Parallel Analysis: a Method for Determining Significant Principal Components

Numerous ecological studies use Principal Components Analysis (PCA) for exploratory analysis and data reduction. Determination of the number of components to retain is the most crucial problem confronting the researcher when using PCA. An incorrect choice may lead to the underextraction of components, but commonly results in overextraction. Of several methods proposed to determine the significance of principal components, Parallel Analysis (PA) has proven consistently accurate in determining the threshold for significant components, variable loadings, and analytical statistics when decomposing a correlation matrix. In this procedure, eigenvalues from a data set prior to rotation are compared with those from a matrix of random values of the same dimensionality (p variables and n samples). PCA eigenvalues from the data greater than PA eigenvalues from the corresponding random data can be retained. All components with eigenvalues below this threshold value should be considered spurious. We illustrate Parallel Analysis on an environmental data set. We reviewed all articles utilizing PCA or Factor Analysis (FA) from 1987 to 1993 from Ecology, Ecological Monographs, Journal of Vegetation Science and Journal of Ecology. Analyses were first separated into those PCA which decomposed a correlation matrix and those PCA which decomposed a covariance matrix. Parallel Analysis (PA) was applied for each PCA/FA found in the literature. Of 39 analyses (in 22 articles), 29 (74.4%) considered no threshold rule, presumably retaining interpretable components. According to the PA results, 26 (66.7%) overextracted components. This overextraction may have resulted in potentially misleading interpretation of spurious components. It is suggested that the routine use of PA in multivariate ordination will increase confidence in the results and reduce the subjective interpretation of supposedly objective methods

Distinct transcriptional responses of mouse sensory neurons in models of human chronic pain conditions.

Background: Sensory neurons play an essential role in almost all pain conditions, and have recently been classified into distinct subsets on the basis of their transcriptomes. Here we have analysed alterations in dorsal root ganglia (DRG) gene expression using microarrays in mouse models related to human chronic pain. Methods: Six different pain models were studied in male C57BL/6J mice: (1) bone cancer pain using cancer cell injection in the intramedullary space of the femur; (2) neuropathic pain using partial sciatic nerve ligation; (3) osteoarthritis pain using mechanical joint loading; (4) chemotherapy-induced pain with oxaliplatin; (5) chronic muscle pain using hyperalgesic priming; and (6) inflammatory pain using intraplantar complete Freund's adjuvant. Microarray analyses were performed using RNA isolated from dorsal root ganglia and compared to sham/vehicle treated controls. Results: Differentially expressed genes (DEGs) were identified. Known and previously unreported genes were found to be dysregulated in each pain model. The transcriptomic profiles for each model were compared and expression profiles of DEGs within subsets of DRG neuronal populations were analysed to determine whether specific neuronal subsets could be linked to each of the pain models.  Conclusions: Each pain model exhibits a unique set of altered transcripts implying distinct cellular responses to different painful stimuli. No simple direct link between genetically distinct sets of neurons and particular pain models could be discerned