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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74 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, ...
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0answers
22 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'...
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1answer
106 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 ...
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88 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 $\...
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1answer
50 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 ...
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1answer
40 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 ...
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60 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, ...
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2answers
154 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 ...
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16 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....
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127 views

Multiclass Logistic Regression: How does sklearn model.coef_ return K well-identified sets of coefficients for K classes?

I am looking to fit a multinomial logistic regression model in Python using sklearn, some pseudo python code below (does not include my data): ...
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1answer
93 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., ...
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1answer
38 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 ...
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1answer
22 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 ...
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65 views

Rank condition for identification

In Basic Econometrics, Gujarati and Porter define a rank condition for identification of simultaneous equations: What would be its proof?
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1answer
128 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{...
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31 views

Identifiability of ANOVA model

Suppose that random variables $Y_{ij}$ are observed according to the overparameterised one way ANOVA model i.e $$Y_{ij}=\mu+T_i+\epsilon_{ij}$$ Show that without some restriction on the parameters, ...
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1answer
45 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 ...
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1answer
130 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 ...
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1answer
87 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 ...
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1answer
76 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 ...
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2answers
77 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
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1answer
272 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....
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1answer
29 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, ...
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1answer
1k 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 ...
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0answers
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_{...
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1answer
117 views

What are the “moment conditions” in the GMM method? Also: GMM vs IV vs 2SLS?

I keep seeing talk of 'moment conditions' or 'moment equations', but don't exactly understand the context. Consider a very standard regression model: $$y_i = \beta x_i + u_i $$ where $u_i$ is an ...
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0answers
98 views

What is an intuitive of definition of “point identification” (point identified parameter) in econometrics?

I've recently come across the notion of point identification in several econometric papers. See, e.g., https://scholar.harvard.edu/files/tamer/files/pie.pdf, who mentions point identification ...
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1answer
49 views

Can anyone show how the concept of Identifiability is geometrically/intuitively presented?

The motivation for this question comes from the following: When I was studying statistics for the first time long ago, no one presented the mathematical concepts behind linear regression, like the one ...
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1answer
37 views

How to deal with product coefficients in a nonlinear model?

I am considering a nonlinear regression model as the following: y=(ax)*(bz)+u, where the sample are IID, u is random error term such that E(u|x,z)=0, and a and b ...
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1answer
20 views

calculate mean of normal distribution given SD and probability corresponding to a single range

Suppose that I have a normally distributed variable with unknown mean and known SD: $X \sim N(\mu, 1)$. I also know that $P(-2 < X < 2) = 0.3.$ Is it possible to calculate $\mu$ from this ...
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3answers
112 views

Parameter identification v. causal identification

As others, it seems (Identification of parameters problem), I get confused about the use of the word "identification" in econometrics. It seems some people talk about "identification" in the sense ...
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0answers
89 views

Identifiability vs. equivalence of probability measures

I'm a bit confused about the notion of identifiability vs. equivalence of probability measures. The following definition of identifiability I am familiar with: Let $\{P_\theta : \theta \in \...
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1answer
33 views

Marginal posterior distribution, likelihood mean sum of two standardnormal priors

How would I compute the marginal posterior distribution of $\mu_1$ and $\mu_2$ if the likelihood $(y | \mu_1,\mu_2) \sim N(\mu_1+\mu_2,1)$ and $\mu_i \sim N(0,1)$
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0answers
114 views

Time series DGP: No convergence to true parameter - Identification problem?

I set up a model, simulated some data and tried to infer the wanted parameter $\alpha$. However it seems that there may be no convergence to the true parameter (result is either $-\alpha$ or $+\alpha$)...
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0answers
25 views

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 ...
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0answers
15 views

Can I combine equations to produce overidentifying restrictions?

Say theory tells me that $$ y = f(x_1,x_2|\theta_f) $$ where $\theta_f$ is a set of parameters Similarly, theory tells me that $$ y = g(x_1,x_3|\theta_g) $$ where $\theta_g$ is another set of ...
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0answers
186 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 $\Bbb P_{\theta}$ ...
3
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2answers
111 views

Identification from implicit function

Suppose my observed data $y$ and $x$ is generated by the following relationship for each observation $i$: $$ y_i = h(y_i,\theta) + x_i + \varepsilon_i$$ where $x_i$ is a strictly exogenous variable ,...
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0answers
107 views

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
160 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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0answers
38 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 ...
2
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1answer
73 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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1answer
194 views

Inconsistent Ljung-Box test result and plot of autocorrelation function of residuals

I get an inconsistent result for the Ljung-Box test: in fact when I run it using the Box.test function it doesn't make me reject the null hypothesis of residuals being white noise, but when I plot the ...
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0answers
52 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
529 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
38 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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0answers
399 views

Fitting a Beta distribution only using coin flips from the biased coins it generates

I have a Beta distribution $D$ with unknown parameters $\alpha$ and $\beta$ which I wish to estimate. If I was given samples $p_1, \ldots, p_n$ from $D$, then it's relatively straightforward to fit $...
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0answers
69 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 (...
5
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1answer
153 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(...
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1answer
99 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{...