Comments on PCA and Multivariate Normality

# Comments on PCA and Multivariate Normality -...

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Comments, Thoughts, etc Concerning Principal Component Analysis (PCA) 1) Exploratory in nature a. implies that assumptions can be somewhat relaxed i. normality is not critical if only interest is in dimension reduction 2) PCA strongly depends on the correlation structure of the variables used in the analysis a. requires linear relationships among variables b. requires sufficient sample sizes to accurately represent the correlation structure i. some texts recommend at least 200 observations ii. if data are highly variable (high variance) then more observations are better than less observations iii. if variables are highly correlated than fewer observations are needed than when correlation is not strong iv. if few variables are important in the PCA, then need fewer observations than when many variables are important 3) Missing values a. PCA does not use an observation if any of the variables has a missing value b. when the pattern of missingness is not completely at random, then the results of the PCA can be compromised c. possible fixes: i. remove variables that have a high number of missing values ii. use imputation techniques to predict the likely value of the missing variables 1. e.g. suppose X1 and X2 are highly correlated and X2 tends to be filled on but X1 has some missing values a. regress X1 on X2 using the observed data to get predicted values for the missing data. Replace the missing values

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## This note was uploaded on 07/22/2011 for the course STA 4702 taught by Professor Staff during the Spring '08 term at University of Florida.

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Comments on PCA and Multivariate Normality -...

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