Timeline for How to determine or show if two solutions to linear regression are different
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Aug 5 at 16:05 | comment | added | whuber♦ | Because it makes this a standard question in regression with standard, routine solutions implemented in all kinds of software: no special calculations or theory are needed. For details see stats.stackexchange.com/questions/12797 (it's the same question as yours). | |
| Aug 5 at 15:18 | comment | added | Finncent Price | I suppose I could just make the $A$ matrix block-diagonal, but I don't see how that is any different from running two separate regressions and then comparing the coefficients. What is the point of the single measurement construction? Why does that matter? | |
| Aug 5 at 15:13 | comment | added | whuber♦ | They will be zeros. The relationship is determined by the rules of matrix multiplication. It can help to work it out with a tiny example, such as two sets of observations with one regressor (where $A$ is a $2\times 1$ matrix). | |
| Aug 5 at 14:52 | comment | added | Finncent Price | I still do not understand the 900x90 part. At the moment, I have two 450x45 matrices. It isn't obvious how to put that data into a 900x90 matrix. No matter which way I do, half of the entries in the matrix are going to be unknown (zero?) because I literally do not have enough data to fill all of those entries. | |
| Aug 3 at 20:20 | comment | added | whuber♦ | It would be $450\times 90$ if the regressors $A$ had been identical in both cases. But since you are estimating $90$ coefficients, you cannot reduce the second dimension. I believe your question has been asked and answered at stats.stackexchange.com/questions/13112 (among others), where you can read the details. | |
| Aug 3 at 18:39 | comment | added | Finncent Price | Wouldn’t the single measurement be 900x45? 45 equalities is straightforward as you say, but in this situation, I’m using the parameters to reconstruct an image and I’m not sure what it means for the image if, for example, all the terms are significant but one. Your comment/question has made me think about whether looking at the individual coefficients will get me what I want, though. Thank you. | |
| Aug 3 at 18:04 | comment | added | whuber♦ | Consider a system in which the input is the collection of your two measurements and the outputs are the collected results. This system can be represented as a single measurement involving a $900\times 90$ matrix and an parameter estimate $\beta$ that is the concatenation of $x_1$ and $x_2.$ You simply need to test the hypothesis $x_1=x_2$ (that's a set of $45$ equalities), which is a standard and extremely well established technique. What about your situation would preclude this straightforward solution? | |
| Aug 2 at 23:46 | history | asked | Finncent Price | CC BY-SA 4.0 |