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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Failing to implement random individual-specific variables in mlogit and gmnl models

I have a response variable that is 4 categories of behaviors (ly, rs,al and fd). I am trying to use a multinomial model with 7 habitat-related predictors as fixed factors and individuals ("bird.ID") ...
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21 views

Difference between naive Bayes / multinomial / Bernoulli / SVM

i have a question to what consider the Naive Bayes algorithms, i am confused about the difference between the 3 algorithms: 1)The original Naive Bayes, 2)Bernoulli Naïve Bayes, 3)Multinomial Naive ...
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66 views

Sample size for multinomial distribution

Suppose we have multinomial distribution with $k$ outcomes having the same probability $1/k$. What sample size do we need to guarantee with the probability $95\%$ that $m$ of the oucomes occur at ...
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13 views

Parameter Estimates and redundancy

I was wondering if someone can help report the finding on this table. I'm so confused with my Exp(B) being so high and theme nations being redundant. Thank you
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1answer
17 views

Expected value of a function of a multinomially distributed random variable

I have a scalar function, $g(x)$, where $x$ is an $n$-vector following a multinomial distribution with mass $f(x;p, N)$, for some probability-vector $p$, such that $\sum p_i=1$ and where $\sum x_i = ...
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78 views

what is this property? $\int p(x,\pi)d\pi=p(x|E[\pi])$?

Sorry if the title does not make sense, from the answer of this question Mistake in derivation about categorical distribution and Dirichlet distribution? it can be shown that say $p(x|\pi)$ follows ...
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1answer
17 views

Differences between categorical classification algorithms

Given data where the class is categorical (finite and discrete), there are multiple ways to come up with a classifier. One could use multinomial logistic regression, or support vector clustering ...
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40 views

Mistake in derivation about categorical distribution and Dirichlet distribution?

$p(x|\pi)$ follows the categorical distribution (the multinomial with one observation), where $\sum\pi_i=1$ and $x$ is a one-hot vector, and $p(\pi|\alpha)$ follows the Dirichlet distribution. ...
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25 views

Likert-type data in Logistic Regression

I have Likert-type data (ranked as 1 least important to 7 most important) for both dependent and independent variables. Can I use multinomial logistic regression? My second question is, if the ...
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15 views

Estimating multinomial probabilities under constraints

Assume a multinomail model with probabilities p_1, ..., p_K and sample size n. Let n_k be the number of observations of the value k (so that n_1 + ... + n_K = n). Of course the usual maximum ...
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1answer
26 views

Treatment of categorical data in R [closed]

I work most of my time with categorical data (predictors and outcome), I usually do a trees in SPSS to make groups and rank which groups are more predominant to buy / not buy. But now I'm into R, and ...
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2answers
40 views

Multinomial logistic regression: Interpretation of odds ratios as relative risks

In the context of an epidemiological study, a multinomial regression analysis was used to obtain odds ratios for an outcome variable with four different categories. ...
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Difference between multinomial and one vs rest schemes in logistic regression

I am dealing with multiclass classification problem where I have 10 classes to predict. I came across Logistic regression model in scikit-learn which can be applied to multiclass settings as well. The ...
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472 views

Expected number of times to roll a die until each side has appeared 3 times

What is the expected number of times you must roll a die until each side has appeared 3 times? This question was asked in primary school in New Zealand and it was solved using simulations. What is ...
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21 views

Log-likelihood function for Multinomial Logistic Regression

Can you help me to calculate log-likelihood function in R code for multinomial logistic regression, if I have X as design matrix(N x K+1), Y is dependent variable matrix(N x J-1), and B as coefficient ...
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12 views

Multinomial logit with multiple and possibly correlated choices

I am working with a data set of the following kind: ...
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27 views

First Derivative of Log-Likelihood of Multinomial Logistic Regression

I want to create my own Multinomial Logistic Regression function in R and get stuck on the first derivative of Log likelihood matrix. The matrix have (J-1)(K+1) rows and (J-1)(K+1) columns, where K is ...
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8 views

Categorial Variables for a MNL model using mlogit on R

I have to build a multinomial logit model of transportation mode choice. Here is the data set I have to study: CASENUM is the ID of the respondent. Each respondent faces between 2 and 4 ...
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14 views

Does the sample size for the dependent variable should be the same for all the values of the independent variable in Peason Chi-square?

I have a question about the sample size when using chi-square test of independence or multinomial logistic regression. I would if you provide me with your feedback since I search a lot and I could not ...
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64 views

Is it correct to compare likelihood ratio indices between logistic regression and multinomial logistic regression models?

In the paper "Including Transfer-Out Behavior in Retention Models: Using the NSLC Enrollment Search Data" (http://www.studentclearinghouse.org/colleges/files/ST_UofMD_casestudy.pdf) the author ...
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17 views

Multinomial logit / time-series fixed effects / multivariate regression: Which one to use in this case?

Friends, As part of a larger study, we have collected a wealth of data on the interactions customers engage in when buying and using a service. Particularly, we have distinguished this process into ...
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16 views

Why is multinomial variance different from covariance between the same two random variables?

We know that if $\big(X_1,X_2...X_k) \sim multinomial(n;p_1,p_2...p_k)$ then $X_i \sim bin(n;p_i) $ Then, $var(X_i) = np_i(1-p_i)$. But we have $cov(X_i,X_j) = -np_ip_j$. So doesnt that imply ...
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46 views

Interpreting interaction term that only includes some of the variables in the model

I have a multinomial regression model with 5 variables (forced to enter the model), and all 2 way interactions between those variables (forward stepwise). The variables are: age, education level, ...
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23 views

Running regressions in R

I am running a multinomial regression in R, and the p value of a lot of variables is 0. Just $0$, not $0.00000$ or anything. And we have 8 dependent variable choices, and the p value for a certain X ...
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13 views

applying stats to ratings of products

Which should I trust more, a 4.5 stars rating with 46 votes, or 4 stars with 66 votes? This isn't Amazon where I can look at the distribution. Can I treat this like a binomial confidence interval? ...
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15 views

Multinomial Logistic Regression aka Softmax Regression

In optimization point of view of generalized linear modeling, there is a transfer function that maps a linear score to a final target. There is also a loss function that is minimized in training to ...
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8 views

Q: Probability of category k yielding the maximum occurrence count after N IID trials

Assume we have a categorical distribution for random variable $X$ with $M$ categories. We generate $N$ IID realizations of the random variable and count the occurrences of each category in the sample, ...
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20 views

find the distribution of the test statistic

The question is as follows: Suppose we are given a set of parameters $\theta_i$ for $i \in \{1...n\}$ and n is a finite number. Given data $D$, find the parameter that maximizes a likelihood $L(D | ...
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20 views

Upper bound for most likely category in multinomial random vector NOT being max count realized

This is a repost from a question posed at Math stack exchange: http://math.stackexchange.com/questions/1750148/upper-bound-for-most-likely-category-in-multinomial-random-vector-not-being-max Let ...
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25 views

Fitting a multinomial regression with multiple dependent variables and random factors (R)

I have a dataset with multiple dependent variables, which are counts of about 53 different categories of debris found on beaches. I also have a variety of independent variables, some of which I am ...
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65 views

Entropy of the multinomial distribution

In my work I've found myself in the position of needing to calculate the entropy of the multinomial distribution: $$\text{Multinomial}({\bf x};\; n,{\bf p})$$ I imagine it would be too much to ...
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29 views

Set of 3 binary logistic regressions versus a single multinomial regression

I have reviewed these posts here and here. I'd like to ask a slightly different question about using a set of binary logistic regressions instead of a single multinomial regression. I am using ...
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10 views

Can an unordered generalised logit model be used to model descriptive models?

I'm trying to do a cross sectional country analysis of various factors (corruption, inequality, region, etc) affecting the standard of living of a country (Using an index of GDP and HDI). I was ...
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11 views

How to interpret coefficients in ordinal logistic regression with partially relaxed proportional odds/parallel lines assumption?

Suppose I estimate an ordinal logistic regression model: $Y$ ~ $\beta_1X + \beta_2Z$ where $Y$ is the ordinal-scale dependent variable with $y = 1, 2...k$ responses. $X$ and $Z$ are independent ...
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6 views

Interpreting MNL results and the coefficients of interaction terms (RPL) in NLogit

I conducted a project with 12 scenarios, each scenario has 4 choices and each attribute has 3 or 4 options. For example, the attribute “X” has 3 options: “never mind”, “low” and “high”. If they are ...
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16 views

Likelihood ratio test seems to show little difference between models with AICc difference of 3

I'm running a multinomial logistic regression analysis of the behavioural responses of deer to camera traps using no reaction, reaction and strong reaction as dependent variables and season, camera ...
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22 views

Propensity Score Matching w/ 3 levels Rx

I'm trying to match consecutive patients by fitting a Propensity Score. The treatment has 3 levels (Controls, Treat_1, Treat_2). The "MatcheIt" package, is designed to work only with 2 levels ...
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1answer
44 views

categorical data Analysis with too many levels

I am running multinomial logistic regression Model for rating Hotels. I have a variable called CHAIN ID which is a bunch of numbers but there are too many such ...
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23 views

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 ...
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22 views

How to test that two vectors of histogram counts over the same bins come from the same multinomial distribution

Preamble: When testing goodness of fit with null distribution with atoms using an EDF-based statistics $T_n$, random variable $n\sqrt{T_n}$ converges in law. Empirically, the law observed with ...
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31 views

I want to make a Logit regression with lagged explanatory variables - but differenced

First of all a little information on my thesis. We are trying to analyze which hedging strategies yielded the highest cash flows when exchanging USD to EUR. To do this we priced all strategies ...
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28 views

multinomial and ordinal regression

Given a set of objects $\{x_1,x_2,\dots,x_n\}$ we can define an order to them and re-arrange them in that order. For example, if $n$ objects in the set and we define the object $x_i$ to be the integer ...
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76 views

How can I create a topic model with a mixture of multinomials and EM?

I'm trying to create a topic model with a mixture of multinomials and the EM algorithm. I do not want to use a package. For reference, I'm implementing this in Python with numpy. Data Sets I have ...
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23 views

Predicted probabilities with confidence intervals after running mlogit function in R

The following generates the predicted probability of choosing each alternative after running the mlogit command in R for a given value of the predictors: ...
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21 views

Instrumental variable standard errors smaller than naive estimator standard errors

I recently estimated the following model using 2 different estimators, multinomial probit and instrumental variable (IV) multinomial probit: $Product_{i}=\beta_0 + ...
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19 views

Multinomial logit coefficient interpretation confusion

In my lecture slides two different ways of interpreting coefficients for the multinomial logit model are discussed. However, numerical values differ and I don't see how they are related. Could anyone ...
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1answer
25 views

Multinomial vs Poisson for Modelling Count Data

Say that I was modelling the counts for two different treatments. Afterwards, I would fit a particular type of distribution to each treatment population respectively. The data is count-based. What ...
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16 views

How to compute residuals in multinomial logit for a choice model?

I am using maximum likelihood method to estimate the parameters for my choice model in R. However, I do not have any idea about how I can estimate residuals after estimating the parameters. I would be ...
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1answer
23 views

Most likely event in a multinomial distribution setting

I'm looking at the following scenario: $k$ categories, distributed by a multinomial ($p_1,\dots,p_k$) such that $p_1 \ge \dots \ge p_k$. Draw $n$ samples. I'm interested in estimators/lower bounds ...
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16 views

Expression for the expectation of joint bivariate binomial random variables

I am working with pairs of variables, $x_i$ and $x_j$ from $x_1,\ldots,x_k$ that follow a multinomial distribution with $k$ variables, $N$ trials and probabilities $p_1, p_2, \ldots, p_k$. If I work ...