# 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.

279 questions
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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 ...
2answers
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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 ...
1answer
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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-...
1answer
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### 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 ...
1answer
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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 ...
1answer
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### 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 ...
1answer
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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 ...
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 ...
1answer
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