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2
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2answers
31 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 ...
1
vote
0answers
39 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, ...
1
vote
1answer
34 views

How to prove the identifiability of a likelihood

Consider the likelihood function for parameter vector ...
1
vote
0answers
47 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 ...
2
votes
1answer
43 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 ...
1
vote
0answers
28 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 ...
1
vote
1answer
35 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 ...
1
vote
0answers
68 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 ...
2
votes
1answer
23 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 ...
0
votes
0answers
61 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 ...
3
votes
2answers
109 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, ...
1
vote
0answers
123 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 ...
1
vote
1answer
126 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 ...
2
votes
0answers
42 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, ...
5
votes
0answers
62 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} = ...
7
votes
2answers
238 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 ...
1
vote
0answers
66 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 ...
0
votes
0answers
78 views

Identifiability issues for linear mixed models with cross-classified data

I have a dataset that could be easily simulated like this: ...
1
vote
1answer
100 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, ...
0
votes
0answers
53 views

Multivariate regression with 3 dependent variables and only 1 independent variable?

I need to compare the marginal effect of one independent variable (X) in 3 different dependent variables (Y). I did a multivariate regression using Stata commands manova and mvreg, but I am doubting ...
1
vote
2answers
90 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, . . . , ...
2
votes
1answer
105 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 ...
2
votes
0answers
22 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 ...
3
votes
1answer
138 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 ...
0
votes
0answers
68 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 $\varepsilon \sim \mathcal{N}(0,\sigma_1^2)$ ...
0
votes
1answer
46 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 ...
2
votes
0answers
89 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 ...
1
vote
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 + ...
3
votes
1answer
57 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 ...
4
votes
0answers
370 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 ...
5
votes
1answer
290 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 ...
1
vote
0answers
341 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 ...
3
votes
2answers
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 ...
0
votes
1answer
209 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 ...
2
votes
1answer
149 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 ...
1
vote
0answers
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 ...
7
votes
0answers
137 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) ...
2
votes
1answer
102 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 + ...
1
vote
1answer
417 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 + ...
2
votes
1answer
135 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 ...
1
vote
0answers
155 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 ...
0
votes
0answers
196 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 ...
3
votes
1answer
161 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 ...
23
votes
2answers
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 ...
3
votes
2answers
853 views

When does a logistic regression model have a unique solution?

Mathematically speaking, for which data does a logistic regression model have a unique solution?
6
votes
2answers
349 views

Possible identifiability issue in hierarchical model

I'm trying to fit some data using a hierarchical normal model $y_i \sim N(\theta_i,\sigma^2)$ $\theta_i \sim N(\mu, \sigma_\theta^2)$ $(\mu,\sigma^2,\sigma_\theta^2) \sim diffuse$ I fit this ...