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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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 ...
2
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0answers
60 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 ...
3
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2answers
142 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 ...
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14 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 ...
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1answer
20 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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29 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-...
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1answer
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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0answers
20 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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36 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 ...
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31 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 (...
2
votes
1answer
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 $$y_i=\eta(...
0
votes
1answer
89 views
Identification of discrete choice models
Consider the classical Logit model. In particular, let $\mathcal{Y}\equiv (0,1,...,L)$ be the set of options available to consumers, where $0$ denotes the outside option. Let
$$
u_y\equiv \begin{...
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63 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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votes
0answers
15 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
votes
0answers
44 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
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 ...
3
votes
1answer
81 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
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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0answers
111 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 ...
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92 views
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 ...
6
votes
2answers
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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0answers
23 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 ...
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0answers
52 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
vote
0answers
20 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
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 ...
8
votes
1answer
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
$$ \mathbb{P} (y = 1 \;|\; x) = \frac{\exp(w^T x)}{1 + \exp(w^T x)} \\
\mathbb{P} (y =...
2
votes
2answers
172 views
Is this model identified?
Is this model identified? The paper is in plosone, but it seems to be that the combination of regression paths from PCS ~ MCS and ...
0
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1answer
995 views
just-identified model and over-identified model in the context of instrumental variable
According to this pdf, when number of instrument variable equals to the number of endogenous components, the model is said to be just-identified; if number of instrument variable is bigger than the ...
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0answers
52 views
Can every identifiable model be estimated by GMM?
Assume a model with parameters $\theta$ is identifiable. Then that means that for every probability distribution over observable variables $p(x|\theta)$, there is a unique parameter value $\theta$.
...
2
votes
1answer
116 views
What is a “weakly identified” parameterization?
I understand that a parameterization is identified if it's true that
$$
\theta_1 \neq \theta_2 \Rightarrow p(y|\theta_1) \neq p(y|\theta_2)
$$
Intuitively, it means that two different parameter ...
1
vote
1answer
1k 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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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
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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1answer
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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2answers
659 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 ...
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vote
1answer
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)$$
Doesn't this pinpoint the value of $\beta$, assuming that the sample size $...
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0answers
40 views
State Space model identification with Kalman Filter [duplicate]
If I have a standard state-space model where all parameters are unknown (coefficients and covariance matrices for both the state equation and observation equation) and I want to estimate it with the ...
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0answers
15 views
How to empirically identify trends exactly offseting each other?
Say a random variable $Y$ is affected by both $X$ and $Z$, in the following way (data generation process):
$$ y_t = a + bx_t + cz_t + \epsilon_t $$
where $\epsilon_t$ is a white noise.
Furthermore,...
2
votes
1answer
37 views
In Bayesian estimation, when can regression coefficients and scale parameter be jointly identifiable? When not?
Exercise 14.2 in Koop, Poirier and Tobias's book (i.e. Bayesian econometric methods) talks about the case that in probit model, the regression and scale parameter are not jointly identified.
I ...
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2answers
318 views
Is the following model parameterization identifiable?
Let $X_i's$ be independent $i=1,2...n$ with $X_i\sim N(\mu+\alpha_i, \sigma^2)$ for each $i$. Let $\theta=(\alpha_1,...\alpha_p,\mu,\sigma)$ and $P_\theta$ be the joint pdf of the $X_i's$.
So, $P_\...
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0answers
53 views
Verifying model identifiability via simulations
I'm working on a nonlinear mixed effects model with 4 parameters. I've simulated some data to fit my model to, and I would like to check that the model is identifiable. I'm trying to outline some ...
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0answers
212 views
Identifiability of Gaussian process parameters
The Gaussian process model (GP) is written as
$$y(x)=h(x)^{t}\boldsymbol\beta + f(x)+\epsilon(x)\qquad[1]$$
where $h(x)^{t}$ is a regression function such as $\left [1,x,x^{2} \right ]$ ; $\...
0
votes
1answer
322 views
Identifiability of Poisson parameters
Assume that you have two Poisson random variables, $y_{jk} ∼ Poi(\lambda_{jk} \psi_j)$ and $y_{kj}∼Poi(\lambda_{jk}\psi_k)$. I've read that this parameterization is not unique, but for me it is not ...
2
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2answers
128 views
How can we see that this model is identified?
Let the density function be given by
$$ 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 ...
1
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0answers
213 views
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|...
1
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1answer
79 views
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 $\beta$ ...
7
votes
1answer
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 ...
