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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questions
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Identifiability of ANOVA model
Suppose that random variables $Y_{ij}$ are observed according to the overparameterised one way ANOVA model i.e
$$Y_{ij}=\mu+T_i+\epsilon_{ij}$$
Show that without some restriction on the parameters, ...
4
votes
1answer
82 views
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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1answer
58 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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1answer
82 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
26 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
25 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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0answers
33 views
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
48 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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The Hansen-Sargan test for overidentification and the choice of quadratic loss function
According to my professor, the Hansen-Sargan statistic is: $HS=nQ(b_{2sls})$ ~ $\chi ^2_{L-K} $ asymptotically, where $L$ is the number of moment restrictions, $K$ is the number of unknown parameters, ...
2
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1answer
35 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 ...
1
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1answer
16 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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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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1answer
30 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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113 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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25 views
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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0answers
132 views
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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153 views
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 ...
2
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0answers
28 views
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 ...
2
votes
1answer
42 views
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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41 views
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-...
0
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1answer
248 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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0answers
29 views
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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48 views
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 ...
0
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0answers
46 views
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 (...
4
votes
1answer
109 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 $$y_i=\eta(...
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1answer
97 views
Identification of discrete choice models
Consider the classical Logit model. In particular, let $\mathcal{Y}\equiv (0,1,...,L)$ be the set of options available to consumers, where $0$ denotes the outside option. Let
$$
u_y\equiv \begin{...
3
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0answers
131 views
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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0answers
18 views
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 ...
3
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0answers
49 views
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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1answer
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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 ...
4
votes
1answer
94 views
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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1answer
137 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:
$$
ATE ā” E[Y_i(1) ā Y_i(0)]
$$
They pose the following question: Can we identify the $ATE$...
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0answers
246 views
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 ...
6
votes
2answers
563 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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0answers
36 views
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 ...
2
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0answers
68 views
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 ...
1
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0answers
24 views
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 ...
0
votes
1answer
258 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 ...
8
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1answer
766 views
Definition of softmax function
This question follows up on stats.stackexchange.com/q/233658
The logistic regression model for classes {0, 1} is
$$ \mathbb{P} (y = 1 \;|\; x) = \frac{\exp(w^T x)}{1 + \exp(w^T x)} \\
\mathbb{P} (y =...
2
votes
2answers
238 views
Is this model identified?
Is this model identified? The paper is in plosone, but it seems to be that the combination of regression paths from PCS ~ MCS and ...
0
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1answer
2k views
just-identified model and over-identified model in the context of instrumental variable
According to this pdf, when number of instrument variable equals to the number of endogenous components, the model is said to be just-identified; if number of instrument variable is bigger than the ...
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0answers
58 views
Can every identifiable model be estimated by GMM?
Assume a model with parameters $\theta$ is identifiable. Then that means that for every probability distribution over observable variables $p(x|\theta)$, there is a unique parameter value $\theta$.
...
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votes
2answers
172 views
What is a “weakly identified” parameterization?
I understand that a parameterization is identified if it's true that
$$
\theta_1 \neq \theta_2 \Rightarrow p(y|\theta_1) \neq p(y|\theta_2)
$$
Intuitively, it means that two different parameter ...
2
votes
1answer
2k views
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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0answers
39 views
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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2answers
270 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"...
0
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1answer
69 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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0answers
440 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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2answers
906 views
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 ...
