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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20 views

Is a multinomial distribution appropriate for modelling this variable?

I'm currently trying to model subject performance on a learning task (Wisconsin Card Sorting Task) in Rjags. One of the outcome variables is a 3x1 matching matrix. Each row of the matrix corresponds a ...
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Confidence intervals for bootstrapped multinomial proportions: Sison-Glaz?

I read the rules and looked for similar posts, but couldn't find any. New to the platform, so if I missed anything, pardon me. I have started looking into uncertainty quantification and I want to ...
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Rank-ordered data - dealing with increased randomness among lower ranks

What is the best way to analyze rank-ordered data when there are signs that respondents were less diligent/able to assign lower ranks? Is it sufficient to introduce a dummy for lower/earlier ranks ...
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32 views

Dirichlet distribution vs Multinomial distribution?

Both Dirichlet and multinomial distributions are distributions over vectors, and both Dirichlet and multinomial distributions are constrained so that all of the elements of these vectors sum to a ...
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68 views

Probability of linear separation in a dataset with categorical response

I am simulating datasets to which I fit polytomous logistic regression models. The maximum likelihood estimator of this model is undefined when all categories are linearly separated (and it is quite ...
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Nested Multinomial Logit Estimation

I am trying to estimate a nested multinomial logit model for transportation mode - the decision tree of how consumers choose a travel mode for a trip. One way of estimating the nested multinomial ...
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31 views

How to assess geographical representativity of a sub-area?

My geographical zone $A$ is subdivided in $k$ different types of areas: $A_1 + A_2 + \dots{} + A_k = A$. These have been measured on a map with neglictible uncertainty: i.e. for any point on the map, ...
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Interpretation of coefficients from multinomial logistic regression

I have run a multinomial logistic regression model with a four level response variable (walk, bike, bus and car) and two predictor variables being their gender (female/male) and where they live (urban/...
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How to compare categorical distributions?

I have a 4 by 4 tables. Rows corresponds to people group and columns are their decisions types. The ij of the table is the percentages of people type i who have decision type j. ...
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58 views

Algorithm did not converge - Multinomial mixed model (mblogit)

I'm trying to fit a multinomial mixed model with the mclogit package (using the mblogit function). But, as I adjusted the model, I'm receiving the following message and I could't find any info about ...
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Poissonization use for sampling size

I'm interested in using the Poissonization trick to solve the following problem, which I made up: Suppose I have a categorical random variable $X$ taking values $1$, $2$, and $3$, with ...
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14 views

How to do post-hoc comparisons for multinomial model with emmeans

When doing post-hoc pairwise comparisons for a multinomial model using emmeans package, do I use mode = "latent" or mode = "prob."? I'm interested in understanding if the response variable (with 3 ...
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Is there a probability distribution like the binomial distribution but with continuous rather than binary trial outputs?

I'm using a uniform random variable (0 mean, 1 variance) to generate white noise. Then I'm doing a moving average on those samples. I'm trying to figure out the variance of this output distribution. ...
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32 views

Confidence interval for categorical data

I have the following data about companies who respond timely or untimely and another category of the answer: ...
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Significance test for a discrete symmetric ordinal distribution

What are possible extensions to the binomial test for a multinomial distribution? Here is a concrete examples: let's say I have 5 positive and 10 negative outcomes with a one-sided test for the null ...
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23 views

How to compute multinomial confidence interval for proportion if some categories have fewer than 5 counts

I want to compute multinomial confidence intervals for proportions, and I was planning to use one of the methodologies listed here. The goodman method [1] is based on approximating a statistic ...
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Modeling stated preference alternative labels vs alternative characteristic levels

I have data from a stated preference survey in which each respondent answers 3 questions each with 3 alternatives. A status_quo / opt-out alternative is the first option for all questions. The ...
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What model should I use for multiple binary response variables?

Consider many traders j = 1, 2, ..., J who can make the following trading decisions: a) buy, b) sell, c) do nothing since they have not previously bought, or d) do ...
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On what basis do I set the baseline for a multinomial logistic regression model?

I am interested in comparing the microhabitat choices made by juvenile lobsters. Lobsters were presented with a patch of seagrass and another habitat type (ie bare sand) at different seagrass ...
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What do the intercepts of multinomial logistic regression model mean?

I am interested in comparing the microhabitat choices made by juvenile lobsters. Lobsters were presented with a patch of seagrass and another habitat type (ie bare sand) at different seagrass ...
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18 views

Posterior probability distribution from multinomial sample

I want to get the posterior from a multinomial sample and want to know if the following derivation is correct. Suppose when drawing (with replacement) a sample of $N$ balls from a urn with $K$ ...
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Is it possible to use a multinomial outcome after a propensity score matching?

I would like to use a propensity score matching (PSM) to evaluate the effect of a treatment T on an outcome Y. In most of the papers that I have read, the outcome is continuous: health expenditures, ...
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106 views

Feature Importance for Multinomial Logistic Regression

I have trained a logistic regression model with 4 possible output labels. I want to determine the overall feature importance for each feature irrespective of a specific output label. In case of binary ...
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¿Do i need to normalize/transform data in a multinomial (nnet:multinom) model? + Dropping variables by Likehood

So, im working with a dataset with controls and 4 diseases, its indeed a nested model cause they are 2 diseases with 2 level each, but i do not know well how to model it. The thing is i got over 40 ...
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Multinomial and Poisson relationship in contingency tables

I am researching the relationship between multinomial and Poisson distribution in contingency tables. Is what I have said below right? For context, the multinomial pmf is below. $$P(X_1=x_1,...,X_N=...
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(Generalised) Negative Multinomial Distribution

Fix some probability vector $( p_1, \ldots, p_N)$, and let $X$ be a categorical random variable with these probabilities, i.e. $$P ( X = x ) = p_x \quad \text{for } x \in \{ 1, \ldots, N \}.$$ ...
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How to predict probabilities from multinomial models, when levels are coded?

I'm using a discrete choice experiment (DCE), and I've estimated the answers with a nested logit model (using mlogit package of r software), which gives quite good results. However, I've coded ...
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Low probability of a multinomial for expected values

given a population with 4 groups for which their frecuencies are: A = 0.46 B = 0.075 C = 0.035 D = 0.43 The expected number of individuals for each group in a ...
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Does $\chi^{2}$ statistic always works for multinomial hypothesis testing?

The $\chi^2$ statistic has been frequently employed in the hypothesis testing of the multinomial distributions. But after looking at the derivation of such a process (where they use Taylor expansion ...
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How can I assess the number of cases needed to distinguish whether responses are from one of several probability distributions?

In my experiment, participants choose one of three options on every trial (the trials are 3x3 versions of the well known Prisoner's Dilemma game). What decision rule they use determines the ...
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What model should I use to predict football outcomes?

I have a project for my statistics course (STATA based) and we are asked to forecast match results based on independent variables that we will choose. My question is, what kind of model should I use ...
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2answers
212 views

Multi- Class probabilities of Random Forest inside caret Model

Im facing a problem with the results of a multi-class random forest model. I want to use a) the predictions of the model and b) the class probabilities of these predictions for further work. I did a ...
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Expected number of trials until all categories are observed at least once in a multinomial distribution

The title basically sums up my question, but suppose I have a multinomial distribution with k categories. What is the expected number of trials until I observe every category occur at least once? ...
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How can I derive goodness-of-fit measures (R-squared and chi-square values) from multinom (multinomial logistic regression) in R?

I am running multinomial logistic regression using multinom command in R. However, I could not figure out how to derive R-squared and chi-squared values from it. I somewhat approached my own way to ...
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The baseline-category coefficient in the multinomial regression

After I run multinomial regression, I get N-1 beta coefficients. I need to obtain also the last coefficient, which is the baseline category. Any suggestions in R? Thanks
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Difference of two probabilities with repeating components

Consider a multinomial distribution with five outcomes. $x_i$ denotes the number of occurences of the $i^{th}$ outcome, and the $i^{th}$ outcome occurs with probability $p_i$, $i=1,2,3,4,5$. Let $n$ ...
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32 views

Given an outcome distribution, how to predict summed outcome of N trials

If I have a game that has a know distribution of outcomes, for example, 5% of the time the outcome is 0 10% of the time the outcome is 1 15% of the time the outcome is 5 8% of the time the outcome ...
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56 views

Why does Fisher’s exact test use the hyper geometric distribution rather than the multi nomial distribution?

To understand hypergeometric and multinomial better, I’d like to know why fisher exact test used hypergeometric rather than multinomial distribution.
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Confusion over dmultinom function arguments and meaning with respect to Math [closed]

What do the arguments in the dmultinom function mean? ...
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27 views

Multinomial Logit

I'm trying to fit a model with statsmodels, Multinomial Logit Model. This works fine, but I'm quite unsure if it is the right model for my case and how to treat my independent variables. So my ...
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The second order moments of the Gaussian multivariate distribution

I am really quite confused to how to calculate and get the result from to I know the symmetry will recduce the sum of j to sum of i(yiyj to yiyi),but however, it is still difficult for me to think ...
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Testing for difference from chance for a ternary choice

I'm analyzing data from an experiment which has the following setup: Independent variables: Age: {16, 17, 18} Testing order: {forward, reverse} Question type: {negative, positive} Testing order and ...
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1answer
42 views

Confusion over multinomial and multivariate- hypergeometric distributions

You, your parents, your sister, go to visit grandma for her birthday. Grandma made a cake for the party. If she puts $20$ raisins in the cake at random in the cake, and she divides the cake into $5$ ...
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48 views

How to calculate probability of a survey sample

I'm working on a school project and I need to calculate the probabilities of new real and/or hypothetical samples given the already collected survey data. The survey data is encoded as a bunch of ...
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1answer
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Is there a way to know what features a Multinomial Naive Bayes classifier is taking into account to predict categories?

I have created a Multinomial Naive Bayes classifier. The dataset looks like this: ...
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31 views

Expected frequency differences when sampling from a uniform?

Imagine I put people into different groups based on a uniformly distributed random variable $y = f(x)$ (e.g. microseconds of their arrival to a website). After a while, I observe how many people are ...
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Sample size for uniform multinomial to control minimum

I'm interested in controlling the minimum for a uniform multinomial distribution. Specifically, What would be the sample size to have the following inequality regarding the minimum? Do you know of ...
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Multigroup multinomial logistic regression in R?

I am using multinomial logistic regression (nnet package in R) to predict a categorical outcome (four categories) with three independent variables. As my data come from different countries, instead ...
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1answer
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How can a multinomial naive Bayes classifier be used here?

I'm doing a problem from a textbook where the data (found here) are students and the features include sex, family size, health, age, etc. The problem asks to make a naive Bayes classifier from scratch ...
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38 views

Inference on Dirichlet hyper-parameter

I'm working on a Gibbs sampler for a (somewhat custom version of) Latent Dirichlet Allocation model. In short, I have data that comes from a $K$-dimensional Dirichlet-Multinomial distribution, i.e. $$...

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