Safety+-+Principal+Component+Analysis+(PCA)

== > ==Safety 091211-0923 ==> Principal Components Analysis (PCA) (Multivariate Methods) (GWU EMSE-271)==

Index | Topics (Logical Lectures) | Lectures | Problems | Readings | Nomenclature | Concepts > "Principal components analyis is a method that can be used to reduce the dimensionality of mulitvariate data." -Lattin > > "Principal component analysis is a method for re-expressing multivariate data. It allows the research to reorient the data so that the first few dimensions account for as much of the available information as possible. The researcher must decide the number of dimensions to use, trading of simplicity for completeness." - EMSE 271, Fall 2009, Slide 235 > > **Steps in a Principal Component Analysis** > || **Step** || **Approach** || **Comment** || > || Exploratory Data Analysis and PCA ||  || VD did not talk about this, but seemed to do it in the sample problem. || > || - View Correlation Matrix || Excel Conditional Formatting || Thresholds will vary with problem. || > ||  ||   ||   || > || - Perform check for highly correlated || Bartlett's Sphericity Test || Later in VD's sample, but it seem appropriate here to me. || > || - Balance with need for dimension reduction ||  || Bartlett's is not enough (EMSE 271, Fall 2009, Slide 275) || > || - Scale Data ||  || If needed or it looks like the right thing to do || > || Principal Component Analysis ||  || Can do PCA without raw data; only need correlation matrix (can be computed from covariance matrix (of standardized data; so underlying variances don't skew results. (Slide 275). If non-standardized, need to explain why. || > || - Run PCA Minitab ||  || Note: Minitab PCA function  requires raw data. || > || - Or Excel PCA Correlation Matrix Analysis ||  ||   || > || - Eignevanalysis of Correlation Matrix ||  ||   || > || - Dimension Reduction ||  ||   || > || - Review Correlation Matrix ||  || Seeing if one component might be enough || > || - Review Loading Plot(s) ||  || Probably only 1st two. || > || - Review Scatter Plot ||  ||   || > || **Retaining Components** ||  ||   || > || - Scree Plot ||  ||   || > || - Kaiser's Rule ||  ||   || > || - Horn's Procedure ||  ||   || > || - Explained Variance ||  ||   || > ||  ||   ||   || > ||   ||   ||   || > ||   ||   ||   || > || Assess Validity ||   ||   || > || - Jackknife Validation ||  ||   || > || - Bootstrap Validation ||  ||   || > || Interpretation ||  ||   || > || - Patterns of Association || Output Loadiing Martix ||  || > || - Interpretation ||  ||   || > ||  ||   ||   || > ||   ||   ||   || > > > **Sources:** ==
 * Analyzing Multivariate Data, by James Lattin, Douglas Carroll and Green, (c) 2003 ([|Amazon]), Chapter 4
 * EMSE 271, Fall 2009