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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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
$$
u_y\equiv \begin{...
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Fixed Effects: Group level variables but individual level outcomes
tl;dr: In fixed effects and first difference estimation, does having sets of individuals where the change in $X_{it}$ over time is identical lead to estimation problems?
When using fixed effects (FE) ...
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0answers
13 views
Identifiability of parameters in a linear model when covariates are random
Suppose we have a linear model (in $\mathbb{R}^n$, say), $$y = X\beta + \epsilon $$
where $\bf{\epsilon}$ is Gaussian with mean $0$ and covariance matrix $\Sigma(\theta)$ where $\theta$ is an unknown ...
3
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0answers
39 views
Why is model unidentifiability a problem?
I am new to the concept of model identifiability, but from my understanding it is possible to learn the true parameter values of the model after obtaining an infinite number of observations from it. ...
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1answer
65 views
What does the sum to zero constraint mean?
In an ANOVA model, there is a constraint that the coefficients must sum to zero. What does this actually mean? I do understand the reason why you might want to make them sum to zero, i.e. to have two ...
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1answer
75 views
What does it mean to “non-parametrically” identify a causal effect within the super-population perspective in causal inference?
I am wondering, within the context of causal inference, what it means to "non-parametrically" identify a causal effect within the super-population perspective. For example, in Hernan/Robins Causal ...
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1answer
89 views
What does it mean if the Average Treatment Effect (ATE) in causal inference is not identifiable?
I read from the following slides on observational studies, pg. 16, Observational Studies, Keio,
that given:
$$
ATE ≡ E[Y_i(1) − Y_i(0)]
$$
They pose the following question: Can we identify the $ATE$...
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What is “identification assumptions” in econometrics? [closed]
I'm starting to study econometrics from Wooldridge's book. But some doubts arise regarding to the role of Conditional Expectations in Econometrics.
Wooldridge says that although it is not always ...
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57 views
Error variance may not be identified. LISREL
I am conducting CFA for a variable in my study. It has two sub-dimensions, say D1 and D2. On conducting CFA with only first-order factors, my model runs fine and there is a strong correlation among ...
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2answers
553 views
Can anyone help explain this basic example of posterior
I am having trouble understanding the authors reasoning here. It is from "The Bayesian Choice"
I am confused about why the posterior is initially written without depending on the data, and why we ...
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0answers
20 views
Alternatives to calculating the rank of the information matrix in determining if the model is identifiable
I have a known non-linear model $h \in \mathbf{R}^n$:
$$
y = h(\theta) + \epsilon,
$$
where $\theta\in \mathbf{R}^m$ is a parameter vector, and $\epsilon$ is a normal random variable with zero mean ...
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44 views
VECM with Multicollinearity
I have fit a vector error correction model (VECM) to some macroeconomic data. In particular, I am interested in three relationships
real GDP as a function of employment and real wages
employment as a ...
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0answers
18 views
Uniqueness on bayesian factor model's loading matrix
I'm doing uniqueness on factor loading matrix in a factor model.
$ y = \Lambda f + \epsilon$
where $ f \sim N(0,\Sigma)$ , $\epsilon \sim N(0,\Omega) $ and $\epsilon \perp f$.
It's well known that ...
0
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1answer
75 views
Reference smooth + smooth by all levels of a factor: is my GAM still identifiable?
I have speech signals sampled in 10-ms intervals ('$time$') in 8 different geographical regions ('$region$'), from 20 subjects each. For each of these regions, I want to know if the sampled trajectory ...
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1answer
535 views
Definition of softmax function
This question follows up on stats.stackexchange.com/q/233658
The logistic regression model for classes {0, 1} is
$$ \mathbb{P} (y = 1 \;|\; x) = \frac{\exp(w^T x)}{1 + \exp(w^T x)} \\
\mathbb{P} (y =...
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2answers
139 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 ...
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1answer
677 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
43 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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1answer
92 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
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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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0answers
38 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
180 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
49 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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255 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
532 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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1answer
117 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
32 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,...
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0answers
25 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
240 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
52 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
173 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
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1answer
209 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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2answers
122 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 ...
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0answers
180 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|...
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1answer
77 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 $\beta$ ...
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1answer
265 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 ...
2
votes
1answer
2k views
Sum-to-zero constraint in one-way ANOVA
I'm trying to understand my lecture notes but am a bit stuck on the concept of identifiability.
In one-way ANOVA, could someone please explain the reason for the constraint $\sum_{i=1}^{m} \beta_{j} = ...
4
votes
1answer
155 views
Fitting least squares when number of predictors are larger than instances
A statement from the book Introduction to Statistical learning with applications in R, didn't quite make sense to me. It says, "In cases when number of predictors are greater than the instances we ...
1
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1answer
98 views
Identifiability Versus Convexity
I'm a little unclear on the definitions of "identifiable" and "convex." Consider the case where $X_1, \ldots, X_n \overset{iid}{\sim} \text{Bernoulli}(p)$. Then our likelihood function is $L(p) = p^{\...
4
votes
3answers
101 views
Is there a term for dividing out a parameter to make model identifiable?
Suppose I have a nonlinear model of the form:
\begin{align}EY|X = \frac{aX}{aX+b}\end{align} where $a, X, b > 0$. I reparameterize the model as
\begin{align}
EY|X =\frac{\beta X}{1 + \beta X}
\...
2
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0answers
120 views
Choice specific variables in multinomial logistic regression
For a MNL regression, is it possible to include independent variables that are only populated for one of the choices? Let's say there are 3 choices an individual has. However, only choice 3 has an ...
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0answers
80 views
Identifying the parameters of a linear state-space-model using Kalman Filter
I have a linear state space model (SSM) that looks like this
\begin{align}
{\dot {x}} & = {\rm \textbf{A}}{x} + {\rm \textbf{B}}{u} \\
{y} & = {\...
1
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0answers
50 views
How to check if the parameter of a statistical model is identified?
I understand the definition of identifiability but I'm not sure how to check for it.
Could I just take the expectation of the distribution with two different parameters and show they are different in ...
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0answers
53 views
Linear moment inequality for layman
Can someone please explain Manski's approach to Partial Identification of Probability Distributions in very basic terms? I have gone through a lot of stuff but failed to find an intuitive explanation. ...
2
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1answer
171 views
Identifiability of ordered regression cutpoints
I have an ordered regression model as described in ?polr:
The ordered factor which is observed is which bin Y_i falls into with
breakpoints
zeta_0 = -Inf &...
1
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1answer
209 views
Alternative construction of ARMA(1,1) process
My question is related to the exercise 2.9, p. 79 in Brockwell & Davis, An Introduction to Time Series Analysis and Forecasting, 2nd edition, New-York, Springer, 2002 (It is also related to ...
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0answers
74 views
identification condition in factor model
Consider the following factor structure:
$\Sigma=\Lambda \Lambda' + \Phi$
where $\Sigma$ is $p \times p$, $\Lambda$ is $p \times m$ without any restrictions and $\Phi$ is a $p \times p$ diagonal ...
2
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0answers
37 views
Is this simultaneous equation model identified?
I have a 3 equation simultaneous equation model where all 3 dependent variables depend on each other (i.e. Y1 is based on Y2 and Y3; Y2 is based on Y1 and Y3; Y3 is based on Y1 and Y2).
Would all 3 ...
