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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 construct class proportion confidence interval for an LLM classifier with known bias and precision and recall?

Let's say I have a dataset, $D$, with known ground truth labels. I nonetheless use a few-shot LLM classifier on this dataset to predict $k$ classes for each label. From the LLM results, I get ...
Estimate the estimators's user avatar
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Significance of the coefficients of a multinomial mixed regression built with npmlt function

I fitted (using npmlt function) a mixte multinomial regression model which ran without errors. I expected that the outputs of the model include p-values that I didn't find. My need now is that someone ...
Romaine TCHEDJI's user avatar
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How to perform model comparison based on multinom( ) function of nnet package in R? [duplicate]

My independent variables are gender and sequence, and the dependent variable is intervention (including 3 intervention methods). I established a multinomial logistic regression model to examine the ...
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post-hoc test for multinomial logistic regression brm model (categorical response)

I apologise as I am very new to this package and I really appreciate any help I can get. I have a brms model with a categorical response variable (Species) with the ...
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How to manually calculate marginal effects from output of a multinomial logistic regression

I need to calculate marginal effects based on coefficients from a mutlinomial logistic regression Here is some toy R code (apologies users of other software but concepts translate across platforms so ...
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Is multinomial naive Bayes classification not naive Bayes classification?

Suppose I am thinking about a classification problem and I have my features $X = (X_1,...,X_n)$ and my classification $C$ (taking values in some finite set of classes $c_1,...,c_k$). The naive Bayes ...
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Multinomial logistic regression sample size

I'm an undergrad student completing my dissertation research proposal. I am trying to calculate a sample size for my multinomial logistic regression analysis. The criterion variable is degree type ...
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Were two 2x2 tables drawn from the same population?

How might one test the null hypothesis that two 2x2 tables (of frequencies) were drawn from the same population? More specifically, I have two 2x2 samples of unequal sample size. I would like to test ...
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Multinomial one-sided confidence intervals

Building on this question: Confidence interval and sample size multinomial probabilities In a binomial confidence interval, a 90% two-sided CI corresponds to a 95% one-sided CI. The question above ...
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What is the probability that the most likely side of a biased die occurs most frequently?

Consider counting occurrences of the sides of a $k$-sided die rolled $n$ times. The die is biased towards the first side having probability $p > \frac{1}{k}$ and the remaining sides all have equal ...
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Detailed derivation for the log likelihood of a logistic multinomial model

I am working with some Bayesian model development involving the logistic-normal multinomial model. However, I am quite confused about how to express the multinomial part. Traditionally, the full ...
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Multinomial logistic regression 0 classification rate

I am running a multinomial logistic regression with SPSS and I have encountered a problem (?) with my data. I have a dependent variable: foreign language enjoyment (FLE) (DV) with five categories ...
Vivien Gao's user avatar
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Are ordinal models technically a GLM?

I'm following Agresti's book. Specifically, chapter 6 which deals with multinomial models. In that he shows how a nominal response can be modeled by a baseline category GLM, and shows it can be viewed ...
Maverick Meerkat's user avatar
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Confidence intervals for proportions and independence

Suppose a company sells various products at different prices. I would like to compute confidence intervals for the contribution of each product to overal sales, preferably in terms of currency (e.g., ...
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Multinomial distribution approach as negative binomial?

I was asked to solve a problem, following the multinomial distribution (if you think is the correct approach, which I actually think it is). I paste the whole problem just in case I am approaching, ...
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How to test whether the "prevalence ratio" of one marker is higher than that of another

Here is my setup. I have two sets of DNA sequences, one bound by a protein (transcription factor), another not bound by the protein. Let's say I have two candidate motifs, or DNA patterns the protein ...
ffffffyyyy's user avatar
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Best practice for multinomial confidence bounds, given only data from a few categories

I have a multinomial distribution with $k$ categories, and my goal is to establish statements of the form: "I am $1-\alpha$ confident that the true frequency of category $i$ is below $x$". ...
Terence C's user avatar
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Test for change of proportion pattern

I am struggling with how to test for the change of a proportion pattern. The dependent variable $t$ is an amount of time which itself is partitioned into $n\geq3$ phases $t_i$. Thus, $t=\sum_{i=1}^n ...
diffset's user avatar
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Necessary condition for constrained optimization

Suppose $X=(X_1,\cdots,X_k)$ follows the multinomial distribution with a known size $n$ and an unknown probability vector $(p_1,\cdots,p_k)$. Find the necessary conditions for the solution to the ...
Nothing's user avatar
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Modification of Pearson's Chi-square test

At first glance, Pearson's chi-squared test seems flawed in a major way. Can you help me identify the error in my logic? I have a multinomial distribution with $k$ outcomes, and $p_i$ denotes the ...
Terence C's user avatar
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R - multinomial logistic regression with relative frequencies as response variable

My colleagues observed in an experiment involving categorical and continuous independent variables, how the species composition changes. Approximately equal numbers of microbes were used in the ...
Anti's user avatar
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Probability of at least one element for each class in a multinomial distribution

Given a multinomial distribution $$X \sim \mathcal{M}(n, p_1, \ldots , p_K)$$ If I know $p_1 \ldots p_n$ I can easily obtain the following probability by repeatedly sampling from a multinomial ...
Manuel's user avatar
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Testing the hypothesis that $\sum_i^N p_i^2 =(N-1)/2N$ given $\sum_i^N p_i=1$

In ecology there is a simple index for measuring diversity known as the Simpson index. In it simplest formula, it takes a series of proportions, representing the relative abundance (number of ...
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Multiple goodness of fit tests for multinomial proportions of unbalanced classes

I am considering a case where I have a nominal variable with $L$ levels (let us say $L=2$ for simplicity) and a bunch of continuous features. I would like to test if the most centrally located point ...
HeyCool08's user avatar
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What's the relation between the output of a neural network and a Multinomial distribution?

I am reading this paper, which has the following paragraph - "The gold standard for deep neural nets is to use the softmax operator to convert the continuous activations of the output layer to ...
desert_ranger's user avatar
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How to interpret multinomial logistic regression results in r with ordered independent variable?

If there is a independent variable X that is a ordered factor (low, medium, high) - high being the base class, the results of the multinomial regression for each class in X should be interpreted as ...
Deb's user avatar
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Assessing differences in effect size of an independent variable: multinomial logistic regression or one-vs-rest binary logistic regression

My question pertains to this Cross Validated post, but I specifically aim to compare the effect size of an independent variable between categories of the dependent variable. In practice, I have a non-...
Abel Aussant's user avatar
2 votes
1 answer
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The test point’s standard deviation from the origin (ESL’s Exercise)

This is Ex.2.4 from The Elements of Statistical Learning. I don’t understand the sentence that I underline in the image. I know that $\sqrt{10}$ is approximately equal to 3.1, but I don’t know how to ...
chenqile's user avatar
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Which parameters optimise the weighted cross-entropy loss for a pre-specified categorical distribution?

Question: Given a categorical distribution $C_q$ with parameters $q_1, \ldots, q_K$ with $K > 2$, $\sum_k q_k = 1$, which (new) categorical distribution $C_p$ with parameters $p_1, \ldots, p_K$ ...
montol's user avatar
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Testing two proportions of a multinomial distribution

I am wondering if there is a statistical procedure to test if two proportions from a multinomial are equal. For instance: I take a sample of animals in a reserve in South-Africa and count the number ...
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Generalized Linear Mixed Modeling questions

I have a dataset with assessments taken at different visits: baseline (visit=1), and then various post-baseline visits (2, 3, 4), and the following variables: DISEASE - the outcome, is an ordinal ...
R. Simian's user avatar
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Closed form formula for distance of multinomial sample from underlying distribution

Suppose that I have a probability vector $p$ e.g. of size 10, and that I draw a multinomial sample of size $n$ from $p$. Does there exist a closed form formula to compute the expected total variation ...
Caldym's user avatar
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Multinomial gam diagnostic help

I have created a Generalized additive model of a multinomial distribution using the mgcv package, I have used check.gam to do some diagnostic tests but they look ...
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What's the Issue with Modeling Admissions as Multinomial?

I am reading Chapter 4 (Testing and Confidence Regions: Basic Theory) of Mathematical Statistics by Bickel and Doksum. In Example 4.1.1, the authors use the study of sex bias in graduate admissions at ...
Extrava's user avatar
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Determine unknown probabilities from sample of multinomial distribution

Let there be a bag with arbitrarily many balls in k colours (presume we know k). There is a set (but unknown) probability p1, p2... pk of drawing a ball of a given colour. I take a sample of g balls (...
aemona's user avatar
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What kind of relationship is there, if any, between simultaneous confidence intervals for multinomial proportions and chi-squared residuals?

I'm trying to understand if/how the chi-square test relates to simultaneous confidence intervals for multinomial proportions. It doesn't relate to a practical problem to solve, so this is just a ...
Coris's user avatar
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Distribution of vector of $n$ Bernoulli trials

I have a random variable $X\in\{-1, 1\}^n$ that is just a vector of length $n$ containing either $-1$ or $+1$. I know that $\rho$ is the probability of the event $X = +1$. I would like to describe the ...
Physics_Student's user avatar
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How to obtain the multinomial logistic regression via the framework of GLMs?

From wikipedia, the assumption we are making in multinomial logistic regression is that we take one class as "reference", say class $K$, and we assume that $\ln\left(\frac{\mathbb{P}(X=k_0)}{...
AyamGorengPedes's user avatar
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What would be an appropriate way to analyze a dataset with nominal dependent variables with reapeated measures for some but not all subjects

I am trying to find the correlation between several clinical observations/demographic characteristics and the presence of certain electroencephalographic (EEG) features. The EEG features are my ...
maglorismyspiritanimal's user avatar
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49 views

Expected number of multinomial samples to cover a multiset

Consider a multinomial distribution $[p_1, \ldots, p_n]$ and a collection of counts $[a_1, \ldots, a_n]$. I would like to know the expected number of multinomial samples needed until every element $i$ ...
John Jumper's user avatar
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How does a fast Fourier transform yield the probabilities for a multinomial random variable?

Let $(A,B,C)$ follow a multinomial distribution: $$(A,B,C) \sim \text{MultiNom}\left(n=100,p_1=p_2=p_3=\frac13\right).$$ Define $X$, a discrete random variable as $$X = f(A,C) = 2A + 3B + 4C = 2A + 3(...
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Is there a non-brute-force solution to this single-valued random variable transformation problem?

Note:  I'm happy to edit and rename the “question title” for this problem if someone proposes a better (and concise) way of asking about this problem. In brief, the problem I'm presenting below was ...
Gregg H's user avatar
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Metrics for multiclass classification

Background Consider a clustering problem where a dataset of measurements $Z\triangleq\{z_i\}_{i=1}^m$ must be partioned in $n$ clusters, where $n$ is unknown and must be estimated. Here the term "...
matteogost's user avatar
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1 answer
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Right way to compute pairwise significance for a multiple choice survey question?

Say I ask people via survey, "Pick your one favorite option: A, B, C, or D." What is the proper way to compute pairwise significance between the answer options? Can we say whether there is a ...
smile-rko's user avatar
6 votes
1 answer
402 views

Obtaining the chi-squared test statistic via geometry

I’m trying to informally derive the chi-squared test statistic using a combination of basic geometry and algebra. I’m successfully able to obtain a system of equations that contain Karl Pearson’s chi-...
Rez99's user avatar
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How do you estimate multiple poisson rates simultaneously?

I have data showing the number of cause-specific deaths in a cohort. I want to use Poisson regression to estimate the cause-specific rate by age. The complication is that I want the predicted cause-...
Dan's user avatar
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2 votes
2 answers
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Comparing emmeans values multinom model

I am performing quite some binomial/multinomial models for my thesis. After doing the emmeans statement, I used the contrast statement to compare the emmeans of the different groups. But, I ...
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What are the option for a post-hoc test after running a multinomial model?

Currently, I am trying to run the multinomial model Age = Gender to investigate the effect of Gender on the probability that my study animal belongs to a particular age class. I am not necessarily ...
S_vdp's user avatar
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2 votes
2 answers
291 views

Help with rigorous derivation of multinomial distribution

$$ \newcommand{\pset}[1]{2^{#1}} \newcommand{\NN}{\mathbb{N}} \newcommand{\PP}{\mathbf{P}} \newcommand{\OO}{\Omega} \newcommand{\oo}{\omega} \newcommand{\sal}{$\sigma$-algebra\...
Novice's user avatar
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Show that two conditional distributions are the same

Let $\mathbf{Y}=\begin{pmatrix} \mathbf{Y_1}\\\mathbf{Y_2} \end{pmatrix}\sim N\left (\boldsymbol{\mu},\boldsymbol{\Sigma} \right ), $ $\boldsymbol{\mu}=\begin{pmatrix} \boldsymbol{\mu_1}\\\...
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