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

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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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22 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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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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11 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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88 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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23 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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17 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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29 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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13 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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64 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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9 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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20 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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125 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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92 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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1answer
31 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
24 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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12 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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15 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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24 views

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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64 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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162 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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56 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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50 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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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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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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39 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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Sparse PLS: algorithm for variable selection and model fitting

In the spls package in R (based on the manuscript by Chun and KeleĊŸ [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) = ...
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30 views

Ways to express the relationship between a latent variable and observables

How do I express concisely the idea that the values of a number of observables is determined stochastically by the value of a latent variable? Can I say: The value of the latent variable is ...
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Conceptual links and differences between generalized and latent models

Please bear with me, as I'm trying to better understand these aspects. My understanding is that (finite) mixture models (MM) are characterized by a presence of a number of sub-populations in a ...
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34 views

Mixture distribution fitting for latent variable analysis

Are there any analytic approaches to using mixture distribution fitting for latent variable analysis? I'm specifically interested in existing approaches to determining whether mixture components ...
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62 views

What is the role/purpose of hidden variables in graphical models?

Is there a formal treatment of the role/power of latent/hidden variables in graphical models and other machine learning models (e.g., structural equation models)? For example, the Restricted Boltzman ...
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identifying latent variables in this model

I have been trying to understand EM and I am having a hard time understanding what a latent variable is. In particular, I am having issues in identifying whether in a particular model that I am using, ...
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225 views

How to choose an optimal number of latent factors in non-negative matrix factorization?

Given a matrix $\mathbf V^{m \times n}$, Non-negative Matrix Factorization (NMF) finds two non-negative matrices $\mathbf W^{m \times k}$ and $\mathbf H^{k \times n}$ (i.e. with all elements $\ge 0$) ...
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How to model occurrence counts in groups with latent membership?

I have a dataset that describes the daily history of occurrences of a certain phenomenon P among a certain population. (These are subdivided into certain classes or forms that the phenomenon can take: ...
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94 views

How to use factors (from CFA) as independent variable in Regression Analysis

I calculated 4 factors as latent constructs in a Confirmatory Factor Analysis (I use AMOS). Now I am wondering if it is possible to extract some kind of a factor score like I know it from Exploratory ...
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160 views

Binary version of Probabilistic Matrix Factorization in pymc?

I'm a newby in statistics, this is my first post, sorry for any possible mistake. There is a good Bayesian Probabilistic Matrix Factorization model introduced in: Bayesian Probabilistic Matrix ...
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Mixture model for dependent observations with additive group-level confounders

I'm looking for a special type of mixture model (described below) and I'm hoping to get some hints with regards to relevant literature to look at or names to be searching for. On the general level, ...
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65 views

Estimation parameters for latent (unobserved) variable

Here is my problem: I have 3 variables $X,Y,Z$ : $X$ is the number of clicks we observed on an web advertisement; $Y$ is the number of time a customer do a sign-up on the website after clicking ...
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127 views

Partial Least Squares structural equation modeling

Im calculating a Structural Equation model with Partial Least Squares (with R). Lets say a simple example: two Response values (R1, R2) are combined to a latent variable RespLV = weight1*R1 + ...
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How to compute a latent variable (as a composite index)

Can I calculate a latent variable (construct) after the formula: Sum of (summated scale for factor i * variance explained by factor i), i taking values from 1 to n (n being the number of factors)? Or ...
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Summated scales for factors (latent variables)

For summated scales: can I use all the variables that load on a factor or is it necessary to use only the variables with high loading (over 0.70, for example)?
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Summated scales (after factor analysis)

Is it okay to calculate summated scales if I am undertaking an exploratory study and some of the factors that result are somewhat different from what I have found in the literature? (I have read that ...
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59 views

latent variables versus model parameters

I am quite confused with the distinction between a latent variable and model parameters. So say I have two observed variables $x$ and $y$ and they have some unknown relationship between them i.e. $y ...
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27 views

Splines, latent variables and model identification

For $J$ units of observations my basic model contains latent variables $\theta_j, j = 1, ..., J$ identified by the marginal assumption $\theta \sim N(0,1)$. The latent variables are connected to a ...
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Is there an extension of multinomial process models that can model several dependent variables?

In the setting of psychological experiments, where a categorical response has to be given, the same response can, in theory, be generated by different latent processes. For example, in an experiment ...
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111 views

Bayes' theorem in 1-d EM algorithm

I'm watching a video on the EM algorithm, When we use Bayes' Theorem to calculate $b_i$, how do I find $P(b)$ and $P(a)$ initially? It says we can estimate the priors $P(b)$ and $P(a)$ but that's ...