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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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A model suffering from omitted variable bias can be said to be unidentified?

If my regression model $$ y_i = \alpha + \beta x_i + \epsilon_i $$ suffers from OVB the error contains one variable which we assume correlated with $$ \epsilon_i = \gamma w_i + u_i $$ my estimate of $\...
Three Diag's user avatar
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Connection between multicollinearity and problem of identification in Simultaneous Equations Model

Is there any connection between multicollinearity and problem of identification in Simultaneous Equations Model? I know Multicollinearity is the occurrence of high intercorrelations among two or more ...
CrunchySia24's user avatar
3 votes
1 answer
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Understanding how to evaluate the integral causal-effect expression

I have this expression $$ p( Y \mid \text{do}(Z=z)) = \int_{B, S, W, X} dBdSdWdX \ \ P(B | S) P(W | B, S) P(X | B, S, Z=z) \left[ \int_{Z'} dZ' P(Z'| B,S,W) P(Y | B, S, W, X, Z') P(S) \right] $$ ...
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Identification problems in the Heckit model

Consider the Heckit model with observables $(y,x,z,d)$ for which \begin{align*} y^*&=x'\theta+\epsilon\\ y&=dy^*\\ d&=\mathbb{1}(x'\pi_1+z'\pi_2\geq-\eta)\\ (\epsilon,\eta)&\perp (x,z)\...
Ludwig Gershwin's user avatar
1 vote
1 answer
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mgcv GAM identifiability constraints

When fitting GAMs in mgcv package in R using smooth function, an identifiability constraint is typically imposed, such that smooth function should sum to zero (thus, addition of the main effect is ...
NeuroPanda's user avatar
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Matern covariance increasing with smoothness

Consider the Matern covariance function with the following parametrization: $$C_{\nu,\phi,\sigma}(h) = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)}\left(\sqrt{2\nu}\frac{h}{\phi} \right)^\nu K_\nu (\sqrt{2\...
Tommy Tang's user avatar
7 votes
1 answer
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How to identify parameters to test asymmetric effect in a structural model

I am estimating an likelihood function (a structural model). A part of the likelihood function is that $$ p_t=p_{t-1}k_1+x_t(1-k_1) \quad if \ x_t=1 $$ $$ p_t=p_{t-1}k_2+x_t(1-k_2) \quad if \ x_t=0 $$ ...
jasmine's user avatar
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2 votes
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Interpreting eigenvalues of non-normalized covariance matrix of physical system

Cross-posted from physics stackexchange Summary: Eigenvalues of a "non-normalized" covariance matrix of time-series measurements from a linear system have units of Action (energy * time). ...
user3716267's user avatar
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What type of rotational invariance information can I get from interest points (coordinates) of corners from an image?

Assume that you are using the FAST algoritm for corner/feature detection. You pick an image and run the FAST algorithm. Question: All these green dots are actully coordinates in x and y direction. ...
euraad's user avatar
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biased estimation of variable correlated with endogenous variable

I have the following model: $ X = \alpha_1 + aZ + \epsilon_1 \\ Y = \alpha_2 + bZ + cX + \epsilon_2 $ Suppose that $Z$ is randomly assigned but $X$ is correlated with the error term $\epsilon_2$, in ...
Eaman's user avatar
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1 vote
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Matching Simulated Moments Perfectly in Practice

Several sources suggest that when estimating a model using the simulated method of moments (SMM), one ought to always be able to get the difference between the empirical and simulated moments to be 0 ...
user400346's user avatar
1 vote
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24 views

Does endogeneity imply non-identification?

My understanding of identification is that it means we can uniquely determine a value of a parameter in a model, given an infinite amount of data of the variables in our model. E.g. If we had a simple ...
Will's user avatar
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Imposing an arbitrary constraint on a overparametrized ANOVA model

Casella & Berger 2nd ed. stated that $\tag{11.2.2}Y_{ij}=\mu+\tau_i+\epsilon_{ij},\quad i=1,\cdots,k,\quad j=1,\cdots,n_i$ is an overparameterized model such that a constraint on $\tau_i$ should ...
wdg's user avatar
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Determining the Identifiability of Models

I am completing exercises in the book Mathematical Statistics: Basic Ideas and Selected Topics regarding proving or disproving that a model is identifiable. The problem I am struggling with considers $...
YessuhYessuhYessuh's user avatar
2 votes
1 answer
138 views

Latent growth curve model: The variance-covariance matrix of the estimated parameters (vcov) does not appear to be positive definite

I have run a latent growth curve model in R using lavaan and got the below warning. It would be good to hear suggestions on how to resolve this warning. The full output is below. Note that I dummy-...
Aepkr's user avatar
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1 vote
2 answers
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Why do we need to generate a random prediction in logistic regression? [closed]

I am trying to understand theory from my Model Identification And Data Analysis course at University. The example I am referring to is the probability of predicting a heart attack. Essentially, from ...
Mattia Iezzi's user avatar
2 votes
1 answer
127 views

Constructing a structural equation model/causal graph

I would like to understand some intuitions behind the following causal graph/SCM. Where as $X_1, X_2$ are expenditure on promotional activities. My main interest lies in understanding the fact that ...
jack's user avatar
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0 answers
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Are one-to-one levels structurally identifiable in a multilevel model?

I have three categorical variables $A$, $B$, and $C$ representing three different levels of spatial regions. Every element of the image of $C$ is a proper subregion of $B$, and likewise for $B$ in ...
Galen's user avatar
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Linear Model, Identification of Structural Parameter

I'm reviewing the foundations of linear regression using Wooldridge's Econometric Analysis of Cross Section and Panel Data and Cameron and Trivedi's Microeconometrics : Methods and Applications. The ...
ECON10105's user avatar
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Is ARMA fit well-defined?

My question is whether unique time series has a unique set of ARMA parameters that fit it best, once order of AR and MA have been chosen. For simplicity, I will ask only about ARMA(1,1) process. Lets ...
Cryo's user avatar
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Is identification assumption a necessary condition for causal inference?

I am confused about the identification assumptions mentioned in learning pearls causal inference book . May I ask is identification assumption a necessary condition for causal inference?
Leonard's user avatar
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6 votes
1 answer
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No more than $n$ moose, but how many?

Introduction I am thinking about how to estimate the number of individual moose from wildlife camera photos. I have the latitude and longitude position of each observation, along with a datetime of ...
Galen's user avatar
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1 vote
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Identification of Non-Gaussian State Space Model

The following paper details necessary assumptions in order to have a non-gaussian state-space model be identifiable (see A1-A5); 'A General Linear Non-Gaussian State-Space Model: Identifiability, ...
PatrickStar's user avatar
3 votes
2 answers
161 views

Estimating parameters of hypergeometric distribution when population size is unknown

I am given a bag containing marbles of two colors, with an unknown total number of marbles $N$. I randomly sample $n$ marbles ($n=n_1+n_2 < N$, where $n_1$ and $n_2$ are the number or marbles of ...
jpg0101's user avatar
  • 31
3 votes
2 answers
414 views

How do we Deal with Identifiability Problems in Statistics?

In statistics, are there any common strategies to deal with non-identifiable models? For example, I have heard that mixture models (i.e. based on weighted sums of normal probability distributions) can ...
stats_noob's user avatar
2 votes
0 answers
43 views

Are the weights of a linear combination of identifiable Bayesian parameters predicting another variable also identifiable?

Suppose I have a statistical model with observed random variables $X_1, \ldots, X_m$ and Bayesian parameters $\theta_1, \ldots, \theta_n$ that are identifiable. Now I want to extend my model by ...
Galen's user avatar
  • 9,381
1 vote
1 answer
182 views

Understanding Identifiability problem of multiple smooths in GAMs/Additive models

I am a beginner into additive models and GAMs, but have good enough knowledge of linear regression. I was going through this wikipedia article to understand more, but can't seem to understand the ...
user101874's user avatar
2 votes
0 answers
15 views

Uniqueness of a Latent Representation Under Monotonicity Condition?

Suppose that I observe a bi-variate joint distribution over two random variables, $(X_1,X_2)$. I want to represent this joint distribution as arising from a function $F$ applied to i.i.d. uniform ...
stats_model's user avatar
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2 votes
1 answer
38 views

In what cases is identification not possible in causal inference?

In step one of judea pearls causal inference book it is to define your graphical causal model. The second step is identification of the estimand for estimation in step 3. Are there any cases where ...
Maths12's user avatar
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2 answers
40 views

How do you know when the reason for a SEM being unidentified is because of the very variables that you put in?

How do you know when a SEM shows as unidentified not because of the path diagram but because of the actual variables that you put in? The following model is well-identified according to AMOS, but when ...
Arnaud Mortier's user avatar
0 votes
1 answer
65 views

Instrumental variable identifiability in a linear setting in the presence of unobserved confounders

Long story short, I'm seeing in the literature that linear instrumental variables models are identifiable, even in the presence of unobserved confounders. The unobserved confounding aspect befuddles ...
mortonjt's user avatar
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0 answers
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How to stationarise a univariate time series in R when auto.arima gives a model to fit that doesn't stationarise it? [closed]

I am currently working on a univariate time series that I try to modelize (following the Box-Jenkins methodology, I try to identify the model before I estimate it, using correlograms, in order to ...
gerardlambert's user avatar
0 votes
1 answer
1k views

Probit with "fixed effects"

I know that it is not possible to run a fixed effects probit model, when fixed effects are at the individual level. In other words, it is not possible to estimate $\alpha_i$ for each individual $i$ in ...
eades's user avatar
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7 votes
2 answers
238 views

Is the class of models for which the MLE exists also the one for which flat priors are permissible?

By "permissible" (for lack of a better term) I mean models which despite of a "flat" (improper) prior (i.e., $\int_{\Theta} p(\theta) d \theta = + \infty$) nevertheless produce a ...
Durden's user avatar
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0 votes
1 answer
129 views

How can I solve identifiability problems in my STAN estimation?

So I am trying to validate my STAN model before using real data and am having some trouble estimating parameters separately. My data structure contains count data with people on the rows, and test ...
Gregtt's user avatar
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1 vote
0 answers
42 views

Confidence regions with non-unique maximum likelihood

Short version Can bootstrap be used to find disconnected confidence regions when MLE is not unique? Long version Let $\theta$ be a parameter and $P_\theta=\mathrm{Normal}(\theta, 1)$ be a ...
Paweł Czyż's user avatar
2 votes
0 answers
50 views

Post-hoc identifiability for Bayesian multilevel regression model

In [1], Ogle & Barber discuss a method for ensuring identifiability of certain Bayesian multilevel regression models; they call this method "post-sweeping". I have a couple of related ...
covert's user avatar
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1 vote
0 answers
24 views

CFA with lavaan: Standard errors not computable [duplicate]

I am not that much experiencend in R and I want to run a CFA. The code is as follows: ...
user384307's user avatar
2 votes
0 answers
35 views

Identifiability of models on RKHS

I have just started learning about using reproducing kernel hilbert spaces for regularisation in machine learning. I am looking for some examples of reproducing kernels that produce identifiable and ...
Codie's user avatar
  • 51
0 votes
0 answers
24 views

How to solve non-identifiability problem in point estimation

I am working with a normal model $X \sim N(0, \sigma^2(\theta))$, where $\sigma^2(\theta) = \frac{1}{e}\cos^2(\theta)+e\sin^2(\theta)$. My goal is to estimate $\theta$ within the range $[0, 2\pi]$. My ...
Marco R's user avatar
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4 votes
1 answer
160 views

Can nonlinear regression identify this equation?

I want to estimate the following regression equation: $y = a + \frac{b}{r*x + 1}$ x is the independent variable, and a, b and r are parameters to be estimated. I have been told that the model is not ...
William Foley's user avatar
3 votes
1 answer
769 views

SEM: Difference between unidentified, underidentified, and underdetermined models?

It's been asserted to me that there is a difference between underidentified and unidentified models in that: Underidentified models can still be estimated and solutions can be obtained, but they are ...
user1205901 - Слава Україні's user avatar
0 votes
0 answers
48 views

Identification in a non-linear simultaneous equation model

I have the following model: \begin{align*} &\ln(cs_t)=c_1+c_2\ln(cs_{t-1})+c_3\ln(y_t)+c_4q1_t+c_5q2_t+c_6q3_t+u_{1t}\newline &\ln(i_t)=c_7+c_8\ln(i_{t-1})+c_9\ln(b_t)+c_{10}(\ln(y_t)-\ln(y_{t-...
honkhonk's user avatar
3 votes
0 answers
106 views

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 ...
jasmine's user avatar
  • 367
0 votes
0 answers
129 views

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?
Dr. T's user avatar
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0 answers
49 views

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, ...
Ant's user avatar
  • 439
0 votes
0 answers
29 views

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}...
cet's user avatar
  • 1
8 votes
3 answers
215 views

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\...
Panel Noob's user avatar
1 vote
0 answers
90 views

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 ...
Niklas's user avatar
  • 11
3 votes
3 answers
113 views

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 ...
Ludwig Gershwin's user avatar

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