tag:blogger.com,1999:blog-9192597712746432631.post8585351135220453712..comments2017-02-20T23:51:26.561+00:00Comments on Notes from Two Scientific Psychologists: Nonlinear Covariation Analysis (MÃ¼ller & Sternad, 2003)Andrew Wilsonhttps://plus.google.com/100841335754826929747noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-9192597712746432631.post-10548123909732666052016-11-08T11:09:32.719+00:002016-11-08T11:09:32.719+00:00Thanks for all that! Very useful :)Thanks for all that! Very useful :)Andrew Wilsonhttp://www.blogger.com/profile/16732977871048876430noreply@blogger.comtag:blogger.com,1999:blog-9192597712746432631.post-6077773014915571462016-11-06T14:59:22.600+00:002016-11-06T14:59:22.600+00:00Hi Andrew
Re (2) - IMO, z-transforming variables ...Hi Andrew<br /><br />Re (2) - IMO, z-transforming variables actually takes away the value of these analyses because there is no longer a well-defined relation between the "task outcome variable" and the elemental variables - i.e., if I know the joint angles directly, I know where the end-point of the effector is, but if I only know the z-transformed joint angle, I probably have no way of estimating the position of the end-point. More conceptually, in the original framework having "more" or "less" variance in certain joint angles is meaningful because it directly relates to how much they contribute to the task (whereas the unit variance of the z-transform destroys that)<br /><br />One sort of compromise is done in some of the UCM postural control papers, where they try to relate muscle activity to changes in the center-of-pressure. Here, there is no clear empirical relation between these two (unlike the joint angle vs end effector) - so they estimate this relation using a regression (assuming that deviations from the mean are small that they can be approximated by a matrix)<br /><br />One last point - the UCM (at least in its original formulation) requires the input variables to be "elemental variables" - i.e. they at least in principle should be uncorrelated. This is why in force production studies because there is "enslaving" between the fingers (i.e. a force produced in one finger also causes small forces in other fingers), the elemental variables are no longer "finger forces" , but rather "finger modes" (which account for the fact that there is enslaving)<br /><br /><br /><br /><br /> <br />Rajiv Ranganathanhttp://www.blogger.com/profile/16826795270905545127noreply@blogger.comtag:blogger.com,1999:blog-9192597712746432631.post-75461214832230609412016-11-01T10:41:14.860+00:002016-11-01T10:41:14.860+00:00Thanks for all your help finding these papers etc,...Thanks for all your help finding these papers etc, I appreciate it! I'm really enjoying them all a lot and I'll take all the help I can get on figuring them out.<br /><br />1. Well then good, if that's in there that's great. I'm thinking of coding up their example to work through it some more, actually, so that might help. <br /><br />2. re integrating this and UCM; I'm working on a project to test an idea I have for filling a gap in all these analyses, specifically formalising what the perceived task goal is. So I'm looking to apply my solution to all these 'motor abundance' analyses and develop a detailed analysis pipeline that can get applied by anyone else. If they don't specifically integrate, that's fine; complementary works too. But I don't see anyone working with all these analyses yet, it seems to have quickly devolved into camps. <br /><br />re different dimensional variables; can you z transform the variance to get them on an equivalent scale? Or does that mess with something?<br /><br />3. The Goal Equivalent Manifold is the last of my four motor abundance methods to review (thanks to you for all the references earlier on Twitter!)<br /><br />Glad this is useful! Always happy to hear students will get something from this. And these are not my final thoughts, I'm still learning, so if I'm wrong or missing something let me know!Andrew Wilsonhttp://www.blogger.com/profile/16732977871048876430noreply@blogger.comtag:blogger.com,1999:blog-9192597712746432631.post-69351351026256568762016-10-30T18:57:24.938+00:002016-10-30T18:57:24.938+00:00Great summary Andrew! Adding some comments here (s...Great summary Andrew! Adding some comments here (so that it does not seem like a Twitter rant)<br />1. The TNC method "does" in fact identify the manifold of goal equivalent states. The function "f" that maps input to output variables is the "manifold" of equivalent solutions. The co-variation element is the equivalent of the "vucm/vort" metric in UCM. (generally true, but see reference below) <br /><br />2. Regarding combining UCM and TNC - I'm not sure what the point would be unless it is for different aspects of a task. Because UCM is based on variance, it requires dimensionally similar elemental variables (either all forces, or all joint angles etc.) - there is no way to do a UCM analysis with dimensionally dissimilar variables like velocity and angle. The TNC gets around this issue by comparing the effects of variability at the "output" level. <br /><br />Did you have anything specific in mind when you talked about combining them?<br /><br />There is a nice paper comparing the two methods that detail some of the differences:<br />https://www.ncbi.nlm.nih.gov/pubmed/17715459<br /><br />3. Finally, to complete the trio - there is also the GEM, where the biggest advance is that "time/trial order" is also now part of the analysis (both UCM and TNC at least in their original formulation are based only on variance - so trial order makes no difference). A good review of the GEM method is here:<br />https://www.ncbi.nlm.nih.gov/pubmed/24210574<br /><br />Hope this helps - thanks again for doing this - your explanations are exceptionally clear! I'm going to refer my students to your blog from now onRajiv Ranganathanhttp://www.blogger.com/profile/16826795270905545127noreply@blogger.com