# 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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### Using probability estimates as independent variables in a multinomial model

I'm testing market efficiency on a fixed odds betting market, and a way of carrying out efficiency test as a statistical hypothesis is by using the multinomial model. However, I'm used to fit ...
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### Questions about pmf of multinomial distribution with indicator variables

I was reading through the textbook of Introduction to Machine Learning, it introduces $z^{t} = (z_{1}^{t},...,z_{k}^{t})$, where $z_{i}$ is an indicator variable, each with probability $\pi_{i}$, then ...
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### Calculating the standard error of difference in proportions from paired multinomial variables

I have a data set where respondents are placed into one of four categories at two time points. I've worked up an example in R. ...
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### Multinomial Logistic Regression with Likert, Count and Categorical data

I want to predict a variable that has a likert format (satisfaction 1 to 4). However, the independent variables available to me are a series of count variables (e.g. counting frequency up to 6 ...
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### Calculate the difference between the multinomial probability

I have an example data as follows: ...
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### A Multinomial Geometric distribution? What is this distribution called?

In a problem I am dealing with I repeatedly interact with a distribution of the following form, $$p(n_1, n_2, \ldots n_M)=\binom{\sum_{i=1}^Mn_i}{n_1\cdots n_m} w_0\prod_{i=1}^Mw_i^{n_i}$$ where $p$ ...
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### Appropriate Model to predict food preference with high number of dependent variables

I am trying to build a model that delivers a prediction for which food a person may like based on information the person has entered into the system beforehand, e.g. they input that they like (beef, ...
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### Independence test or multinomial distribution test

I have a contingece table as follows: I can use the Chi-square test to check the independent of the column and row variable. You will compute the difference between the actual frequency and expected ...
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### Dirchlet Process Mixture of Multinomials

The Dirichlet Process Mixture of Gaussians has been well studied and shown to work. I have never seen DPM of Multinomials and tried to implement one. What I notice is the likelihood tends to dominate ...
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### Logistic regression model; too many independent variables?

I'm building a logistical regression model to predict the gender of users based on listening duration of music genres. My main worry is that I have over 40 different genre's and I'm concerned that ...
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### Testing for equality in single-response-category proportions in a multinomial sample

Problem: I have a multinomial variable with three response categories. I am asked to test the effect of certain categorical predictors on the proportion of each category. To my understanding, this ...
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### Ordinal predictors treated as continuous in multinomial logistic regresion

Can an ordinal predictor variable (independent, 4 levels - 0, 10, 20 and 30) be treated as a continuous variable in a multinomial logistic regression? Thank you for your help.
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### Multinomial distribution: probability that one outcome is greater than another

Consider a multinomial distribution with three outcomes. Let $x_i$ denote the number of occurences of the $i^{th}$ outcome, and the $i^{th}$ outcome occurs with probability $p_i$, $i=1,2,3$. Let $n$ ...
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### Including probabilistic information in the model fit assessment of multivariate nominal regression

I have a ground truth nominal variable $Y$ and a continuous predictor variable $X$. I have split these up into a training dataset, $Y_1$ and $X_1$, and a testing dataset, $Y_2$ and $X_2$. I want to ...
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### Multinomial Distribution

I am trying to quantify a belief that the proportions of testing conditions I have subjected my test units to is representative of my population proportions(known). My data is a number of hours spent ...
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### Measure for in equality of prediction quality in mutlclass classification

I have got a balanced dataset of 10 different classes $y\in\{0,\dots 9\}$. After fitting a ML model I get classification results $y^*$. Despite the data being balanced, the results are not. I want a ...
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### A multinomial problem has been solved programmatically, could someone please give a hint about how to solved it mathematically?

This post gives an example of Multinomial Distribution. Two chess players have the probability Player A would win is 0.40, Player B would win is 0.35, game would end in a draw is 0.25. The ...
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### Sampling distribution of modified multinomial MLE

I have $n$ observations of a categorical random variable with the following distribution: $$\text{Categorical}(A\cdot p)$$ Where $A$ is a known $m \times s$ matrix and $p\in\mathbb{R}^s$ ($p_i\geq 0$, ...
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### Non-trivial ways to sample the size of the bins of a Multinomial

I'm trying to develop some entropy-efficient algorithms. For part of the process, I'm sampling $(X_1,\dots, X_n)\sim\mathsf{Mult}(n, \vec{p})$, where $\vec{p} = (1/B,\dots,1/B)$. I then do some ...
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### Symmetrical distributed variable in multi-nominal classification ML model

I was trying to build a multi-nomial model on a 5-level dependent variable. There is one variable X that I really want to include in model, but show no importance in final output. It is a (0,1) ...
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### What is the econometric unordered (alternative-specific) multinomial probit model?

Possibly a very trivial question, however I am somehow unable to find any mathematical definition of this model. From other posts on this website I perfectly understand the difference between an ...
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### How to approximate the distribution of the sum of multiple multinomial random variables?

Say we have $T$ independent Multinomial random variables $X_1,X_2\dots X_T$, with $p(X_t=m)=p_{t,m},m\in\{1,2,...M\}$. What would be the distribution of $X_1+X_2+...+X_T$? If there is no closed-form, ...
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### Bayesian approaches to study multi-variate binomial case

I'm currently working on a machine learning problem and want to clarify my research question. Consider two coins $A$ and $B$, each of which respectively has Heads probability $p_A$ and $p_B$. ...
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### 3D ROC surface from multinomial logistic regression with more than one predictor

How do you construct a 3D ROC surface in R from a multinomial logistic regression? I have been able to form a 3D ROC surface for the individual models within a multinomial logistic regression, but not ...
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### How to interpret coefficients of a multinomial elastic net (glmnet) regression

I'm trying to model a membership in one of three well-being clusters (flourisher, normative, languisher) based on a set of predictors, using elastic net for both variable selection & modelling. I ...
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### Treating missing data in making Bayesian inference

Suppose we have two biased coins $X_1,X_2$ that are possibly correlated to each other. In each round, when both the coins are tossed, there can be four possible outcomes: $(HH,HT,TH,TT).$ Let's ...
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### Number of times an object gets sampled when sampling $N$ times with replacement from $M$ objects [closed]

Take $N$ draws with replacement from $M$ unique objects. As $N$ goes up, what is the distribution over the increment to the number of times I get each $M$? So say $M$ is 3 and $N$ is one. The ...
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### Multinomial vs multivariate logistic regression

I have a list of cancer cases with details. They belong to various stages like 1a/b, 2a/b/c, 3a/3b/3c, and Stage 4a/b/c, unknown and blank(missing). I combined early stage cancer cases consisting of ...
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### Use Lift charts with multinomial classification model

This is the example I’m trying to understand. I’m trying to understand the use of Lift charts with multinomial classification model in the evaluation phase. I can see only one category can be ...
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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, ...