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

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How to determine time complexity of EM algorithm of probabilistic PCA?

I was studying probabilistic PCA from Bishop's book. There an EM algorithm is provided to calculate principal subspace: Here $\mathbf M$ is $M\times M$ matrix, $\mathbf W$ is $D\times M$ matrix ...
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32 views

Understanding LDA inference

It is said that the key inferential problem that needs to be solved to use LDA (latent dirichlet allocation) is that of computing the posterior distribution $p(\theta,z | w, \alpha ,\beta)$. I know ...
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38 views

Word-topic matrix in Latent Dirichlet Allocation

In the Latend Dirichllet Allocation model described in Wikipedia (https://en.wikipedia.org/wiki/Latent_Dirichlet_allocation), is $\beta$ the word-topic matrix? I understand that $\beta$ is the ...
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71 views

What is principal subspace in probabilistic PCA?

if $X$ is observed data matrix and $Y$ is latent variable then $$X=WY+\mu+\epsilon$$ Where $\mu$ is the mean of observed data, and $\epsilon$ is the Gaussian error/noise in data, and $W$ is called ...
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11 views

How to classify new observations to class with parameters from latent class models?

I am using LatentGold to estimate latent class models (LCM). I wanted to create an equation using my parameters to classify new observations to classes. To do this, LatentGold explains that one has ...
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96 views

Probabilistic models for partial least squares, reduced rank regression, and canonical correlation analysis?

This question results from the discussion following a previous question: What is the connection between partial least squares, reduced rank regression, and principal component regression? For ...
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86 views

Beginner references to understand probabilistic principal component analysis (PPCA)

I am totally new to machine learning. I started studying PCA from Jonathan Shlens, 2005, A Tutorial on Principal Component Analysis. The paper provides some concrete examples, and background ...
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24 views

How to estimate the parameters of the following log-likelihood function?

I would like to estimate the parameters based on the famous Merton model used probability of default modelling: Suppose firms' logarithmic returns are following the standard normal distribution and ...
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16 views

Defining a paradox in proxy variables

I'm looking for a formal name or write-up of this phenomenon: When you are using a proxy variable (A) to measure a true variable (B), taking actions based on the proxy variable can decrease the ...
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27 views

Mixture model: 3 binomial components (using WinBugs)

I've a BUGS question I've been unsuccessfully trying to define the likelihood for a mixture of 3 binomial distributions. I'd like to estimate the mixing proportions for a given dataset. Once this is ...
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11 views

Sampling a Latent Variable with Unspecified Distribution

This question is an extension of Product probability , although I will use a linear function here in hopes it is more tractable. Suppose you observe a sample of iid random variables $Z_1,...,Z_n$. ...
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33 views

A question regarding maximum likelihood conditional on observed and unobserved variables

Please consider the following likelihood function, $$ L(\theta)=\int_{\Re^u} f(y|x,u,\theta)h(u|\xi)\partial u, $$ where $y$ is a vector of observed dependent variables, $u$ is a vector of unobserved, ...
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52 views

When does the marginal MLE converge to the complete data MLE?

What I mean by the title is suppose we have a distribution $p(x,z\;|\;\theta)$, where the $x$ are observed and each $x_i$ depends on a hidden $z_i$. Then the marginal MLE is given by ...
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25 views

Does it make sense for pairwise correlation to be uniformly higher than an ability?

I am fitting a graded response model to analyze a 16 item, 5 ordered response category scale. It shows univariate properties in an EFA with one very strong principal component. The distribution of ...
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21 views

PCA (with phi/tetrachoric correlation matrix) or LTM to study the correlation of (true) dichotomous variables?

I am doing a study were I have to initially do an exploratory analysis by grouping diseases that coexist in my study population. For that I have x diseases/variables that are (true) dichotomous ...
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15 views

Intuition behind Latent SVM

The relevant paper (I think) is : Felzenszwalb, Pedro F., et al. "Object detection with discriminatively trained part-based models." Pattern Analysis and Machine Intelligence, IEEE Transactions on ...
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13 views

Under the latent variable formulation, can we use the Tobit model for count or categorical dependent variables?

Suppose we are using the Latent Variable Formulation (i.e. not the Generalized Linear Modeling) for a multiple regression model: Can the Tobit model be used if the dependent variable is not ...
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54 views

Why does probabilistic PCA use Gaussian prior over latent variables?

I am currently reading papers about probabilistic PCA and I am wondering why is Gaussian prior (and not some other prior) chosen for the latent variables? Is it just because it's simple or is there ...
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8 views

Modeling target effect as latent variable - Why not possible?

I have a dataset with participants nested in groups of six, and each participant is rating the other participants in his group with respect to trustworthiness. The average rating of all other ...
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106 views

What's the difference between a MIMIC factor and a composite with indicators (SEM)?

In structural equation modeling with latent variables (SEM), a common model formulation is "Multiple Indicator, Multiple Cause" (MIMIC) where a latent variable is caused by some variables and ...
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51 views

What is the motivation for the entropy term in the proof of EM algorithm?

Reading through the proof that EM algorithm monotonically increases the log-likelihood (until it converges), I noticed that the most important ingredient of the proof is the introduction of an entropy ...
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21 views

SEM with zero-inflated outcome

I'm working on a project and my advisor wants me to do SEM in MPLUS because we can do latent modeling, but I have no clue where to start. I've only ever done regressions but I said I'd be up for ...
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27 views

Signal-to-noise ratio for probabilistic PCA

Consider the probabilistic PCA model where you have $n$ i.i.d centered obserbations $x_1,...,x_n\in \mathbb{R}^p$ drawn from $$\forall i\leq n, \; \; \; \; x_i = W y_i + \varepsilon_i,$$ where $W$ is ...
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23 views

Latent Dirichlet Allocation and text Pre-Processing

I think I understand the basic principles of LDA. However, browsing the githubs of people who applied this method, I noticed they pre-process the Corpus very specifically. For example, about the ...
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13 views

Constraining the mean latent slope in lavaan

In lavaan, I can constrain the intercepts of the latent slope and latent intercept, like so: ...
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107 views

Comparing AIC/BIC Between Continuous (CFA) and Categorical (LCA) Latent Models

Some colleagues and I have a set of variables that we would like to represent more parsimoniously/latently. Originally, my colleagues used an exploratory and confirmatory factor-analysis approach to ...
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1answer
79 views

Advantage of latent SVM for part-based object detection

In the famous paper Object Detection with Discriminatively Trained Part Based Models, the authors use a Latent SVM approach to learn the detector of each part, because the localization of the parts in ...
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70 views

Mathematics behind factor loading in Confirmatory factor analysis/ Structural Equation Modeling

I'm curious about how are the loading in a simple confirmatory factor analysis determined mathematically. Also, the intuition is also hazy to me as to how are the factor loads determined when a ...
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33 views

Fitting a logistic function to a latent growth curve model in lavaan

Assume I have the following latent growth curve model in lavaan: ...
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30 views

SEM/Bayesnets: does creating a latent variable always reduce the fit?

assume there are 3 variables (x1, x2, x3) that each correlate tightly with each other, and also correlate tightly with y. if we add a latent/hidden variable that merges information from x1, x2 and x3 ...
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41 views

Rotation in (Univariate) Partial Least Squares Regression

according to a not so recent paper (http://www.sciencedirect.com/science/article/pii/S0167947303003049), it is a good idea to Varimax-rotate the factors that have emerged by Partial Least Squares. ...
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26 views

Non-time-varying covariates in latent growth curve modeling?

I know that if I'm doing a latent growth curve model I can use time-varying covariates, i.e. a covariate that has one value for each time point. What if I have a variable that has one value for each ...
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34 views

Gradient of Expectation in latent variable model

I am reading a paper that talks about minimizing the variational lower bound $\mathcal{L}(\theta,\phi;x) = -KL(q_\phi(z|x) ||p_\theta(z)) + \mathbb{E}_{q_\phi(z|x)} log(p_\theta(x|z) $ wrt. to the ...
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37 views

What is the conceptual link between the chi-square distribution and indices of fit in structural equation modeling?

I understand that the fitting function in SEM is obtained from the difference between the observed and model-implied covariance matrices. I can't find a simple and intuitive explanation of -why- it is ...
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50 views

Can you write a probability based on the relative entropy?

Suppose we have a graphical model $X\rightarrow \Theta \rightarrow D$ where all the distributions are Gaussian Mixture Models. Suppose further that the distribution of $X$ has more components than the ...
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31 views

Regression on Inferred Variables

Given a set of labels $y$ and design matrix $X$ we often compute a linear regression to find a set of parameters $\hat{\beta}$ such that $E[y|X] = X\hat{\beta}$. However, how does one perform ...
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38 views

Regression with latent variable response

I have a dataset with the following structure: $(x_1,x_2,x_3,...,x_n, y)$ where $x_k$ are some categorical predictors and $y$ the numerical (integer) response. Assuming that $x_1 \in \{a,b,c\}$, ...
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1answer
54 views

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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45 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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1answer
43 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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464 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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69 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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45 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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14 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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91 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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69 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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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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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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239 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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54 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 ...