Dear researchers,
I am trying to develop two scales for a project I'm working on
there are no specific scales in the literature so we decided we could try to create the scales we needed.
I used cronbach's alpha to determine reliability, and i used principle component analysis. But I'm having some difficulites interpreting the results and knowing what I need exactly from PCA
For the first scale
it consists of 11 items
cronbach's alpha is about 0.85 and mean inter item correlation was 0.35
I used PCA and after parallel analysis i ended with one component/factor
based on the component matrix all variables loaded strongly on the component (0.5+)
Since all items loaded on one component, is that considered good for a scale?
As for the second scale
cronbach's alpha was about 0.83 and inter item correlation was about 0.26
I also used PCA and after parallel analysis I ended up with two factors
the first factor had a big eigenvalue while the second factor was just barely above "significance"
Based on the component matrix, all variables loaded pretty well on the first component (0.3+) but some variables loaded on both components, either positively or negatively
I removed some variables that loaded on two components,
cronbachs alpha became a bit lower but mean inter item correlation increased to 0.29
after PCA and parallel analysis only one factor was retained and all variables loaded nicely on that component
To recap, my questions are:
for the first scale, is having one component a sign of a good scale?
and for the second scale, how do interpret negative loadings on one component and positive loadings on the other, and how do i interpret loadings on two components
last but not least, is what i did for the second scale (removing some variables) a good or bad decision?
Dear Dr. Jawad thank you very much indeed for the question.
I am taking information from Alyami, M., Henning, M., Krägeloh, C. U., & Alyami, H. (2020). Psychometric Evaluation of the Arabic Version of the Fear of COVID-19 Scale. International journal of mental health and addiction, 1–14. Advance online publication. https://doi.org/10.1007/s11469-020-00316-x
to answer your question.
I quote directly from the statistical section of this paper
"1. They assessed nternal consistency using Cronbach alpha coefficients (α), inter-item correlations as well as corrected item-total correlations.
2. According to DeVellis (2016); Nunnally and Bernstein (1994) a Cronbach’s α of .70 or higher indicates acceptable reliability
3. According to Ferketich (1991).” Inter-item correlations and corrected item-total correlations between .30 and .70 indicate medium to strong associations between items."
If all the components are having strong factor loadings this is an indication that the items are good.
For the second scale if you have 2 components you look at the rotated component matrix
.795 -.178
.843 -.202
If you have 2 components and one is positive and one is negative you go for the one which is positive and having higher value.
I hope this really helps. All the very best
Dr. Nabeel thank you for your response,
for the second scale some items had major cross loadings (whether both positive or positive/negative)
I'm thinking of deleting variables with low inter item correlations, and seeing if it becomes a one factor solution, what do you think?
By right we should use the 'real' EFA (eg. Principal Axis Factoring) instead of PCA when developing a new scale@instrument. PCA is a default function for factor analysis. PCA is appropriately used when we adapt or adopt other scale. Usually people would not argue which one as long as we got the best factor solution.
Dear Dr.Jawad,
II think you can look at the reliability tests splly the Cronbach's Alpha. Over there you would have Alpha after item deletion try removing the items with low values and also remove items with low ICC inter item correlation coefficient. All the very best God Willing u will surely succeed.
When using CFA prior to EFA, the Cronbach's Alpha doesn't help much. Most importantly in most cases to obtain a good model fit in CFA, loading higher than 0.7 in EFA would be recommended.
I am preparing E-Readiness Index for farmers, extension personnel and agricultural scientist separately to measure the degree of an individual to utilize tools of ICT in agriculture. I have selected sub-groups as well as indicators for the same but i am stuck how to obtain e-readiness score ? As per my reading of literature i realized that PCA or Factor Analysis provides relevancy and accuracy to indicators but my confusion is when to apply PCA ? On which data - data obtained from pre-testing data or the final collected data? Or without any data collected ? Please guide.
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