# 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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17 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 ...
60 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 $\Bbb P_{\theta}$ ...
94 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 ...
142 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 ...
14 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 ...
20 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 ...
29 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-...
63 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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### 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 ...
36 views

### Profile Likelihood confidence interval

I am interested in obtaining profile likelihood confidence intervals for parameter identifiability. My cost function is the least square error between the data and some fitted approximation depending ...
31 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 (...
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### 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) ...
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### 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 ...
44 views

### Why is model unidentifiability a problem?

I am new to the concept of model identifiability, but from my understanding it is possible to learn the true parameter values of the model after obtaining an infinite number of observations from it. ...
396 views

### What does the sum to zero constraint mean?

In an ANOVA model, there is a constraint that the coefficients must sum to zero. What does this actually mean? I do understand the reason why you might want to make them sum to zero, i.e. to have two ...
81 views

### What does it mean to “non-parametrically” identify a causal effect within the super-population perspective in causal inference?

I am wondering, within the context of causal inference, what it means to "non-parametrically" identify a causal effect within the super-population perspective. For example, in Hernan/Robins Causal ...
114 views

### GLMM in R doesn't converge, nearly unidentifiable [duplicate]

I'm building my GLMM using r. ...
109 views

### What does it mean if the Average Treatment Effect (ATE) in causal inference is not identifiable?

I read from the following slides on observational studies, pg. 16, Observational Studies, Keio, that given: $$ATE ≡ E[Y_i(1) − Y_i(0)]$$ They pose the following question: Can we identify the $ATE$...
111 views

### What is “identification assumptions” in econometrics? [closed]

I'm starting to study econometrics from Wooldridge's book. But some doubts arise regarding to the role of Conditional Expectations in Econometrics. Wooldridge says that although it is not always ...
92 views

### Error variance may not be identified. LISREL

I am conducting CFA for a variable in my study. It has two sub-dimensions, say D1 and D2. On conducting CFA with only first-order factors, my model runs fine and there is a strong correlation among ...
556 views

### Can anyone help explain this basic example of posterior

I am having trouble understanding the authors reasoning here. It is from "The Bayesian Choice" I am confused about why the posterior is initially written without depending on the data, and why we ...
23 views

### Alternatives to calculating the rank of the information matrix in determining if the model is identifiable

I have a known non-linear model $h \in \mathbf{R}^n$: $$y = h(\theta) + \epsilon,$$ where $\theta\in \mathbf{R}^m$ is a parameter vector, and $\epsilon$ is a normal random variable with zero mean ...
52 views

### VECM with Multicollinearity

I have fit a vector error correction model (VECM) to some macroeconomic data. In particular, I am interested in three relationships real GDP as a function of employment and real wages employment as a ...
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I'm doing uniqueness on factor loading matrix in a factor model. $y = \Lambda f + \epsilon$ where $f \sim N(0,\Sigma)$ , $\epsilon \sim N(0,\Omega)$ and $\epsilon \perp f$. It's well known that ...
144 views

### Reference smooth + smooth by all levels of a factor: is my GAM still identifiable?

I have speech signals sampled in 10-ms intervals ('$time$') in 8 different geographical regions ('$region$'), from 20 subjects each. For each of these regions, I want to know if the sampled trajectory ...