Questions tagged [identifiability]
A model is identifiable if a single set of parameters can be found that will yield the best fit.
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Understanding why volatility in diffusion process $(X_t)_{t \in[0,T]}$ is identifiable/known for continuous observations, but the drift is not?
Why is it that when dealing with continuous time observations of a diffusion process $(X_t)_{t \in[0,T]}$, we say that the volatility $\sigma^2$ is "perfectly identifiable" and just usually ...
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Identification of the transition probability of a time homogeneous MDP with subsampling
I am dealing with a MDP (or a temporal causal SEM) problem with missing observations. I want to know under what assumptions the transition probability can be identified from the observation.
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Identification of Richer Conditional Expectation from Less Rich Ones
Let $X_1,X_2$ be uniformly distributed and suppose that we know the quantities $E[Y | c_1 X_1 + c_2 X_2 = v]$ for all values of $c_1,c_2,v$ (i.e. we know all of the expectation of $Y$ conditional on ...
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An estimation method/algorithm for estimating the value of a specific parameter in a convex function
I am looking for an estimation/iteration process to estimate the value of a specific unobserved parameter of a convex function that fits the observed data of the other variables closely. Specifically, ...
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How to get a confidence interval for each parameter in an stochastic optimization problem?
I'm using Differential Evolution to locate the global minimum in a search space with the objective function being the Root Mean Squared Error. I'm using a mathematical model with number of parameters $...
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Beta distributed transition probability in CEA
I am reading a paper on cost-effective analysis and trying to replicate their results. (paper: https://ascopubs.org/doi/full/10.1200/GO.20.00288)
The probabilistic model in the paper assumes that the ...
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Identification techniques when $E(u_i|\text{do}(X_i))\not=0$
In this article Chen & Pearl make the following 2 statements:
"Identification techniques are available for models in which X is far from satisfying $E(u_i|X_i)=0$" in response to Stock &...
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Joint inference vs composition of estimators
I’m currently playing around with a toy problem at work.
Assume I have a bivariate distribution with four parameters which I want to estimate, two marginal parameters and two which steer dependence. I ...
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How do I handle underidentification in Bifactor ESEMs?
I hope you can help me to find some answers to my questions.
Following Morin, Arens, & Marsh (2016; references below), I’m trying to conduct a bifactor exploratory structural equation model (...
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Near-perfect "multicollinearity" between categorical variables in linear regression analysis
I have a panel dataset which consists of 100,000 observations and 30 variables. Two of the variables, one binary ($x_1$) and one categorical ($x_2$ with ~4000 categories), are nearly "collinear&...
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Are Non-Parametric Models more "Identifiable" compared to Parametric Models?
Are Non-Parametric Models more "Identifiable" compared to Parametric Models?
I have read about the notion of "Identifiability" in statistics - Identifiability (or "Label ...
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Fix second-order factor loadings to equal in all second-order factors with two first-order factor indicators? CFA / SEM
I am conducting a CFA followed up by a SEM analysis. In my original model I had 13 latent variables. As some of these were highly correlated, I created second-order factors, of which 3 are indicated ...
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Expected value of log-likelihood and KL divergence
Background:
Let $x_t = Ax_{t-1} + w_t$ be a discrete linear time invariant system where:
$x_t \in \mathbb{R}^d$ for all time samples $t$ corresponds to the state vector
$A\in \mathbb{R}^{d\times d}$ ...
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What's the purpose of do-calculus?
I understand backdoor adjustment blocks backdoor paths and front door adjustment combines the causal effect of different nodes. The purpose of both is to eventually identify the causal effect of a ...
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Why do we need identification in causal inference?
I am reading Pearl's causality book and it states,
Identifiability ensures that the added assumptions conveyed by $M$ ... will supply the missing information without explicating $M$ in detail.
...
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Identification of structural parameters in a linear model (treatment effect context)
Suppose that we have $N$ observations indexed by $i=1,...,N$.
The observations are partitioned in three groups indexed by $g=1, 2,3$.
Here, we consider potential outcomes $Y_{ig}^0,Y_{ig}^1,Y_{ig}^2$.
...
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Identifiability of multivariate instrumental variable model
I'm interested in estimating the effects of $X_1$ and $X_2$ on $Y$ in the directed acyclic graph below. $U_1$ and $U_2$ are unobserved confounders. Based on Definition 7.4.1 on p. 248 of Causality ...
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Model identifiability based on loadings matrix
For $\textbf{y}=\mathbf{\mu}+\mathbf{\Lambda f}+\mathbf{\epsilon}$, let $\Phi=\textbf{cov}(\textbf{f})$ to be a $m\times m$ symmetric matrix containing $\frac{m(m+1)}{2}$ unique factor variances and ...
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Using a DAG to understand omitted variable bias in OLS vs Binary Dependent Variable Regression
Suppose I have three variables. $A$ and $U$ are continuous variables but $U$ is unobserved. $Y$ is the binary outcome. $A$ and $U$ are independent.
Let the true model be from the typical probit or ...
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A realistic example of a non identifiable model?
Given the definition of statistical model identifiability : identifiable iff $P_\theta = P_{\theta'} \implies \theta = \theta' ~~ \forall \theta, \theta' \in \Theta$ we can see that, for example, $X \...
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Can unobserved heterogeneity with factor loading identified in MLE?
I have a question on the identifiability when I do maximum likelihood estimation with logit model. I use discrete factor random effect model for the unobserved heterogeneity.
B is a binary outcome of ...
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Re-parameterization to resolve non-identifiability in this squiggly model (linear combination of logistic functions)?
So my desire here is to be able to capture a variety of temporal dynamics governing the change in value of some feature of interest. I want the model to be able to represent, for example, bounded:
...
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Maximum Likelihood For the Normal Distribution
I get using Maximum Likelihood Estimation to find unknown parameters of a function.
But in the normal distribution, we know probability density function is f(x)=1/σ√2π(e^−(x−μ)2/(2σ^2)) where μ is ...
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Identifiability of discrete HMM with categorical observations
My setup is simple. I have two categorical distributions with probabilities $p$ and $\tilde{p}$ that generate an observation depending on whether the hidden state is 1 or 0, respectively. In other ...
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A question on identification
This question is about how to show identification of the fixed effects in a static panel linear model.
A1 (model): The model is
$$
Y_{it}=\alpha_i+X_{it}^\top \beta+\epsilon_{it}
$$
for each $i=1,......
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What might be the identification challenges with a generalized DiD model where the treatment variable experiences reversals (switches on/off)?
I have a setting where my treatment variable experiences reversals across the panel units in a staggered adoption setting. To estimate the average treatment effects on the treated in a setting that ...
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Can I compare a just-identified model and an overidentified model?
As far as I understand, a just-identified model has zero degrees of freedom and its model fit indices do not make much sense. On the contrary, overidentified models have a meaningful chi-square, CFI, ...
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Properties of joint distribution over observed data generated after training a latent variable model
I have a Latent variable model like this
White nodes are observed and gray nodes are latent. $\theta = \{\theta_U, \theta_X, \theta_M, \theta_{MY}, \theta_{UY}\}$ are the parameters of this model ...
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How is this model identified?
I've built a pretty complex SEM model. I know computationally it's identified (i.e. it runs in R). But I'm having a hard time figuring out how to prove it's identified. The three sufficient rule doesn'...
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Effect on GARCH innovations after scaling by a constant
I wish to fit the innovations resulting from a GARCH (1,1) process to either a student-t or an NIG distribution. For stability, I had to scale my data before applying GARCH. How will this affect the ...
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What is the difference between Consistency and Identification?
Dear experienced friends, I start to learn Econometrics recently and there is a question really confuses me. Suppose we have a sample linear model
$$
y = \beta*X.
$$
From the definition, we know the ...
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Identifiable but has no consistent estimator
Let $P_\theta$ denote the distribution of the random variable $X$. The distribution depends on the parameter $\theta$ that lies in some parameter space $\Theta$. Consider a function $f(\theta)$ of $\...
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Why does estimability imply identifiability?
Let $P_{\theta}$ be the distribution (known up to a parameter $\theta$ in parameter space $\Theta$) of a random variable.
A parameter (function) $\gamma=g\left(\theta\right)$ is called identifiable if ...
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Is there a word or phrase to describe a model that is basically unidentifiable in practice?
So suppose we have a model $f(x|\theta)$ that is theoretically identifiable, so that $\theta_1 \neq \theta_2$ implies $f(x|\theta_1) \neq f(x|\theta_2)$.
However, suppose that data collection is very ...
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Identification of correlated errors with multinominal probit
Consider the multinational probit model where we observe $Y_i \in \{1, \dots, K + l\}$ with
$$
\begin{align*}
Y_i = l \Leftrightarrow Z_l&\geq \max(Z_1,\dots Z_{K +1}\}
\qquad l \in \{1, \dots, ...
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Identifying the correlation between a slope and a level
Throughout this post, I assume at least second moments exist. Consider a heterogeneous linear treatment effect model of the form:
$$Y_i = \alpha_i + \beta_i X_i$$
where $\alpha_i, \beta_i$ are ...
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Quasi-experiment analysis
I have 5-year sales information from a grocery store in Canada. I want to check the effect of an online campaign that happened in 2017 on food sales. My treatment group is people living in urban areas....
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Estimating LATE from RDD using OLS - Have I understood it correctly?
I am currently running a project using RDD in STATA where I am unable to use the handy "rdrobust" command, and hence have to use the conventional "regress" function instead, i.e., ...
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Parameter identification and causal identification
When people say identification, do "parametric identification" and "causal identification" mean
completely different?
Ex) When performing ML estimation, the sentence that one ...
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How to identify coefficients for all levels of categorical variables when you have multiple of them
I have an equation like y ~ x1 + x2 + x3 + x4 where the first 3 variables are categorical and the last one is continues. I want to identify the coefficients for all ...
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Basic Questions about regression formula, sampling variability, and 'identification'
lets say I run the simple regression, $y_i = \beta_o + \beta_1x_i + \epsilon_i$.. Assume $cov(\epsilon,x)$=0
This yields the formula people write in terms of covariances for the slope parameter:
$\hat{...
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Does 'As Good As Random' Have a rigorous definition in identification strategies?
If using an identificaton strategy such as differences in differences, Regression Discontinuities, or IV's, I see the phrase 'as good as random' used alot. Does this have a rigorous definition, or is ...
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Does estimated fixed effects change if we change reference level?
Consider a fixed effect model $$y_{it}=x_{it}'\beta+\alpha_{i}+\epsilon_{it}$$
To estimate the fixed effects $\alpha_i$ we can add a dummy for each individual and run the least-squares dummy variables ...
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Proving Identifiability Using Law of Large Numbers? [closed]
Well normally proving identifiability follows by showing that $p_{\theta}(x)=p_{\theta'}(x)$ implies $\theta=\theta'$. Usually this proceeds by showing that a function dependent on $\theta$, such as ...
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Parameters identifiability / estimation in Bayesian linear state-space models
Is it possible to tell if the parameters can be uniquely estimated in a Bayesian state-space models from the system equations (beyond redundant parameterisations). If so, how?
For example, should it ...
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Simultaneity in causal diagrams
Lets assume we have simultaneity problem. Variable x causes y and y causes x. As an example i would state alcoholism: the more respondent consumes alcohol, the more 'is' alcoholic (measured for ...
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MLE Asymptotic Normality regularity conditions
I had this lecture of mathematical statistics about asymptotic normality of MLE. In order to prove this, a series of regularity conditions were stated, and the identifiability condition was among them....
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fitting specific formula/model in r - model possibly not identifiable
I would like to fit the following formula in R:
y ~ alpha *(x1_0 * x2_0 * beta_0 + x1_1 * x2_1 * beta_1)
Here: alpha, ...
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Can't compute standard errors: the information matrix could not be inverted
I am trying to compute a Structural equation model.
I have identified one model, in which I have included all the subscales simultaneously. However, when I try to look at the subscales separately, I ...
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How to verify identification of a model?
I have the system of simultaneous equations:
$$
\begin{cases}
y_1 = b_{12}y_2 + b_{13}y_3 + a_{11}x_{12} + a_{13}x_3 \\
y_2 = b_{21}y_1 + a_{21}x_1 + a_{22}x_{2} \\
y_3 = b_{32}y_2 + a_{31}x_1 + a_{...
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