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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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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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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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Explaining Low Predictive Ability

For a university project I am supposed to predict one survey question (with 5 different answers) using 20 other survey questions (each with 4 or 5 different answers i.e. all predictor variables are ...
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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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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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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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Setting up the priors for Bayesian Multilevel Multinomial Mixed Model using BRMS

I am new (understatement!) to Bayesian statistics in general and to brms(). More specifically, I am confused as to how to specify the priors for nested random effects in a multinomial mixed model. ...
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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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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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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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Does Scikit Learn Logistic Regression use Sigmoid Function if We Apply multi_class=multinomial?

By looking at various documentations/blogs, my answer to this above question is No. By default, sklearn.linear_model.LogisticRegression using multi_class = ‘ovr’. I understand Sigmoid function for ...
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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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Multinomial equivalence test?

I was wondering if there is any statistical equivalence test (in r or python) for multinomial data "a contingency table (4x4)" to know whether the observed and the expected values are equivalence?
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Multinomial (Categorical) Multilevel (Hierarchical) Bayesian Model in R

I have a couple of questions, so I hope it is ok that I ask them here. Before that, here is some background information on my data: Outcome variable (1): categorical, 6 categories, N=168 Predictor ...
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Metrics for reporting the fit of a model with a multinomial response

When running a linear model, I like to report the R^2 values to give a simple overview of how well it fits the data. At the moment, I'm working on an analysis with a multinomial response (response ...
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1answer
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what's the difference between multinomial logistic regression and traditional regression?

Could anyone please explain to me what is the difference between multinomial logistic regression and traditional regression? I have used a method called elastic-net as the response variables are in ...
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1answer
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Standard Error of the ratio of multinomial and negative binomial variables

What is the correct way to compute a standard error of the ratio between random variables following multinomial and negative binomial distribution? I asked a question about computing variance in the ...
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1answer
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Relationship between statistical models: mcnemar test vs logistic regression

I always find useful and reliable answers in this forum and I hope this pattern will not change this time. I was spending some time to check whether an intervention program had any effect on an ...
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Discrete version of multivariate normal distribution

Let's say that I have a 2d map, and I would like to explore around my house. Drawing samples from a bivariate gaussian centered at the x, y location of my house makes sense, as I don't want to stray ...
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Distribution of number of objects in Simple Random Sampling with Replacement (SRSWR)

Suppose we have an urn containing $m \in \mathbb{N}$ objects and we sample with replacement $n \in \mathbb{N}$ times with equal chance of sampling any object in any draw. Let $1 \leqslant K \leqslant ...
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How to Interpret Parameter Estimate Output from SPSS [duplicate]

Dear Community Members, Given the outputs of the SPSS analysis, how can the exp (B ) and Beta values be interpreted in terms of odd ratio ? and in relation to how the independent variable affects the ...
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Using one binary classifier in multinomial classification bias?

It's very common to use binary classifiers to solve multiclass classification problems using a number of schemes (one-versus-all, one-vs-one, error encodings, etc.). My question involves using only ...
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Multinomial probabilities

Given a multinomial distribution, X ~ Mult(s1, s2, ..., sn; p1, p2, ..., pn) where all the p's are equal (1/n). What is the probability that ANY of the counts (si) are equal to c? I know we can ...
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Confidence region for multinomial distribution with k=7 - including 5 zero values in dataset

I have a multinomial distribution with $k=7$ and an observed dataset $n_i = \{62, 35, 0, 0, 0, 0, 0\}$. While it was quite expected that $n_i = 0$ for $i \in \{3,4,...,7\}$, there was no way to ...
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How to calculate standardized group differences for multinomial variables?

I am using the tableone::CreateTableOnefunction in R to evaluate differences between three groups regarding baseline variables (like age, gender, education etc.). ...
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Multinomial Probability Exercise

I have this problem: Among 30 students in a group, 6 students received grade "5" for the exam, 10 students - "4", 9 students - "3", the rest - "2". Find the probability that 3 students, called to the ...
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GLMNET: Weights and imbalanced data

I have a multinomial regression problem using glmnet. The training data is imbalanced (1:5:10 roughly). I tried over and undersampling already. Would providing ...
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Looking to see if random sample is uniform or not

I've been tracking data and I am looking to see if it is truly uniformly random. The scenario is there can be a grid of 35 colour tiles with 5 different colours (Blue, Green, Purple, Red and Yellow). ...
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Calculating proportion of variance explained by random effect in multinomial GLMM

I have a multinomial logistic GLMM with one random intercept. The number of response categories $C = 4$. Since a multinomial logit model consists of $C-1$ binomial logit models -- each pairing one non-...
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How to interpret GEE parameter estimate for Multinomial Ordinal Data

I have the following experimental design. There are four diet charts (A, B, and C, D). For each diet, a group of 25 subjects (1, 2, 3…25) was on each of those four diets. And they are supposed to ...
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Maximum a posteriori on Multinomial distribution with a Dirichlet prior can result in negative probabilities?

I am doing a maximum a posteriori (MAP) estimation of a Multinomial distribution $M(c_1,\dots,c_n|p_1,\dots,p_n)$ with a Dirichlet prior $D(p_1,\dots,p_n|\alpha_1,\dots,\alpha_n)$. The experimental ...
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Best method to do multiclass classification on a dataset with just 60 samples

I have a dataset with just 60 samples and for each sample I have about 45 predictors. Some of the predictors are derived from others because they represent the percentage of one predictor relative to ...
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Predict hierarchical outcome data

I am trying to predict an outcome that is hierarchical. Specifically, industry classification codes found here: https://www.naics.com/search/ These are six digit numbers where the first two indicate ...
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Difference in distribution of multinomial distributions

I have some questions regarding how to analyse catagorical data, summarised as percentages on an individual level. In the data in question, for each individual we know the fraction of biological ...
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multinomial distribution aggregation property

Suppose we have multinomial distribution in which we have 4 categories, and each one is associated with a probability of being selected, say $\theta_i$, $i=1,..,4$. And I know for sure that $\...