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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Understanding well some definitions of identification in econometrics
In the context of parametric models with $\Theta$ being the parametr space and
$$\mathbf P :=\{ P_\theta : \theta \in \Theta \}$$
assume that $P$ denote the true distribution of the observed data $X$ ...
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How to interpret coefficient and marginal effect in probit when $\beta$ is not identified
Say we have the latent variable $y_i^*=x_i\beta-\epsilon_i$ and $\epsilon_i \sim N(0, \sigma^2)$.
$y_i^*/\sigma=x_i\beta/\sigma-u_i$ where $u_i=\epsilon_i/\sigma \sim N(0, 1)$, and so can use Probit ...
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Show by derivation why both Order and Rank conditions are needed for identification with instrumental variables
Why are both Order and Rank conditions needed for identification with instrumental variables?
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Enforce identifiability on model predictioins
I have a model (a neural network) which produces estimates for the parameters of latent random variables (e.g. the $\lambda$ param for an exponential distribution).
I don't observe the r.v. directly, ...
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Time-varying parameter estimates
I have some basic conceptual misunderstanding of how to back out parameter estimates from the following function:
$W_{it+1} = \alpha_1 \frac{R_{t+1}}{R_t} W_{it} + \alpha_2 \frac{R_{t+1}}{R_t^2} W_{it}...
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Identification of a model with normalization
Consider a model:
$$Y=\psi(X)+\epsilon$$
where $Y$ is an outcome variable, $X$ is covariates, $\psi(\cdot)$ is an unknown function, and $\epsilon$ is the error term.
Then, $E[Y|X]=\psi(X)+E[\epsilon|X]...
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Relaxing identifiability assumption for asymptotic normality of MLE
One of the regularity conditions for asymptotic normality of MLE is identifiability, for example, from this post is that if $\theta \ne \theta′ \Rightarrow f(x_i;\theta)\ne f(x_i;\theta′)$. From ...
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Online parameter estimation for inverse reinforcement learning
We have developed a novel interpretable RL paradigm for continuous actions where agents are compositions of trained prototypical agents with affinities for certain strategies; this aids strategy ...
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Formal Definition of Identification
This definition of identification (the bracketed part) is confusing to me because (based on my obvious misunderstanding) it fails for probit:
Probit with 2 covariates: $f=\Theta(X_1\theta_1+X_2\...
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Identifiability of a model with a marginalized parameter implies on the identifiability of the model without the marginalization?
I am researching the identifiability of a class of models with latent variables. Those models depend on some continuous parameters and some latent categorical variables. I found some results about the ...
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Using factor smooths as varying coefficients: Identifiability and identifiability constraints
I would like to use mgcv to build a model in which the effect of a covariable is modelled using a factor smooth as varying coefficient, i.e. the model
...
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How do we identify parameters in this simple model?
Consider the following model:
$$ y_{it}=\nu_{it}+\epsilon_{it}$$
$$\nu_{it}=\rho \nu_{it-1}+\zeta_{it}$$
Where $y_{it}$ is the income for $i$ at time $t$. $\epsilon_{it}$ is the idiosyncratic income ...
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How do we identify the parameters in this factor model?
Consider the following model:
$$ y_{it}=\nu_{it}+\epsilon_{it}$$
$$\nu_{it}=\rho \nu_{it-1}+\zeta_{it}$$
Where $y_{it}$ is the income for $i$ at time $t$. $\epsilon_{it}$ is the idiosyncratic income ...
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Can the parameters be identified separately in this model?
Suppose we have a model
$y_i=\epsilon_i^1+\epsilon_i^2$
$\epsilon_i^1\sim N(0,\sigma_1^2)$
$\epsilon_i^2\sim N(0,\sigma_2^2)$
$\epsilon_i^1\perp\epsilon_i^2$
Assume $y_i$ is i.i.d. I have derived the ...
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Identification of Latent Variables in Latent Dirichlet Allocation
I am building an Latent Dirichlet Allocation (LDA) model which estimates a version of the Author-Topic model developed by Rosen-Zvi, Griffiths, Steyvers and Smyth. The original paper is here
The ...
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Subspace method fails at identifying parameters in a state space system
I am trying to infer the parameters of a linear multivariate time-invariant state space system using a subspace method. However, the inferred parameters do not match the ground-truth parameters used ...
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Binomial Distribution $N, p$ parameters identifiability
Suppose that we have generated data from a Binomial distribution
$$ C_{1}, C_{2},..., C_{K} \sim Bin(N,p)$$
and our goal is to estimate both the parameters $N$ and $p$. I've see numerically (just ...
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How do Sparsity Priors help for Identifiability?
Let's say we have a Factor Analysis model with a latent variable $\mathbf{z}_t \in \mathbb{R}^k$:
$$x_t = A z_t + \epsilon_t, \qquad \epsilon_t \sim \mathcal{N}(0, \Sigma)$$
Let $A \in \mathbb{R}^{g\...
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How to transform parameters to obtain an "unbounded" Johnson distribution?
When applying the R fucntion SuppDists::FitJohnson() to data, the Johnson distribution parameters are automatically calculated, ...
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GEE correlation structure's number of parameters
I am kind of confused on GEE correlation structure's number of parameters. Say I have 10 students(or clusters) and I measure their physical strength 10 times for each of them with their corresponding ...
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Standardize table identifiers/names and merge them efficiently
I hope this is the right place to ask the following question.
I have N tables (N>1000). The rows (all, or some of them) of each table may (or may not) be merged with other rows in other tables, ...
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Is there an analytical equation for the uncertainty in an estimate of Weibull Modulus?
If I have a sample of $N$ measurements that follow a two-parameter Weibull distribution, how does the uncertainty in the estimate of the shape parameter (Weibull modulus, $k$) vary with $N$?
I've done ...
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Mathematical Definition of Parameters
I am currently trying to differentiate the parameters in the beta generalized Gompertz distribution by Benkhelifa which has the following CDF
and the following PDF
with all parameters being larger ...
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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 ...
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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.
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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 ...
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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, ...
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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 $...
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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 ...
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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 &...
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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 ...
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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 (...
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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&...
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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 ...
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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 ...
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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.
...
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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 $Y_{ig}^0,Y_{ig}^1,Y_{ig}^2$.
...
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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 ...
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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 ...
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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 \...
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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:
...
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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 ...
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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 ...
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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,......
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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 ...
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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, ...
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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'...
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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 ...
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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 $\...
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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 ...
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