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Q方法的统计分析基于因子分析,然后进行因子旋转。 当前,最常见的因子提取方法是质心和主成分提取,而因子旋转的常见技术是手动旋转和varimax旋转。 但是,还有一些其他因子提取方法(例如主轴因子分解)和因子旋转方法(例如quartimax和equamax)没有被Q用户使用,因为它们尚未在任何主要的Q程序中实现。 在本文中,我们简要介绍了一些主要因素提取和因素旋转技术,并使用三个数据集比较了这些技术。 我们对三个实际数据集应用了主成分和主轴因式分解方法,以进行因子提取以及varimax,equamax和quartimax因子旋转技术。 我们根据加载在每个因子上的Q排序的数量,每个因子上的区分语句的数量以及排除的Q排序比较了这些技术。 主成分和主轴因子分解因子提取之间没有太大差异。 本文的主要发现包括基于quartimax旋转的一般因素的出现和较少数量的排除Q排序。 另一个有趣的发现是,与varimax和equamax旋转相比,基于quartimax旋转的因子的区别性陈述数量更少。 这些发现不是结论性的,需要对更多数据集进行进一步分析。
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Open Journal of Applied Sciences, 2017, 7, 147-156
http://www.scirp.org/journal/ojapps
ISSN Online: 2165-3925
ISSN Print: 2165-3917
DOI: 10.4236/ojapps.2017.74013
April 30, 2017
A Comparison between Major Factor
Extraction and Factor Rotation Techniques in
Q-Methodology
Noori Akhtar-Danesh
School of Nursing, McMaster University, Hamilton, Canada
Abstract
The statistical analysis in Q-methodology is based on factor analysis
followed
by a factor rotation. Currently, the most common factor extraction methods
are centroid and principal component extractions and the common tec
h-
niques for factor rotation are manual rotation and varimax rotation. However,
there are some other factor extraction methods such as principal axis facto
r-
ing and factor rotation methods such as quartimax and equamax which are
not used by Q-
users because they have not been implemented in any major
Q-program. In this article we briefly explain some major fact
or extraction and
factor rotation techniques and compare these techniques using three datasets.
We applied principal component and principal axis factoring methods for
factor extraction and varimax, equamax, and quartimax factor rotation tec
h-
niques to thre
e actual datasets. We compared these techniques based on the
number of Q-sorts loaded on each factor, number of distinguishing stat
e-
ments on each factor, and excluded Q-sorts.
There was not much difference
between principal component and principal axis fac
toring factor extractions.
The main findings of this article include emergence of a general factor and a
smaller number of excluded Q-
sorts based on quartimax rotation. Another
interesting finding was that a smaller number of distinguishing statements for
factors based on quartimax rotation compared to varimax and equamax rot
a-
tions. These findings are not conclusive and further analysis on more datasets
is needed.
Keywords
Q-Methodology, Factor Analysis, Factor Extraction, Factor Rotation
1. Introduction
The statistical analysis in Q-methodology is based on factor analysis, which is
How to cite this paper:
Akhtar-Danesh,
N.
(201
7) A Comparison between Major Fac-
tor Extraction and Factor Rotation Tec
h-
niques in Q
-Methodology.
Open Journal of
Applied Sciences
,
7
, 147-156.
https://doi.org/10.4236/ojapps.2017.7401
3
Received:
March 13, 2017
Accepted:
April 25, 2017
Published:
April 30, 2017
Copyright © 201
7 by author and
Scientific Research Publishing Inc.
This work is licensed under the Creative
Commons
Attribution-NonCommercial
International License (
CC BY-NC 4.0).
http://creativecommons.org/licenses/by
-nc/4.0/
Open Access
N. Akhtar-Danesh
148
typically followed by a factor rotation. Currently, the most common factor ex-
traction methods are centroid and principal component extractions and the
common techniques for factor rotation are manual rotation and varimax rota-
tion. Indeed, these factor extraction and factor rotation techniques are the only
methods available in the widely used PQMethod program [1]. However, there
are some other factor extraction methods such as principal axis factoring and
factor rotation methods such as quartimax and equamax which are not used by
Q-users because they have not been implemented in any major Q-program. In
this article we briefly explain some major factor extraction and factor rotation
techniques and compare them using three actual datasets.
2. Background
2.1. Q-Methodology
Q-methodology was introduced in 1935 by Stephenson [2] [3] and is used to
identify common attitudes, perceptions, preferences, and feelings among a group
of participants. In Q-methodology subjective viewpoints are collected and ana-
lyzed using a combination of qualitative and quantitative techniques [4]. A Q-
methodological study involves a) development of a sample of statements, Q-
sample, related to the topic of interest and b) rank-ordering of the Q-sample by a
group of individuals from their points of views about the statements using a
Q-sort table (a grid) with a quasi-normal distribution (see
Figure 1). After data
collection using this grid a by-person factor analysis (
i.e.
, the factor analysis is
performed on persons not variables or traits) is used to analyze these Q-sorts
where each Q-sort represents one individual rather than one variable or trait.
However, for the rest of this article Q-sort and variable are used interchangeably.
Using such by-person factor analysis, similar Q-sorts (individuals) are grouped
together as factors where each factor represents a group of individuals with sim-
ilar views, feelings, or preferences about the theme of the study. One individual
is loaded on one factor if his/her factor loading is statistically significant (
p
≤
0.05). A factor loading is simply the correlation between a Q-sort and the factor
itself. Then, each factor is interpreted based on its
distinguishing
statements and
statements with high or low factor scores. Distinguishing statements usually de-
fine the uniqueness of each factor.
2.2. Factor Extraction Methods
General statistical programs such as SPSS, R, Stata, and SAS include several fac-
Figure 1. A Q-sort table with anchors of −5 and +5.
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