Timeline for Solving linear regression with weights and constraints
Current License: CC BY-SA 3.0
20 events
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| Sep 10, 2014 at 14:54 | comment | added | whuber♦ | No, I think it means something is not quite right about the code in the present solution. Perhaps I just am not interpreting its output correctly... | |
| Sep 10, 2014 at 10:10 | comment | added | Datageek | @whuber Does it mean linear regression is not as good as some other solvers in this case? I originally used Excel solver and got really close results as well. I need to solve this problem in R, and preferably with one of the cran libraries that doesn't require installation of additional software. | |
| Sep 9, 2014 at 14:04 | comment | added | Sycorax♦ |
@whuber You're right that the results are incredibly precise. But b_hat is simply computed from the drawn (and transformed) sim_x value, so it is evaluated once for each draw. b_hat is not read in as if it were data.
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| Sep 9, 2014 at 14:00 | comment | added | whuber♦ |
There are problems with such a comparison, Datageek. First, the constraints automatically hold for any reasonable fit to these data. Second, the results shown in this answer are way too good: the distributions of the estimates are far too narrow (by one to two orders of magnitude) to be consistent with the actual data. Since I'm unfamiliar with rstan I cannot diagnose the problem. I believe, though, that it is unfairly using the true parameters b_hat in a simulation, so it is unclear to me to what extent it actually is testing the fitting procedure at all.
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| Sep 9, 2014 at 12:25 | comment | added | Sycorax♦ | If you use weighted least squares with the data in my snippet, the parameter estimates satisfy the constraint. There's not too much to show. | |
| Sep 9, 2014 at 12:17 | history | edited | Sycorax♦ | CC BY-SA 3.0 |
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| Sep 9, 2014 at 10:12 | comment | added | Datageek | @whuber this is great, thanks. Would you mind adding this as an answer? Would be great to see it produces the same results on the same data as user777. | |
| Sep 8, 2014 at 20:50 | comment | added | Sycorax♦ | With the expanded explanation, your meaning is, indeed, obvious. The great thing about CV is that I literally never stop learning. | |
| Sep 8, 2014 at 19:54 | comment | added | whuber♦ | The second one, if it exists, is guaranteed to meet the constraints, by construction. Otherwise, there is no solution. (But there always will be when the weights are positive.) Here's an example: fit a line $y=ax+b$ to $(x,y)$ data with the constraint $a+b\le 5$. If the OLS estimates do not satisfy that constraint, now fit the model $y=ax+5-a$ to those data. (You could easily do that by fitting the no-intercept model $y-5=a(x-1)$ to the data $(x-1,y-5)$, for instance.) I hope it's obvious the constraint will be met and that no special software is needed. | |
| Sep 8, 2014 at 19:32 | comment | added | Sycorax♦ | @whuber I'm not sure I fully understand. What happens when neither solutions meets the constraints? | |
| Sep 8, 2014 at 19:30 | comment | added | whuber♦ | I'm not exactly sure what @ssdecontrol is referring to :-), but as far as the other answers go, one (as I recall) suggested finding the weighted least squares solution. If it does not satisfy the constraint, then find the equality-constrained solution. Observe that (1) this requires only two least squares calculations, so it is efficient and fast and (2) in either case you obtain a covariance matrix for the estimates. Continuing in the analogical vein, that would make this problem about as easy as breaking a saltine into your soup, so you can put away the jackhammer :-). | |
| Sep 8, 2014 at 19:24 | comment | added | shadowtalker | When you have a jackhammer, everything looks like a sidewalk. | |
| Sep 8, 2014 at 18:43 | comment | added | Datageek | This is awesome, thanks @user777! I wonder how difficult it would be to do the same with one of the methods @whuber suggested. | |
| Sep 8, 2014 at 18:29 | vote | accept | Datageek | ||
| Sep 10, 2014 at 18:28 | |||||
| Sep 8, 2014 at 18:13 | history | edited | Sycorax♦ | CC BY-SA 3.0 |
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| Sep 8, 2014 at 17:19 | history | undeleted | Sycorax♦ | ||
| Sep 8, 2014 at 15:57 | history | deleted | Sycorax♦ | via Vote | |
| Sep 8, 2014 at 15:35 | history | edited | Sycorax♦ | CC BY-SA 3.0 |
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| Sep 8, 2014 at 15:28 | history | edited | Sycorax♦ | CC BY-SA 3.0 |
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| Sep 8, 2014 at 15:20 | history | answered | Sycorax♦ | CC BY-SA 3.0 |