i am analysing the associations between social sustainability practices (62 observed indicators) that are grouped under 8 social categories, and sustainability enablers (10 observed indicators)
it is theoretically hypothesised that there is positive correlation between social sustainability practices and the enablers.
i'am interested in knowing the observed indicators and drawing conclusion based on that, i do not want to draw conclusions based on constructs.
can i use canonical correlation analysis (CCA) to analyse the strength of associations between 62 social indicator (dependent set) and another set of the 10 enablers ( independent set)?
or is it better to use structural equation modelling (SEM) and analyse path coefficients from independent variable (enablers) ----------------> 8 social categories each forming a latent dependent variable?
Yes you can, and I think CCA is much more suited than SEM in your case because is a less demanding procedure. My suggestion is to perform CCA not directly on the indicator variables but on the two separate sets of principal components of social indicators (set Y) and enablers (set X). In this way, given principal components are each other independent by construction, when you will perform CCA on the two X and Y component spaces you already eliminates within-set correlations and the emerging solution will only depend on the bertween-sets relational structure, see:
Article Breaking down the climate effects on cod recruitment by prin...
and
https://www.nature.com/articles/s41397-019-0080-6
Thank you for your valuable answer, i used the manova syntax on spss, i added all the social indicators (62) before WITH and the 10 enablers + 5 barriers after. thus, forming a set of (15 barriers and enablers , this is what you mean?
Can i send you the final model to tell me if i did it right?
Unfortunately, the 5 barriers show insignificant positive correlation coefficient with the practices. It should be negatively correlated in theory, should i remove them from the model? Or keep them since they are insignificant
Dear Chehab BEFORE PERFORMING CCA you should compoue the PCA of the 62 indicators, let's suppose you get a 5 component solution (eigenvalues > 1), well take the scores of these 5 components (SOC1-SOC5) they will be your VAR set. Then do the same with the enablers and barriers, let's suèppose you will get 3 principal components (ENAB1-ENAB3).
Well, now you are ready for CCA using SOC1.SOC5 as VAR set and ENAB1-ENAB3 as WITH set.
After CCA you will get different canonical correlations, start with the most relevant one and see which are the SOC and ENAB component that drive the canonical relation, well, let's imagine they are SOC1 and ENAB1 ..well go to the component loading matrix and intepret the meaning of the components that drive the relation between the two sets of variables.
Thanks a lot for your generous explanation, i will make it and see how it works.
Dear professor, what if all the 62 observed indicators are collected using survey (168 responses) derived from literature review process , and i need to keep the data specificity without reducing them in order to observe each of them and contrast with the literature can i run the CCA without PCA?
The results showed a statistically significant association Wilks < 0.05, therefore, r2=1-0 = 1, which indicates that the full model explained a large portion, about 100% of the variance shared between the variable sets.
ten canonical functions from the full CCA process but only the first two are statistically significant (p < 0.01) and hence, good candidates to be used for interpreting the results. The first function explains 48.3% and the second function explain 15.2% of the variation in the first set. The remaining 8 functions are not significant for the interpretation as their statistical significance test is uninformative since p > 0.01 for all of them.
Although the second function is statistically significant, it has no practical significance since it only explains 1.2% of variance in the second set of dependent variables explained by canonical function.
Therefore, the first function will only be considered in the analysis as it explains 35.3% of variance in dependent variables.
OK is good, as for the interpretation of the results you must look to the principal component scores (SOC and ENAB) most loaded on canonical variates. The original variables loadings on their components will allowyou to interpret the meaning of the principal components and then of the canonical solution, see for interpretation of components by their loadings (correlation coefficient between variables and their components) see the attached file. (Chapter: Catching the sense of experimental results: a case study on animal behavior).
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