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Questions tagged [latent-variable]

Latent variables refer to variables that cannot be directly observed. These variable are defined in terms of observable variables. In narrow sense, "latent variable" is seen/modeled as what generates the observed variables in an implied data generation process. Also called hidden or lurking variables.

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what is the difference between a multilayered autoencoder and a hierarchical latent variable model?

I have been trying to understand how hierarchical latent variable models are different from multilayered autoencoders and in specific the argument below Autoencoder networks resemble in many ways ...
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How can I analyse simmilarities/differences of one nominal variable of two different groups?

I have two different samples. I want to measure how similar is each individual of the first group with the second group in terms of Var 1 (nominal not ordered), given that they are both categorized ...
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SEM: issue with two correlated latent variables

I am fitting a SEM model that includes socio-economic status (SES) for a household and environmental conditions (env) surrounding this household (road condition, sanitation etc). My (obvious) ...
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Linear mixed model with unknown variable

I would like to implement a linear mixed model (LMM), however additionally to the normal covariates also with a variable that I do not observe directly, rather I observe the probability for its ...
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Confusion with the E-step of the EM algorithm for Gaussian Mixture Models

So I was reviewing the E-step for the Gaussian Mixture model on Wikipedia. And it looks like in the E-step all you really need to compute is the conditional distribution of Z because that is all that ...
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What happens if the observations are connected in a hidden Markov model (HMM)?

Suppose that we have an HMM with hidden variables $X_t$ and observed variables $Y_t$. Why do we always assume $p(Y_t|X_t)$? What happens if we have $p(Y_t|X_t, Y_{t-1})$? Is it because that wouldn't ...
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Singular values for a latent-factor model

Suppose we build a latent-factor model using alternating least squares (ALS) or stochastic gradient descent (SGD). Can we calculate weights for each latent factor, in a similar way to how the singular-...
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27 views

Estimating common slope across two traits for a parallel growth curve model

I am using a parallel growth curve model with 5 waves longitudinal data to evaluate correlated change among 2 traits. For models that showed the effects of correlated change among traits, I'm ...
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Neural network with unknown layers

Say I have a neural network with some unknown number $N$ of hidden layers. Assume I know the structure (e.g. feedforward, convolutional, or recurrent) of the first $k$ of these hidden layers but know ...
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Markov property of manifest variables in longitudinal ESM

I am working on a longitudinal ESM model were the indicators are (highly) autocorrelated. This means that the classic cross-lagged models of panel data analysis cannot be used directly. I have ...
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1answer
30 views

likelihood of latent state space model

Im trying to calculate the likelihood function of my latent state space model. My model has Poisson observations $p(y_t|\beta_t;x_t) \sim \mathcal{Poiss}(z)$. where $z$ is the rate of the poisson ...
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AIC for latent variable models

I'm trying to use BIC/AIC for model comparison and want to know what the number of parameters is. The models I'm unsure about are linear Gaussian state space models with nonlinear observations. ...
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Latent variable interaction: different number of indicators 4 vs 1

I am trying to calculate a latent variable interaction using the unconstrained product indicator approach (Marsh 2004) with double centering (Lin et al. 2010). My data: two latent predictor ...
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Question about validity of an MCMC algorithm

Let suppose I want to sample from the posterior distribution of $X_1,X_2|y$ using an MCMC algorithm and let indicate with $X_i^t$ the value of $X_j$ at the $t-$th iterations. I want to know if the ...
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Conducting a three-step Latent Class Analysis in R

I'm trying to conduct a Latent Class Analysis in R using the poLCA package, and I have now become stuck on two aspects of the process. I have conducted Latent Class Analysis separately for males and ...
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Estimating latent mean and variance for a Gaussian

I have a latent Gaussian model with unknown parameters $\mu$ and $\sigma^2$. I can estimate these parameters using MLE and an EM-ish algorithm. However the solution is not stable; I end up in local ...
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Modelling latent variables: lavaan warning: covariance matrix of latent variables is not positive definite

I have 3 independent variables (linguistic, onk2_sc3 and dsk2_sc3) and one dependent variable (Reading) in SEM multigroups (3 groups) comparison: ...
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Partial Least Squares Regression : deflation of the Y matrix

I am digging deep into the PLSR algorithms and while I have found multiple flavours of if (different normalisations, SIMPLS,..), there is always something in the Y deflation that is throwing me off ...
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Linear Regression Perfectly Predicts Latent Variables

I'm having trouble understanding the relationship between the latent variables produced by the CFA function in R's Lavaan package, and linear regression. I have used one of Lavaan's built-in data ...
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Likert scales and Latent variables constraints

I have series of Likert scale questions (1-10) from which I have derived two latent variables using PCA. The Likert scale variables are obviously constrained, in that you can't score above 10 or ...
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Interpreting the latent growth model output

I started to go through this interesting structural equation model called latent growth curve model. When i go through some research articles that involved latent growth curve models, I found this ...
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Creating a weighted composite score from standardized lavaan latent beta weights that retains the scale of the original measures?

I did a latent factor analysis in Lavaan which had a good fit and gave me the following estimates of standardized beta weights for three latent variables called Eta1, Eta2, and Eta3. ...
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Can we apply Gaussian mixture model to all kinds of scensrios where some variables are unobserved?

I learned from this answer that: A mixture distribution combines different component distributions with weights that typically sum to one (or can be renormalized). A gaussian-mixture is the ...
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PLS (Partial Least Squares) deflation and graphics

I have been working with pls for a little while now. I have a question in terms of the deflation of both the $X$ and $Y$ matrices. In the literature I have found different methods over which deflation ...
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1answer
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Are direct effects between latent variable indicators ever appropriate?

I have a longitudinal structural model regressing 1 endogenous latent variable at Time 2 on 4 exogenous latent variables at Time 1. The modification indices in Mplus suggest including a direct effect ...
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Help with PCA Question

The conventional model for probabilistic principal component analysis has a standard normal latent $\vec{y}$ and a loading matrix $\Lambda$: $P(\vec{y}) \sim N(\vec{0}, I)$, $P(\vec{x}|\vec{y}) \sim ...
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What type of transformation for Latent Growth Curve analysis with lavaan when observed variances are over 40,000,000?

Edit: I believe a linear transformation is just fine - divide each number by 100 for example. Just make sure you change back your units when you are interpreting the output! In fact, when I do this, ...
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Path analysis of latent variable relationships over time for hypothesis testing

Consider that I have a sample of 30 people (my real data are much bigger), and we ask them how often the would like to eat three types of food (candy, vegetables, and meat) at four points in their ...
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1answer
71 views

Deriving non-Gaussian uncertainties using Gaussian process regression

I came across this work on "Gaussian Process Regression with Heteroscedastic or Non-Gaussian Residuals" which is intriguing, but I believe I am failing to properly interpret its results. Namely, it ...
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50 views

Low average variance extracted (AVE) for a construct that measures self-reported behavior

I want to use a latent variable as a dependent variable in a path analysis. The indicators of the variable are self-reported behaviors like donate to an environmental NGO, recycle, and use public ...
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Create an index tracking belief-change “moderation”

Let's say I ask participants to evaluate, on a scale from 0-100 (with 0 representing "completely disagree" and 100 representing "completely agree) the extent to which they believe a number of ...
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probabilistic model from expectation of another probabilistic model

In Goodfellow's deep learning book Chapter 13 first paragraph (https://www.deeplearningbook.org/contents/linear_factors.html) Many of the research frontiers in deep learning involve building a ...
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Are latent variable models the same as latent source models?

I am interested in the research done in this thesis and accompanying paper. This research discusses models termed latent source models. I have never heard of this specific term and the papers don't ...
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Generative autoencoders - how important is agreement of latent variable distribution e.g. with Gaussian?

Autoencoders want to minimize distortion of encoding-decoding process, preferably alongside evaluation by discriminant. Generative autoencoders additionally would like latent variable from a chosen ...
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Identification and estimation of my structural model with a latent variable

I am having some trouble trying to identify the parameters in the following structural model that I am trying to estimate. $$ y = a'x_1 + \beta\eta + \epsilon_1 $$ $$ \eta = b'x_2 + \delta T+\...
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54 views

Categorical data & Gaussian latent variables

I am learning about imposing structure on the latent variables in autoencoders. In that context I have looked at variational autoencoders (VAEs) and adversarial autoencoders (AAEs). This paper ...
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Discrete latent variables in Bayesian Network

I am creating a Bayesian Network where all nodes are discrete. Using the available data, I have learned the structure of the network using the Hill-Climb algorithm (...
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1answer
161 views

PyMC3: Mixture Model with Latent Variables

I have a rather basic knowledge of Bayesian inference and I'm somewhat new to MCMC and PyMC3. Can I model data that looks like this? ...
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364 views

Question about the latent variable in EM algorithm

In mixture models, Expectation maximization algorithm (EM) is a commonly used method to estimate the model parameters. Suppose that I have bivariate mixture model with two mixture components, with ...
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49 views

How can one get consistent (i.e. direct+indirect=total) effects in a Meta-Analytic SEM model with latent variables?

I have a mediation model with latent variables using datasets from a few studies. In particular, one of the latent variables is the outcome, while the others are tested as possible mediators of a ...
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item selection procedure for a questionnaire representing several latent variables / constructs

i have drafted 51 items that are supposed to measure 9 distinct but related constructs, and have collected data on this questionnaire from 530 people. ultimately, i want to use these data for a sem. ...
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1answer
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computing values of a latent variable

Is there an easy way to compute the (standardized) values of latent variables so that it generates a new variable to the dataset. I am working with Stata. The SEM model builder doesn't seem to offer ...
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1answer
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Trying to understand a latent curve model in terms of mixed effects regression

I'm trying to understand exactly what the following model is trying to represent: (taken from Beaujean's Latent Variable Modeling Using R book) The text indicates that this is a random intercept/...
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1answer
100 views

Expectation of latent variables in Factor analysis Model

I am going to through the theory behind factor analysis models given here Let's say our model is \begin{align} y_i = \mathcal \Lambda x_i +\epsilon, \end{align} where $y_i$ is the $p$-dimensional ...
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113 views

What is the relationship between latent factors in matrix factorization?

I am working on a project that involves using ALS to factor a m x n matrix $A$ into two latent matrices $UV$T, with dimensions m x k and n x k respectively. I was wondering, what is the relationship ...
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Latent growth curve model with more time points than participants

I can't quite figure out if having more time points in a latent growth curve model reduces power or increases it. I don't have the data yet so I can't experiment. The study has around 300 measurement ...
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Combining AEVB with conjugate exponential family observations

I'm trying to build a probabilistic model that is a combination of a neural network and a graphical model; namely it uses a MLP as an encoder network, and the "decoder" is an exponential family ...
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66 views

What's a good way to enforce shared latent space for multi-modal data

I have two separate data sets (of different types) $A$ and $B$. I can train two independent generative models (with different architectures for $A$ and $B$) such that $q_A(z|x)$ and $q_B(z|x)$ are the ...
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Comparing population averages while accounting for changes in composition

I have two populations (i.e., men / women) with different average measurements (let's say height). I observe the combined average of their height decreases. I also observe the proportion of women ...
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Encouraging deep probabilistic model to make use of all available latent dimensions

I have a deep probabilistic model that models a data generating process $$p(x, z) =p(z_0)\sum_{t=1}^{T-1}p(z_t|z_{t-1})p(x|z).$$ It works on simulated data, but when I reduce the SNR it quite often ...