Factor Analysis Example - Harvard University

[Pages:43]Factor Analysis Example

Qian-Li Xue

Biostatistics Program Harvard Catalyst | The Harvard Clinical & Translational Science

Center Short course, October 28, 2016

1

Example: Frailty

? Frailty is "a biologic syndrome of decreased reserve and resistance to stressors, resulting from cumulative declines across multiple physiologic systems, and causing vulnerability to adverse outcomes" (Fried et al. 2001)

? Common phenotypes of "frailty" in geriatrics include "weakness, fatigue, weight loss, decreased balance, low levels of physical activity, slowed motor processing and performance, social withdrawal, mild cognitive changes, and increased vulnerability to stressors" (Walston et al. 2006)

2

Example: Frailty

Manifest Variables of Frailty:

Body composition: Arm circumference Tricep skinfold thickness

Body mass index

Slowed motor processing and performance:

Speed of fast walk

Speed of Pegboard test

Speed of usual walk

Time to do chair stands

Muscle Strength: Grip strength Knee extension

Hip extension

3

Recap of Basic Characteristics of Exploratory Factor Analysis (EFA)

? Most EFA extract orthogonal factors, which may not be a reasonable assumption

? Distinction between common and unique variances

? EFA is underidentified (i.e. no unique solution)

? Remember rotation? Equally good fit with different rotations!

? All measures are related to each factor

4

Major steps in EFA

1. Data collection and preparation 2. Choose number of factors to extract 3. Extracting initial factors 4. Rotation to a final solution 5. Model diagnosis/refinement 6. Derivation of factor scales to be

used in further analysis

5

Step 1. Data collection and preparation

v Factor analysis is totally dependent on

correlations between variables.

v Factor analysis summarizes correlation

structure

v1.........vk

O1 . . . .

v1.........vk

v1 . . . vk

F1.....Fj v1 . . . vk

. .

Correlation Factor pattern

.

Matrix

Matrix

.

On

Data Matrix

6

Example: Frailty

(N=547)

Observed Data Correlation Matrix

bmi arm skin grip knee hip uslwalk fastwk chrstand peg

----------------------------------------------------------------------------

bmi 1.00

arm 0.89 1.00

skin 0.65 0.72 1.00

grip 0.25 0.32 0.23 1.00

knee -0.41 -0.36 -0.12 0.01 1.00

hip -0.34 -0.34 -0.10 0.00 0.62 1.00

uslwalk -0.11 -0.03 0.09 0.14 0.26 0.12 1.00

fastwk -0.10 0.01 0.13 0.17 0.29 0.15 0.89 1.00

chrstand 0.04 0.02 -0.08 -0.09 -0.26 -0.14 -0.41 -0.41

1.00

peg 0.05 0.10 0.18 0.24 0.13 0.08 0.33 0.35 -0.29 1.00

------------------------------------------------------------------------------------------------------------------------

7

Step 2. Choose number of factors

v Intuitively: The number of uncorrelated constructs that are jointly measured by the Y's.

v Only useful if number of factors is less than number of Y's (recall "data reduction").

v Estimability: Is there enough information in the data to estimate all of the parameters in the factor analysis? May be constrained to a certain number of factors.

8

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download