Re: [R] linear functional relationships with heteroscedastic non-Gaussian errors - any packages around?
On Tue, 2 Dec 2008, Jarle Brinchmann wrote: Yes I think so if the errors were normally distributed. Unfortunately I'm far from that but the combination of sem its bootstrap is a good way to deal with it in the normal case. I must admit as a non-statistician I'm a not 100% sure what the difference (if there is one) between a linear functional relationship and a linear structural equation model is as they both deal with hidden variables as far as I can see. U and V are not 'variables' (not random variables) in a linear functional relationship (they are in the closely related linear structural relationship). J. On Tue, Dec 2, 2008 at 9:33 PM, Spencer Graves [EMAIL PROTECTED] wrote: Isn't this a special case of structural equation modeling, handled by the 'sem' package? Spencer Jarle Brinchmann wrote: Thanks for the reply! On Tue, Dec 2, 2008 at 6:34 PM, Prof Brian Ripley [EMAIL PROTECTED] wrote: I wonder if you are using this term in its correct technical sense. A linear functional relationship is V = a + bU X = U + e Y = V + f e and f are random errors (often but not necessarily independent) with distributions possibly depending on U and V respectively. This is indeed what I mean, poor phrasing of me. What I have is the effectively the PDF for e f for each instance, and I wish to get a b. For Gaussian errors there are certainly various ways to approach it and the maximum-likelihood estimator is fine and is what I normally use when my errors are sort-of-normal. However in this instance my uncertainty estimates are strongly non-Gaussian and even defining the mode of the distribution becomes rather iffy so I really prefer to sample the likelihoods properly. Using the maximum-likelihood estimator naively in this case is not terribly useful and I have no idea what the derived confidence limits means. Ah well, I guess what I have to do at the moment is to use brute force and try to calculate P(a,b|X,Y) properly using a marginalisation over U (I hadn't done that before, I expect that was part of my problem). Hopefully that will give reasonable uncertainty estimates, lots of pain for a figure nobody will look at for much time :) Thanks, Jarle. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. -- Brian D. Ripley, [EMAIL PROTECTED] Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UKFax: +44 1865 272595 __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
[R] linear functional relationships with heteroscedastic non-Gaussian errors - any packages around?
[apologies if this appears twice] Hi, I have a situation where I have a set of pairs of X Y variables for each of which I have a (fairly) well-defined PDF. The PDF(x_i) 's and PDF(y_i)'s are unfortunately often rather non-Gaussian although most of the time not multi-modal. For these data (estimates of gas content in galaxies), I need to quantify a linear functional relationship and I am trying to do this as carefully as I can. At the moment I am carrying out a Monte Carlo estimation, sampling from each PDF(x_i) and PDF(y_i) and using a orthogonal linear fit for each realisation but that is not very satisfactory as it leads to different linear relationships depending on whether I do the orhtogonal fit on x or y (as the errors on X Y are quite different non-Gaussian using the covariance matrix isn't all that useful either) Does anybody know of code in R to do this kind of fitting in a Bayesian framework? My concern isn't so much on getting _the_ best slope estimate but rather to have a good estimate of the uncertainty on the slope. Cheers, Jarle. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] linear functional relationships with heteroscedastic non-Gaussian errors - any packages around?
I wonder if you are using this term in its correct technical sense. A linear functional relationship is V = a + bU X = U + e Y = V + f e and f are random errors (often but not necessarily independent) with distributions possibly depending on U and V respectively. and pairs from (X,Y) are observed. As U and V are not random, there is no PDF of X or Y: each X_i has a different distribution. If you know the error distribution for each X_i and Y_i, you can easily write down a log-likelihood and maximize it. The first hit I got on Google, http://www.rsc.org/Membership/Networking/InterestGroups/Analytical/AMC/Software/FREML.asp, has a reference to a paper for the Gaussian case. But finding R code for the non-Gaussian case seems a very long shot. Jarle Brinchmann wrote: [apologies if this appears twice] It did ... Hi, I have a situation where I have a set of pairs of X Y variables for each of which I have a (fairly) well-defined PDF. The PDF(x_i) 's and PDF(y_i)'s are unfortunately often rather non-Gaussian although most of the time not multi-modal. For these data (estimates of gas content in galaxies), I need to quantify a linear functional relationship and I am trying to do this as carefully as I can. At the moment I am carrying out a Monte Carlo estimation, sampling from each PDF(x_i) and PDF(y_i) and using a orthogonal linear fit for each realisation but that is not very satisfactory as it leads to different linear relationships depending on whether I do the orhtogonal fit on x or y (as the errors on X Y are quite different non-Gaussian using the covariance matrix isn't all that useful either) Does anybody know of code in R to do this kind of fitting in a Bayesian framework? My concern isn't so much on getting _the_ best slope estimate but rather to have a good estimate of the uncertainty on the slope. Cheers, Jarle. -- Brian D. Ripley, [EMAIL PROTECTED] Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UKFax: +44 1865 272595 __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] linear functional relationships with heteroscedastic non-Gaussian errors - any packages around?
I wonder if you are using this term in its correct technical sense. A linear functional relationship is V = a + bU X = U + e Y = V + f e and f are random errors (often but not necessarily independent) with distributions possibly depending on U and V respectively. and pairs from (X,Y) are observed. As U and V are not random, there is no PDF of X or Y: each X_i has a different distribution. If you know the error distribution for each X_i and Y_i, you can easily write down a log-likelihood and maximize it. The first hit I got on Google, http://www.rsc.org/Membership/Networking/InterestGroups/Analytical/AMC/Software/FREML.asp, has a reference to a paper for the Gaussian case. But finding R code for the non-Gaussian case seems a very long shot. Jarle Brinchmann wrote: [apologies if this appears twice] It did ... Hi, I have a situation where I have a set of pairs of X Y variables for each of which I have a (fairly) well-defined PDF. The PDF(x_i) 's and PDF(y_i)'s are unfortunately often rather non-Gaussian although most of the time not multi-modal. For these data (estimates of gas content in galaxies), I need to quantify a linear functional relationship and I am trying to do this as carefully as I can. At the moment I am carrying out a Monte Carlo estimation, sampling from each PDF(x_i) and PDF(y_i) and using a orthogonal linear fit for each realisation but that is not very satisfactory as it leads to different linear relationships depending on whether I do the orhtogonal fit on x or y (as the errors on X Y are quite different non-Gaussian using the covariance matrix isn't all that useful either) Does anybody know of code in R to do this kind of fitting in a Bayesian framework? My concern isn't so much on getting _the_ best slope estimate but rather to have a good estimate of the uncertainty on the slope. Cheers, Jarle. -- Brian D. Ripley, [EMAIL PROTECTED] Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UKFax: +44 1865 272595 __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] linear functional relationships with heteroscedastic non-Gaussian errors - any packages around?
Thanks for the reply! On Tue, Dec 2, 2008 at 6:34 PM, Prof Brian Ripley [EMAIL PROTECTED] wrote: I wonder if you are using this term in its correct technical sense. A linear functional relationship is V = a + bU X = U + e Y = V + f e and f are random errors (often but not necessarily independent) with distributions possibly depending on U and V respectively. This is indeed what I mean, poor phrasing of me. What I have is the effectively the PDF for e f for each instance, and I wish to get a b. For Gaussian errors there are certainly various ways to approach it and the maximum-likelihood estimator is fine and is what I normally use when my errors are sort-of-normal. However in this instance my uncertainty estimates are strongly non-Gaussian and even defining the mode of the distribution becomes rather iffy so I really prefer to sample the likelihoods properly. Using the maximum-likelihood estimator naively in this case is not terribly useful and I have no idea what the derived confidence limits means. Ah well, I guess what I have to do at the moment is to use brute force and try to calculate P(a,b|X,Y) properly using a marginalisation over U (I hadn't done that before, I expect that was part of my problem). Hopefully that will give reasonable uncertainty estimates, lots of pain for a figure nobody will look at for much time :) Thanks, Jarle. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] linear functional relationships with heteroscedastic non-Gaussian errors - any packages around?
Isn't this a special case of structural equation modeling, handled by the 'sem' package? Spencer Jarle Brinchmann wrote: Thanks for the reply! On Tue, Dec 2, 2008 at 6:34 PM, Prof Brian Ripley [EMAIL PROTECTED] wrote: I wonder if you are using this term in its correct technical sense. A linear functional relationship is V = a + bU X = U + e Y = V + f e and f are random errors (often but not necessarily independent) with distributions possibly depending on U and V respectively. This is indeed what I mean, poor phrasing of me. What I have is the effectively the PDF for e f for each instance, and I wish to get a b. For Gaussian errors there are certainly various ways to approach it and the maximum-likelihood estimator is fine and is what I normally use when my errors are sort-of-normal. However in this instance my uncertainty estimates are strongly non-Gaussian and even defining the mode of the distribution becomes rather iffy so I really prefer to sample the likelihoods properly. Using the maximum-likelihood estimator naively in this case is not terribly useful and I have no idea what the derived confidence limits means. Ah well, I guess what I have to do at the moment is to use brute force and try to calculate P(a,b|X,Y) properly using a marginalisation over U (I hadn't done that before, I expect that was part of my problem). Hopefully that will give reasonable uncertainty estimates, lots of pain for a figure nobody will look at for much time :) Thanks, Jarle. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] linear functional relationships with heteroscedastic non-Gaussian errors - any packages around?
Yes I think so if the errors were normally distributed. Unfortunately I'm far from that but the combination of sem its bootstrap is a good way to deal with it in the normal case. I must admit as a non-statistician I'm a not 100% sure what the difference (if there is one) between a linear functional relationship and a linear structural equation model is as they both deal with hidden variables as far as I can see. J. On Tue, Dec 2, 2008 at 9:33 PM, Spencer Graves [EMAIL PROTECTED] wrote: Isn't this a special case of structural equation modeling, handled by the 'sem' package? Spencer Jarle Brinchmann wrote: Thanks for the reply! On Tue, Dec 2, 2008 at 6:34 PM, Prof Brian Ripley [EMAIL PROTECTED] wrote: I wonder if you are using this term in its correct technical sense. A linear functional relationship is V = a + bU X = U + e Y = V + f e and f are random errors (often but not necessarily independent) with distributions possibly depending on U and V respectively. This is indeed what I mean, poor phrasing of me. What I have is the effectively the PDF for e f for each instance, and I wish to get a b. For Gaussian errors there are certainly various ways to approach it and the maximum-likelihood estimator is fine and is what I normally use when my errors are sort-of-normal. However in this instance my uncertainty estimates are strongly non-Gaussian and even defining the mode of the distribution becomes rather iffy so I really prefer to sample the likelihoods properly. Using the maximum-likelihood estimator naively in this case is not terribly useful and I have no idea what the derived confidence limits means. Ah well, I guess what I have to do at the moment is to use brute force and try to calculate P(a,b|X,Y) properly using a marginalisation over U (I hadn't done that before, I expect that was part of my problem). Hopefully that will give reasonable uncertainty estimates, lots of pain for a figure nobody will look at for much time :) Thanks, Jarle. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
[R] linear functional relationships with heteroscedastic non-Gaussian errors - any packages around?
Hi, I have a situation where I have a set of pairs of X Y variables for each of which I have a (fairly) well-defined PDF. The PDF(x_i) 's and PDF(y_i)'s are unfortunately often rather non-Gaussian although most of the time not multi--modal. For these data (estimates of gas content in galaxies), I need to quantify a linear functional relationship and I am trying to do this as carefully as I can. At the moment I am carrying out a Monte Carlo estimation, sampling from each PDF(x_i) and PDF(y_i) and using a orthogonal linear fit for each realisation but that is not very satisfactory as it leads to different linear relationships depending on whether I do the orhtogonal fit on x or y (as the errors on X Y are quite different using the covariance matrix isn't all that useful either) Does anybody know of code in R to do this kind of fitting in a Bayesian framework? My concern isn't so much on getting _the_ best slope estimate but rather to have a good estimate of the uncertainty on the slope. Cheers, Jarle. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
