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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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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94 views

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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1answer
139 views

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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173 views

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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57 views

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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130 views

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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Caveats regarding the choice of the elementary panel model

Lets compare three panel most basic models: pooled, random effects, fixed effects. I observe common belief, that the fixed effect model estimation is "less biased", than in the other models. ...
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1answer
95 views

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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75 views

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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163 views

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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1answer
202 views

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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1answer
49 views

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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1answer
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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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243 views

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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1answer
396 views

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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1answer
31 views

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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1answer
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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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1answer
319 views

What are the "moment conditions" in the GMM method? Also: GMM vs IV vs 2SLS?

I keep seeing talk of 'moment conditions' or 'moment equations', but don't exactly understand the context. Consider a very standard regression model: $$y_i = \beta x_i + u_i $$ where $u_i$ is an ...
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What is an intuitive of definition of "point identification" (point identified parameter) in econometrics?

I've recently come across the notion of point identification in several econometric papers. See, e.g., https://scholar.harvard.edu/files/tamer/files/pie.pdf, who mentions point identification ...
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1answer
49 views

Can anyone show how the concept of Identifiability is geometrically/intuitively presented?

The motivation for this question comes from the following: When I was studying statistics for the first time long ago, no one presented the mathematical concepts behind linear regression, like the one ...
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1answer
39 views

How to deal with product coefficients in a nonlinear model?

I am considering a nonlinear regression model as the following: y=(ax)*(bz)+u, where the sample are IID, u is random error term such that E(u|x,z)=0, and a and b ...

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