THE VALIDITY OF EXPLORATORY
Date
2011-05-13
Authors
Maddern, Kevin Richard
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Abstract
The purpose of this research was to determine the impact that ordinal data
(Likert type responses) has on principle axis method exploratory factor analysis,
and whether these results could be improved through first rescaling the ordinal
data using the distribution fitting method proposed by Stacey (2005), or using
analysis that ignores the inter scale distances by using Spearman-rank
correlation analysis, prior to performing exploratory factor analysis.
This research was a simulation study. It simulated the continuous
attitudes/beliefs of respondents given a known (unobserved) factor structure,
and then used these to create responses on an ordinal scale. The study
compared the robustness of exploratory factor analysis using varimax rotation
when applied; directly to the ordinal data, to the Spearman-rank correlation
matrix of the same ordinal data, and to the transformed ordinal data using a
distribution fitting algorithmic approach. Comparison was done between these
methods and the known factors of the contrived ‘latent’ continuous population
from which the ordinal data was derived.
The research found that discretisation creates both a negative bias and an
increase in the variance in the factor loading results. The amount of negative
bias and variance increase both as the number of categories used in the
response scale decrease, and as the underlying communalities in the factor
structure decrease. Given various forms of scale distortion introduced during
the discretisation process (skew, kurtosis, and bimodality), it was found that
both the negative bias and the variance of the results will increase even further
as the scale distortion increases. These scale distortions are akin to the various
biases that a group of respondents may exhibit when completing an ordinal
scale questionnaire. Skewed distortion was found to be the most destructive,
followed by bimodal distortion. Although no improvement was found in the
results when using normal distribution fitting algorithm prior to exploratory factor
analysis, it was found that, in cases of skewed or bimodal distortion, performing
exploratory factor analysis on the Spearman-rank correlation matrix of the
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ordinal data was superior to performing the factor analysis directly on the
ordinal data.
These results are relevant to many fields of research, including business, given
the prolific use of ordinal scales to gather data due to their simplicity and ease
of use, and given the need by researchers to simplify or further analyse the
ordinal data using multivariate techniques intended for interval level data (such
as exploratory factor analysis). It was found that researchers need to take care
in the selection of the response scale for their analysis, since it is shown that
the correct choice in category size is the most effective way to ensure that data
loss due to discretisation error is minimised. Data loss was shown to constitute
both a strengthening and a weakening in the observed factor loading when
compared to the unobserved (intended) factor structure. The risk is therefore
shown that a researcher may unknowingly discard good data, or include
spurious data, through the incorrect use of the response scale. These results
begin to guide the researcher to avoid these pitfalls.
Description
MBA - WBS
Keywords
Ordinal data, Ordinal scales