We developed a 10-item scale in order to assess the level of acceptance of aggression. Each item was measured on a 3-point ordinal scale. So far, the factor analysis requires interval or ratio scores. Can we still use these three points ordinal measures for factor solution? What could be the alternative solution?
Dear Rabiul Karim,
From my perspective, it is not sure whether you can take your 10-point scale of acceptance level into a 3-point ordinal scale. However, your 10-point acceptance level can be categories into 3 attributes. They are namely: Not accepted, Marginally accepted and Accepted. As it is understood that your 10-point scale is from 1 to 10 and scale 5 indicates the level of neutral, it would be wise to have a confidence level estimate based on the mid-scale 5, by considering the standard deviation of a variable. It will be easy and statistically acceptable.
If you need, you can refer to the paper that I have given its link below.
Article The Relationship of Brand Equity to Purchase Intention
In the paper, it was considered a 5-point scale and the mid-point scale is 3.
You can refer to page 6 of the paper for the assumptions and how the interval estimates can be done to have the three levels of acceptance attributes. According to your 10-point scale, you have 5 as the mid-point scale, instead of 3 for the 5-point scale.
Hope this will help you. Good luck in your studies.
Regards,
S. Senthilnathan
The scale has 10 items. The items were measured on a 3-point scale, e.g., 0 = not accepted, 1= little accepted, 2 = strongly accepte. Thank you so much
There are different types of factor analysis (e.g., some for binary data, some for continuous or metric data, and some for ordinal data). Which type of factor analysis (e.g., a graded response IRT model) are you asking about?
I would say no. This is because you dont give your participnats enough options to answer your questions. Usually for factor analysis i would recommended at least 5. That should cover all your basis.
Dear Rabiul Karim,
If you have gone through my suggestions, you might have some answers for your question. If you have still some problems, I am willing to help you formulate the acceptance attributes with a 95% confidence limit. If so, you need to provide me with the name of variables, their respective means and standard deviations to set the confidence limits. Good luck.
Hello Rabiul,
In addition to the good suggestions given previously (especially Daniel Wright 's, which was pointing you in the direction of IRT models...very useful for getting past the usual objections to Likert-type response scale values being treated as if interval strength), let me make two other observations.
1. For common factor analysis, it would make sense to consider using polychoric correlations instead of Pearson or Spearman correlations.
2. Likert's own perspective (1932) was that the successive integer scaling of response values (1, 2, 3, ... k) was that, compared to the then more rigorous scaling methods available at the time, his integer scaling correlated in the .90s with the "rigorous" scaling values. While he (Likert) argued that the summated scale scores are the ones to use (and not individual item scores), this supposes that the scale is in fact, unidimensional. And that's the question that factoring can help to answer (or, IRT scaling can explore dimensionality as well).
https://legacy.voteview.com/pdf/Likert_1932.pdf
Good luck with your work.
Hi Rabiul,
You can use exploratory and confirmatory factor analysis to gather evidence for construct validity. You can use polychoric correlation/covariance matrix for this analysis. There is some articles about factor analysis with categorical data.
Bests
Article Best Practices in Exploratory Factor Analysis: Four Recommen...
Book Best Practices in Exploratory Factor Analysis
Article Factor analysis of variables with 2, 3, 5 and 7 response cat...
Article Confirmatory factor analysis of ordered categorical variable...
Article Confirmatory Factor Analysis of Ordinal Variables With Missp...
https://www.frontiersin.org/articles/10.3389/fpsyg.2014.01515/full
https://dergipark.org.tr/tr/download/article-file/1222063
Rather, it would be preferable to use the Likert scale with 5 or 7 possible responses.
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