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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Is this empirical likelihood parameter identified?

I am writing my empirical likelihood function, but I do not know whether my model parameters can be identified. The data contains 4 columns, Z is treatment assignment, D is treatment, Y is metric and ...
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Why is $X$ not an identifiable statistical model

In my textbook, Identifiablity is defined as so: For any $\theta_1, \theta_2 \in \Theta$ , if $\theta_1 \neq \theta_2 \Rightarrow \Bbb P_{\theta_1} \neq \Bbb P_{\theta_2}$ , where $\Bbb P_{\theta}$ ...
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Moments of $Y=X_1 + X_2 X_3 + X_4 X_5 X_6 +\cdots$

The $X_i$'s are i.i.d. and $X$ denotes any of these random variables. We assume here that $|E(X)|<1$ to guarantee convergence. I am interested in particular in the third moment $E(Y^3)$. For the ...
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If $|E(X)|< 1$ and $E(X^2)<1$, can we have $1 - E(X^2) = (1 - E(X))^2$?

Of course $X=0$ works, but I am looking for a non-singular solution. I haven't made much progress to solve this problem. However, let $\mu_2 = E(X^2)$ and $\mu_1 = E(X)$. For the equality to hold, we ...
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Identifiability of a probability given a set of conditional independence statements and distributions

I am seeking help for finding papers demonstrating the identifiability of a probability given a set of conditional independence statements and a set of probability distributions. More specifically, I ...
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For MLE, why does the information inequality imply identifiability

Let $X = \langle X_1, \dots, X_n \rangle^{\top}$ be a finite sample of observation $X$ where $X \sim \mathbb{P}_{\theta_0}$ with $\theta_0 \in \Theta$ and density $f_X(x; \theta_0)$. The true ...
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parameters of ARMA process

Let $z_{t}$ be ARMA(1,1) process. $$ z_{t+1} = \phi z_{t} + \theta\varepsilon_{t} + \varepsilon_{t+1} $$ In order to have a stationary process we must have $|\phi| < 1$. This is clear. The auto-...
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63 views

ARMA model with MA coefficient greater than 1

Assume we have the following ARMA(1, 1) model: $$ z_{t+1} = \phi z_{t} + \theta \varepsilon_{t} + \varepsilon_{t+1}, $$ where $\varepsilon_{t}$ are i.i.d. with $var(\varepsilon_{t}) = \sigma^2$. A ...
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Identifiability in this Hierarchical Dynamic Factor Model

I am studying the dynamic factor model presented in "Dynamic Hierarchical Factor Models" by Moench, Ng, and Potter. A copy can be found here if you're interested in reading on your own. Consider the ...
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Profile Likelihood confidence interval

I am interested in obtaining profile likelihood confidence intervals for parameter identifiability. My cost function is the least square error between the data and some fitted approximation depending ...
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Model identifiability in SEM

I am trying to fit a model with a structure similar to others already published (see Nees et al., 2012 Neuropsychopharmacology). In particular, the model structure is organized in 3 latent variables (...
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61 views

Gaussian Processes and Identification/Identifiability Issues

I'm looking for references of Gaussian Processes and identification issues that may occur. For example, in Kennedy and O'Hagan's (2001) Bayesian Calibration of Computer Models, we have $$y_i=\eta(...
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Identification of discrete choice models

Consider the classical Logit model. In particular, let $\mathcal{Y}\equiv (0,1,...,L)$ be the set of options available to consumers, where $0$ denotes the outside option. Let $$ u_y\equiv \begin{...
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Fixed Effects: Group level variables but individual level outcomes

tl;dr: In fixed effects and first difference estimation, does having sets of individuals where the change in $X_{it}$ over time is identical lead to estimation problems? When using fixed effects (FE) ...
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Identifiability of parameters in a linear model when covariates are random

Suppose we have a linear model (in $\mathbb{R}^n$, say), $$y = X\beta + \epsilon $$ where $\bf{\epsilon}$ is Gaussian with mean $0$ and covariance matrix $\Sigma(\theta)$ where $\theta$ is an unknown ...
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Why is model unidentifiability a problem?

I am new to the concept of model identifiability, but from my understanding it is possible to learn the true parameter values of the model after obtaining an infinite number of observations from it. ...
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396 views

What does the sum to zero constraint mean?

In an ANOVA model, there is a constraint that the coefficients must sum to zero. What does this actually mean? I do understand the reason why you might want to make them sum to zero, i.e. to have two ...
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What does it mean to “non-parametrically” identify a causal effect within the super-population perspective in causal inference?

I am wondering, within the context of causal inference, what it means to "non-parametrically" identify a causal effect within the super-population perspective. For example, in Hernan/Robins Causal ...
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GLMM in R doesn't converge, nearly unidentifiable [duplicate]

I'm building my GLMM using r. ...
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1answer
109 views

What does it mean if the Average Treatment Effect (ATE) in causal inference is not identifiable?

I read from the following slides on observational studies, pg. 16, Observational Studies, Keio, that given: $$ ATE ≡ E[Y_i(1) − Y_i(0)] $$ They pose the following question: Can we identify the $ATE$...
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What is “identification assumptions” in econometrics? [closed]

I'm starting to study econometrics from Wooldridge's book. But some doubts arise regarding to the role of Conditional Expectations in Econometrics. Wooldridge says that although it is not always ...
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Error variance may not be identified. LISREL

I am conducting CFA for a variable in my study. It has two sub-dimensions, say D1 and D2. On conducting CFA with only first-order factors, my model runs fine and there is a strong correlation among ...
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556 views

Can anyone help explain this basic example of posterior

I am having trouble understanding the authors reasoning here. It is from "The Bayesian Choice" I am confused about why the posterior is initially written without depending on the data, and why we ...
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Alternatives to calculating the rank of the information matrix in determining if the model is identifiable

I have a known non-linear model $h \in \mathbf{R}^n$: $$ y = h(\theta) + \epsilon, $$ where $\theta\in \mathbf{R}^m$ is a parameter vector, and $\epsilon$ is a normal random variable with zero mean ...
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VECM with Multicollinearity

I have fit a vector error correction model (VECM) to some macroeconomic data. In particular, I am interested in three relationships real GDP as a function of employment and real wages employment as a ...
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Uniqueness on bayesian factor model's loading matrix

I'm doing uniqueness on factor loading matrix in a factor model. $ y = \Lambda f + \epsilon$ where $ f \sim N(0,\Sigma)$ , $\epsilon \sim N(0,\Omega) $ and $\epsilon \perp f$. It's well known that ...
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144 views

Reference smooth + smooth by all levels of a factor: is my GAM still identifiable?

I have speech signals sampled in 10-ms intervals ('$time$') in 8 different geographical regions ('$region$'), from 20 subjects each. For each of these regions, I want to know if the sampled trajectory ...
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616 views

Definition of softmax function

This question follows up on stats.stackexchange.com/q/233658 The logistic regression model for classes {0, 1} is $$ \mathbb{P} (y = 1 \;|\; x) = \frac{\exp(w^T x)}{1 + \exp(w^T x)} \\ \mathbb{P} (y =...
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Is this model identified?

Is this model identified? The paper is in plosone, but it seems to be that the combination of regression paths from PCS ~ MCS and ...
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995 views

just-identified model and over-identified model in the context of instrumental variable

According to this pdf, when number of instrument variable equals to the number of endogenous components, the model is said to be just-identified; if number of instrument variable is bigger than the ...
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Can every identifiable model be estimated by GMM?

Assume a model with parameters $\theta$ is identifiable. Then that means that for every probability distribution over observable variables $p(x|\theta)$, there is a unique parameter value $\theta$. ...
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116 views

What is a “weakly identified” parameterization?

I understand that a parameterization is identified if it's true that $$ \theta_1 \neq \theta_2 \Rightarrow p(y|\theta_1) \neq p(y|\theta_2) $$ Intuitively, it means that two different parameter ...
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1answer
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Assumptions of MLE

I am currently reading up on Maximum Likelihood Estimation in Studies in Econometric Method. When describing the requirements for MLE to be consistent, they described it as the following: A number ...
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A test of my understanding of identification

I've been asking a few questions about identification lately, so forgive me for another one: Throughout this question, let $\mathbb P$ denote the set of probability distributions consistent with the ...
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213 views

When a prior distribution would not be overwhelmed by data, regardless of the sample size?

I came across a question 8 at the end of chapter 3 of the book: "Give two simple examples showing a case in which a prior distribution would not be overwhelmed by data, regardless of the sample size"...
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51 views

Estimate a parameter from subset of the data, other parameters from all data

I use Bayesian random effects models [$y_i \sim bernoulli\_logit(\beta + \alpha_{subj})$ $\alpha_{subj} \sim normal(0, \gamma)$], the $y$ outcome is binary. Part of the subjects have two observations,...
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324 views

Linear regression model identifiable?

I understand the concept of identifiability in the context of distributions. This is $f$ is identifiable if $f(x;\theta) = f(x;\theta')$ for all $x$, if and only if $\theta=\theta'$. However, in the ...
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Identifiability of neural network models

It's quite intuitive that most neural network topologies/architectures are not identifiable. But what are some well-known results in the field? Are there simple conditions which allow/prevent ...
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131 views

What's wrong with this argument that the parameter $\beta$ is always identified in the linear regression model?

If we have a linear regression model $y=X\beta + e$, then $E(y)=E(X\beta)+E(e)=E(X)\beta + 0$ Therefore $$E(X)\beta = E(y)$$ Doesn't this pinpoint the value of $\beta$, assuming that the sample size $...
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State Space model identification with Kalman Filter [duplicate]

If I have a standard state-space model where all parameters are unknown (coefficients and covariance matrices for both the state equation and observation equation) and I want to estimate it with the ...
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How to empirically identify trends exactly offseting each other?

Say a random variable $Y$ is affected by both $X$ and $Z$, in the following way (data generation process): $$ y_t = a + bx_t + cz_t + \epsilon_t $$ where $\epsilon_t$ is a white noise. Furthermore,...
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In Bayesian estimation, when can regression coefficients and scale parameter be jointly identifiable? When not?

Exercise 14.2 in Koop, Poirier and Tobias's book (i.e. Bayesian econometric methods) talks about the case that in probit model, the regression and scale parameter are not jointly identified. I ...
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318 views

Is the following model parameterization identifiable?

Let $X_i's$ be independent $i=1,2...n$ with $X_i\sim N(\mu+\alpha_i, \sigma^2)$ for each $i$. Let $\theta=(\alpha_1,...\alpha_p,\mu,\sigma)$ and $P_\theta$ be the joint pdf of the $X_i's$. So, $P_\...
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Verifying model identifiability via simulations

I'm working on a nonlinear mixed effects model with 4 parameters. I've simulated some data to fit my model to, and I would like to check that the model is identifiable. I'm trying to outline some ...
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Identifiability of Gaussian process parameters

The Gaussian process model (GP) is written as $$y(x)=h(x)^{t}\boldsymbol\beta + f(x)+\epsilon(x)\qquad[1]$$ where $h(x)^{t}$ is a regression function such as $\left [1,x,x^{2} \right ]$ ; $\...
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322 views

Identifiability of Poisson parameters

Assume that you have two Poisson random variables, $y_{jk} ∼ Poi(\lambda_{jk} \psi_j)$ and $y_{kj}∼Poi(\lambda_{jk}\psi_k)$. I've read that this parameterization is not unique, but for me it is not ...
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How can we see that this model is identified?

Let the density function be given by $$ f(x;a,b) = \frac{a + 2 b g(x) + (1-a-b) g(x)^2}{(1-x)(2 b g(x) + (1-a-b) g(x)^2)}$$ where $a$ and $b$ are parameters of interest and $g(x)$ is a known ...
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Get different results with different sampling order in Gibbs sampling: what could be wrong?

In sampling a complex spatio-temporal model by Gibbs sampling, I found if I change the order of sampling (for example, to sample $P(\theta_1,\theta_2|D)$, in one try, I sample $\theta_1\sim P(\theta_1|...
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1answer
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Stochastic volatility model - why not identified?

For the following model $y_t = \beta e^{h_t/2} \epsilon_t$ $h_{t+1} = \mu + \phi(h_t - \mu) + \sigma_n \eta_t$ this Kim et al (1998) paper writes that For identifiability reasons either $\beta$ ...
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310 views

Identifiability in a nonlinear regression problem

Suppose I'm working with the following model $y_i = \alpha(1-\exp(-\beta t_i))+\gamma(1-\exp(-\delta t_i)) + \varepsilon_i$. The $\varepsilon_i$ are i.i.d. gaussian with zero mean and I'm trying to ...