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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Mixture of factor analyzers: Correct expression for likelihood function?
I'm reading these notes about mixtures of factor analyzers, where the following generative model is described:
The conditional distribution of the data $x$ is stated (in Sec 3, eqn 9) as:
$$
P(x \mid ...
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Why do we need to marginalize when finding p(data) when latent variables are involved? (part of elbo derivation)
so confused with the derivation of elbo. In part of the derivation p(data) is intractable as it involves an integral over a high dimensional latent variable. I cant understand why the latent ...
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Comparing unsupervised approaches to topic prevalence detection in semi-structured nested textual data
I am trying to understand approaches to (ideally, probabilistically) detecting the prevalence of latent topics in semi-structured, nested textual data. Specifically, there appear to be at least two ...
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Finding level curves for a latent variable model
I have a latent variable model that represents p(x) using two Gaussian distributions p(z) and p(x|z). The mean and covariance of p(x|z) is represented by some function of z using a neural network.
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df (mis)calculation with efa models in lavaan
I've been working on some functionality to wrap EFA scripting in lavaan, and noticed some df's that seemed off. I'm now wondering if I'm goofing/overlooking something, or rather, if something ...
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Exploring vae latent space
I recently trained a AE and a VAE and used the latent variables of each for a clustering task. It seemed to work well, sensible clusters. The main reason for training the VAE was too gain more ...
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Can you use a binary outcome variable in a longitudinal latent-growth mediation model
I am wanting to create a LGCM in which I am assessing whether two latent factors (the intercept and slope) mediate the relationship between a continuous predictor and binary outcome variable but am ...
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Why is the forward process referred to as the "ground truth" in diffusion models?
I've seen in many tutorials on diffusion models refer to the distribution of the latent variables induced by the forward process as "ground truth". I wonder why. What we can actually see is ...
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How to determine the ideal number of components for PLSR using RMSE?
I would like to determine a non-visual, numeric based approach to determine the ideal number of components for my PLSR model.
There are 10 components in the model for 1 target variable.
If I simply ...
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Predicting future states in hidden Markov models -- use the Viterbi algorithm?
The Viterbi algorithm is used to decode hidden states in hidden Markov models (HMMs) by working out which sequence of states is most likely. To do this, it first identifies which state $j \in \{1, ...,...
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Why reverse diffusion process is not a gaussian distribution?
The forward diffusion process, which goes from x_t to x_{t+1} is Gaussian, which is very reasonable as we go the next state by adding random gaussian noise. However, I do not understand why the ...
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Is the behavior of log-likelihood and number of parameters correct in probabilistic PCA?
I am studying the behavior of Probabilistic PCA as described by Tipping and Bishop (1999). I am using the R package "Rdimtools" to help. I am puzzled about the number of parameters in the ...
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For EM algorithm, why we assign an independent distribution $Q_i$ for each sample index
I'm learning the expectation maximization algorithm with Andrew's CS229 lecture notes https://pillowlab.princeton.edu/teaching/statneuro2020/notes/notes18_LatentVariableModels.pdf
The derivation and ...
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Conditioning once or twice?
Let's say we have two random variables $Z \in \mathcal{Z}$ and $X \in \mathcal{X}$ with joint density $p_{Z,X}(z,x)$ with respect to a base measure. The density is assumed to factor as
$$ p_{Z,X}(z,x) ...
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Statistical test for change in time series with one group
I have conducted a latent class trajectory analysis using growth mixture models on a sample of 150 individuals. Individuals are assigned to 2 classes - 1 consisting of 18 individuals and the second ...
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Linear Model Equivalence regarding Latent Variables
While reading a paper (surprises in high-dimensional ridgeless least squares interpolation), I was stuck to a part of a section (5.4, page 16~18).
Consider coviariates $x_i = (x_{i,1},\dots,x_{i,p}) \...
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Demystifying CFA Models for Longitudinal Analysis of Latent Variables
TLDR; there are 3 approaches I have come across to longitudinal CFA (not SEM) and I am not sure which one is appropriate for simple dimensionality reduction.
I have come across 3 common flavors of CFA ...
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Interpretation of $\sigma$ in Gaussian mixture
I have a distribution of a variable that was normalized with plt.hist and then fitted with a sum of gaussian curves $g_M = \displaystyle\sum_i\frac{w_i}{\sigma_i \...
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Is it possible to fit a latent class regression where the latent class is grouped by 1 variable, but there is a random intercept by another variable?
The data generating process I am interested in is the following:
$$y_i=\beta_g x_i+\epsilon_t+\epsilon_i$$
$$S(i)=s, G(s)=g$$
What this means is that that the $i$th observation, which is made of ...
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VAE with linear decoder and nonlinear encoder, does this just learn a linear decomposition of the data?
There are a number of variational autoencoder(VAE) methods that have nonlinear encoders and linear decoders. The concept of using the linear decoder is to improve the interpretability (which features ...
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Can I covary exogenous and endogenous latent variables in SEM in lavaan
I am editing the question as it was too meandering. I am sorry about that.
I am running an extended Theory of planned behavior (TPB) model of digital piracy and I have a question that boils down to - ...
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Help needed fitting a general latent variable model in glmmTMB
as Ben Bolker suggested here I should ask this question in this forum!
I am trying to fit a GLVM similar to the one presented in this vignette: https://cran.r-project.org/web/packages/glmmTMB/...
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Does measurement invariance analysis assume equal latent scores across groups?
I have completed a measurement invariance analysis comparing high-school aged boys to high-school aged girls on a measure of depression. The results suggest that scores are not (scalar) invariant; ...
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Least Square Estimate and Latent Space
I'm currently studying regression coefficient w.r.t latent space in a paper Surprises in High-Dimensional Ridgeless Least Squares Interpolation by Trevor Hastie etc. This topic occurs in chapter 5.4 (...
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Response style as an alternative explanation for latent mean differences under scalar invariance?
I established scalar measurement invariance for a two-group CFA. The output from my final model showed that the latent mean in group 1 is lower than the latent mean in group 2. Can this difference in ...
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Modelling count data with variable upper bound
I have been unable to find references to understand how count data can be modeled where each count observation has an unknown upper bound lying in a particular range.
Let's consider the following ...
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Testing a multifactor asset pricing model against another one
I have a sample of $(Y_{i,t},X_{1,i,t},X_{2,i,t})$ for $i=1,\dots,N$ and $t=1,\dots,T$. I want to figure out which data generating process (DGP) it comes from, DGP1 or DGP2.
DGP1:
$$
Y_{i,t}=\lambda_0+...
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IRT hybrid model predict latent estimate using bayesian method
I'm having some problem about an item response theory (IRT) prediction model.
When I use IRT hybrid model, it cannot predict the latent value even it has successfully converge during the IRT model ...
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Inference on latent variable with observation of its convolution with itself
Problem
I have an inference problem where the data observed are univariate random numbers whose distribution is obtained as follows. A latent random variable X is first sampled from a parametric ...
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When does SEM have little to no benefit over multiple regression, and there is a distinction without a difference between two approaches?
My understanding of SEM and it's advantages over multiple regression is:
Model Comparison: Contraining paths, or fixing paths to other estimates, or specifying other possible models to see which is ...
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Growth Mixture Model/Latent Class Growth Analysis for binary/binomial outcome in R?
Latent Class Growth Analysis and Growth Mixture Models (synonyous; henceforth referred to as GMM) explain between-subject heterogeneity in growth on an outcome by identifying latent classes with ...
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How do different sets of restrictions in a SEM with moderation affect results?
I'm trying to run a latent moderated mediation analysis SEM with R lavaan. It is essentially "First Stage Moderation", per Edwards & Lambert (2007), with a few extra factors. I'm using ...
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How to interpret standardized simple slopes and indirect effects in R with semTools and lavaan?
I am attempting to obtain a standardized solution for simple slopes and indirect effects in a SEM in R using lavaan and semTools::probe2WayMC, following the methods of Schoemann & Jorgensen (2021) ...
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EM algorithm for mixture with latent regression?
I have in the past implemented the EM algorithm for certain cases of mixture distributions. However, I'm attempting to implement it now for a given problem that's exposing my lack of understanding of ...
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Is reinforcement learning conceptually equivalent to time-series with a latent dependent variable?
In reinforcement learning, there is a state $s_t$, an action $a_t$, and a policy $\pi(a|s)$ that maps states to the Probability Distribution Function (PDF) of actions. The goal is to choose the ...
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How can I calculate the required sample size for Latent Growth Curve Modelling?
I am looking to calculate what sample size I would need for my study by running an a priori power analysis.
Is there any way (e.g an R package) I can calculate the required sample size required for ...
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How to model a difference score for cross-sectional, hierarchical survey data
What is the best way to model a difference score that is based on cross-sectional survey data, while also taking into account the hierarchical structure of the survey data?
I have the following survey ...
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On the expressivity of latent variable models
Empirically, we have seen that VAEs can approximate very complex distributions. I am interested in knowing if there are any theoretical results showing how expressive latent variable models can be. ...
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Is FAMD (Factor Analysis of Mixed Data) truly a factor analysis technique? or it is a dimension reduction technique?
PCA is distinct from factor analysis; it's a dimension reduction technique. PCA does not account for individual variable noise. On the other hand, FAMD (Factor Analysis of Mixed Data) combines PCA and ...
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Latent growth curve model with a continuous time-invariant covariate, multi-group or covariate model?
A Latent growth curve model with a time-invariant covariant can be specified with (at least) two ways, by using the multigroup model approach or the "regression approach".
By regression ...
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Is it possible to have an Indicator-spesific Trait factor model within a multiple indicator second order growth model?
I am running a multiple-indicator growth curve model over 7 time points.
One of my items has a large residual variance and seems to covary very well among themselves.
Thus, I assumed that it has a ...
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How can one estimate the parameters of unobserved variables?
Consider three discrete variables $X, Y , Z$ where
$$X \sim B(p_x)$$
$$P(Y = 1 |X = 1) = p_y,\ P(Y = 0 |X = 1) = 1 - p_y,\ P(Y = 1 |X = 0) = 0$$ I think I can say that $$Y \sim B(p_xp_y)$$
And
$$S = ...
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LCA with covariates: is it still worthwhile to use 1 step approach?
Dear statisticians' community,
I am trying to compute a Latent Class Analysis through Stata and/or R.
I built a 5 classes LCA model using poLCA on R and added a set of covariates.
It seems from the ...
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How do I incorporate sample size as a random variable in a latent interval censored model
I've got a dataset wherein only every third success in a series of n trials is observed. I had originally used the following Bayesian model:
$$
y_i \sim \mathtt{floor}(z_i / 3) \\
z_i \sim B(n_i, p_z) ...
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Multivariate longitudinal/repeated measures models: change in latent variables vs. latent change
Researchers often employ multivariate longitudinal/repeated meatures models when they collect multiple measures ($k\in K$) on each of multiple occasions ($t\in T$) for each of multiple units ($i \in N$...
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define latent variables and measurment model in SEM
Does a latent variable in SEM need to be defined by validated scale or can you "imagine" one?
For instance, I work on school participation (defined in research by attendance to school and ...
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Is there a way to estimate dependence between an observed variable and an unobserved variable?
I'm attempting to do some open-ended exploratory analysis/model building on real-valued time series data.
I am explicitly not assuming that all elements of my class of models are linear in the lagged ...
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Why do matrices of simulation data generated in R create strongly related latent variables?
When creating examples of matrices for CFA in R for students, I still have a problem with getting data that looks realistic - specifically, that between latent variables I often have covariance path ...
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When building a latent class model, what should be done with demographic variables?
To expand on the issue I'm having a bit:
I am trying to build a latent class model. The dataset I am working with contains some scales related to shopping habits, plus several demographic items (age, ...
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Can we use "subscale scores" as "observed variables" in SEM ? + dividing a model?
I am new to SEM. My aim is to determine which factors (several intrisic and serveral extrinsic) influence school participation in children with disabilities. Some of my latent variables are scores to ...