) model was used to identify processes underlying...

increases. Estimation methods are available either by approximating a multinomial distribution or by bootstrapping. When used for binary attributes, the...

statistical models include the following: normal mixtures, binomial mixtures, multinomial mixtures, Bayesian networks, neural networks, radial basis functions...

Three Commonly Used Crash Severity Models on Sample Size Requirements: Multinomial Logit, Ordered Probit and Mixed Logit Models. Analytic Methods in Accident...

permutation of q → {\displaystyle {\vec {q}}} can be represented by a multinomial as N ! ∏ j = 0 k n j ! {\displaystyle {\frac {N!}{\prod _{j=0}^{k}n_{j}...

ISBN 978-0-444-89942-2. Riefer, David M.; Batchelder, William H. (1988). "Multinomial modeling and the measurement of cognitive processes" (PDF). Psychological...

"Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model". Transportation Research Part B: Methodological. 35 (7):...

so we get the special case of the quadratic kernel. After using the multinomial theorem (twice—the outermost application is the binomial theorem) and...

Train has well documented steps for implementing this algorithm for a multinomial probit model. What follows here will apply to the binary multivariate...

mathematical study of combinatorics spinning, but even theology was impacted. Multinomial distribution Bernoulli trial Law of large numbers Bernoulli numbers Binomial...

application areas: the econometrics of choice data (logit and probit, multinomial and ordered choice, truncated and censored data, and duration data) and...

Multiset coefficients should not be confused with the multinomial coefficients that occur in the multinomial theorem. The value of multiset coefficients can...

the complete homogeneous symmetric polynomials as special cases of the multinomial coefficient that appears in the MacMahon expression. Performing some...

binomial coefficient Partition (number theory) Twelvefold way Dirichlet-multinomial distribution Batterson, J. Competition Math for Middle School. Art of...

numbers. The clustering is performed using Gibbs sampling Dirichlet multinomial mixture model algorithm. The citation statistics are provided derived...

coefficients of ⁠ f . {\displaystyle f.} ⁠ The analogue of Lucas's theorem for multinomial coefficients p ! i ! j ! k ! {\displaystyle {\frac {p!}{i!j!k!}}} says...

k = 2 {\textstyle \sum _{k=1}^{6}{C_{k}}=2} and the counts have the multinomial distribution f ( c 1 , … , c 6 ) = Pr ( C 1 = c 1  and  …  and  C 6 =...

Skeaff, Sheila; Slooten, Liz; Strack, Mick; Shephard, Kerry (2014). "Multinomial-Regression Modeling of the Environmental Attitudes of Higher Education...

S2CID 86867575. ———; McFadden, Daniel (1984). "Specification Tests for the Multinomial Logit Model". Econometrica. 52 (5): 1219–1240. doi:10.2307/1910997. hdl:1721...

multiplying the vector part. These two scalar functions are series sums of multinomials in the number that is the scalar part and the number that is the vector...

parameters. This is later generalized for multi-class classification, with multinomial logistic regression experts. One paper proposed mixture of softmaxes...

M) is n, then the number of multiset permutations of M is given by a multinomial coefficient: ( n m 1 , m 2 , … , m l ) = n ! m 1 ! m 2 ! ⋯ m l ! = (...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

be performed in any order, the number of such paths is given by the multinomial coefficient ( m + n − k k , m − k , n − k ) = ( m + n − k m ) ( m k )...

bootstrap samples items from a list of size n with counts drawn from a multinomial distribution. If W i {\displaystyle W_{i}} denotes the number times element...

(2015). "Source and destination memory in face-to-face interaction: A multinomial modeling approach". Journal of Experimental Psychology. 21 (2): 195–204...

variable Trial data, trial data is simulated as a Monte Carlo sample from a Multinomial distribution. For example, when Trial_size=100, each Monte Carlo sample...

and, in each stratum, a 2x2 table showing the paired binary responses. Multinomial confidence intervals are used for matched pairs binary data. Pearson's...

, … , x m {\displaystyle x_{1},\ x_{2},\ldots ,x_{m}} is called the multinomial and has the form: f ( x 1 , x 2 , … , x m ∣ p 1 , p 2 , … , p m ) = n...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

{\tilde {w}}_{i}} for each word i {\displaystyle i} , such that we have a multinomial logistic regression: w i T w ~ j + b i + b ~ j ≈ ln ⁡ P i j {\displaystyle...

gamma variance prior. This model is then optimized using a customized multinomial probit approach with a Gibbs sampler. These methods have been used successfully...

Affiliation as listed on her publications "Estimating the Size of a Multinomial Population" (1972, doi:10.1214/aoms/1177692709) and "Estimating the Size...

Poisson regression, ordinal logistic regression, quantile regression and multinomial logistic regression that described by Fallah in 2009. Similar to RBFNN...

Dirichlet's approximation theorem Hilbert's paradox of the Grand Hotel Multinomial theorem Pochhammer symbol Ramsey's theorem Herstein 1964, p. 90 Rittaud...

{\displaystyle \ (\ x_{11},x_{10}\ ,x_{01}\ ,x_{00}\ )\ } follows a multinomial distribution with probability vector   ( p 11   , p 10   , p 01   , p...

relationship to the beta function is analogous to the relationship between multinomial coefficients and binomial coefficients. For example, it satisfies a similar...

implemented in the RRF package Decision tree Memetic algorithm Random multinomial logit (RMNL) Auto-encoding networks with a bottleneck-layer Submodular...

such as pH. In addition, this is the transform most commonly used for multinomial logistic regression. The alr transform is not an isometry, meaning that...

2-dimensional, unlike Pascal's simplex, whose rows are the multinomial coefficients of the nth multinomial series expansion. When m = 2, the problem will be equivalent...

S.E. et al. (1999). Source monitoring deficits in patients with schizophrenia; a multinomial modeling analysis. Psychological Medicine, 29, 903–914....

problems. Models used in binomial regression can often be extended to multinomial data. There are many methods of generating the values of μ in systematic...

newer alternative is probabilistic latent semantic analysis, based on a multinomial model, which is reported to give better results than standard LSA. In...

{\alpha _{i}+c_{i}}{\sum _{i}\alpha _{i}+n}}\end{aligned}}} (categorical) Multinomial p (probability vector), k (number of categories; i.e., size of p) Dirichlet...

is generalized Dirichlet, and that Y ∣ X {\displaystyle Y\mid X} is multinomial with n {\displaystyle n} trials (here Y = ( Y 1 , … , Y k ) {\displaystyle...

{K}{k_{1},\ldots ,k_{n}}}\equiv {\frac {K!}{k_{1}!\cdots k_{n}!}}} is a multinomial coefficient. The Kronecker deltas in the above formulas restrict the...

the ROC) Logistic regression (a.k.a. logit model) Logit Probit model Multinomial probit Q–Q plot Continuous function Monotonic function Quantile function...

the Beta-binomial model, the Gaussian–Gaussian model, the Dirichlet-multinomial model, as well specific models for Bayesian linear regression (see below)...

and healthy groups. The concept translates to higher dimensions D if multinomials x 1 i x 2 j ⋯ x D k {\displaystyle x_{1}^{i}x_{2}^{j}\cdots x_{D}^{k}}...

Note that all the combinatorial proofs above use either binomials or multinomials of n {\displaystyle n} . Therefore if p {\displaystyle p} is prime, then:...

2}}/2=3}} ways of choosing 2 pairs of points from 4 points (counting via the multinomial coefficient, and accounting for the overcount by a factor of 2 that (...

J.-M. (2003). An introduction to the imprecise Dirichlet model for multinomial data. Tutorial for the Third International Symposium on Imprecise Probabilities...

variance. Hoeffding, Wassily (1965). "Asymptotically Optimal Tests for Multinomial Distributions". The Annals of Mathematical Statistics. 36 (2): 369–401...

more variables, an analogous expression holds, but with an appropriate multinomial expansion rather than binomial expansion. Higher order differentials...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

continuous- discrete Rectified Gaussian Multivariate (joint) Discrete: Ewens Multinomial Dirichlet Negative Continuous: Dirichlet Generalized Multivariate Laplace...

Setting a uniform prior over the initial m categories, and 2) using the multinomial distribution as the likelihood function (which is the multivariate generalisation...

d_{i}} specified for each vertex i {\displaystyle i} is equal to the multinomial coefficient ( n − 2 d 1 − 1 , d 2 − 1 , … , d n − 1 ) = ( n − 2 ) ! (...

Cramér's V, which can be equal to 1 for any rectangular table. If we have a multinomial sample of size n, the usual way to estimate T from the data is via the...

which can be binomial when the opinion applies to a binary variable or multinomial when it applies to an n-ary variable. A subjective opinion thus applies...

}\end{aligned}}} where ( j α ) {\displaystyle {\tbinom {j}{\alpha }}} is the multinomial coefficient. Since 1 j ! ( j α ) = 1 α ! {\displaystyle {\tfrac {1}{j...

com/2007/09/interview-with-jack-meacham.html Smith, R., & Bayen, U. (2004). A multinomial model of event-based prospective memory. Journal of Experimental Psychology:...

theory of irrationals expounded in Euclid, Book x., from binomial to multinomial and from ordered to unordered irrationals (see extracts from Pappus's...

In this "memoryless" model, every I/O reference represents an i.i.d multinomial random variable, whose outcome is the location of the next reference...

minimax character of the sample distribution function and of the classical multinomial estimator", Annals of Mathematical Statistics, 27 (3): 642–669, doi:10...

been observed if the agent faced different general choice sets, with multinomial choices being a natural way to analyze multiple treatments. More formally...

corresponding two-index inverse relations for sequences of two indices, and to multinomial inversion formulas for sequences of j ≥ 3 {\displaystyle j\geq 3} indices...

Fonseca-Fuentes, Marisela; Elórtegui-Gómez, Claudio (1 September 2021). "Multinomial Logistic Regression to Estimate the Financial Education and Financial...

^{\mathrm {T} }.} C n {\displaystyle C_{n}} is the covariance matrix of the multinomial distribution, in the special case where the parameters of that distribution...

the NEF described below. An example of the multivariate case is the multinomial distribution with known number of trials. The properties of the natural...

combinatorisch-analytischer Abhandlungen, which contained a claim that de Moivre's multinomial theorem was “the most important proposition in all of mathematical analysis”...

continuous- discrete Rectified Gaussian Multivariate (joint) Discrete: Ewens Multinomial Dirichlet Negative Continuous: Dirichlet Generalized Multivariate Laplace...

generalized extreme value, multinomial probit, or mixed logit. For the case where ε n i t {\displaystyle \varepsilon _{nit}} is multinomial logit (i.e. drawn iid...

λ of the Poisson distribution, the probability p in the binomial or multinomial distribution. Consider the model of a normal distribution with unknown...

{\displaystyle \ F(\ x;\ -\ln \sigma ,\ {\tfrac {\ 1\ }{\alpha }},\ 0\ )~.} Multinomial logit models, and certain other types of logistic regression, can be...

u , 1 ) {\displaystyle (u+du,1)} respectively. This equals (refer to multinomial distribution for details) n ! ( k − 1 ) ! ( n − k ) ! u k − 1 ⋅ d u ⋅...

step-size. For multiple underlyers – e.g. Rainbow- and Basket options – "multinomial lattices" can be built. Each underlyer will have its own tree, and the...

2}}=3}} ways of choosing 2 pairs of points from 4 points (counting via the multinomial coefficient). For example, given the four points ( ± 1 , ± 1 ) , {\displaystyle...

corresponded was expanded by De Moivre, who found the expansion of a multinomial. De Moivre also found the formula for derangements using the principle...

century. Statistical Science 13: 95–122. P. Walley (1996). Inferences from multinomial data: learning about a bag of marbles. Journal of the Royal Statistical...

models (DDM), Random Utility Models (RUM) or, in its most used form, the multinomial logit model (MNL). Choice models have attracted a lot of attention and...

\prod _{\ell =a,b,\ldots }^{k}{\frac {1}{N_{\ell }!}}} This is just the multinomial coefficient, the number of ways of arranging N items into k boxes, the...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

(Bretagnolle–Huber–Carol Inequality is a variation of Concentration inequality for multinomially distributed random variables which bounds the total variation distance...

most probable result. The probability of any particular result is the multinomial distribution, P r ( p ) = W ⋅ m − N {\displaystyle Pr(\mathbf {p} )=W\cdot...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

(F:D) McCullagh's parametrization of the Cauchy distributions / (1:C) Multinomial distribution / (F:D) Multivariate normal distribution / Gau Negative...

machine during World War II. Turing at first modelled the frequencies as a multinomial distribution, but found it inaccurate. Good developed smoothing algorithms...

current state-of-the-art methods on benchmark datasets. InstaNovo+, a multinomial diffusion model built upon human intuition, further improves performance...

Liew; Survival Models for Altitude Decompression Sickness - N Kannan; Multinomial Bubble Score Model - P Tikuisis, KA. Gault; Probabilistic Models of DCS...

of explanatory (independent) variables, using a logistic function or multinomial distribution. Logistic regression measures the relationship between a...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

Program on the Utilization of Obstetrical Services in Mexico, 2001-2006: A Multinomial Probit Model with a Discrete Endogenous Variable. Journal of Health Economics...

symbols) is 1. Each column can therefore be regarded as an independent multinomial distribution. This makes it easy to calculate the probability of a sequence...

regression Binary regression Logistic regression Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson...

"Entropy of the sum of independent Bernoulli random variables and of the multinomial distribution". In Gani, J.; Rohatgi, V.K. (eds.). Contributions to probability:...

Generalized linear models Logistic regression Multinomial logit Ordered logit Probit model Multinomial probit Ordered probit Poisson regression Maximum...

model Relative species abundances in the UNTB model follow a zero-sum multinomial distribution. The shape of this distribution is a function of the immigration...

31(01):143–159, 1996. Randall C Campbell and R Carter Hill. "Predicting multinomial choices using maximum entropy". Economics Letters, 64(3):263–269, 1999...

the voters are independent and identically distributed according to a multinomial distribution conditional on a prior uniform draw … This prior is a special...

doi:10.1214/aoms/1177728549. Mosimann, James E. (1962). "On the compound multinomial distribution, the multivariate β {\displaystyle \beta } distribution...

time, the tool was tested with success for the Okapi BM25 model, and a multinomial language model, but also includes divergence from randomness models....

ordering does not matter, however, is comparable to describing a single multinomial distribution of N draws from an X-fold category, where only the number...

when this was not present in the data. They noted that the use of the multinomial distribution may be more appropriate than the use of a Poisson distribution...

balls are observed. Negative binomial distribution Dirichlet negative multinomial distribution Johnson et al. (1993) Johnson, N.L.; Kotz, S.; Kemp, A.W...

(IIS) are two early algorithms used to fit log-linear models, notably multinomial logistic regression (MaxEnt) classifiers and extensions of it such as...

with Tor Helleseth titled “New commutative semifields defined by new PN multinomials”. In 2022 another paper co-authored by Budaghyan led to Emil Artin Junior...

Minka, Thomas P. (2011). "Non-conjugate Variational Message Passing for Multinomial and Binary Regression" (PDF). NeurIPS. Infer.NET: an inference framework...

stratification, the number of elements at each stratum can be modeled as a multinomial distribution with different p h {\displaystyle p_{h}} inclusion probabilities...

data. Summary statistics for model selection have been obtained using multinomial logistic regression on simulated data, treating competing models as the...

Problems involving categorical or nominal predictions, both binomial and multinomial; Problems involving binary or Boolean predictions. The first type of...

Richard; Jonsson, Jan O. (October 2000). "Analyzing Educational Careers: A Multinomial Transition Model". American Sociological Review. 65 (5): 754–772. doi:10...

Linear Discriminant Analysis Linear Regression Nonlinear Regression Multinomial Logit Classification Nearest Neighbor Regression and Classification Neighborhood...

application areas: the econometrics of choice data (logit and probit, multinomial and ordered choice, truncated and censored data, and duration data) and...

the Fisher information matrix. The design allowed the estimation of a multinomial logistic regression model with 50 parameters: 10 parameters for main...

Calanchini, J., Rivers, A. M., Klauer, K. C., & Sherman, J. W. (2018). Multinomial processing trees as theoretical bridges between cognitive and social...

Review. 76 (5): 87–99. PMID 10185434. Can also be 'multi-period' or 'multinomial' option Pennock, Michael (2010). "Multistage real options". The Economics...

functions that employ Range Queries are: NPV, XNPV, IRR, XIRR, MIRR, MULTINOMIAL, and SERIESSUM. Within the application these functions are identified...

Duncan KH, Sunghoon Kim, Zhe Chen, and Wayne S. DeSarbo. "A Bayesian Multinomial Probit Model for the Analysis of Panel Choice Data." Psychometrika 81...

Topaloglu, H. (2021). Assortment optimization and pricing under the multinomial logit model with impatient customers: Sequential recommendation and selection...

continuous- discrete Rectified Gaussian Multivariate (joint) Discrete: Ewens Multinomial Dirichlet Negative Continuous: Dirichlet Generalized Multivariate Laplace...

{\displaystyle {e_{\alpha }(z)={z^{\alpha } \over {\sqrt {\alpha !}}}}} for α a multinomial. For f in F n {\displaystyle {\mathcal {F}}_{n}} and z in Cn, the operators...

(microsatellites, SNP-array genotyping, BayeScan (which uses the Dirichlet-multinomial distribution)) to place them into defined conservational units. This...

judgments. Expanding on this work, Gawronski and colleagues developed a multinomial model called the CNI model, which quantifies (a) sensitivity to consequences...

pm-research.com. Madan, Dilip B.; Milne, Frank; Shefrin, Hersh (1989). "The Multinomial Option Pricing Model and its Brownian and Poisson Limits". The Review...

values vegetarian/non-vegetarian, Grandmaster/or not), or an ordered multinomial categorical variable (e.g. level of final educational attainment, skiers'...

"Client demands and the allocation of home care in the Netherlands. A multinomial logit model of client types, care needs and referrals". Health Policy...

Lave developed the first disaggregate automobile choice model, using multinomial logit 1985 – Gordon Fielding, Timlynn Babistky, and Mary Brenner identified...

Jenny (April 2020), "Finding a flexible hot-deck imputation method for multinomial data", Journal of Survey Statistics and Methodology, 9 (4) smaa005, doi:10...