# Questions tagged [identifiability]

A model is identifiable if a single set of parameters can be found that will yield the best fit.

203 questions
Filter by
Sorted by
Tagged with
19 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 ...
18 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 ...
12 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 $A\in \mathbb{R}^{d\times d}$ ...
66 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 ...
62 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. ...
25 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 $Y_{ig}^0,Y_{ig}^1,Y_{ig}^2$. ...
23 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 ...
11 views

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 ...
128 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 ...
60 views

82 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 ...
149 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, ...
21 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 ...
25 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'...
54 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 ...
247 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 ...
126 views

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 $\... 0answers 6 views ### Caveats regarding the choice of the elementary panel model Lets compare three panel most basic models: pooled, random effects, fixed effects. I observe common belief, that the fixed effect model estimation is "less biased", than in the other models. ... 1answer 81 views ### Why does estimability imply identifiability? Let$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)$is called identifiable if ... 1answer 42 views ### Is there a word or phrase to describe a model that is basically unidentifiable in practice? So suppose we have a model$f(x|\theta)$that is theoretically identifiable, so that$\theta_1 \neq \theta_2$implies$f(x|\theta_1) \neq f(x|\theta_2)$. However, suppose that data collection is very ... 0answers 74 views ### Identification of correlated errors with multinominal probit Consider the multinational probit model where we observe$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, ... 2answers 162 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$$where \alpha_i, \beta_i are ... 0answers 18 views ### Quasi-experiment analysis I have 5-year sales information from a grocery store in Canada. I want to check the effect of an online campaign that happened in 2017 on food sales. My treatment group is people living in urban areas.... 1answer 152 views ### Estimating LATE from RDD using OLS - Have I understood it correctly? I am currently running a project using RDD in STATA where I am unable to use the handy "rdrobust" command, and hence have to use the conventional "regress" function instead, i.e., ... 1answer 45 views ### Parameter identification and causal identification When people say identification, do "parametric identification" and "causal identification" mean completely different? Ex) When performing ML estimation, the sentence that one ... 1answer 28 views ### How to identify coefficients for all levels of categorical variables when you have multiple of them I have an equation like y ~ x1 + x2 + x3 + x4 where the first 3 variables are categorical and the last one is continues. I want to identify the coefficients for all ... 1answer 136 views ### Basic Questions about regression formula, sampling variability, and 'identification' lets say I run the simple regression, y_i = \beta_o + \beta_1x_i + \epsilon_i.. Assume cov(\epsilon,x)=0 This yields the formula people write in terms of covariances for the slope parameter: \hat{... 1answer 45 views ### Does 'As Good As Random' Have a rigorous definition in identification strategies? If using an identificaton strategy such as differences in differences, Regression Discontinuities, or IV's, I see the phrase 'as good as random' used alot. Does this have a rigorous definition, or is ... 1answer 213 views ### Does estimated fixed effects change if we change reference level? Consider a fixed effect model$$y_{it}=x_{it}'\beta+\alpha_{i}+\epsilon_{it}$$To estimate the fixed effects \alpha_i we can add a dummy for each individual and run the least-squares dummy variables ... 1answer 89 views ### Proving Identifiability Using Law of Large Numbers? [closed] Well normally proving identifiability follows by showing that p_{\theta}(x)=p_{\theta'}(x) implies \theta=\theta'. Usually this proceeds by showing that a function dependent on \theta, such as ... 1answer 93 views ### Parameters identifiability / estimation in Bayesian linear state-space models Is it possible to tell if the parameters can be uniquely estimated in a Bayesian state-space models from the system equations (beyond redundant parameterisations). If so, how? For example, should it ... 2answers 114 views ### Simultaneity in causal diagrams Lets assume we have simultaneity problem. Variable x causes y and y causes x. As an example i would state alcoholism: the more respondent consumes alcohol, the more 'is' alcoholic (measured for ... 1answer 363 views ### MLE Asymptotic Normality regularity conditions I had this lecture of mathematical statistics about asymptotic normality of MLE. In order to prove this, a series of regularity conditions were stated, and the identifiability condition was among them.... 1answer 31 views ### fitting specific formula/model in r - model possibly not identifiable I would like to fit the following formula in R: y ~ alpha *(x1_0 * x2_0 * beta_0 + x1_1 * x2_1 * beta_1) Here: alpha, ... 1answer 2k views ### Can't compute standard errors: the information matrix could not be inverted I am trying to compute a Structural equation model. I have identified one model, in which I have included all the subscales simultaneously. However, when I try to look at the subscales separately, I ... 0answers 17 views ### How to verify identification of a model? I have the system of simultaneous equations:$$ \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_{... 1answer 234 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: $$y_i = \beta x_i + u_i$$ whereu_i$is an ... 0answers 163 views ### What is an intuitive of definition of "point identification" (point identified parameter) in econometrics? I've recently come across the notion of point identification in several econometric papers. See, e.g., https://scholar.harvard.edu/files/tamer/files/pie.pdf, who mentions point identification ... 1answer 49 views ### Can anyone show how the concept of Identifiability is geometrically/intuitively presented? The motivation for this question comes from the following: When I was studying statistics for the first time long ago, no one presented the mathematical concepts behind linear regression, like the one ... 1answer 39 views ### How to deal with product coefficients in a nonlinear model? I am considering a nonlinear regression model as the following: y=(ax)*(bz)+u, where the sample are IID, u is random error term such that E(u|x,z)=0, and a and b ... 1answer 38 views ### calculate mean of normal distribution given SD and probability corresponding to a single range Suppose that I have a normally distributed variable with unknown mean and known SD:$X \sim N(\mu, 1)$. I also know that$P(-2 < X < 2) = 0.3.$Is it possible to calculate$\mu$from this ... 3answers 125 views ### Parameter identification v. causal identification As others, it seems (Identification of parameters problem), I get confused about the use of the word "identification" in econometrics. It seems some people talk about "identification" in the sense ... 0answers 101 views ### Identifiability vs. equivalence of probability measures I'm a bit confused about the notion of identifiability vs. equivalence of probability measures. The following definition of identifiability I am familiar with: Let$\{P_\theta : \theta \in \...
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 $\mu_i \sim N(0,1)$
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 $+\alpha$)...