Timeline for Why are "Linear" Models so Important?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 19, 2022 at 0:17 | comment | added | Glen_b | @MBA_Grad_Student_2022 re 1) see en.wikipedia.org/wiki/Nonlinear_regression There are also generalized nonlinear models (with similar replacement of the linear predictor with a function that's nonlinear in parameters). More generally still, you could have nonlinear models where the distribution of the conditional response [Y|X=x] is outside the exponential dispersion family. | |
| Sep 18, 2022 at 12:33 | comment | added | user603 | @Tim: from linearity also comes some equivariance properties such as affine equivariance which are important in practice, specially for forecasting | |
| Sep 18, 2022 at 5:34 | comment | added | Tim | 2) Usually yes. But not always. For example, a decision tree is non-linear and easy to fit. | |
| Sep 18, 2022 at 5:34 | comment | added | User1865345 | @Tim +1 for the compilation of those posts. | |
| Sep 18, 2022 at 5:32 | comment | added | Tim | @MBA_Grad_Student_2022 1) check the links I provided. Any model that is not linear in parameters is non-linear. | |
| Sep 18, 2022 at 5:32 | comment | added | User1865345 | @MBA_Grad_Student_2022 when response variable is related with the predictor variables through non-linear function, say, $y = \theta_1\exp(\theta_2x) +\varepsilon.$ The normal equations corresponding to non-linear least squares aren't that easy to solve compared to the linear counterparts. | |
| Sep 18, 2022 at 5:31 | history | edited | Tim | CC BY-SA 4.0 |
added 6 characters in body
|
| Sep 18, 2022 at 2:40 | comment | added | stats_noob | 2) Do GLM's allow for easier estimation of regression coefficients compared to non-linear models? | |
| Sep 18, 2022 at 2:39 | comment | added | stats_noob | 1) What is an example of a non-linear model? | |
| Sep 18, 2022 at 2:39 | comment | added | stats_noob | Thank you so much for addressing these points! Just two questions I had: | |
| Sep 17, 2022 at 22:37 | comment | added | Frank Harrell | I would temper "remarkably well" a bit. Linear models can be ruined by outliers and by not already knowing a good transformation for Y on which to base the analysis. | |
| Sep 17, 2022 at 22:13 | history | edited | Tim | CC BY-SA 4.0 |
added 120 characters in body
|
| Sep 17, 2022 at 21:49 | history | answered | Tim | CC BY-SA 4.0 |