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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446 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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786 views

Dealing with poor fit in an Item Response Theory model

I'm studying an online course with about 3000 students who each took several quizzes and I'm trying to apply Item Response Theory (using the ltm package in R) to model the questions, determine which ...
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404 views

How to save individual residuals from an observed endogenous variable in a structural equation model?

I am estimating a structural equation model in which two latent variables (with 4 indicators each) and the interaction between the two latent variables predict a single observed variable. I would like ...
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3answers
145 views

Hierarchical model: does leaving out a latent variable (hierarchy level) result in an equivalent model?

Say we have a hierarchical model: $$z_i \sim \mbox{Bernoulli}(\pi_i); \mbox{logit}(\pi_i) = ... \text{(linear function of covariates for site i)}$$ $$y_{i,j} \sim \mbox{Bernoulli}(z_i \cdot p_{i,j}) ...
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35 views

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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126 views

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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134 views

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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43 views

Measuring latent traits: Searching for a suitable model

There is a kind of a problem related to psychometrics I keep coming across in my research again and again. Unfortunately, I failed to find appropriate statistical model to solve it. Can anybody ...
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245 views

Expectation of Covariance Matrix for Deep Gaussian Processes

I am currently reading the paper entitled "Variational Auto-Encoded Deep Gaussian Processes" by Dai et al, a copy of which may be found here. The paper proposes a stacking of Gaussian Process Latent ...
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112 views

What happens when assumptions about the distribution of the latent variable in a GLMM are violated?

I am struggling with one assumption usually made when using linear mixed models: the nature of the distribution of the random factor. (The first part of the question is more about biology --whether ...
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559 views

How does the word distribution of a document relate to its topic distribution in LDA?

Suppose I trained an LDA model (latent dirichlet allocation). This gives me for each topic a word-distribution. Now I receive a new document and I want to calculate what the distribution of topics is ...
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298 views

Hidden Markov Model with several observations

I am a little bit familiar with Hidden Markov Models. I have always seen cases with only one layer of hidden states and one layer of observations. Now I wonder to see if there is a possibility to add ...
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34 views

Can I try several CFAs on the same data before choosing one for generating factor scores?

I'm interested in matching on latent constructs (see Raykov, 2012), and one way to do so is to match on factor scores generated by CFAs of the items (One could also match on the items themselves, but ...
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140 views

Appropriateness of Rasch for formative measurement models

I've spent several months thinking about the issue of whether or not it is appropriate to apply Rasch models to formative measurement models, and I'm looking to see whether anybody else has considered ...
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131 views

Can we reconstruct the hidden (latent) variables after executing EM?

The question is in the title. I know that EM algorithm could do maximum likelihood estimation for models that have latent variables. I would like to know can we get the (estimated) value of these ...
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53 views

How to get one composite score to represent a MIMIC factor (including both formative variables and reflective indicators)

I have a MIMIC model where the latent variable of interest has both formative causes and reflective indicators (as depicted in the figure). My question is: is there a way to get one composite score ...
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104 views

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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1answer
93 views

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
50 views

Significance testing on two groups (distributions) of many binomial distributions

Basically I have two (or more) different success probability generating distributions. In other words, there are two (or more) different (non-normal) distributions, which realize success probabilities ...
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64 views

Adjusting for selection bias in a structural topic model

I want to build a structural topic model that adjusts for selection bias into the sample of entities about whom documents are written. I wanted to use the stm R ...
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0answers
217 views

Latent variable model vs Random effects model?

What is the difference between a latent variable model and a random effects model. It appears to me that the idea is to model unobservable variables or heterogeneity in both models? Or, is latent ...
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0answers
272 views

Ordered Probit Model in R: Latent Variable and Threshold Parameters

I have recently started to improve my methodological skills and programming in R. For a study term paper I now want to run an ordered logit/probit model. The data I use are taken from the European ...
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16 views

Process monitoring: determining number of expected bad widgets in your sample. model set up

Set up: We are testing widgets. If a widget passed testing it moves out of the factory. If it failed we will test it up to 3 times. There are some number of widgets that will never pass even if we ...
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1answer
209 views

Gaussian Process Latent Variable Model Optimisation

I am attempting to implement the Nonlinear Gaussian Process Latent Variable Model, as per Lawrence 2005 and have the gradient with respect to the kernel as follows(Eq 10 in paper): $\frac{\partial L}{...
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111 views

Does a latent class model become unstable with large samples and dimensions?

I have a dataset of approx 2million individuals with 40 dichotomous variables signifying presence or not of diseases (e.g heart disease, asthma, etc.) along with some sociodemographic info. I have ...
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166 views

How to estimate a spatial weight matrix empirically?

Let $y$ be an n-vector of observations on the dependent variable and $X$ be the $n \times k$ design matrix with observations for $n$ units on $k$ variables. I aim to estimate a time-series cross-...
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0answers
51 views

Comparing approximating mixture distributions

Setup: Say I have some Bayesian predictive model I assume to be true for each observation $x_1$. Each $x_2$ is a latent/unseen/hidden random variable. The parameters are $\theta$. It's a mixture ...
2
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197 views

What is the preferred way to use deep learning to learn output distributions instead of point estimates?

I was wondering what would be the preferred model to use deep learning to learn an output distribution instead of a point estimate. Specifically, there might be the case that certain types of ...
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0answers
294 views

How to determine time complexity of EM algorithm of probabilistic PCA?

I was studying probabilistic PCA from Bishop's book. There an EM algorithm is provided to calculate principal subspace: Here $\mathbf M$ is $M\times M$ matrix, $\mathbf W$ is $D\times M$ matrix and $...
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0answers
101 views

A question regarding maximum likelihood conditional on observed and unobserved variables

Please consider the following likelihood function, $$ L(\theta)=\int_{\Re^u} f(y|x,u,\theta)h(u|\xi)\partial u, $$ where $y$ is a vector of observed dependent variables, $u$ is a vector of unobserved, ...
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185 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 (...
2
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0answers
218 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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315 views

latent variables versus model parameters

I am quite confused with the distinction between a latent variable and model parameters. So say I have two observed variables $x$ and $y$ and they have some unknown relationship between them i.e. $y =...
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293 views

Model validation in Bayesian statistics from a model with latent variables

I am working with some two-regime autoregressive models first introduced by Hamilton in 1989. The specific models is of no great concern to my question, but some variables within my autoregressive ...
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0answers
90 views

How to model the distribution over payouts from aggregate (sum) data?

The setting A user is presented with a number of options related to her search query. She chooses one of them. As a result, a payout is generated. The payout lies in the range [0.05, 0.50], but the ...
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0answers
63 views

Tricky latent parameter problem

I'm reinterpreting the data of some colleagues to see if I can't get at heterogeneity in grouped outcomes. Start with a decay process with two pools: $$ C_{it} = P_i e^{-k_{i}^{fast}t} + (1-P_i)e^{-...
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171 views

Testing graded response model thresholds for significance?

I have a data set in which two raters have each rated N samples using a 5-point ordinal rating scale. My primary interest is in whether these two raters make significantly different use of those ...
2
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0answers
100 views

Estimating the quantiles of a latent variable

I am trying to estimate the quantiles of the function $f(x_i)$ in the equation: $$ y_{it} = \alpha_i + f(x1_{it}, x2_{it}) + \epsilon_{it} $$ My current, probably naive, approach is to run the ...
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28 views

Can latent variables be used in Bayesian networks?

I have successfully implemented a hill climbing approach to Bayesian structure learning using a Gaussian Bayesian network. I want to now implement a more sophisticated model with latent variables. ...
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1answer
46 views

Estimate for structural equation model

I tried to find the estimate for SEM using R and Stata but I found that both estimates are different. ...
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0answers
128 views

Bayesian Nonparametric Latent feature model

For quite a long time I've been trying to understand the paper "Bayesian Nonparametric Latent feature model" (by Zoubin Ghahramani et al.) [http://mlg.eng.cam.ac.uk/zoubin/papers/GhaGriSol06.pdf]. In ...
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80 views

How is vector arithmetic and interpolation possible in the latent space of GANs?

In the DCGAN paper (Alec Radford et al.), the authors were able to perform vector arithmetic for semantic analogies by averaging the latent vectors of generated images with the same class. They've ...
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1answer
70 views

Outlier Detection Using VAE Latent Space

I am trying to perform outlier detection using VAE. Before I was performing the same task using normal autoencoder and I used reconstruction error. I trained the network, then I passed new samples as ...
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0answers
34 views

Variable reduction method for factor variables

I have answers from 16 multiple-choice questions, each with 4 unordered options, and I would like to apply a dimensionality reduction method on them. I was thinking of going for PCA, but then I ...
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0answers
36 views

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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0answers
57 views

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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2answers
847 views

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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2answers
34 views

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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0answers
997 views

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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0answers
108 views

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 ...