Principal Components Analysis and Factor Analysis by Dr. Winai Bodhisuwan

Principal Component Analysis Principal components analysis transforms the original set of variables into a smaller set of linear combinations that account for most of the variance in the original set. The purpose of PCA is to determine factors (i.e., principal components) in order to explain as much of the total variation in the data as possible.

Principal Component Analysis The are 2 bases of analysis. Based on Covariance Matrices Based on Correlation Matrices

Radiotherapy Data Study The data consist of average ratings over the course of treatment for patients undergoing radiotherapy. Variables measured include x 1 (number of symptoms, such as sore throat or nausea); x 2 (amount of activity, on a 1-5 scale); x 3 (amount of sleep, on a 1-5 scale); x 4 (amount of food consumed, on a 1-5 scale); x 5 (appetite, on a 1-5 scale); and x 6 (skin reaction, on a 0-3 scale) *Refer to the data set file, radiotherapy.MTW

Mineral Contents in Bones At the start of a study to determine whether exercise or dietary supplements would slow bone loss in older women, an investigator measured the mineral content of bones by photon absorptiometry. Measurements were recorded for three bones on the dominant and nondominant sides. *Refer to the data set file, mineralcontents.MTW

Air Pollutions The data set file are 42 measurements on air-pollution variables recorded at 12:00 noon in the Los Angeles area on different days. *Refer to the data set file, airpollution.MTW

Principal Component Analysis Minitab Command: Using the menu: Stat >> Multivariate >> Principal Components

Principal Component Analysis Minitab Command: Click Graphs and Storage to produce score plot and store the resulted score.

Factor Analysis Factor analysis is a multivariate tool that is very similar to PCA. Factor analysis is also used to condense a set of observed variables into smaller of transformed variables called factors.

Rotated Factor Matrix Correlation Matrix or Covariance Matrix Data Collection MLE Factor Model PCA Unrotated Factor Matrix

Factor Analysis Minitab Command: Using the menu: Stat >> Multivariate >> Factor Analysis

Factor Analysis Minitab Command: Using the menu: Stat >> Multivariate >> Factor Analysis

Factor Analysis Minitab Command: Using the menu: Stat >> Multivariate >> Factor Analysis