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.

learn more… | top users | synonyms

1
vote
0answers
10 views

The marginals of a truncated multinomial are truncated binomials?

The multinomial distribution for a vector $\vec x$ of non-negative integers assigns a probability of: $$f(\vec x) = n!\prod_i p_i^{x_i}/x_i!$$ to every vector $\vec x$ of non-negative integers in ...
3
votes
1answer
22 views

Correlation multinomial distribution

Problem 1.14 from Categorical Data Analysis 2nd. For the multinomial distribution, show that $$corr(n_j,n_k)=\frac{-\pi_j\pi_k}{\sqrt{\pi_j(1-\pi_j)\pi_k(1-\pi_k)}}$$ Show that $corr(n_1,...
3
votes
1answer
34 views

How to sample a truncated multinomial distribution?

I need an algorithm to sample a truncated multinomial distribution. That is, $$\vec x \sim \frac{1}{Z} \frac{p_1^{x_1} \dots p_k^{x_k}}{x_1!\dots x_k!}$$ where $Z$ is a normalization constant, $\vec ...
0
votes
1answer
39 views

Multinomial Probability Question

A lift starts with 5 passengers and stops at 8 floors. Find the probability that no two or more passengers leave at the same floor. Assume that all arrangements of discharging passengers have the same ...
-3
votes
0answers
21 views

STATA COMMAND ON MATCHING PROTOCOLE FOR MULTIVALUED TREATMENT [on hold]

Good morning, i would like to assess the impact of level of environmental compliance (treatment variable: 0=non compliance; 1=fair compliance; 2=good compliance; 3=excellent compliance) on firm ...
0
votes
0answers
25 views

Estimator for E[A]/E[B]^2

If I have 2 random variables $A$ and $B$, with unknown means (denoted $\mu_A$ and $\mu_B$), and I want to estimate $\mu_A/\mu_B^2$ from $n$ samples of each, $\frac{\sum A_i/n}{(\sum B_i/n)^2}$ is ...
0
votes
0answers
12 views

Missing Value in SPSS Output

I'm running a multinomial regression and I can't figure out why SPSS is giving me a missing value under ACountry. Any thoughts? Thanks!
0
votes
0answers
22 views

Case-specific and alternative-specific regressors

Can someone give me a brief explanation and some examples, about the difference between case-specific and alternative-specific regressor variable in multinomial /conditional logit models? I don'...
0
votes
1answer
24 views

Multinomial Model of Discrete Choice

Can anyone explain me the differences between Multinomial Logit Model and Conditional Multinomial Logit Model? Multinomial Logit Model $$P(y_n=j|z_n=z)=\frac{exp(z'a_j)}{1+\sum exp(z'a)}$$ ...
0
votes
0answers
51 views

IIA assumption in multinomial model

I try to verify the IIA assumption by using the suest. I have 4 categories of the outcome and I use : ...
1
vote
1answer
28 views

Elasticities for Multinomial Logit Model (Stata)

I estimat a multinomial logit model in Stata. Is it possible to compute elasticities from the MLogit model? If so, do I need to take the logarithm of the y and x variable, or only the log of x? I ask ...
1
vote
1answer
21 views

What is the mode of Dirichlet-Multinomial (Polya) distribution?

What is the ML estimate of the parameter $e_i$ for the Dirichlet-Multinomial (Polya) distribution defined below? $p(\mathbf{x}|\mathbf{e}) = \frac{N!}{\prod_i^d x_i!}\frac{\Gamma(A)}{\Gamma(N+A)}\...
0
votes
0answers
4 views

comparing subgroups in a clogit model (significant difference?)

I have a question about comparing two subgroups in a conditional logit model. We obtained exact the same preference data from psychians and patients and want to test whether there exist a significant ...
1
vote
1answer
44 views

number of parameters for a Bayesian network over binary random variables

I am working through the exercises of a book (Bayesian Reasoning and Machine Learning) for machine learning but I got stuck (I do not understand the question). The following three variable ...
0
votes
0answers
16 views

Assess the model of Multinomial Logistic Regression

Some people told me that AIC and residual deviance are good statistics to assess multinomial logistic regression model. But I don't know how to use it in multinomial logistic regression. Anyone here ...
1
vote
0answers
7 views

Asymptotic Behavior of Probabilities mapped to Discrete Outcomes

I'm having trouble finding a solution to the following problem: Assume that there are $N$ observations and each observation is associated with $K$ probabilities. For each $i \in N$, the ...
1
vote
1answer
26 views

Study design using multinomial vs logistic regression?

Suppose that I have a categorical response variable that consists of group 1-3, and I hope to see if predictors can differentiate group 1 vs group 3 (group 2 not included). The response variable is ...
0
votes
0answers
3 views

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

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") ...
0
votes
0answers
29 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 ...
3
votes
0answers
68 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 ...
0
votes
0answers
14 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
0
votes
1answer
21 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 $\sum x_i = N$...
3
votes
0answers
81 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 ...
1
vote
1answer
21 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 (...
0
votes
1answer
42 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. $p(x|\...
1
vote
1answer
34 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 ...
0
votes
0answers
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 ...
1
vote
0answers
28 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 ...
0
votes
2answers
45 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. ...
1
vote
0answers
19 views

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 ...
15
votes
2answers
513 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 ...
0
votes
0answers
25 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 ...
2
votes
0answers
15 views

Multinomial logit with multiple and possibly correlated choices

I am working with a data set of the following kind: ...
0
votes
0answers
31 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 ...
0
votes
0answers
10 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 ...
0
votes
1answer
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 ...
1
vote
2answers
70 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 ...
0
votes
0answers
18 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 ...
0
votes
1answer
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 ...
0
votes
0answers
49 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, ...
0
votes
0answers
24 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 ...
0
votes
0answers
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? ...
0
votes
0answers
23 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 ...
0
votes
0answers
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, ...
0
votes
0answers
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 | \...
0
votes
0answers
22 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 $(...
1
vote
0answers
26 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 ...
1
vote
1answer
71 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 ...
0
votes
0answers
32 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 ...
0
votes
0answers
11 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 ...