Timeline for "Prediction interval" for a slope of a model fitted to new data
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Feb 23, 2023 at 13:33 | vote | accept | Martin Modrák | ||
| Feb 13, 2023 at 17:31 | comment | added | Martin Modrák | @JarleTufto indeed, this works. Expanded on that a bit and added as answer. Thanks! | |
| Feb 13, 2023 at 17:30 | answer | added | Martin Modrák | timeline score: 2 | |
| Feb 13, 2023 at 15:45 | comment | added | Jarle Tufto | Construct a pivotal quantity by dividing $\tilde\beta_1 - \hat\beta_1$ by its standard error. This involves the $x_i$'s for the new unobserved data so these must be known. Replacing $\sigma$ in the denominator by its estimate $s$ based on the observed part of the data, the resulting quantity is $t$-distributed with $n-2$ degrees of freedom, where $n$ is the sample size of the observed data. | |
| Feb 13, 2023 at 14:59 | comment | added | Martin Modrák | Let us continue this discussion in chat. | |
| Feb 13, 2023 at 14:57 | comment | added | Tim | In what scenario you would have new data generated from an estimated model? | |
| Feb 13, 2023 at 14:56 | comment | added | Martin Modrák |
@Tim I agree confidence intervals shouldn't work here - but wanted to include them since you suggested that this might be what I am after. Note that the intervals I need (and approximate via simulations) are just somewhat widened CIs, so it is not like CIs are totally unrelated.... Note that both fit and fitbar share the same "true" values, so one should provide some information about the other.
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| Feb 13, 2023 at 14:54 | history | edited | Martin Modrák | CC BY-SA 4.0 |
Added figure of the results
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| Feb 13, 2023 at 14:42 | comment | added | Tim | There's no reason for your simulation to work because you check if parameters from completely different models match confidence intervals from another model. | |
| Feb 13, 2023 at 14:25 | history | edited | Martin Modrák | CC BY-SA 4.0 |
Fixed typo in code
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| Feb 13, 2023 at 14:07 | comment | added | Martin Modrák | @Tim I added a code example showing what I am after. | |
| Feb 13, 2023 at 14:06 | history | edited | Martin Modrák | CC BY-SA 4.0 |
Added a code example
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| Feb 13, 2023 at 12:22 | comment | added | Tim | Could you give us an example illustrating the problem? It's not perfectly clear from your description. | |
| Feb 13, 2023 at 11:54 | history | edited | Martin Modrák | CC BY-SA 4.0 |
Added more explanation about the sense in which i use "prediction interval"
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| Feb 13, 2023 at 11:48 | comment | added | Martin Modrák | @Tim Agree that "prediction interval" might not be the best naming. The idea is this: I can make predictions for $\bar{y}$ given $\bar{x}$ - if my understanding of prediction intervals is correct, this is going the be a random vector of correlated t-distributed variables. I then should be able to transform predictions for $\bar{y}$ into predictions for some function of $\bar{y}$. $\bar{\beta}_1$ - the MLE of regression slope given $\bar{x}, \bar{y}$ is such a function. I want to construct a prediction interval for the value of this function. Does that clarify? | |
| Feb 13, 2023 at 10:53 | comment | added | Tim | Prediction intervals are usually meant for the intervals around predictions rather than parameters. What do you mean here? Aren't you interested in confidence intervals? | |
| Feb 13, 2023 at 10:45 | history | asked | Martin Modrák | CC BY-SA 4.0 |