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 can I calculate margin of error in a NPS (Net Promoter Score) result?

I'll let Wikipedia explain how NPS is calculated: The Net Promoter Score is obtained by asking customers a single question on a 0 to 10 rating scale, where 10 is "extremely likely" and 0 is "...
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Multinomial logistic regression vs one-vs-rest binary logistic regression

Lets say we have a dependent variable $Y$ with few categories and set of independent variables. What are the advantages of multinomial logistic regression over set of binary logistic regressions (i....
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39 votes
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How to do logistic regression in R when outcome is fractional (a ratio of two counts)?

I'm reviewing a paper which has the following biological experiment. A device is used to expose cells to varying amounts of fluid shear stress. As greater shear stress is applied to the cells, more of ...
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Interpreting exp(B) in multinomial logistic regression

This is somewhat of a beginner's question, but how does one interpret an exp(B) result of 6.012 in a multinomial logistic regression model? 1) is it 6.012-1.0 = 5.012 = 5012% increase in risk? or 2)...
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Sample size for categorical data

I have a population of phone calls - 200,000. There are different reasons for each call, but lets assume the number of reasons is known. i.e. 7 different call reasons: 1) Check on order 2) Cancel ...
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What makes the formula for fitting logistic regression models in Hastie et al "maximum likelihood"?

I am learning logistic regression from The elements of statistical learning: data mining, inference, and prediction, by Trevor Hastie, Robert Tibshirani, Jerome H. Friedman. Suppose $G$ is a random ...
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Analyze proportions

I have a dataset containing multiple proportions that add up to 1. I am interested in the change of these proportions along a gradient (see below for example data). ...
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Can multinomial distribution be simulated by a sequence of binomial draws?

I wonder if single multinomial distribution (I will use the notation from JAGS/WinBUGS, but in fact, this is principial thing rather than of particular language) ...
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Can a Multinomial(1/n, ..., 1/n) be characterized as a discretized Dirichlet(1, .., 1)?

So this question is slightly messy, but I'll include colourful graphs to make up for that! First the Background then the Question(s). Background Say you have a $n$-dimensional multinomial ...
Rasmus Bååth's user avatar
19 votes
2 answers
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Linear combination of two dependent multivariate normal random variables

Suppose we have two vectors of random variables, both are normal, i.e., $X \sim N(\mu_X, \Sigma_X)$ and $Y \sim N(\mu_Y, \Sigma_Y)$. We are interested in the distribution of their linear combination $...
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What is the normal approximation of the multinomial distribution?

If there are multiple possible approximations, I'm looking for the most basic one.
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Test whether two multinomial samples come from the same distribution

This should be a very elementary question, yet I cannot figure out where I am going wrong. The matrix below contains data on the colour distributions of balls in two urns. I am looking for a formal ...
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Asymptotic distribution of multinomial

I'm looking for the limiting distribution of multinomial distribution over d outcomes. IE, the distribution of the following $$\lim_{n\to \infty} n^{-\frac{1}{2}} \mathbf{X_n}$$ Where $\mathbf{X_n}$ ...
Yaroslav Bulatov's user avatar
9 votes
1 answer
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Conditional Distribution of Poisson Variables, given $\sum X_i$

An exercise asks me to show that if $X_1,X_2,\ldots,X_n$ is a random sample from a Poisson distribution with parameter $\theta$, the conditional distribution of $X_1,X_2,\ldots, X_{n-1}$, given $Y=\...
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How to sample $n$ observations from a multinomial distribution using binomial (or poisson) sampling?

Context I have $n$ observations which I'd like to sample with replacement for the purpose of bootstrap. A way to think about it is that we have a multinomial distribution with $n$ classes and that we'...
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Simultaneous confidence intervals for multinomial parameters, for small samples, many classes?

Suppose I have a sample from a multinomial distribution $\text{Multi}(p_1,\ldots,p_k)$, where $p_1+\dots+p_k=1$. I'd like simultaneous confidence intervals for the $p_i$'s. That is, for any $\alpha\...
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Probability of drawing all balls in a non-uniformly distributed population

I am wondering if there is a way of calculating the following: I have a bag with 5 balls numbered from 1 through 5 that are going to be drawn. Due to different weights, the balls have different ...
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2 answers
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Generating a propensity score for multiple treatment using multinomial logistic regression

I am analyzing data from a representative cohort (>10,000 persons, 10 years follow-up) and I would like to perform a retrospective cohort study comparing the effect of a treatment on the outcomes. ...
Vincent's user avatar
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1 answer
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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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2 votes
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Multinomial logit regression with ordinal independent variables

I've got some ordinal variables b and a and a categorized variable c. I would like to fit a multinomial logit regression from the library car. I tried to ignore the ordinal scale. I have the ...
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2 votes
1 answer
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Distribution of complex results for pool of ten-sided dice, specific to custom tabletop RPG system

I'm no statistician, but I do find the area of mathematics fun and fascinating. I have a friend who has designed a "roll-mid" dice system for his custom tabletop RPG and as part of the game balancing, ...
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2 votes
1 answer
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How to use the Dirichlet prior for estimating the multinomial parameters? [closed]

I know that the multinomial distribution gives the likelihood of some vector D of occurrences to happen given a probability vector (parameters) P' i.e. P(D|P'). Now with a Dirichlet prior we are ...
Mosab Shaheen's user avatar
31 votes
5 answers
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Getting p-values for "multinom" in R (nnet package)

How do I get p-values using the multinom function of nnet package in R? I have a dataset ...
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What are some distributions over the probability simplex?

Let $\Delta_{K}$ be the probability simplex of dimension $K-1$, i.e. $x \in \Delta_{K}$ is such that $x_i \ge 0$ and $\sum_i x_i = 1$. What distributions which are frequently (or well-known, or ...
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Multinomial-Dirichlet model with hyperprior distribution on the concentration parameters

I will try to describe the problem at hand as general as possible. I am modeling observations as a categorical distribution with a parameter probability vector theta. Then, I assume the parameter ...
Dnaiel's user avatar
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14 votes
2 answers
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glmnet: How to make sense of multinomial parameterization?

Following problem: I want to predict a categorical response variable with one (or more) categorical variables using glmnet(). However, I cannot make sense of the output glmnet gives me. Ok, first ...
jmb's user avatar
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Confidence interval and sample size multinomial probabilities

I'm an absolute beginner in statistics. Please excuse any wrong assumptions or missing information in my question. I have a question that relates to a multinomial distribution (not even 100% sure ...
Dirk's user avatar
  • 311
13 votes
2 answers
4k views

Several logistic regressions vs multinomial regression

Is it viable to do several binary logistic regressions instead of doing a multinomial regression? From this question: Multinomial logistic regression vs one-vs-rest binary logistic regression I see ...
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Multinomial logistic regression assumptions

What are the proper assumptions of Multinomial Logistic Regression? And what are the best tests to satisfy these assumptions using SPSS 18?
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conditional on the total, what is the distribution of negative binomials

If $x_1, x_2, \ldots, x_n$ are i.i.d. negative binomial, then what is the distribution of $(x_1, x_2, \ldots, x_n)$ given $x_1 + x_2 + \ldots + x_n = N\quad$? $N$ is fixed. If $x_1, x_2, \ldots, ...
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8 votes
3 answers
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Expected number of uniques in a non-uniformly distributed population

I am wondering if there is any reasonably simple way of calculating the following problem: Drawing, with replacement, $n$ balls from a bin of $N$ different colored balls, with a known probability of ...
lgaud's user avatar
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1 answer
522 views

Analyzing changes in a repeated categorical measure

I am trying to analyze why some individuals change their response to a categorical survey item Y between time T1 and T2, given some explanatory variables X1 and X2 Specifically, the data looks like ...
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2 answers
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How to threshold multiclass probability prediction to get confusion matrix?

Lets say my multinomial logistic regression predict that a chance of a sample belonging to a each class is A=0.6, B=0.3, C=0.1 How do I threshold this values to get just binary prediction of a sample ...
rep_ho's user avatar
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6 votes
2 answers
470 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 ...
Ben's user avatar
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How to validate a Multinomial Logit and Probit Model fit?

I would like to know how do you determine the performance of your models. That is, if you fit a multinomial logit or probit model for un-ordered discrete choice. What do you use to evaluate whether ...
rbetan's user avatar
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5 votes
1 answer
4k views

"Better fit" using aggregated data in comparison to disaggregated data: explanation?

I have fitted multionomial regression models to two different datasets, but from the same country, corresponding to the same event. Dataset A is an aggregated dataset (at country level), relating a ...
Neodyme's user avatar
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4 votes
0 answers
427 views

The marginals of a truncated multinomial are truncated binomials?

The multinomial distribution for a vector $\vec x$ of non-negative integers assigns a probability of: $$f(\vec x) = n!\prod_i p_i^{x_i}/x_i!$$ to every vector $\vec x$ of non-negative integers in ...
a06e's user avatar
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4 votes
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656 views

False-error rate in a Pearson test, when approximation by a $\chi^2$ distribution is invalid?

The question arises in a cryptographic context involving a regulatory test of a physical source or random bits, with null hypothesis that they are independent and unbiased. $n$ samples of 4 bits are ...
fgrieu's user avatar
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4 votes
0 answers
2k views

Why glmnet can be calculated parameters for all category? [closed]

For my understanding, multinomial logit model requires to restrict the parameters for one category to zeros. However, package{glmnet} seems to allow different parameters to every class. Could someone ...
Tky's user avatar
  • 139
3 votes
1 answer
152 views

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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3 votes
1 answer
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Multinomial mixed models with glmmADMB

I want to run a multinomial mixed effects model with the glmmADMB package of R. I have read the available information of the programm but i couldn't find which family or link has to be used for ...
Ana María Prieto's user avatar
3 votes
3 answers
6k views

Unable to provide random parameter with mlogit

I'm having trouble with rpar argument in the mlogit function (package mlogit). My dataset looks like this: ...
Lyly's user avatar
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1 vote
0 answers
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Likelihood Ratio Testing in Multinomial logistic regression using SPSS [duplicate]

I am doing multinomial logistic regression. Dependent variable is categorical with 6 categories. 6 Independent variables are measured on an interval scale (included as covariates in SPSS) Now I am ...
jochem damen's user avatar
24 votes
3 answers
33k views

How to set up and estimate a multinomial logit model in R?

I ran a multinomial logit model in JMP and got back results which included the AIC as well chi-squared p-values for each parameter estimate. The model has one categorical outcome and 7 categorical ...
paul's user avatar
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15 votes
1 answer
2k views

Cost functions for contextual bandits

I'm using vowpal wabbit to solve a contextual-bandit problem. I'm showing ads to users, and I have a fair bit of information about the context in which the ad is shown (e.g. who the user is, what ...
Zach's user avatar
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15 votes
3 answers
37k views

Multinomial Logistic Loss vs (Cross Entropy vs Square Error)

I observed that Caffe (a deep learning framework) used the Softmax Loss Layer SoftmaxWithLoss as output layer for most of the model samples. As far as I know, ...
karfai's user avatar
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14 votes
1 answer
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What is the difference between multinomial and ordinal logistic regression?

Can somebody explain it with a simple example!
Puneet Jindal's user avatar
13 votes
3 answers
874 views

What do I gain if I consider the outcome as ordinal instead of categorical?

There are different methods for prediction of ordinal and categorical variables. What I do not understand, is how this distinction matters. Is there a simple example which can make clear what goes ...
Karsten W.'s user avatar
12 votes
1 answer
5k views

What is "Multinomial Deviance" in the glmnet package?

I am fitting a multinomial logistic regression using the glmnet package in R: ...
Zach's user avatar
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11 votes
3 answers
2k views

How to sample a truncated multinomial distribution?

I need an algorithm to sample a truncated multinomial distribution. That is, $$\vec x \sim \frac{1}{Z} \frac{p_1^{x_1} \dots p_k^{x_k}}{x_1!\dots x_k!}$$ where $Z$ is a normalization constant, $\vec ...
a06e's user avatar
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