Questions tagged [identifiability]
A model is identifiable if a single set of parameters can be found that will yield the best fit.
185
questions
2
votes
1answer
34 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
0answers
48 views
Identification of correlated errors with multinominal probit
Consider the multinational probit model where we observe $Y_i \in \{1, \dots, K + l\}$ with
$$
\begin{align*}
Y_i = l \Leftrightarrow Z_l&\geq \max(Z_1,\dots Z_{K +1}\}
\qquad l \in \{1, \dots, ...
6
votes
2answers
140 views
Identifying the correlation between a slope and a level
Throughout this post, I assume at least second moments exist. Consider a heterogeneous linear treatment effect model of the form:
$$Y_i = \alpha_i + \beta_i X_i$$
where $\alpha_i, \beta_i$ are ...
1
vote
0answers
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....
0
votes
0answers
26 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):
...
0
votes
1answer
41 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
1answer
29 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
1answer
18 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 ...
0
votes
0answers
28 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?
5
votes
1answer
119 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
0answers
16 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}$$
Show that without some restriction on the parameters, ...
0
votes
1answer
39 views
Does 'As Good As Random' Have a rigorous definition in identification strategies?
If using an identificaton strategy such as differences in differences, Regression Discontinuities, or IV's, I see the phrase 'as good as random' used alot. Does this have a rigorous definition, or is ...
2
votes
1answer
66 views
Does estimated fixed effects change if we change reference level?
Consider a fixed effect model $$y_{it}=x_{it}'\beta+\alpha_{i}+\epsilon_{it}$$
To estimate the fixed effects $\alpha_i$ we can add a dummy for each individual and run the least-squares dummy variables ...
4
votes
1answer
85 views
Proving Identifiability Using Law of Large Numbers? [closed]
Well normally proving identifiability follows by showing that $p_{\theta}(x)=p_{\theta'}(x)$ implies $\theta=\theta'$. Usually this proceeds by showing that a function dependent on $\theta$, such as ...
0
votes
1answer
64 views
Parameters identifiability / estimation in Bayesian linear state-space models
Is it possible to tell if the parameters can be uniquely estimated in a Bayesian state-space models from the system equations (beyond redundant parameterisations). If so, how?
For example, should it ...
2
votes
2answers
64 views
Simultaneity in causal diagrams
Lets assume we have simultaneity problem. Variable x causes y and y causes x. As an example i would state alcoholism: the more respondent consumes alcohol, the more 'is' alcoholic (measured for ...
2
votes
1answer
177 views
MLE Asymptotic Normality regularity conditions
I had this lecture of mathematical statistics about asymptotic normality of MLE. In order to prove this, a series of regularity conditions were stated, and the identifiability condition was among them....
0
votes
1answer
27 views
fitting specific formula/model in r - model possibly not identifiable
I would like to fit the following formula in R:
y ~ alpha *(x1_0 * x2_0 * beta_0 + x1_1 * x2_1 * beta_1)
Here: alpha, ...
1
vote
1answer
680 views
Can't compute standard errors: the information matrix could not be inverted
I am trying to compute a Structural equation model.
I have identified one model, in which I have included all the subscales simultaneously. However, when I try to look at the subscales separately, I ...
1
vote
0answers
17 views
How to verify identification of a model?
I have the system of simultaneous equations:
$$
\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_{...
0
votes
1answer
64 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 ...
1
vote
0answers
68 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 ...
2
votes
1answer
48 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 ...
0
votes
0answers
10 views
The Hansen-Sargan test for overidentification and the choice of quadratic loss function
According to my professor, the Hansen-Sargan statistic is: $HS=nQ(b_{2sls})$ ~ $\chi ^2_{L-K} $ asymptotically, where $L$ is the number of moment restrictions, $K$ is the number of unknown parameters, ...
2
votes
1answer
36 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 ...
0
votes
0answers
14 views
Instrumental variables, do we only need cov(z,e)=0 for exogeneity, and not E[e|z]=0?
Looking at the formula for instrumental variables estimator, we have :
B_iv = B + (z'x)^-1(z'e)
and then taking probability limits it becomes evident that we need cov(e,z)=0 and cov(z,x)=/=0..
but ...
1
vote
1answer
17 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 ...
0
votes
0answers
15 views
What kinds of variation am I able to explore using panel data with 3 fixed effects?
this question is similar to an unanswered question of mine.
My data explores variation at three possible dimensions: $a$ area, $s$ sector, and $t$ time. There are 400 areas, 13 sectors and 8 time ...
4
votes
3answers
104 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 ...
1
vote
0answers
72 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 \...
0
votes
1answer
32 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 $\mu_i \sim N(0,1)$
1
vote
0answers
113 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 $+\alpha$)...
0
votes
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 ...
1
vote
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 ...
3
votes
0answers
153 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
votes
2answers
110 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 ,...
6
votes
0answers
106 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
votes
2answers
157 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 ...
2
votes
0answers
35 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
votes
1answer
56 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 ...
1
vote
1answer
138 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 ...
1
vote
0answers
46 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-...
0
votes
1answer
390 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 ...
2
votes
0answers
29 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 ...
3
votes
0answers
321 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 $...
0
votes
0answers
58 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
votes
1answer
137 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 $$y_i=\eta(...
1
vote
1answer
97 views
Identification of discrete choice models
Consider the classical Logit model. In particular, let $\mathcal{Y}\equiv (0,1,...,L)$ be the set of options available to consumers, where $0$ denotes the outside option. Let
$$
u_y\equiv \begin{...
3
votes
0answers
168 views
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) ...
2
votes
0answers
18 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 ...
