Questions tagged [identifiability]
A model is identifiable if a single set of parameters can be found that will yield the best fit.
210
questions
1
vote
0
answers
14
views
Understanding why volatility in diffusion process $(X_t)_{t \in[0,T]}$ is identifiable/known for continuous observations, but the drift is not?
Why is it that when dealing with continuous time observations of a diffusion process $(X_t)_{t \in[0,T]}$, we say that the volatility $\sigma^2$ is "perfectly identifiable" and just usually ...
0
votes
0
answers
24
views
Identification of the transition probability of a time homogeneous MDP with subsampling
I am dealing with a MDP (or a temporal causal SEM) problem with missing observations. I want to know under what assumptions the transition probability can be identified from the observation.
...
0
votes
0
answers
6
views
Identification of Richer Conditional Expectation from Less Rich Ones
Let $X_1,X_2$ be uniformly distributed and suppose that we know the quantities $E[Y | c_1 X_1 + c_2 X_2 = v]$ for all values of $c_1,c_2,v$ (i.e. we know all of the expectation of $Y$ conditional on ...
2
votes
0
answers
30
views
An estimation method/algorithm for estimating the value of a specific parameter in a convex function
I am looking for an estimation/iteration process to estimate the value of a specific unobserved parameter of a convex function that fits the observed data of the other variables closely. Specifically, ...
1
vote
0
answers
15
views
How to get a confidence interval for each parameter in an stochastic optimization problem?
I'm using Differential Evolution to locate the global minimum in a search space with the objective function being the Root Mean Squared Error. I'm using a mathematical model with number of parameters $...
0
votes
1
answer
32
views
Beta distributed transition probability in CEA
I am reading a paper on cost-effective analysis and trying to replicate their results. (paper: https://ascopubs.org/doi/full/10.1200/GO.20.00288)
The probabilistic model in the paper assumes that the ...
2
votes
0
answers
55
views
Identification techniques when $E(u_i|\text{do}(X_i))\not=0$
In this article Chen & Pearl make the following 2 statements:
"Identification techniques are available for models in which X is far from satisfying $E(u_i|X_i)=0$" in response to Stock &...
0
votes
0
answers
15
views
Joint inference vs composition of estimators
I’m currently playing around with a toy problem at work.
Assume I have a bivariate distribution with four parameters which I want to estimate, two marginal parameters and two which steer dependence. I ...
0
votes
0
answers
9
views
How do I handle underidentification in Bifactor ESEMs?
I hope you can help me to find some answers to my questions.
Following Morin, Arens, & Marsh (2016; references below), I’m trying to conduct a bifactor exploratory structural equation model (...
0
votes
0
answers
22
views
Near-perfect "multicollinearity" between categorical variables in linear regression analysis
I have a panel dataset which consists of 100,000 observations and 30 variables. Two of the variables, one binary ($x_1$) and one categorical ($x_2$ with ~4000 categories), are nearly "collinear&...
0
votes
0
answers
26
views
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 ...
1
vote
1
answer
139
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 ...
0
votes
0
answers
27
views
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
$A\in \mathbb{R}^{d\times d}$ ...
2
votes
1
answer
110
views
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 ...
5
votes
3
answers
394
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.
...
1
vote
1
answer
29
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 $Y_{ig}^0,Y_{ig}^1,Y_{ig}^2$.
...
3
votes
1
answer
33
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 ...
0
votes
0
answers
13
views
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 ...
3
votes
2
answers
137
views
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 ...
2
votes
2
answers
175
views
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 \...
0
votes
0
answers
10
views
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 ...
1
vote
0
answers
28
views
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:
...
0
votes
0
answers
419
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 ...
1
vote
1
answer
48
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 ...
1
vote
1
answer
97
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,......
3
votes
1
answer
219
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 ...
4
votes
2
answers
281
views
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, ...
0
votes
0
answers
22
views
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 ...
2
votes
0
answers
27
views
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'...
0
votes
1
answer
89
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 ...
7
votes
1
answer
463
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 ...
1
vote
0
answers
140
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 $\...
1
vote
1
answer
112
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 ...
2
votes
1
answer
48
views
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 ...
1
vote
0
answers
82
views
Identification of correlated errors with multinominal probit
Consider the multinational probit model where we observe $Y_i \in \{1, \dots, K + l\}$ with
$$
\begin{align*}
Y_i = l \Leftrightarrow Z_l&\geq \max(Z_1,\dots Z_{K +1}\}
\qquad l \in \{1, \dots, ...
6
votes
2
answers
168
views
Identifying the correlation between a slope and a level
Throughout this post, I assume at least second moments exist. Consider a heterogeneous linear treatment effect model of the form:
$$Y_i = \alpha_i + \beta_i X_i$$
where $\alpha_i, \beta_i$ are ...
1
vote
0
answers
19
views
Quasi-experiment analysis
I have 5-year sales information from a grocery store in Canada. I want to check the effect of an online campaign that happened in 2017 on food sales. My treatment group is people living in urban areas....
0
votes
1
answer
275
views
Estimating LATE from RDD using OLS - Have I understood it correctly?
I am currently running a project using RDD in STATA where I am unable to use the handy "rdrobust" command, and hence have to use the conventional "regress" function instead, i.e., ...
1
vote
1
answer
57
views
Parameter identification and causal identification
When people say identification, do "parametric identification" and "causal identification" mean
completely different?
Ex) When performing ML estimation, the sentence that one ...
1
vote
1
answer
48
views
How to identify coefficients for all levels of categorical variables when you have multiple of them
I have an equation like y ~ x1 + x2 + x3 + x4 where the first 3 variables are categorical and the last one is continues. I want to identify the coefficients for all ...
5
votes
1
answer
149
views
Basic Questions about regression formula, sampling variability, and 'identification'
lets say I run the simple regression, $y_i = \beta_o + \beta_1x_i + \epsilon_i$.. Assume $cov(\epsilon,x)$=0
This yields the formula people write in terms of covariances for the slope parameter:
$\hat{...
0
votes
1
answer
53
views
Does 'As Good As Random' Have a rigorous definition in identification strategies?
If using an identificaton strategy such as differences in differences, Regression Discontinuities, or IV's, I see the phrase 'as good as random' used alot. Does this have a rigorous definition, or is ...
2
votes
1
answer
309
views
Does estimated fixed effects change if we change reference level?
Consider a fixed effect model $$y_{it}=x_{it}'\beta+\alpha_{i}+\epsilon_{it}$$
To estimate the fixed effects $\alpha_i$ we can add a dummy for each individual and run the least-squares dummy variables ...
4
votes
1
answer
92
views
Proving Identifiability Using Law of Large Numbers? [closed]
Well normally proving identifiability follows by showing that $p_{\theta}(x)=p_{\theta'}(x)$ implies $\theta=\theta'$. Usually this proceeds by showing that a function dependent on $\theta$, such as ...
1
vote
1
answer
122
views
Parameters identifiability / estimation in Bayesian linear state-space models
Is it possible to tell if the parameters can be uniquely estimated in a Bayesian state-space models from the system equations (beyond redundant parameterisations). If so, how?
For example, should it ...
3
votes
2
answers
146
views
Simultaneity in causal diagrams
Lets assume we have simultaneity problem. Variable x causes y and y causes x. As an example i would state alcoholism: the more respondent consumes alcohol, the more 'is' alcoholic (measured for ...
2
votes
1
answer
472
views
MLE Asymptotic Normality regularity conditions
I had this lecture of mathematical statistics about asymptotic normality of MLE. In order to prove this, a series of regularity conditions were stated, and the identifiability condition was among them....
0
votes
1
answer
32
views
fitting specific formula/model in r - model possibly not identifiable
I would like to fit the following formula in R:
y ~ alpha *(x1_0 * x2_0 * beta_0 + x1_1 * x2_1 * beta_1)
Here: alpha, ...
2
votes
1
answer
3k
views
Can't compute standard errors: the information matrix could not be inverted
I am trying to compute a Structural equation model.
I have identified one model, in which I have included all the subscales simultaneously. However, when I try to look at the subscales separately, I ...
1
vote
0
answers
17
views
How to verify identification of a model?
I have the system of simultaneous equations:
$$
\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_{...