Let's say I've got a scale measuring a person's ability to build rapport with children. It has 3 dimensions based on EFA/CFA. In what case can we sum the scores across all 3 dimensions into a single score of ability to build rapport? Or should it be left as 3 separate scores for each dimension? Is it based on correlation among dimensions? Is there a specific cut-off value?
You can use bi-factor confirmatory factor analysis, if this procedure improve the fit your model, you can use the factor scores of the second order factor. If this procedure don't improve your model I don't advise summing all items. You will loose the individual contributions of each item.
You can use bi-factor confirmatory factor analysis, if this procedure improve the fit your model, you can use the factor scores of the second order factor. If this procedure don't improve your model I don't advise summing all items. You will loose the individual contributions of each item.
The issue is essentially the same as with the separate items that went into each scale: It depends on how strongly the three dimensions are correlated. If they are all measuring similar content (i.e., highly correlated), then it would make sense to treat them as a single, larger construct.
If the dimensions have been derived from EFA/CFA you would, in theory, lose valuable information by combining them. If with your sample the scales are highly correlated then you could combine them. The definition of "highly correlated" seems to vary across authors and this is reflected in the different criteria recommended for considering multicollinearity.
I see no point in reducing the factors. While it's easy to say 'ability to build rapport', this clearly involves a number of component skills, just as 'ability to build a house'. This skills may have differential effects on different aspects of rapport, or in different situations.
You risk missing all this by forcing the scale to represent a unitary dimension which finds poor support in the data.
Which leaves unanswered the question - why is it that you want to do so? Are you dealing with the problem of three separate outcome measures that are giving overlapping results to a predictor? Are you struggling with a small sample size in which only one predictor (not three) can be analyzed? The answer to that question will shape what we think are useful responses...
If two sub-scales are "highly correlated" then, in terms of the statistical analyses, measure essentially the same thing. The difference in fit between a 3-factor and a 1-factor (or 2-factor) model is directly testable through CFA, so this should probably be an empirical question.
Dear all,
The only thing perhaps that i can add in relation to "In what case can we sum the scores across all 3 dimensions into a single score of ability to build rapport? ": 1.when we sum, we are assuming a linear combination of the 3 scores; 2. if the factors do not have the same relevance we should do a weighted sum; 3. it will be easier to obtain an average of those score weight, but in this way i think that you were assuming unidimensionality, and its internal consistency would be high because all 3 would measure the same....
Have a nice time
Helena
This is not new in scales development to have subscales and the {sum} refers to the total scale.
each subscale have its similar items meaning, while all the items under the 3 dimensions also give general meaning for the phenomenon under study.
I think you can add the dimensions if all the dimensions are measuring same latent trait. If correlation is too high, doubt the possibility of loading in two different factors. Otherwise you can confirm with discriminant and convergent validity calculations (Statistical Procedure).
I do not know why you want to add them? But, I do not find any mistake in them.
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