I am trying to find the correlation between two latent variables. Let's call them A and B.
- A has two dimensions. Let's call them Dimension 1 and 2.
- B also has two dimensions. Let's call them Dimension 3 and 4.
- The four dimensions (1, 2, 3 and 4) have several indicators each. Let's call them (a) and (b) for Dimension 1, (c), (d) and (e) for Dimension 2, (f) and (g) for Dimension 3 and (h), (i) and (j) for Dimension 4.
- I have measured the ten indicators (a, b, c, d, e, f, g, h, i and j) on a likert scale or else using cardinal numbers (e.g. one, two, three, four, etc.).
- I have then weighted the indicators using the likert scale codes that I created (e.g. 0 = not important, 1 = low importance, 2 = medium importance, 3 = high importance and 4 = absolute importance)
- I have then added the scores for all indicators to arrive at the dimension scores. This is my first weighting.
- I have then said that each dimension contributes 50% to the composite score of A or B and have standardised the dimension scores to 50% each. This is my second weighting.
- Finally I added the dimension scores to arrive at the composite score.
To give an example:
If I have a score of 2 for (a) and 3 for (b) then my total for Dimension 1 is 5. Similarly, if I have a score of 3 for (c), 4 for (d) and 2 for (e), then my total for Dimension 2 is 9. The score of 5 and 9 are the dimension scores, based on likert scale weights.
As I said that each dimension contributes 50%, I have divided the obtained score by the total score for each dimension and multiplied it by 50%. So I have got the following:
(2+3)/8 (remember this is based on two likert scale responses so the maximum score is 4 plus 4) x 50% = 0.31
(3+4+2)/12 (remember this is based on three likert scale responses so the maximum score is 4 plus 4 plus 4) x 50% = 0.38
I then added 0.31 and 0.38 and got 0.69. This is my composite score for Composite Variable A (which has 2 dimensions and 5 indicators; 2 for the first dimension and 3 for the second dimension).
To make it comprehensible, I have multipled 0.69 by 100 to get 69 out of 100 scores. I want to run corrleation on the composite scores of A and B to see the relationship between them.
As you would see, I have not done any complex statistical modeling using factor analysis etc but arrived at my final score using a system of subjective weighting based on relative importance (which is aligned to the likert scale coding in the first instance) and equal weighting in the second instance. I have used this approach to keep everything simple. I know it is subjecive weighting but I can justify it to some extent with theory and the rest with commonsense!
Am I doing this right? Is this approach robust enough? Remember, I don't want to complicate things! I am not statistically minded!
Can I do correlation analysis on the composite scores of A and B? They are rank scores (based on weights) so is the Spearman Rank Correlation the way to go for the analysis?