Latent variables refer to variables that cannot be directly observed. These variable are defined in terms of observable variables.

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Difference between latent and auxiliary variables

In a Gaussian mixture model, the labels assigned to the data points are often called auxiliary variables, whereas the cluster means and covariances are called latent variables. Since both types of ...
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20 views

How to compare latent mean difference from Measurement Invariance with cohen's d from a meta-analysis?

I was wondering if it is possible to compare latent mean differences estimated in a scalar invariance model to an overall Cohen's d found in a meta-analysis. Is there a way to convert one value to the ...
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22 views

Penalizing common words in LDA analysis

I have a corpus I want to perform an LDA on, however it has very few total words and some words occur extremely often. I want to penalize these words. A tfidf at first seemed intuitive (and I have ...
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60 views

Latent Dirichlet Allocation vs. pLSA

In the original LDA paper it is stated that: The parameters for a k-topic pLSI model are k multinomial distributions of size V and M mixtures over the k hidden topics. This gives kV +kM ...
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24 views

Is it possible to get a prediction interval for logistic regression via a latent variable?

carbocation asked how to compute prediction intervals for logistic regression. The answer was that prediction intervals don't make sense for logistic regression because the response variable only ...
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6 views

Material on plate notation of bayesian hidden markov model

Does any one know some materials on plate notation of Bayesian Hidden Markov Model? Say, given multiple observed sequences, how to infer the posterior distribution of the parameters, and the ...
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11 views

Is SEM appropriate for this problem?

I want to estimate some latent variables but I'm not 100% sure that Structural Equation Modelling is the correct way to do it, or if there are any easier solutions. I have a pretty basic graph <50 ...
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1answer
42 views

Latent variable values in structural models

I am beginning to go through SEM textbooks and research in order to understand the logic and reasoning for the analysis. I believe that I will be using this type of analysis in the near future for my ...
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41 views

Derivation of likelihood function for latent variable model made explicit

I am trying to make the steps deriving the likelihood function for the following latent variable model as explicit as possible: $$Y^0=X\beta + u$$ where $$u \sim NID(0,\sigma^2).$$ The observed data ...
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16 views

Methods to deal with latent variables

I had a general question about methods to adjust for the effect of latent variables (specially variables that are suspected to be confounder) in observational studies. In particular, I'm working on a ...
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20 views

Different Methods for clustering skills in text

Consider a talent pool in which each member has some set of skills. Some of these talent are submitted to orders as potential candidates of which one is selected. It is reasonable to assume that the ...
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2answers
57 views

Student's t-test with a covariate?

I am testing the different between some variables $X$ and $Y$ using the Student's t-test. I suspect that there might be a latent variable $Z$ that has an effect on both $X$ and $Y$. How could I ...
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18 views

How to fix a scale of latent variable measured by dichotomous indicators in SEM

How can I fix a scale of latent variable measured by dichotomous indicators in a structural equation model to estimate the mean of that latent variable? I know the mean of that variable (because I ...
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21 views

Comparing growth estimates of multigroup growth curve model

I have fitted a growth curve model to describe the trajectories of a variable in 4 groups across three assessment points. I am interested in doing some pair-wise comparisons of the slopes between some ...
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37 views

Quasi-Newton Accelerator (QN1) for EM Algorithm

I am trying to implement what is called a "very simple to implement" accelerator for the EM algorithm. Specifically I am talking about the QN1 algorithm, described here, and am using a multivariate ...
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17 views

disease progression R markov chains

hello i have a dataframe, some of the columns include: remission,height,weight,time from diagnosis, age ethnicity, age, patient id remission is 1 or 0 just to be clear i want to fit an appropriate ...
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1answer
71 views

Expectation-Maximization Algorithm for Binomial

I have a multinomial distribution with four outcomes, with a pdf: $$p(x_1,x_2,x_3,x_4)=\frac{n!}{x_1!x_2!x_3!x_4!}p_1^{x_1}p_2^{x_2}p_3^{x_3}p_4^{x_4}, \sum_{i=1}^4x_i=n, \sum_{i=1}^4p_i=1$$ The ...
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35 views

Growth mixture modeling with latent variables in R with lcmm

I am trying to replicate the analysis that was used to make this figure: I have measured the depression levels (a quantitative variable) in my subjects at the following time points (in months): ...
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31 views

Should I be concerned that the correlation between factors changes sharply when I move from EFA to CFA?

I am running an EFA and CFA on the same data (I realise this would not normally be appropriate). I've found that when I do an EFA (direct oblimin rotation) with a four-factor solution there is a ...
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251 views

LDA vs word2vec

I am trying to understand what is similarity between Latent Dirichlet Allocation and word2vec for calculating word similarity. As I understand, LDA maps words to a vector of probabilities of latent ...
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16 views

linear discriminative analysis for regression

LDA computes a projection matrix to maximize class conditional probability. Similar to this, is there any exisiting method or library for jointly learning latent space and minimizing the regression ...
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24 views

Is the bias of a coin a latent variable or a parameter?

Consider the standard Bayesian estimation problem in which the bias $p$ of a coin is picked uniformly at random from $[0, 1]$, the coin is tossed a few times, and $p$ is then estimated from the ...
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40 views

Intuition for understanding latent variables

I am having difficulty understanding and proving the GMM/LDA model, for I think I do not really understand latent variables. To be more exact, I cannot understand the latent variable z_k(categorical ...
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27 views

How to label observations based on latent class analysis

I perform a latent class analysis to a dataset of binary variables with ...
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117 views

Can logistic regression be modified to predict a distribution, not just point-estimate? Other ways to learn a beta distribution from binary events?

Currently I'm using high dimensional logistic regression to predict the probability of a rare event. I use this probability for both ranking and for other calculations which need it to be ...
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25 views

Dangers of treating residuals as latent variable?

I have data on variables ($y, x_1, x_2$), a linear model with the following form: $$ y = \beta_0 + \beta_1x_1 + \beta_2x_2 $$ and a theoretical assumption that the residuals represent a latent ...
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18 views

Resolve dispute over permanently latent variable?

I have data on variables ($y, x_1, x_2$), a linear model with the following form: $$ y = \beta_0 + \beta_1x_1 + \beta_2x_2 $$ and a theoretical model that the residuals represent a latent variable ...
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32 views

How to answer skeptic who points to latent variable?

I have a linear model with the following form: $$ y = \beta_0 + \beta_1x_1 + \beta_2x_2 $$ As $y$ is considered a "moral" behavior, I expect resistance and skepticism of the following kind: the ...
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1answer
16 views

Factoring a probability distribution containing a latent variable

I distribution which involves 3 parameters, which I'll call (for now) $P(z | y, x)$. However, one of the parameters is a function of another. For instance, let the random variable $y$ be a ...
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1answer
95 views

Generating data from Probit regression, cut off 0 and variance 1 necessary?

I am trying to create a dataset using a Probit regression model in R, where I have an intercept and three covariates. I first fix a set of coefficients for the three covariates, generate these ...
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11 views

Sub-space / latent-space covariance

I am not entirely sure what I should be googling for this in my present context. Basically I am working with a set of latent variable models such as the Gaussian Processes latent variable model ...
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24 views

Estimate the conditional distribution of an latent variable?

What techniques might best illuminate the underlying conditional distribution of a latent variable and what information or assumptions would improve that illumination? For example, if we have data ...
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173 views

Selecting the number of mixtures / hidden states / latent variables

My question is regarding Gaussian Mixture models, Hidden Markov models (HMM) or any type of clustering or latent variable model, for which we can devise a likelihood function. Specifically, I train a ...
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117 views

Parameters vs latent variables

I have asked about this before and have really been struggling with identifying what makes a model parameter and what makes it a latent variable. So looking at various threads on this topic on this ...
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36 views

Universal approximation of probability distribution with latent variable model

I want to show that under certain circumstances this form can approximate any probability distribution. For that, I came up with the following argument. Consider a directed graphical model of the ...
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1answer
34 views

Structural Equation Model - Construct Operationalization

I'm building a Structural Equation Model and I'm trying to operationalize my Dependent Variable, the construct of "Investor Behaviour" (= whether or not an investor is willing to invest in a startup). ...
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16 views

Extracting latent factor from ranking data

I want to construct a model to link between a set of quantitative engineering parameters (e.g. Sm, Ra) of 9 material samples to a set subjective qualitative rankings of 6 perceived attributes, e.g. ...
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16 views

Suggestions of a statistical model with IID data and latent variables

While this might be an unusual request, I am looking for a statistical model with certain properties to test my numerical method on and thought I might ask here. The model ought to have the following ...
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How can I infer the joint distribution of an observed and a latent variable?

I have a dataset of school children with three features: Age $x$ of the student answering the survey Year group $a$ of the student answering the survey Year group $b$ of the best friend of the ...
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1answer
170 views

When a CFA model has a “covariance matrix was not positive definite” problem, is it due to the dataset or the model?

I am testing several CFA measurement models with Lavaan in R. The questionnaire that I am investigating has been shown to be composed of 1-factor, 3-factor, and 4-factor. In the dataset, I found ...
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239 views

Combining several variables into one outcome score: How is it done in the machine learning community?

I have got 8 cognitive (continuous) behaviour variables and would like to combine them into a composite score. I would then like to find the best predictors of this outcome (from about 50 predictors). ...
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59 views

Easy and common way to separate latent classes from Likert-scale survey?

Let say, there are two 5-points Likert-scale questions "How do you like a flavor?" applied for two product samples. That is, each respondent tries two samples and evaluate them on Likert scale. ...
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1answer
75 views

Mean field variational inference

In Chris Bishop PRML book p.465 equation 10.6, the derivation doesn't explain why exactly the term $\int q_j ln(q_j) dz_j $ was generated, is not that term supposed to be multiplied by constant, did ...
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19 views

How do you correctly scale a formative latent variables in a structural equation model?

How does one scale a formative latent variable? I know that one option is to multiply one indicator by 1. What I do not understand is that if depending on which indicator is multiplied the direction ...
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32 views

Comparing a model with a latent variable to one without

I would like to test whether my 3 dependent variables all load onto an underlying latent variable or if a latent variable is not necessary to explain the relationship between the IVs and the DVs. In ...
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1answer
59 views

Explain: Latent Variable (e.g for Latent Dirichlet Allocation)

I am trying to understand the Latent Dirichlet Allocation but therefore I need the basic understanding about what exactly a latent variable is in that sense. I know that the basic idea of a latent ...
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43 views

Sparse PLS: algorithm for variable selection and model fitting

In the spls package in R (based on the manuscript by Chun and Keleş [1]), there is a separate specification for the variable selection and fitting in the main function, ...
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Should the rivals models include the same number of observed variables?

The question is about comparing models that include different number of observed variables. For example consider I have an 80-items questionnaire and I want to do confirmatory factor analysis (CFA) in ...
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Latent Class Analysis vs. Cluster Analysis - differences in inferences?

What are the differences in inferences that can be made from a latent class analysis (LCA) versus a cluster analysis? Is it correct that a LCA assumes an underlying latent variable that gives rise to ...
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26 views

Confusing definition of Potts model

I came across some Markov random field models and noticed something that didn't make sense to me. One of these models for a set of latent variables $\{z_{i}\}$ is the following: $$p(z) = ...