-------- Original Message -------- Subject: Application of partial least squares regression Date: Sat, 10 Mar 2012 09:58:12 -0500 From: Emily Kane <ekane...@ucr.edu> To: morphmet@morphometrics.org Hello, I am at UC Riverside and my advisor (Tim Higham) and I are interested in applying partial least squares regression to functional data (kinematics) in fishes. Given the use of this technique in the morphometrics community, I was hoping that someone might be able to answer some questions I have regarding the use of PLSR to address integration as well as some more atypical analyses of changes in integration. I am interested in how animals integrate the locomotor and feeding systems during prey capture. Most of the work on functional integration has utilized univariate statistical techniques such as correlation or regression. However, this doesn’t seem like the most appropriate approach for analyzing the integration of multiple systems, which are each defined by many variables. My questions are as follows: 1 - I have video of 4 species of fishes feeding on evasive and non-evasive prey types. Is there a way to incorporate these levels of variation into PLSR, for example as a covariate or a nested design? I have received some suggestions to use a multi-block PLS, but I am not sure whether this might be the most appropriate. 2 - Regarding power of the test, I know that PLSR is robust to datasets where traditional analyses (such as multiple linear regression) would have low statistical power due to low sample size, but I am unsure what the limit on sample size is for PLSR. I have 2 datasets with ~60 variables each, and within each species I will have 50 trials (25 for each prey type). If power will be a concern for this analysis, I have received some suggestions to use PCA to reduce each dataset prior to running PLSR, however I am concerned that PCA would distort the covariance relationships. Are there any other suggestions to rectify a low power situation? 3 - In the case that PLSR would result in more than two or three significant singular axes, is there a way to visualize all axes simultaneously in a single "integration space"? I plan to use phenotypic vector analysis to determine the flexibility of integration across species and prey types, which requires a 2D representation of the data. A solution I was thinking of is to perform a PCA on all significant PLSR axes to obtain the "integration space" since the PLSR axes describe the integration. However, I would like feedback as to whether this technique would be valid. Please send feedback to ekane...@ucr.edu <mailto:ekane...@ucr.edu>. I would also be more than happy to Skype with anyone who would be willing to discuss this further. Thank you. * Emily Kane* University of California, Riverside Department of Biology 900 University Avenue Riverside, CA 92521 Lab: (951) 827-2386 http://student.ucr.edu/~ekane001
