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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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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, ...,...
user_15's user avatar
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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 ...
levitatmas's user avatar
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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 ...
Daniel Caetano's user avatar
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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 ...
BlackSith's user avatar
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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) ...
PAM's user avatar
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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 ...
j.rahilly_UCL's user avatar
5 votes
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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}) \...
jason 1's user avatar
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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 ...
Maurice Pasternak's user avatar
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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 \...
poki456's user avatar
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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 ...
sanK's user avatar
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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 - ...
Miljan's user avatar
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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/...
Max M's user avatar
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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; ...
ila's user avatar
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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 (...
jason 1's user avatar
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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 ...
user321797's user avatar
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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 ...
medium-dimensional's user avatar
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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+...
Richard Hardy's user avatar
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irt hybrid model predict latent estimate using bayesian method

I'm having some problem about irt prediction model. When i use irt hybrid model, it cannot predict the latent value even it has successfully converge during the irt model processed. It contain binary ...
梁聖宇's user avatar
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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 ...
Riccardo Buscicchio's user avatar
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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?

I recently saw a case where someone fit a SEM with 20 latent variables (with many indicators each) predicting a single latent variable (of several indicators), and suggested it was evidence for some ...
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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 ...
Chris's user avatar
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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) ...
Chris's user avatar
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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 ...
statsplease's user avatar
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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 ...
Colin T Bowers's user avatar
3 votes
2 answers
270 views

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 ...
Matt W's user avatar
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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 ...
Alina's user avatar
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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. ...
Saeed Hedayatian's user avatar
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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 ...
Diego Andrés's user avatar
2 votes
1 answer
90 views

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 ...
EmH's user avatar
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1 answer
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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 = ...
Knz's user avatar
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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 ...
Irene 's user avatar
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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) ...
Lemonici's user avatar
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Methods to identify a latent sistematic source of noise

I am working on modeling the relationship between various biomedical variables (age, sex, diseases ...) and DNA methylation data. DNA methylation data consists of percentages of methylation at many ...
SunScript's user avatar
2 votes
1 answer
60 views

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 ($i \in N$...
socialscientist's user avatar
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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 ...
Adeline Lacroix's user avatar
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31 views

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 ...
QMath's user avatar
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3 votes
3 answers
152 views

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 ...
kwadratens's user avatar
1 vote
1 answer
98 views

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, ...
Sven Ferguson's user avatar
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1 answer
185 views

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 ...
Adeline Lacroix's user avatar
2 votes
0 answers
15 views

Uniqueness of a Latent Representation Under Monotonicity Condition?

Suppose that I observe a bi-variate joint distribution over two random variables, $(X_1,X_2)$. I want to represent this joint distribution as arising from a function $F$ applied to i.i.d. uniform ...
stats_model's user avatar
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2 answers
106 views

How to understand the binary latent variable z in GMM model?

GMM(Gaussian Mixture Model) itself is a mixture of Gaussian with each having the proportion of $\pi_k$, $$\sum_{k=1}^{K}\pi_k=1$$this is easy to understand. But when introducing the latent, I don't ...
user3153824's user avatar
1 vote
2 answers
73 views

Risk perception measurement using CFA - Items with different scale

I am working on my risk perception model using three measures- probability, affection, and severity. I have one item on a Likert scale (1-5) for each probability and affection. However, for the ...
Snehalata Sainjoo's user avatar
1 vote
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142 views

Implementing bias-adjustion for step3 latent profile analysis in R [closed]

I am identifying a latent profile model with the Mclust package in R. After identifying an optimal number of cluster I would like to identify possible covariates and distal outcomes via logistic/...
David Janda's user avatar
3 votes
2 answers
355 views

In measurement invariance testing, how can one differentiate between differences in response styles and differences in latent means?

I am trying to establish measurement invariance between two groups on a depression measure: high-school aged boys and high-school aged girls. Though my entire sample reports elevated depression ...
ila's user avatar
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3 votes
2 answers
75 views

Causal modeling in the presence of a latent variable

Suppose that four variables of $X$, $Y$, $L$, and $C$ have the following relationships in the form of directed acyclic graph. $X$, $Y$, and $C$ are observable variables while $L$ is a latent (...
bluepole's user avatar
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What is the difference between a Latent variable model and a Tobit model?

Wooldridge Introductory Econometrics: A Modern Approach (2018), pages 561 and 572, gives the following definitions: Latent variable model (LVM): $$ y^*=\beta_0+\mathbf{x} \boldsymbol{\beta}+e, y=1\...
Tomas R's user avatar
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Cross-level influence in multilevel model for longitudinal data with time-invariant outcome

I don't have a lot of experience with multilevel models and Mplus, so I'm unsure if my approach is appropriate. I would therefore be very grateful for any help and feedback! I have data from an ...
Jonas's user avatar
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