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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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Does Scikit Learn Logistic Regression use Sigmoid Function if We Apply multi_class=multinomial?

By looking at various documentations/blogs, my answer to this above question is No. By default, sklearn.linear_model.LogisticRegression using multi_class = ‘ovr’. I understand Sigmoid function for ...
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Regression for combination of categorical and continuous dependent variables?

I am dealing with a model that has several categorical independent variables, 4 continuous dependent variables, and 2 categorical dependent variables. My goal is to examine how the IV's affect the DV'...
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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 ...
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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 ...
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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?
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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 ...
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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 ...
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1answer
57 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 ...
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1answer
32 views

Standard Error of the ratio of multinomial and negative binomial variables

What is the correct way to compute a standard error of the ratio between random variables following multinomial and negative binomial distribution? I asked a question about computing variance in the ...
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1answer
50 views

Relationship between statistical models: mcnemar test vs logistic regression

I always find useful and reliable answers in this forum and I hope this pattern will not change this time. I was spending some time to check whether an intervention program had any effect on an ...
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21 views

Discrete version of multivariate normal distribution

Let's say that I have a 2d map, and I would like to explore around my house. Drawing samples from a bivariate gaussian centered at the x, y location of my house makes sense, as I don't want to stray ...
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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 ...
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How to Interpret Parameter Estimate Output from SPSS [duplicate]

Dear Community Members, Given the outputs of the SPSS analysis, how can the exp (B ) and Beta values be interpreted in terms of odd ratio ? and in relation to how the independent variable affects the ...
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Using one binary classifier in multinomial classification bias?

It's very common to use binary classifiers to solve multiclass classification problems using a number of schemes (one-versus-all, one-vs-one, error encodings, etc.). My question involves using only ...
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19 views

Multinomial probabilities

Given a multinomial distribution, X ~ Mult(s1, s2, ..., sn; p1, p2, ..., pn) where all the p's are equal (1/n). What is the probability that ANY of the counts (si) are equal to c? I know we can ...
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Confidence region for multinomial distribution with k=7 - including 5 zero values in dataset

I have a multinomial distribution with $k=7$ and an observed dataset $n_i = \{62, 35, 0, 0, 0, 0, 0\}$. While it was quite expected that $n_i = 0$ for $i \in \{3,4,...,7\}$, there was no way to ...
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How to calculate standardized group differences for multinomial variables?

I am using the tableone::CreateTableOnefunction in R to evaluate differences between three groups regarding baseline variables (like age, gender, education etc.). ...
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Multinomial Probability Exercise

I have this problem: Among 30 students in a group, 6 students received grade "5" for the exam, 10 students - "4", 9 students - "3", the rest - "2". Find the probability that 3 students, called to the ...
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GLMNET: Weights and imbalanced data

I have a multinomial regression problem using glmnet. The training data is imbalanced (1:5:10 roughly). I tried over and undersampling already. Would providing ...
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2answers
243 views

Looking to see if random sample is uniform or not

I've been tracking data and I am looking to see if it is truly uniformly random. The scenario is there can be a grid of 35 colour tiles with 5 different colours (Blue, Green, Purple, Red and Yellow). ...
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Calculating proportion of variance explained by random effect in multinomial GLMM

I have a multinomial logistic GLMM with one random intercept. The number of response categories $C = 4$. Since a multinomial logit model consists of $C-1$ binomial logit models -- each pairing one non-...
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How to interpret GEE parameter estimate for Multinomial Ordinal Data

I have the following experimental design. There are four diet charts (A, B, and C, D). For each diet, a group of 25 subjects (1, 2, 3…25) was on each of those four diets. And they are supposed to ...
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1answer
77 views

Maximum a posteriori on Multinomial distribution with a Dirichlet prior can result in negative probabilities?

I am doing a maximum a posteriori (MAP) estimation of a Multinomial distribution $M(c_1,\dots,c_n|p_1,\dots,p_n)$ with a Dirichlet prior $D(p_1,\dots,p_n|\alpha_1,\dots,\alpha_n)$. The experimental ...
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Best method to do multiclass classification on a dataset with just 60 samples

I have a dataset with just 60 samples and for each sample I have about 45 predictors. Some of the predictors are derived from others because they represent the percentage of one predictor relative to ...
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1answer
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Predict hierarchical outcome data

I am trying to predict an outcome that is hierarchical. Specifically, industry classification codes found here: https://www.naics.com/search/ These are six digit numbers where the first two indicate ...
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33 views

Difference in distribution of multinomial distributions

I have some questions regarding how to analyse catagorical data, summarised as percentages on an individual level. In the data in question, for each individual we know the fraction of biological ...
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1answer
44 views

multinomial distribution aggregation property

Suppose we have multinomial distribution in which we have 4 categories, and each one is associated with a probability of being selected, say $\theta_i$, $i=1,..,4$. And I know for sure that $\...
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23 views

How to interpret Gelman's multivariate Gaussian prior for multinomial distribution?

Andrew Gelman suggested the use of a multivariate Normal distribution as prior for hierarchical models that have a multinomial distribution at the lowest level (http://andrewgelman.com/2009/04/29/...
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1answer
37 views

multinomial model with some certain parameters

I might be asking a naive questions here, sorry. Imaging I have 4 categories, each one has a probability of $\theta_i$ being selelcted, $i=1..4$ and sum of $\theta_i$ is 1. For this simple ...
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35 views

Naive Bayes for classifying columns

Hello StackExchange Community, I have a unique use case for Naive Bayes where I'm trying to train my model to identify output column names based on previous data of input column names. Basically, my ...
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13 views

Creation of a multinomial regression model from a set of data

I have a set of data (X,Y) values. The Y value needs to be modeled as a linear regression. The catch is that there are multiple independent subsets in (X,Y). say (X,Y) = ( (x11,y11), (x12,y12), (x21,...
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Continuous compound Poisson and Binomial

Suppose a random vector $X$ that is distributed: $X|N \sim \text{MN}(N,p_1,p_2...p_J)$ $N \sim \text{Poisson}(\lambda)$ What is the continuous analog of each distribution and the continuous ...
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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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Adjusting probabilities generated by multinomial regression by a fixed percent (for sensitivity analysis)

I have built an agent-based simulation model that has a diversity of different agent "classes" acting in different ways. The class of each agent is assigned at the start of each simulation according ...
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Number of Parameters in a Multinomial Logistic Model (Varying Sample Sizes Across Dependent Variable Groups)

I have a dependent variable which consists of an unordered set of 12 groups (1, 2, 3 ... 12). I'd like to fit a multinomial logistic model, with group 1 as the reference class (essentially a series of ...
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56 views

Partial Least Squares Multinomial Regression

Background: PLS regression is a nice method to develop prediction models from data with large dimensional highly correlated measurements/predictors (e.g., spectral or other frequency domain data with ...
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On testing if a hypothesis that the parameters of a multinomial distribution are related by a given formula

Consider the following example: A population is classified as being one of three blood types; MM, MN, or NN. The proportions of the population that are these types are $\theta_1$, $\theta_2$, $\...
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In a Multinomial Regression can I have different variables depending on my reference category?

I am conducting a Multinomial Regression and my DV has 3 categories (high relationship satisfaction, mid, and low). In my initial analysis, the reference category was set as FIRST (low satisfaction) ...
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using Dirichlet multinomial to solve a problem

Please where do I find a good description or some worked sample using Dirichlet multinomials. I searched several places but could not find anything that can really help.
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311 views

Multinomial logistic regression using glmnet

I have a few questions regarding the use of the glmnet package. I have a data with n observation, p variables and k classes. I use the command ...
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169 views

Multinomial Logistic Regreesion with Lasso penalty in R

I am applying regularized logistic regression (in R) to the handwritten digits data set. I have fitted a logistic multinomial model with lasso penalty to the training data. I am asked to obtain the ...
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Calculation of Bayes Factor for multinomial distributions

I'm trying to follow along with this document: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.11.293&rep=rep1&type=pdf As is also discussed as an answer here: https://stats....
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difference between GOLOGIT and a series of binary logistic regressions

I have recently learned about Generalized Ordered Logit regression, which is something in-between ordered logit regression (ordinal regression) and multinomial regression. It frees us from the ...
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Using binomial confidence intervals for multinomial confidence intervals?

Below is sample code showing the widths of binomial confidence intervals (using a simple normal approximation) and multinomial "simultaneous confidence intervals" (from MultinomialCI). I picked ...
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1answer
93 views

Modes of a multinomial distribution

Is the multinomial distribution an example of a multimodal distribution? I was just curious about this. I know of continuous distributions that are multimodal, but didn't know if you could talk about ...
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1answer
158 views

Maximum number of categorical predictors in multinomial (polytomous) logistic regression

I'm modeling a quaternary response using multinomial logit. N is about 3000, however, there are only 500 occurrences of the rarest event. My usual go-to sources (Agresti 2013: 207; Hosmer et al 2013:...
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Endogeneity in Recursive Probability Models

I am trying to estimate the causal effect of $\{\Psi_i\}_{i=1}^M$ on $Y$. Where $\Psi_i$ are probabilities, and there is simultaneity between $\Psi_i$ and $Y$. The proposed methodology is first to ...
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What do the results differ for any data set or combination of variables between mnlogit and nnet's multinom?

I have been toying around with the mnlogit (like mlogit but a little more refined) package and nnet's multinom function. I understand that the mnlogit fits the model using MLE with Newton's method and ...