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

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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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9 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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11 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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9 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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42 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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42 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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49 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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10 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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23 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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11 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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8 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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82 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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59 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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1answer
32 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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28 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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28 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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27 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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18 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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14 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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1answer
30 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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48 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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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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36 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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35 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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39 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
38 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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318 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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56 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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22 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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13 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
70 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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64 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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17 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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22 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
132 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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39 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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51 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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41 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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25 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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314 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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74 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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45 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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1k 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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17 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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27 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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64 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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53 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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133 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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29 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 ...