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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52 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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16 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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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 ...
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32 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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12 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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11 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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19 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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14 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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23 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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1answer
55 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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0answers
9 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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8 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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4 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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0answers
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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19 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
40 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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22 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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21 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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29 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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1answer
27 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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67 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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21 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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20 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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0answers
18 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
20 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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15 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
21 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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0answers
14 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 ...
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0answers
19 views

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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1answer
25 views

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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10 views

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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1answer
66 views

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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0answers
18 views

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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0answers
13 views

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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1answer
20 views

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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0answers
27 views

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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0answers
22 views

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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0answers
60 views

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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41 views

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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9 views

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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1answer
17 views

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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1answer
41 views

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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29 views

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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43 views

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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6 views

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 ...
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39 views

10-fold cross validation of a Multinomial Regression Model SPSS 20.0

I have a set of 125 people that belong to one of four nominal categories. Each person is described with 7 descriptors with 2-5 nominal variables that I use in my regression model to predict the ...
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59 views

Interpretation of partial dependence plots for multinomial GBM

I've been a big fan of the gbm package for some time, but am having difficulty understanding the output from the partial dependence plots in the case for multinomial classification problems. Below ...