# Tagged Questions

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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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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!
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### 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'...
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### Multinomial Model of Discrete Choice

Can anyone explain me the differences between Multinomial Logit Model and Conditional Multinomial Logit Model? Multinomial Logit Model $$P(y_n=j|z_n=z)=\frac{exp(z'a_j)}{1+\sum exp(z'a)}$$ ...
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### 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 : ...
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### 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 ...
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### 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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### 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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### 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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### 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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### 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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### 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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### Multinomial logit with multiple and possibly correlated choices

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