1. Variable Cluster Analysis: A useful approach to identify underlying dimensions of a questionnaire Usree Kirtania, MS; Cynthia Davis, MS Institute for Community Health Promotion, Nov 2006
BROWN
UNIVERSITY
OBJECTIVE: To identify underlying dimensions of a questionnaire using Variable cluster analysis (VARCLUS) approach.
Introduction
_____________________________________________________
Variable Cluster Analysis, (implemented in SAS through PROC VARCLUS), is another variable reduction method that often has distinct advantages over the traditional Factor Analysis (FA) approach. This method borrowed some ideas from the Factor Analysis method and some from the Hierarchical Clustering method and produces either disjoint or hierarchical clusters. These distinct clusters from VARCLUS help to identify underlying dimensions of a questionnaire which are essential for developing a well constructed scale score.
Data
________________________________________________
We applied the VARCLUS method in a 94 item food habit questionnaire (STFHQ) from the SISTERTALK study,which is a weight control intervention program for African American women (N=461).Each introductory item is followed by several behavioral items. We used 57 behavioral items in the analysis.
Example: Introductory item: How often did you eat bacon or sausage?
Behavioral item: How often was it low fat or turkey bacon?
Multi level responses: (Almost always/often, sometimes, rarely, never).
For all behavioral items higher score indicates higher fat intake behavior.
Missing values generated in behavioral items due to response ‘never’ in an introductory item were imputed with zero.
Fat related eating behaviors using VARCLUS procedure
_________________________________________________
Preliminary VARCLUS suggested 7 distinct clusters.
59% total variation explained by these 7 clusters. Cluster items and
1 –R2 ratio has been presented below.
Restaurant (=0.72)
Sitdn1 (0.41)
Sitdn3 (0.41)
Sitdn5 (0.52)
Sitdn7 (0.50)
Lean fat food (=0.48)
Grdmt1 (0.52)
Grdmt2 (0.59)
Redmt1 (0.62)
Redmt3 (0.52)
Higher fat food (=0.74)
Chick1 (0.39)
Ffish1 (0.56)
Sitdn6 (0.58)
Ffood6 (0.60)
Chinese food (=0.65)
Chins1 (0.32)
Chins2 (0.46)
Chins4 (0.50)
Milk fat (=0.71)
Milk1 (0.19)
Milk21 (0.16)
Fruit as snack/ dessert
(=0.76)
Otdes4 (0.23)
Snack3(0.23)
VARCLUS Procedure
______________________________________________________
VARCLUS procedure vs. Factor Analysis (FA)
______________________________________________
2nd eigenvalue
VARCLUS
Factor Analysis (FA)
Adding fat (=0.59)
Hotcr1 (0.49)
Sandw1 (0.51)
Potat3 (0.57)
X1, X2, X3, X4, X5
X1, X3, X4
X2, X5
X1, X3 X4
All variables start in one cluster.
MAXEIGEN=option
using Correlation matrix OR
PERCENT=option
using Covariance matrix
Estimate communalities
using Squared Multiple
Correlation (SMC)
1.7
Threshold
(Default) 1
2) 2nd eigenvalue > specified
threshold => additional dimensions.
Fat related eating behaviors using Factor Analysis
__________________________________________________
FA produced 7 factors. 62% total variation explained by these 7 factors. Higher fat food factor (8 items α=0.74).Chinese food factor (3 items α=0.65). Restaurant factor (4 items α=0.72). Milk fat factor (3 items α=0.70). Low/lean fat food factor (4 items α=0.44). Fruit as snack/dessert factor (2 items α=0.76). Adding fat factor (2 items α=0.44).
Conclusions
No estimating communalities makes the VARCLUS procedure simple.
Due to distinct clusters, VARCLUS is an easier method to detect and to explain underlying dimensions compared to the Factor Analysis approach, which produces overlapping factors.
So, we should consider the VARCLUS approach and use it more often along with FA because of it’s simplicity and interpretability.
Contact: Usree Kirtania. MS.
Statistical Data Analyst
0.7
Divisive Clustering
3) The initial cluster divided into
two clusters.
Number of clusters
Clusters that meet
2nd eigenvalue < specified
threshold
Number of factors
Scree plot
Kaiser-Guttman rule
6) VARCLUS uses the first principal
component based on correlation matrix
or the first centroid component based
on covariance matrix.
4) The procedure stops when each
cluster satisfies 2nd eigenvalue
< specified threshold criterion.
Rotation
Varimax
Promax
Rotation
Ortho-oblique
7) VARCLUS generates
(1-R2 own cluster)
1-R2 Ratio =
(1-R2next closest cluster)
5) Variables have relatively high
correlation with their own cluster and
low correlation with other clusters.
Cluster representative
(1-R2) ratio
(Lower is better)
Factor representative
Factor loading
(Higher is better)