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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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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18 views

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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62 views

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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25 views

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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23 views

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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79 views

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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38 views

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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88 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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82 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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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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54 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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247 views

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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126 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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81 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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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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162 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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152 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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45 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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28 views

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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213 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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93 views

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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114 views

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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363 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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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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2k views

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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234 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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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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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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38 views

calculate mean of normal distribution given SD and probability corresponding to a single range

Suppose that I have a normally distributed variable with unknown mean and known SD: $X \sim N(\mu, 1)$. I also know that $P(-2 < X < 2) = 0.3.$ Is it possible to calculate $\mu$ from this ...
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125 views

Parameter identification v. causal identification

As others, it seems (Identification of parameters problem), I get confused about the use of the word "identification" in econometrics. It seems some people talk about "identification" in the sense ...
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101 views

Identifiability vs. equivalence of probability measures

I'm a bit confused about the notion of identifiability vs. equivalence of probability measures. The following definition of identifiability I am familiar with: Let $\{P_\theta : \theta \in \...
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34 views

Marginal posterior distribution, likelihood mean sum of two standardnormal priors

How would I compute the marginal posterior distribution of $\mu_1$ and $\mu_2$ if the likelihood $(y | \mu_1,\mu_2) \sim N(\mu_1+\mu_2,1)$ and $\mu_i \sim N(0,1)$
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114 views

Time series DGP: No convergence to true parameter - Identification problem?

I set up a model, simulated some data and tried to infer the wanted parameter $\alpha$. However it seems that there may be no convergence to the true parameter (result is either $-\alpha$ or $+\alpha$)...

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