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0answers
22 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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0answers
22 views

Identifiability issues for linear mixed models with cross-classified data

I have a dataset that could be easily simulated like this: ...
1
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1answer
37 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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0answers
24 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 ...
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2answers
77 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
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1answer
69 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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0answers
21 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
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1answer
121 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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0answers
51 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
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1answer
36 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
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0answers
76 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
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1answer
46 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
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1answer
54 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
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0answers
264 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
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1answer
169 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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0answers
194 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
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2answers
1k 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
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1answer
188 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
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1answer
134 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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0answers
60 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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0answers
106 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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0answers
64 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
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1answer
379 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
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1answer
114 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
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0answers
124 views

Unidentified variables in multinomial model

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
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0answers
166 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
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1answer
157 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 ...
19
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2answers
2k 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
669 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
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2answers
299 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 ...