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
x1 (number of symptoms, such as sore throat or nausea);
x2 (amount of activity, on a 1-5 scale);
x3 (amount of sleep, on a 1-5 scale);
x4 (amount of food consumed, on a 1-5 scale);
x5 (appetite, on a 1-5 scale); and
x6 (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.
Data Collection
Correlation Matrix
or
Covariance Matrix
Factor Model
PCA
MLE
Unrotated
Factor Matrix
Rotated 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