# 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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### Probability distribution over predicted probabilities in multinomial logistics regression

I am currently wondering (and cannot get my head around this) how to get a probability distribution (or something similar to a prediction interval in OLS) for the predicted probabilities of a ...
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### Multinomial logistic regression where two choices are pooled/censored in the data?

I am looking for a lead on estimating a specific type of multinomial choice model. Specifically, assume that I see $N$ people and those people have some vector of characteristic $X$. For ten ...
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### Are there behavior genetic models for multinomial outcomes?

I am thinking of the standard behavior genetic model of decomposing the variance in an outcome variable into ACE components. I will have outcome variables of different kinds: linear, dichotomous, ...
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### In R how can I fit multivariative distribution to data and sample from it?

I collected data on post parcells delivery, each object is a combination of 3 variables: Weight (continuous >0) Destination city (categorial - factor of hundreds) Delivery type (categorial - ...
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### Specifying an HLM model in SPSS (ranking data)

In SPSS, I am receiving the error: The final Hessian matrix is not positive definite although all convergence criteria are satisfied. And when looking at the output, it is telling me that the ...
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### How do I improve the misclassification rate for multiple categories when only two or three categories are causing the problem?

I am building a model in order to classify an observation as one of 20 categories. My model performs quite well, but it struggles to distinguish between 3 of categories. In fact, most of the ...
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### Is it wise to use multiple binary models as opposed to a multinomial model?

Let's say that you have a classification problem where the dependent variable has MANY levels (say 20) and you CANNOT transform the target (i.e. no clustering, combining of levels, etc.). Is it a good ...
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### Multinomial distribution conditional on number of distinct items

I want to sample from the integers $\{1, \dots, k\}$ with probabilities $\{ p_i \}_{i=1}^k$, with replacement, until I see $m$ distinct elements (call that $n$ times). You can view the distribution I ...
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### Multinomial algorithm for probabilistic data

I am trying to predict the suffix a certain word will take based on properties of the word. There three outcomes but they are not absolute, that is, some words can take two or three different suffixes ...
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### Which regression model should I build?

I'm trying to handle a dataset about student performance in 2 Portuguese Schools in the subject of Portuguese. Student grades go from 0 to 20, discrete. I have a set of 30 Regressors (all but 3 ...
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### Path Analysis Vs Multinomial Logit

Would anyone be able to explain the logic behind using a Path Analysis over running several multinomial logits. The theoretical model I am testing has X1-3 mediating Y1. Y1 and X1 predict U1-3 (the ...
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### Method validation in non-regression problems

Assume I have a sample of r species/classes that follow a multinomial distribution, where the vast majority of classes only are observed once. Further, let us say I have k models that all are giving ...
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### Multinomial Count Models

Is it possible to model a dependent variable which is both multinomial and count? If so, how would one do so with a tool such as R? For example, suppose that my dependent variable looks like this: ...
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### Multiple binary logit regressions vs multinomial logit regressions? [duplicate]

Lets assume we have a dependent varible which can take on three values: 1, 2 and 3. Is there any differences in running multiple binary logit regressions(ie. 1 vs 2 and 2 vs 3) or the multinomial ...
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### Possible to estimate a multinomial logit model with a first-stage multinomial logit sample selection model?

I want to estimate the effect of education type (4 categories) on an 8-category outcome variable. Since choice of education has self-selection issues, I want to correct for this using the inverse ...
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### Loss Function for Multinomial Logistic Regression - Cannot find its derivative

For Multinomial Logistic Regression we can define the Loss Function in the following way: \$J(\theta)=\frac{-1}{m}\sum\limits_{i=1}^m\sum\limits_{j=1}^k ...
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### Multinomial logit model and weighted sample

I am doing a multinomial logit analysis on a survey weighted sample of household data in R. I am trying do model if household owns, has access to mobile phone or has none. Since I am beginner in this ...