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Questions tagged [multinomial]

A multivariate, discrete probability distribution used to describe the results of a random experiment where each of $n$ outcomes are placed into one of $k$ nominal categories.

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Interpreting R nnet output Multinomial Regression

I was wondering if anyone would be able to help me interpret my results. I am struggling to find anywhere online which it simple to follow. I have conducted a multinomial regression. I have a ...
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Counting frequencies in Multinomial Naive Bayes

I have noticed some ambiguity/inconsistency in how various authors calculate the p(word|label) estimate in Multinomial Naive Bayes. In some cases, this value is calculated by counting words without ...
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How to calculated a probability for a sum of integers to be equal to a given value if probabilities of addends are known?

Let's assume that we have a process generating some integer numbers with different probabilities. The set of possible integers is small. For example: -2, -1, 0, 1 and 2. We also know probabilities for ...
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Regression for multinomial distribution (negative and positive correlation coefficients)

I have a dependent variable, which is a multinomial distribution resulting from positive and negative correlation coefficients. This is a study from the field of Dendrochronology. Those correlation ...
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Multinomial-dirichlet with fractional counts

Suppose a lepidopterologist wants to estimate the relative proportions of three different species of butterfly. They go out into the field and count $N$ butterflies and record the number of each ...
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Sample size for multinomial response?

Thank you in advance for reading this question! I was wondering, how would I go about calculating an appropriate sample size, given that the output / response is multinomial? I really like the ...
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Interpreting discrete choice experiments with sequential options

Objective: We have fruit fly stocks of different eye-pigment phenotypes, with different visual acuity levels. We want to know if, given a number of environments with different lighting conditions, ...
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Does the multinomial coefficient create combinations or permutations?

I am looking at this formula I just want to make sure I get it. For example, if I want to split a fifty-two card deck into all the possible combinations of four, thirteen card hands, then I get: 52!...
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Dirichlet Multinomial Posterior Predictive Distribution for Language Model

I have been trying to teach myself about Bayesian analysis, and whilst I have been through the theory several times, I am struggling to actually apply it. I have found some questions online to ...
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28 views

Penalized multinomial regression with missing values

I would like to fit some models on a dataset where I have a lot of missing values. I am especially interested in comparing models fit with and without imputed values, because the dataset has so many ...
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Standard error of individual groups in a multinomial distribution

Let's say I have a sample of data from a multinomial distribution with 10 categories. I want to determine the error in my estimate of the % of observations that fall into each of the categories. ...
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My dependent variable is classified in categories ,which regression model to use

My dependent variable is classified in categories as 5-10, 10-15 . Which is the best regression model for this kind of analysis.my dependent variable asks the participant of the survey to mark the ...
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Probability of detecting small bias in a die in the low confidence regime

We are given a biased $m$-sided die: one of the sides has probability $\frac{1}{m} + \gamma$ and all the rest have probability $\frac{1}{m} - \frac{\gamma}{m-1}$ each. The goal is to figure out which ...
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Numerically/approximately integrating over independent gamma variables

Problem Statement For a problem in biology, I am testing out a joint distribution of the form: $$ X \sim Multinomial(\frac{\theta_1}{\sum \theta_i}, ...,\frac{\theta_n}{\sum{\theta_i}}) \\ \theta_i \...
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Transform a multiclass dataset into a multi-label one

I have a dataset of feature/label pairs. My labels are probabilities of each feature vector to belong to the K classes. Here is an example for K = 3: D1 = { (V0, [0.33,0.33,0.33]), (V1, [0.9,0.07,0....
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Calculate a Bayesian 'posterior predictive p-value' for a multinomial logistic regression

For assessing the fit of a model in a Bayesian framework, 'posterior predictive p-values' (PPPs) are often used. Here, a value close to 0.5 indicates a good fit; a value close to 0 or 1 indicates a ...
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1answer
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What are the possible estimates of the parameters of the multinomial distribution?

The expected value of the parameters of the multinomial distribution (taking into account the Dirichlet prior $D(\alpha)$ and the posterior Dirichlet-Multinomial) is: $\pi_i = α_i+ x_i / \sum_{j} α_j+...
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How to use the Dirichlet prior for estimating the multinomial parameters? [closed]

I know that the multinomial distribution gives the likelihood of some vector D of occurrences to happen given a probability vector (parameters) P' i.e. P(D|P'). Now with a Dirichlet prior we are ...
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Why is the conditional distribution from a multinomial a binomial with these parameters?

Say we have a multinational distribution , $$Y=(Y_{1},Y_{2},Y_{3},Y_{4},Y_{5}) \sim multi(n,\frac{1}{2},\frac{\theta}{4},\frac{1-\theta}{4},\frac{1-\theta}{4},\frac{\theta}{4})$$ with observed $X=(...
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standard error of the reference category of the outcome_ multinomial logistic regression

I am working with a multinational Logistic Regression model where I have a 6-category outcome and have a number of predictors(independent variables). I have set category 1 of the target as the ...
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Multinomial Random Variable - significance test & bootstrapping

If I have a random variable $X$ that follows a multinomial distribution $(p_1, p_2, \dotsc, p_n)$, is there anyway to test if two of the levels have equal probability, for example, if $p_1 = p_2$? ...
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Need question answered [closed]

With a universe of 143, 30 of those were queried/sampled at random, giving answers of (dividing into groups of) A, B, C,and D. Question: If all 143 were sampled, what is the probability that the ...
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What is the cost of reconstructing a discrete probability distribution, from samples, within a given error?

I'm aware that there are several methods to estimate the probability distribution from samples (e.g. density estimation methods). However, I haven't been able to find the actual asymptotic costs of ...
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1answer
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Consumer Surplus (Williams 1977 and Rosen 1981)

$U_{nj} = V_{nj} + \epsilon_{nj}$ for all $j$ and $\epsilon_{nj}$ captures the factors that affect utility but are not included in $V_{nj}$. The decision maker chooses the alternative that provides ...
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1answer
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Interpreting R nnet Package Multinomial Regression

I need to interpret this summary. I have a response variable with 5 levels (response) and an explanatory variable (taxon) with 2 levels (raptor and others). Can someone help me? Call: multinom(...
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1answer
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for a multinomial treatment and binary outcome, what is more appropriate, ATC or ATE?

I need help to choose between ATC and ATE for my analysis with multinomial treatment and binary outcome. In the example below taken from here, it seems that ATT does not sound well for multinomial ...
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Question regarding equation in the multinominal distrubution of the exponential family

So this question is regarding to some notes i read in the book Machine learning and pattern recognition in chapter 2 in the section exponential family. First they state: So then they derive this ...
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1answer
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What is the added value of a multivariate Bernoulli distribution over a multinomial distribution?

I came across the multivariate Bernoulli distribution of Dai, Ding & Wahba (2013) that has the following form (in the bivariate case): $P(X_1,X_2)=p_{11}^{x_1 x_2} p_{10}^{x_1 (1-x_2)} p_{01}^{(1-...
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Why with glmnet I obtain different coefficients for the different categories I want to classify?

I am performing a multinomial logistic regression using glmnet. I have 7 classes of trees to predict and different predictors. What I do not understand is why when I plot the coefficents vs. log ...
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1answer
73 views

How to calculate the probability for this multinomial logit model?

In multinomial logit models, the probability of the observed choice ranked 1st among all option is given by this formula: p(choice = j) = exp(x_j*b)/(\sum(x_i*b)) ...
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Regression methods for ordered categorical data with more than 2 levels

I am dealing with an Outcome Variable y which is categorical (0,1,2,3) and ordered. My question is what type of regression models can I try for such a dataset ? I ...
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1answer
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how to estimate prognostic core for a continuous, multinomial, and binary treatment, respectively

Quoting David Hajage and Finbarr Leacy, respectively: "Introduced by Hansen in 2008, the prognostic score (PGS) has been presented as ‘the prognostic analogue of the propensity score’ (PPS). ...
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Count frequency distribution of monomial

If you sample $N$ times from a set of $n$ objects with replacement and then plot the frequency against the count (i.e. the number of times an object has been chosen once, twice,...), you get a ...
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Why there are not (long tail) alternatives to dirichlet-multinomial (while there are for posisson-gamma)

While there are a lot of long tail alternatives to poisson-gamma (negative binomial), for example (Source) I haven't found any work on replacing the dirichlet distribution with a more long tailed ...
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probability to belong to the majority class based on observed proportions

I have a population of several categories and I don't know the proportion of these categories in my population. I want to draw (with replacement) in my population until I can say with 99% certainty ...
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Compare models which use different methods to describe the response

Situation I am trying to predict the stand type of a forest 10 years following a clear cut. I am using GBM models to do the multinomial classification. The problem is I have several competing methods ...
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Binomial logistic regression for multiclass problems

Applying the independence of irrelevant alternatives (IIA) is an inherent assumption in multinomial logistic regression but not binomial. Is it therefore okay and possibly better to use $K$ binomial ...
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4answers
527 views

How to simulate Likert-scale data in R? [closed]

I want to do a Monte-Carlo experiment to check my theoretical finding regarding Likert-scale data. I want to have random test results with N participants, where every question has 5 answers: (0,1,2,3 ...
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Is there a name for “many Multinomial distributions”?

Is there a name for "many Multinomial distributions"? I.e. if I have a set of r.v.s that each obey a multinomial, then what distribution does the set have?
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Multinomial vs Poisson for Histograms

Preliminaries My question came about when reading Lawrence and Chromy's paper on Maximum Likelihood (ML) estimation of histograms (link). I am aware of this question, but I fail to see how that helps ...
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Recovering $\theta$ in Dirichlet-Multinomial (Polya) distribution

I'm working on Latent Dirichlet Allocation with Collapsed Gibbs Sampling. LDA has two Dirichlet-Multinomial distribution and one of them is a document-topic distribution that determines the ...
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Testing if word-count vectors follow a multinomial distribution

I am attempting to make a Naive Bayes classifier for word count vectors (each document is represented as a vector of word counts). For this, I am using SciKit-Learn's MultinomialNB. From what I ...
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104 views

Simulating Random Strings using Binomial/Multinomial Distributions

I am simulating some DNA sequences (containing characters A, C, G, and T) in R through specifying i) the number of sequences to generate (num.seqs) ii) the length of the generated sequences (length....
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Marginal Likelihood of Multinomial Dirichlet model

To find the marginal likelihood of the multinomial Dirichlet model, I tried the following: $$\int_\theta p(N|\theta)p(\theta)d\theta=\frac{n!}{n_1!...n_K!}\frac{\Gamma(\sum_{k=1}^K\alpha_k)}{\Pi_{k=1}^...
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Estimation of emission distribution parameters of HMM using Baum-Welch

It seems like the count-based Baum-Welch method described elsewhere is concerned only with the categorical emission distribution. In Hidden Markov Models, I have normal transition matrix between ...
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1answer
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How to decide on whether it is a hypergeometric or a multinomial?

I am a bit confused whether I should use a hypergeometric or a multinomial distribution when I encounter a questions having more than two X_i and I kinda remember that for multinomial distribution the ...
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Generating Function for sum of N dice [or other multinomial distribution] where lowest N values are “dropped” or removed

Background I found this interesting question Formula for dropping dice (non-brute force) and excellent answer https://stats.stackexchange.com/a/242857/221422, but couldn't figure out how to ...
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Convergence in probability of a multinomial sample correlation coefficient

This problem is from a Ph.D Qualifying Exam on mathematical statistics(also related to probability theory). Let $(X_1,\cdots,X_k)$ be a random vector with multinomial distribution of $n$ trials and ...
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105 views