Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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.

0
votes
0answers
16 views

SAS PROC NLMIXED for correlated ordinal data [on hold]

I have a dataset where its response variable is clustered ordinal data (1, 2, 3). I fit my model using the following code using SAS ...
1
vote
1answer
19 views

Penalized multinomial regression with missing values

I would like to fit some models on a dataset where I have a lot of missing values. I am especially interested in comparing models fit with and without imputed values, because the dataset has so many ...
0
votes
1answer
25 views

Standard error of individual groups in a multinomial distribution

Let's say I have a sample of data from a multinomial distribution with 10 categories. I want to determine the error in my estimate of the % of observations that fall into each of the categories. ...
-1
votes
1answer
33 views

My dependent variable is classified in categories ,which regression model to use

My dependent variable is classified in categories as 5-10, 10-15 . Which is the best regression model for this kind of analysis.my dependent variable asks the participant of the survey to mark the ...
1
vote
0answers
10 views

Probability of detecting small bias in a die in the low confidence regime

We are given a biased $m$-sided die: one of the sides has probability $\frac{1}{m} + \gamma$ and all the rest have probability $\frac{1}{m} - \frac{\gamma}{m-1}$ each. The goal is to figure out which ...
5
votes
2answers
150 views

Numerically/approximately integrating over independent gamma variables

Problem Statement For a problem in biology, I am testing out a joint distribution of the form: $$ X \sim Multinomial(\frac{\theta_1}{\sum \theta_i}, ...,\frac{\theta_n}{\sum{\theta_i}}) \\ \theta_i \...
0
votes
0answers
6 views

Transform a multiclass dataset into a multi-label one

I have a dataset of feature/label pairs. My labels are probabilities of each feature vector to belong to the K classes. Here is an example for K = 3: D1 = { (V0, [0.33,0.33,0.33]), (V1, [0.9,0.07,0....
1
vote
0answers
26 views

Calculate a Bayesian 'posterior predictive p-value' for a multinomial logistic regression

For assessing the fit of a model in a Bayesian framework, 'posterior predictive p-values' (PPPs) are often used. Here, a value close to 0.5 indicates a good fit; a value close to 0 or 1 indicates a ...
0
votes
0answers
10 views

Concrete example of a generative process using the joint distribution of (Dirichlet prior and Multinomial Distribution)?

I am not a statistician as it is not my field. Please bear with me and correct me when I am wrong. Your help is much appreciated. I know that when having a Dirichlet Prior and Multinomial ...
0
votes
1answer
31 views

Can we say that the expected value of the parameters of the multinomial distribution has been calculated using Maximum A Posteriori (MAP)?

I am naive in statistics because it is not my field, so please tolerate my bad writings (it may contain misconceptions). The expected value of the parameters of the multinomial distribution (using ...
1
vote
1answer
51 views

What is the point of Dirichlet prior? [closed]

I understand the multinomial distribution and that it can calculate the likelihood of some vector D to happen given the probability vector P' i.e. P(D|P'). Now with Dirichlet prior we are introducing ...
0
votes
0answers
31 views

Why is the conditional distribution from a multinomial a binomial with these parameters?

Say we have a multinational distribution , $$Y=(Y_{1},Y_{2},Y_{3},Y_{4},Y_{5}) \sim multi(n,\frac{1}{2},\frac{\theta}{4},\frac{1-\theta}{4},\frac{1-\theta}{4},\frac{\theta}{4})$$ with observed $X=(...
0
votes
0answers
19 views

standard error of the reference category of the outcome_ multinomial logistic regression

I am working with a multinational Logistic Regression model where I have a 6-category outcome and have a number of predictors(independent variables). I have set category 1 of the target as the ...
0
votes
0answers
19 views

Multinomial Random Variable - significance test & bootstrapping

If I have a random variable $X$ that follows a multinomial distribution $(p_1, p_2, \dotsc, p_n)$, is there anyway to test if two of the levels have equal probability, for example, if $p_1 = p_2$? ...
1
vote
0answers
33 views

Need question answered [closed]

With a universe of 143, 30 of those were queried/sampled at random, giving answers of (dividing into groups of) A, B, C,and D. Question: If all 143 were sampled, what is the probability that the ...
1
vote
0answers
14 views

What is the cost of reconstructing a discrete probability distribution, from samples, within a given error?

I'm aware that there are several methods to estimate the probability distribution from samples (e.g. density estimation methods). However, I haven't been able to find the actual asymptotic costs of ...
0
votes
1answer
14 views

Consumer Surplus (Williams 1977 and Rosen 1981)

$U_{nj} = V_{nj} + \epsilon_{nj}$ for all $j$ and $\epsilon_{nj}$ captures the factors that affect utility but are not included in $V_{nj}$. The decision maker chooses the alternative that provides ...
0
votes
1answer
26 views

Interpreting R nnet Package Multinomial Regression

I need to interpret this summary. I have a response variable with 5 levels (response) and an explanatory variable (taxon) with 2 levels (raptor and others). Can someone help me? Call: multinom(...
2
votes
1answer
66 views

for a multinomial treatment and binary outcome, what is more appropriate, ATC or ATE?

I need help to choose between ATC and ATE for my analysis with multinomial treatment and binary outcome. In the example below taken from here, it seems that ATT does not sound well for multinomial ...
0
votes
0answers
23 views

Question regarding equation in the multinominal distrubution of the exponential family

So this question is regarding to some notes i read in the book Machine learning and pattern recognition in chapter 2 in the section exponential family. First they state: So then they derive this ...
0
votes
0answers
14 views

What is the added value of a multivariate Bernoulli distribution over a multinomial distribution?

I came across the multivariate Bernoulli distribution of Dai, Ding & Wahba (2013) that has the following form (in the bivariate case): $P(X_1,X_2)=p_{11}^{x_1 x_2} p_{10}^{x_1 (1-x_2)} p_{01}^{(1-...
0
votes
0answers
10 views

Why with glmnet I obtain different coefficients for the different categories I want to classify?

I am performing a multinomial logistic regression using glmnet. I have 7 classes of trees to predict and different predictors. What I do not understand is why when I plot the coefficents vs. log ...
0
votes
1answer
42 views

How to calculate the probability for this multinomial logit model?

In multinomial logit models, the probability of the observed choice ranked 1st among all option is given by this formula: p(choice = j) = exp(x_j*b)/(\sum(x_i*b)) ...
0
votes
0answers
21 views

Explaining Low Predictive Ability

For a university project I am supposed to predict one survey question (with 5 different answers) using 20 other survey questions (each with 4 or 5 different answers i.e. all predictor variables are ...
0
votes
0answers
32 views

Regression methods for ordered categorical data with more than 2 levels

I am dealing with an Outcome Variable y which is categorical (0,1,2,3) and ordered. My question is what type of regression models can I try for such a dataset ? I ...
0
votes
1answer
12 views

how to estimate prognostic core for a continuous, multinomial, and binary treatment, respectively

Quoting David Hajage and Finbarr Leacy, respectively: "Introduced by Hansen in 2008, the prognostic score (PGS) has been presented as ‘the prognostic analogue of the propensity score’ (PPS). ...
0
votes
1answer
63 views
0
votes
1answer
37 views

Count frequency distribution of monomial

If you sample $N$ times from a set of $n$ objects with replacement and then plot the frequency against the count (i.e. the number of times an object has been chosen once, twice,...), you get a ...
1
vote
0answers
31 views

Why there are not (long tail) alternatives to dirichlet-multinomial (while there are for posisson-gamma)

While there are a lot of long tail alternatives to poisson-gamma (negative binomial), for example (Source) I haven't found any work on replacing the dirichlet distribution with a more long tailed ...
0
votes
0answers
10 views

probability to belong to the majority class based on observed proportions

I have a population of several categories and I don't know the proportion of these categories in my population. I want to draw (with replacement) in my population until I can say with 99% certainty ...
1
vote
0answers
62 views

Compare models which use different methods to describe the response

Situation I am trying to predict the stand type of a forest 10 years following a clear cut. I am using GBM models to do the multinomial classification. The problem is I have several competing methods ...
0
votes
1answer
21 views

Binomial logistic regression for multiclass problems

Applying the independence of irrelevant alternatives (IIA) is an inherent assumption in multinomial logistic regression but not binomial. Is it therefore okay and possibly better to use $K$ binomial ...
2
votes
4answers
350 views

How to simulate Likert-scale data in R? [closed]

I want to do a Monte-Carlo experiment to check my theoretical finding regarding Likert-scale data. I want to have random test results with N participants, where every question has 5 answers: (0,1,2,3 ...
0
votes
0answers
18 views

Is there a name for “many Multinomial distributions”?

Is there a name for "many Multinomial distributions"? I.e. if I have a set of r.v.s that each obey a multinomial, then what distribution does the set have?
1
vote
1answer
77 views

Multinomial vs Poisson for Histograms

Preliminaries My question came about when reading Lawrence and Chromy's paper on Maximum Likelihood (ML) estimation of histograms (link). I am aware of this question, but I fail to see how that helps ...
0
votes
0answers
36 views

Recovering $\theta$ in Dirichlet-Multinomial (Polya) distribution

I'm working on Latent Dirichlet Allocation with Collapsed Gibbs Sampling. LDA has two Dirichlet-Multinomial distribution and one of them is a document-topic distribution that determines the ...
0
votes
0answers
21 views

Testing if word-count vectors follow a multinomial distribution

I am attempting to make a Naive Bayes classifier for word count vectors (each document is represented as a vector of word counts). For this, I am using SciKit-Learn's MultinomialNB. From what I ...
0
votes
0answers
66 views

Simulating Random Strings using Binomial/Multinomial Distributions

I am simulating some DNA sequences (containing characters A, C, G, and T) in R through specifying i) the number of sequences to generate (num.seqs) ii) the length of the generated sequences (length....
1
vote
0answers
60 views

Marginal Likelihood of Multinomial Dirichlet model

To find the marginal likelihood of the multinomial Dirichlet model, I tried the following: $$\int_\theta p(N|\theta)p(\theta)d\theta=\frac{n!}{n_1!...n_K!}\frac{\Gamma(\sum_{k=1}^K\alpha_k)}{\Pi_{k=1}^...
0
votes
0answers
21 views

Estimation of emission distribution parameters of HMM using Baum-Welch

It seems like the count-based Baum-Welch method described elsewhere is concerned only with the categorical emission distribution. In Hidden Markov Models, I have normal transition matrix between ...
0
votes
1answer
69 views

How to decide on whether it is a hypergeometric or a multinomial?

I am a bit confused whether I should use a hypergeometric or a multinomial distribution when I encounter a questions having more than two X_i and I kinda remember that for multinomial distribution the ...
2
votes
0answers
98 views

Generating Function for sum of N dice [or other multinomial distribution] where lowest N values are “dropped” or removed

Background I found this interesting question Formula for dropping dice (non-brute force) and excellent answer https://stats.stackexchange.com/a/242857/221422, but couldn't figure out how to ...
0
votes
0answers
33 views
2
votes
0answers
67 views

Convergence in probability of a multinomial sample correlation coefficient

This problem is from a Ph.D Qualifying Exam on mathematical statistics(also related to probability theory). Let $(X_1,\cdots,X_k)$ be a random vector with multinomial distribution of $n$ trials and ...
0
votes
0answers
83 views
0
votes
0answers
33 views

Multinomial equivalence test?

I was wondering if there is any statistical equivalence test (in r or python) for multinomial data "a contingency table (4x4)" to know whether the observed and the expected values are equivalence?
1
vote
0answers
94 views

Multinomial (Categorical) Multilevel (Hierarchical) Bayesian Model in R

I have a couple of questions, so I hope it is ok that I ask them here. Before that, here is some background information on my data: Outcome variable (1): categorical, 6 categories, N=168 Predictor ...
1
vote
1answer
97 views

Interpretation of regression coefficients in latent class regression (using poLCA in R)

I am analysing data on symptoms, signs, and autopsy findings (a set of binary Y/N variables), viral serology, for several viruses, and a few other covariates (Age, gender, site) in pigs. After some ...
0
votes
0answers
9 views

Metrics for reporting the fit of a model with a multinomial response

When running a linear model, I like to report the R^2 values to give a simple overview of how well it fits the data. At the moment, I'm working on an analysis with a multinomial response (response ...
2
votes
1answer
240 views

what's the difference between multinomial logistic regression and traditional regression?

Could anyone please explain to me what is the difference between multinomial logistic regression and traditional regression? I have used a method called elastic-net as the response variables are in ...