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

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25 views

How do weak instruments violate full rank condition?

So I know that if the instruments $(Z_i)$ in 2SLS regression are weak i.e. $X_i$ and $Z_i$ are uncorrelated, then full rank condition for matrix $\Sigma_{ZX}=E[Z_iX_i]$ will fail to hold, but how can ...
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22 views

Identifiability of regression parameter in multinomial logistic regression

In simple logistic model, we have $\log (\frac{\pi}{1-\pi})=\alpha+\beta t$. If we allow our parameters $\alpha$ and $\beta$ to take value in $[-\infty,\infty]$, there will be identifiability problem. ...
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53 views

Identification of Bayesian models

In frequentist estimation, a large degree of emphasis in SEM/CFA modeling is placed on whether the model is identified, that is, whether each parameter can be uniquely estimated from the data. The ...
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1answer
44 views

Why is over identified models preferred over just identified models in Structural Equation Modeling?

It's often stated that for analysis using an SEM technique, it is preferred to use an overidentified model compared to a just identified model. Why is that so ? My intuition says that for an over ...
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1answer
28 views

On identifiability: Why can't you include all levels of the two factors in a linear regression?

In Gelman and Hill, there is a passage on identifiability and it says: "For example, you could not include both of the sex categories and all four of the age categories. It is simpler just to keep ...
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1answer
34 views

Interpretation of estimates from a SEM without intercepts

I am building a model using structural equation modeling in R with the lavaan package. There are only observed variables (no latent variables) and 5000 observations with which to fit the model. I use ...
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2answers
37 views

Identifying method by equation (Related to Factorial Fractional Design)

I'd like to know the name of the method in the picture below. It's the same category as full - and factorial fractional design. It's quite difficult to search the net for this equation - I've tried ...
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46 views

Identifiability in Parameter Estimation Problem

I have a question regarding the identifiability of parameters. I know that if $f(y;\theta)=f(y;\theta')$ then $\theta = \theta'$, otherwise it would be impossible to estimate $\theta$. However, ...
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67 views

How to prove the identifiability of a likelihood

Consider the likelihood function for parameter vector ...
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63 views

Bayesian neural networks: very multimodal posterior?

Question: How do Bayesian treatments of neural networks address the fact that the posterior has an exponentially large number of modes? Background: There seems to be a lot of interest in Bayesian ...
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1answer
98 views

Identifiability of a state space model (Dynamic Linear Model)

Take a general linear Gaussian state space model (SSM)(aka Dynamic Linear Model DLM): $X_{t+1}=FX_t + V_t$ $Y=HX_t+W_t$ $V_t \sim N(0,Q)$ $W_t \sim N(0,R)$ I am interested in the ...
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50 views

What do I do when my second order CFA model is not identified?

I am assessing a measurement model of a three-factor organisational commitment scale for my PhD project. Although congeneric single factor and first order CFA models have produced excellent model fit ...
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1answer
38 views

Estimation of a process

I have this process to estimate: $x_t - x_{t-1} = \lambda(\gamma-x_{t-1}+\varepsilon_{t-1})+\varepsilon_t-\varepsilon_{t-1}$ but as far I can see it is unidentified. Any suggestions how to estimate ...
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1answer
83 views

Relationship between low identifiability and prior weight in Bayesian model

I'm trying to get intuition into the relationship between low identifiability and prior weight in Bayesian model. Is it true to say that in lowly identifiable model + data the prior will have a higher ...
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1answer
25 views

Identifiability of a particular Independent Component Analysis model

I am considering the model : $$ \mathbf{x} = \mathbf{A}\mathbf{s} $$ where $\mathbf A \in \mathcal{M}_{n,p}(\mathbb{R})$ and $\mathbf s \in \mathbb{R}^{p}$ such that the entries of $\mathbf s$ are ...
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81 views

Identifiability in factor analysis

Say we model $\mathbf{x}_t \in \mathbb{R}^d$ as a linear combination of factor loadings: $$\mathbf{x}_t = \mathbf{E}\mathbf{F}_t + \boldsymbol{\epsilon}_t, \qquad \boldsymbol{\epsilon}_t \sim ...
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2answers
200 views

Identifiability of the linear regression model: necessary and sufficient condition

Let $\{(x_i, y_i), 1\le i\le n\}$ be the pairwise values of the observations and responses respectively. Let us fit the linear regression model: $y_i=b_0+b_1 x_i+\epsilon_i, ...
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133 views

Can logistic regression be modified to predict a distribution, not just point-estimate? Other ways to learn a beta distribution from binary events?

Currently I'm using high dimensional logistic regression to predict the probability of a rare event. I use this probability for both ranking and for other calculations which need it to be ...
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1answer
244 views

Identification problems with a structural equation model of experimental data

I have performed an experiment in which I manipulated three factors and I would like to model latent variables that those factors affect and then estimate the effects of the latents on response ...
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0answers
49 views

Asymptotic distribution of $\hat{B_1}$in simple linear regression

I am currently studying how to $\bf{identify}$ the parameter $B_1$ in a simple univariate regression model where we have $Y=B_0+B_1X+\epsilon$ with the usual assumption of $X$ being exogenous, ...
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106 views

Rule of thumb for excluded variable in Heckman selection model?

I'm working on a project that involves the use of a Heckman selection model (more specifically a Roy or move-stay model, which is essentially a two-sided Heckman) of the following form: $$ Y_{i1} = ...
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319 views

Dirichlet Processes for clustering: how to deal with labels?

Q: What is the standard way to cluster data using a Dirichlet Process? When using Gibbs sampling clusters appear and dissapear during the sampling. Besides, we have a identifiability problem since ...
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89 views

Identifiability and estimability

I am somewhat confused about this identifiability and estimability concept with application to binomial example in David Freedman's book (statistical models: theory and practice Page 125-P126). let ...
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88 views

Identifiability issues for linear mixed models with cross-classified data

I have a dataset that could be easily simulated like this: ...
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1answer
155 views

Identifiability in linear regression and time series

The multivariate linear regression model is given by $\mathbf{y} = \mathbf{X}\boldsymbol{\beta} + \boldsymbol{\epsilon}$, where $\boldsymbol{\epsilon} \sim \mathcal{N}(\mathbf{0, ...
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106 views

Identifiability of normal distribution

I am working on an exercise problem and am stuck in this problem: Suppose that $X_1,\dots,X_n$ are independent with $X_i\sim\mathrm{N}(\alpha_i + \nu, \sigma^2)$. Let $\theta = (\alpha_1, . . . , ...
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1answer
122 views

Estimating standard error in a probit: econometrics or programming problem?

This question has two parts, as I do not understand whether my problem is theoretical (identification of the parameters) or practical (insufficient R skills). Econometrics Most "probit" style ...
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30 views

Should IDs be nominal factors or text?

I am getting started with R. I imported by data and R decided that my ID attribute should be a factor. While technically correct, it feels misleading to me. An ID doesn't feel like a factor with ...
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152 views

Is this identifiable?

I am interested in the following model : ($1 \leq i \leq p$, $1 \leq j \leq n_{i}$) $$y_{i,j} = A (1+a_{i})(t_{i,j}+\gamma_{i}) + \varepsilon_{i,j}$$ where $A \in \mathbb{R}$, $(a_{i})_{1 \leq i ...
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73 views

Identifiability in linear regression

If we have a generative model: $X_2=X_1a_1+\varepsilon$, where $\varepsilon \sim \mathcal{N}(0,\sigma_2^2)$, do we have $X_1=X_2a_2+\varepsilon '$, where $\varepsilon \sim \mathcal{N}(0,\sigma_1^2)$ ...
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1answer
49 views

Identifiability and unbiasedness

How do you show that if my model parameter $\theta$ (scalar) is U-estimable (i.e. if there exists an unbiased estimator of $\theta)$, then $\theta$ is identifiable? This makes sense intuitively, but ...
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94 views

Estimating variance for identically non independent data

Let $X_{ij}$ with $1\leq i<j\leq n$ (that are $X_{12},\dots, X_{1n},\dots,X_{(n-1)n}$) be ${n \choose 2}$ identically normal distributed $N(0,\sigma^2)$ such that $ \text{corr}(X_{ij},X_{rs})=\rho ...
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1answer
51 views

Question about identification for this parametrization

Assume I observe a poisson-process with a rate $\boldsymbol{\lambda}$. I would like to model $\boldsymbol{\lambda}$ as: $\boldsymbol{\lambda} = \boldsymbol{\pi}_1\boldsymbol{\lambda}_1 + ...
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1answer
62 views

Separating effects of foods and of food components in nutritional epidemiology

I have data on average long-term intake of common foods of a medium/large cohort (n=500+). It was assessed semi-quantitatively (that is, interval-censored). From these about 100 food items and their ...
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1answer
449 views

What's the problem with model identifiability?

I understand that in a decision perspective, identifiability of a model is needed to ensure the convergence (with increasing number of observations) of the parameters to estimate through a single ...
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366 views

Bayesian inference and degrees of freedom

While learning frequentist linear regressions, one thing the professors always talked about was about the number of degrees of freedom, I never saw this expression in a bayesian book though. Perhaps ...
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425 views

Mixture of binomial distributions

I am experimenting with a mixture of binomial models. Consider a binary variable $y_i$. Furthermore, there are two sub-groups in the population (not known a priori and not observable): $z_i=0$ or ...
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2k views

In my logistic regression model one of the independent variables is redundant with the interaction term. How should I deal with it?

In my logistic regression is the dependent variable a dummy variable and I also have two independent variables. One of those is a dummy variable and the other is a metric variable. I also suppose an ...
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1answer
220 views

Model Identification

Could somebody please explain why this model is "just identified" As I see it, there are 5 * 4 / 2 = 10 variances/covariances, 4 observed means, giving 14 available degrees of freedom 5 DF are ...
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1answer
156 views

Fitting ratios in multiple regression formula

I would like to ask a (probably very simple) question with regards to multiple linear regression. I have an experimental formula in the form: $$ Y \sim \frac{a_0 \cdot X_0}{(a_1 \cdot X1) * (a_2 ...
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62 views

Is data driven identification in a simultaneous equation model possible?

Suppose I have to estimate 3 models: $y_1 = y_2\beta_1 + y_3\beta_2 + X\beta_3 + u_1$ $y_2 = y_1\alpha_1 + y_3\alpha_2 + X\alpha_3 + u_2$ $y_3 = y_1\gamma_1 + y_2\gamma_2 + X\gamma_3 + u_3$ I ...
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1answer
166 views

Identification of parameters problem

I always struggle to get the true essence of identification in econometrics. I know that we state that a parameter (say $\hat{\theta}$) can be identified if by simply looking at its (joint) ...
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1answer
117 views

About Identification in a 3 equation SEM

I got this example and I was wondering about a certain statement: $$ \begin{aligned} y_1 &= \alpha_{12}y_2 + \alpha_{13}y_3 + \beta_{11}z_1 + u_1 \\ y_2 &= \alpha_{21}y_1 + \beta_{21}z_1 + ...
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1answer
440 views

How do I identify this simultaneous equations model?

I have the following model (which is in this form is not identifiable if the $y$'s are indeed endogenous): (1) $y_1 = a_0 + a_1y_2 + a_2y_3 + \boldsymbol{Xa} + \boldsymbol{u}$ (2) $y_2 = b_0 + ...
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1answer
154 views

Understanding basic identifiability

I'm having trouble understanding identifiability. Specifically, I'm not sure, in the following example, why $P\left(C\right)$ cannot be identified. Here's the example: You have 2 unfair coins with ...
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172 views

Unidentified variables in multinomial model [closed]

I am building a simple multinomial logit (MNL) model. I've discovered that the particular variable that I am testing ("pctLS") causes the model to be "unidentified," but I am not sure how to correct ...
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208 views

learning an hierarchical linear model - overfitting / identifiability issues?

I'm currently looking at a paper where they've done this using two layer support vector regression and I'm trying to figure out whether they have biased the performance of their classifier and whether ...
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2answers
309 views

Simple linear regression

Consider the simple regression model $y=\beta_0+\beta_1x+u$, where $\text{corr}(x,u)=1$ and all random variables have normal distributions. Is it possible to provide asymptotically consistent ...
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1answer
166 views

Identifying parameters in BUGS linear regression

With a linear regression defined in BUGS, how should one implement model identification constraints such as having the mean of a group of parameters be zero, or having the group of parameters sum to ...
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4k views

What is model identifiability?

I know that with a model that is not identifiable the data can be said to be generated by multiple different assignments to the model parameters. I know that sometimes it's possible to constrain ...