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 compare models in weighted multinomial logistic regression?
I want to do a regression analysis after a GMM. I have a dependent variable with three categories (classes), which differ in their posterior probabilities. That's why I included the posterior ...
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Why are week and weekday fixed effects not identifiable in a mlogit logit model (R)? What am I doing wrong?
I am estimating a multinomial logit model using R’s mlogit package based on scanner data (store-level purchases).
For each product category, I estimate a choice model conditional on purchase: each ...
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Error bars for slopes on probability scale crosses 0 but interaction is significant
I am trying to understand this multinomial logistic regression model. The dependent variable is subjective class. There are two independent variables and an interaction term (objective class and year)....
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Conditional independence assumption for Naive Bayes with Multinomial distribution
I was going through Naive Bayes Classifier (from Cornell Machine Learning course (link here) and I found quite confusing the use of the Naive Bayes classifier for bag-of-words with the Multinomial ...
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Most powerful test for multinomial distribution
I'm trying to define the most powerful test using Neyman-Pearson lemma for a multinomial distribution.
Writing the likelihood under the null and the alternative and dividing them, I get this:
\begin{...
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Partially observed multinomial distribution?
I am trying to infer the distribution of plausible group counts ($K$)
in a population stratified by $E$ exposures and 1 outcome (all binary); so, we have $N_e = 2^E$ total exposure groups and $N_k = 2 ...
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How to obtain the propensity score weights from Gradient Boosted Model in R
For a gradient boosted model with n data points using multinomial regression where the response variable is a categorical variable "class" with four levels (A, B, C, D), the probabilistic ...
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Experimentally Verifying Frequency of a Multinomial Distribution
I have a question about verifying the frequency distribution of an event.
A wheel has 5 zones. Each time you spin the wheel, 4 zones show up 24.75% of the time, and the 5th zone shows up 1% of the ...
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Simultaneous or binomial confidence intervals for multinomial or ordinal proportions?
We're using random sampling to audit processes that we conceptualize as Bernoulli and scoring sampled items as pass or fail. In the interest of fairness to the auditee, we use the lower bound of an ...
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How to use (or alternatives to) Exact Multinomial Test when the theoretical distribution changes for each test sample
Say I have a process that results in outcomes that can be placed in 5 categories: A, B, C, D, and E. The categories are mutually exclusive and exhaustive, and individual trials through the process ...
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Sampling from a multinomial distribution with K categories by sampling K independent uniform distributions and sorting
Consider a multinomial distribution with $K$ categories, where each of the categories has a probability $p_k, k\in \{1,...,K\}$ of being selected in a random trial such that $\sum_{k}p_k=1$. In ...
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Why do multinomial confidence intervals tighten dramatically when adding other outcomes?
I'm trying to compare the performance of two functions A and B, with confidence intervals to gauge statistical significance.
When passed a random value 100,000 times, the two functions tie 98,175 ...
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Generalized variance of a multinomial distribution
Scalar variance is a univariate notion, so generalized variance gives a generalization to the multivariate setting by taking the determinant of the covariance matrix for the multivariate distribution.
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multinomial covariance matrix is singular?
Consider a multinomial distribution, $\text{multinom}\left(n, \left(p_1,\dots, p_k\right)\right)$. There is a $k\times k$ covariance matrix, $\Sigma$, that depends on the parameters of the multinomial ...
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Multinomial-Like Regression Model with indiscernible Outcomes
I've looked around a bit for the answer to this, and haven't found anything. I'm hoping that someone has already considered this particular system and that there is an existing model. I have a ...
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How to interpret the summary of a multinomial model?
I have a model with 5 multinomial levels coded 0 to 4:
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Can I do a difference-in-difference analysis if my outcome variable is nominal?
When the outcome variable is nominal and has more than two categories that are not in a specific order, can I still perform a difference-in-difference analysis?
I am interested coordination among ...
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Bayesian multinomial dirichlet regression (using user specific information) model for purchase counts across several products
Suppose user $i$ has purchase history of $J$ products $q_i^1,\ldots,q_i^J$. Also, values of $K$ user characteristics (gender, for example) are known $x_i^1,\ldots,x_i^K$. I want to build Bayesian ...
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Dummy encoding for the multinomial response variable
I am reading about multinomial response models from the book Multivariate Statistical Modelling Based on Generalized Linear Models by Fahrmeir and Tutz. I am trying to understand the following ...
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Trend test for multinomial variables
Which test should be used to estimate a p-value for trend when the outcome (dependent) variable is multinomial (with multiple unordered categories like race) and the independent variable is an ordered ...
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Finding the expectation of a categorical variable times a random amount
Say we have $J$ trading cards and each have a dollar value of $u_{j}$ and I am allowed to make 1 draw.
$$
u_{j} \sim N(\mu,1)
$$
Where the value of each trading card is independent and identically ...
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Bias in simulation samples low frequency event at higher rates
I am trying to simulate a dataset of x trials and y subjects, where every trial can be one of 3 categorical vars, associated with a unique probability. For every subject and trial, I also want to add ...
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Likelihood ratio test -- Multiparameter multinomial distribution
This is a problem from Hogg and McKean's "Introduction to Mathematical Statistics" (Exercise $6.5.11.$)
Problem Statement
Let $n$ independent trials of an experiment be such that $x_1,x_2,\...
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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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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 $p_1, \ldots, p_K$ ...
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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 ...
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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 ...
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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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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 (...
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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 ...
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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 ...
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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)}{...
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