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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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probability to be above thresholds 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 95% 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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product multinomial mgf help

I have worked with mgf before with multinomial but need guidance understanding how to show $n.j$ is multinomial with the given parameters.
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1answer
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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
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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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16 views

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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22 views

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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1answer
32 views

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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27 views

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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13 views

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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20 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
33 views

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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38 views

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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0answers
9 views

Regression for combination of categorical and continuous dependent variables?

I am dealing with a model that has several categorical independent variables, 4 continuous dependent variables, and 2 categorical dependent variables. My goal is to examine how the IV's affect the DV'...
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0answers
69 views

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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35 views

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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9 views

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
89 views

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
34 views

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
70 views

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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24 views

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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1answer
141 views

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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35 views

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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20 views

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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36 views

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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34 views

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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1answer
31 views

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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148 views

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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2answers
244 views

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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35 views

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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1answer
160 views

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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23 views

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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1answer
12 views

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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38 views

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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1answer
47 views

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 $\...
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30 views

How to interpret Gelman's multivariate Gaussian prior for multinomial distribution?

Andrew Gelman suggested the use of a multivariate Normal distribution as prior for hierarchical models that have a multinomial distribution at the lowest level (http://andrewgelman.com/2009/04/29/...
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1answer
37 views

multinomial model with some certain parameters

I might be asking a naive questions here, sorry. Imaging I have 4 categories, each one has a probability of $\theta_i$ being selelcted, $i=1..4$ and sum of $\theta_i$ is 1. For this simple ...
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47 views

Naive Bayes for classifying columns

Hello StackExchange Community, I have a unique use case for Naive Bayes where I'm trying to train my model to identify output column names based on previous data of input column names. Basically, my ...
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14 views

Creation of a multinomial regression model from a set of data

I have a set of data (X,Y) values. The Y value needs to be modeled as a linear regression. The catch is that there are multiple independent subsets in (X,Y). say (X,Y) = ( (x11,y11), (x12,y12), (x21,...
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48 views

Continuous compound Poisson and Binomial

Suppose a random vector $X$ that is distributed: $X|N \sim \text{MN}(N,p_1,p_2...p_J)$ $N \sim \text{Poisson}(\lambda)$ What is the continuous analog of each distribution and the continuous ...
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1answer
99 views

Marginal distribution of random variable with multinomial sampling distribution and parameters $(n,\boldsymbol{p})$, where $n \sim $ Poisson

Suppose you have: $X|N \sim \text{MN}(N,p_1,p_2...p_J)$ $N \sim \text{Poisson}(\lambda)$ Where is the marginal distribution of $X$?
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Adjusting probabilities generated by multinomial regression by a fixed percent (for sensitivity analysis)

I have built an agent-based simulation model that has a diversity of different agent "classes" acting in different ways. The class of each agent is assigned at the start of each simulation according ...