# Questions tagged [multinomial-distribution]

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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### How to determine sample size when performing indirect sampling?

Problem Summary I want to know the minimum sample size needed for a given confidence level and margin of error when performing indirect sampling where samples from the two populations are not one-to-...
1 vote
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### Bayesian updates for Dirichlet-multinomial with Gamma prior

Let \begin{aligned} X_i &\sim \text{Dir-multinom}(X\mid\lambda)\\ \lambda_{j} &\sim \text{Gamma}(\lambda_j\mid\alpha,\beta)\\ \end{aligned} where $i$ iterates over observations, $j$ ...
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### Pairwise comparisons for probabilities from multinomial model

Q. How can I do pairwise comparisons for probabilities and associated CI's obtained from a multinomial model? The simple example. We have been conducting some experiments for sediment preference for ...
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### Why do proportions hold across credibility range in multinomial distribution? How to compute probability of deviations from that?

I know I can use pymc3 code like this to find out if die is biased and what side is it that is more prone to show up (taken from here). ...
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### Multinomial logistic regression for proportions in R

I am asking myself the following question: Is a multinomial logistic regression adequate to model a proportion Y_n/Y? f.ex.: Y_n = number of broken phones, divided by Y = number of total phones sold X ...
1 vote
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### Fitting a multinomial glm for a very large dataset

I have compositional data where for two groups, where each is represented by two ages, there are 100 possible categories for which I observed counts: ...
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### Multinomial Logistic Regression vs. Logistic Regression Results in R

I am running multinomial logistic regressions in R using the multinom function from the nnet package. Most of my variables are categorical, and oddly almost all of the variables come out significant. ...
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### Multinomial with small counts and many cells

I have data distributed as multinomial, with $N= 1,000$ observations divided among $n=10,000$ cells, with unequal probabilities $p_i$, for $i=1,...,n$. I would like to assess how likely it is that an ...
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### Why multinomial regression gives huge difference in Odds Ratio when variable treated as continuous and tertile categories?

I am trying to perform a multinomial regression model with the values of Leptin against BMI levels (Normal, Overweight and ...
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### Probability that two samples from a multinomial distribution intersect in a specific way

The following combinatorially difficult problem has obvious applications in information retrieval and bioinformatics but I haven't seen its solution discussed anywhere. I am interested in computing ...
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### Confidence intervals for multinomial proportions

I know that there are a lot of methods to find the confidence intervals for binomial proportions using methods like Agresti-Coull, but is there any important papers mentioning to find confidence ...
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### Question about paper on Bayesian Shrinkage Estimation

I am reading the paper Bayesian Shrinkage Estimation of the Relative Abundance of mRNA Transcripts Using SAGE, and I am trying to work out the calculations for the complete conditionals for the Gibbs ...
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### A regression in R with a categorical response variable

I have a conceptual question. I have a dataset with a categorical response variable (integers from 1 till 10) and numerical predictors (independent variables). I want to be able to predict the value (...
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1 vote
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### Question about a mixture dirichlet MCMC model

I am self-learning Bayesian statistics using the book Computational Bayesian Statistics by Turkman et al. and I am currently stuck on Chapter 6 Problem 10. It can be found here on page 124. I am ...
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### One-vs-rest vs one-vs-one multiclass probability validation: does it matter?

Now that I have figured out how rms::val.prob works to the extent that I have written my own Python implementation, I would like to extend that idea to multiple ...
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### "Cumulative distribution" of a collection of random variables with different distributions

I am working with an application where I have a grid of cells, and I calculate "concentrations" in each cell by randomly placing a number of "particles" across the grid, and ...
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1 vote
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### BASIC: Probability of a box to contain n-keys

Consider the situation in which 4 boxes exist, as well as 4 keys. Each key is stored inside of a randomly chosen box. Now suppose we chose a box at random. What is the probability of the chosen box to ...
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### Multinomial test from finitely many possible multinomial distributions

my area of focus is within pure math, but I've found myself in a situation where I need to run some sort of statistical test, and I am hoping someone can point me towards the correct test or framework....
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### How to choose alternative specific constant (ASC) in multinomial logistic regression in R? (unlabeled choice experiments)

I am trying to replicate my colleague's NLOGIT analysis using R. This analysis was for a discrete choice experiment in which fisherman chose whether to opt into a hypothetical environmental protection ...
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### Outlier detection/influential observations multinomial logit in R

I'm using the mlogit package to fit models using a multinomial likelihood. Does anyone know how to check for outliers or influential observations when fitting multinomial models with this package? ...
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### Probability of a draw between at least two options in an election with n voters and m options

I hope that this question has not been asked before, but i couldn't find an answer to it online or by myself. I came by that question during a project of mine: If i have an election with n voters and ...
1 vote
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### between-group multinomial test

I'm having some trouble to decide what is the best method to analyze a between-groups / multinomial problem. For simplicity, I'll use an example: Let's say I want to compare basketball shooting ...
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### Latent profile analysis and Factor Analysis

How different is Latent Profile Analysis from Factor Analysis and what is the role of Multinomial Regression ? Does anybody have any intuitive ideas to understand the difference? Thanks.
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### GLMM when the dependent variable has three levels

I'm trying to fit mixed models in R for data where the dependent variable is categorical with three levels (choices of True, False, Unsure). My plan was to fit three separate binomial mixed models (...
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1 vote
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### Interpretation of Multinomial Logistic Regression model fit in R

I have fitted a multinomial logistic regression model in R. The data has 35 independent variables and the dependent variable has 3 levels. I do not find information on how to interpret the outcome of ...