For example, if I have 6 items on a 1-5 scale and 6 items on a 1-70 scale, can I do a factor analysis throwing them all into the mix? And, if I can, how do I then create a score (since clearly any mean or sum will be skewed toward the 1-70 scale items)?
So you have 2x6 scales measuring the same latent quantity in different ways. You can view this as if each score measured a linear transformation of the latent quantity with some error, i.e.
score01 = a01 + b01*latent + error01
...
score12 = a12 + b12*latent + error12
The variances of the errors may be different for each scale.
My preferred way of computing this is using the sem (structural equation modelling) package of R. It will estimate you the above a, b coefficients and the error variances, also the values of the latent variable for each subject. If the above assumptions are realistic then the value of the latent variable will be a good measure of the quality all of your scales intended to measure.
Hi,
Usually we run factor analysis based on correlations (that is standardized covariances), for this reason the differences in the scale is not a problem.
To have the score: just “save” in SPSS.
These scores are standardized (mean = 0 and s.d = 1)
Best regards,
Bido
Hi,
If you don’t have SPSS, use the “factor weights” (it isn’t the “factor loadings”) to compute the factor scores, like this:
1) Compute the standardized values of the items.
2) Use the factor weights to compute the unstandardized scores.
Unstandardized Score = w1*x1 + w2 *x2 +w3*x3 +…+wn*xn
Where:
wi = weight score of item i
xi = standardized value of item i
3) Standardize the factor scores.
Remembering that:
Standardized value = (unstandardized – mean) / s.d.
Best regards,
Bido
Agree with Diogenes Bido. Scale of items does'nt matter especially if you either save the output factor scores (I prefer the more direct Regression method) or if you calculate the score yourself from the weights and then standardize it. Save the result into your file and use it as a scale score. BTW this gets complicated if you want to estimate the reliability of the calculated scale. I'd use the factor scores in the reliability analysis instead of the original items - a common mistake.
Thanks for that last tip Alan, I can see how that could be easy to make.
I also agree with all earlier views that difference in scale does not matter for doing FA.
However, I would like to add that if exploring the factor structure is the only goal then there is no need of any transformation either in terms of Z scores or Factor scores or any other form. My view is based on the fact that factor analysis is based on correlation matrix and correlation is free of change of origin and scale. Thus, the difference in the possible range of scores as well as difference in the scale or scaling unit does not influence the correlation. Hence, any analysis (including FA) that is based on correlation will not be influenced by differences in the scale of items.
We compute correlation between weight and height, both having different unis of measurement.
Does anyone have a reference to support the decision to include factors on different scales in an EFA? I was planning to standardize my variables prior to the EFA because of the different scales.
When we run EFA based on correlations, all variables already are standardized.
Just when we used covariances (more common in CFA or SEM), the unit of each variable are included in the analysis. Even in these cases, usually we use the standardized solution.
I agree with Marisol, are there references for including variables on (very) different scales without standardisation in factor analysis. IF so which method is preferred? I would assume maximum likelihood?
having done this tupe of analysis now, it is indeed possible but standardisation is required. there are a number of different ones depending on the goals of the analysis. Though having done this now I would suggest avoiding ML, and doing principle axis (PAF) factor analysis in stata or r.
Thanks Sarah for the timely respond, hugely appreciated. If standardization is required, this should be done prior the factor analysis, right?
Going by this case then: How do one decide to adopt a new scale out of the scales for all the items. For instance, my items are 7 : five of them have a 6 -likert scale, one is a 4 likert and the last one is in 9-likert scale.
The end goal is to construct a measure for one of my independent variable "uncertainty avoidance" : before doing some regression (SPSS).
Yes you'd need to do this before you apply factor analysis and SPSS is very limited with respect to the FA options so you may want to avoid its pitfalls. This is required because FA is dependent on variances, and if youve got different scales you're results will be questionnable/unreliable. There are a number of standardisation techniques, google the references for it. but it varies depending on the goal. With likert scales you may be able to get away with converting everything to the same scale (see what others have done in the literature) but for me personally I have done FA on vastly different scales ( for example combined questionnaire data with lab results), thus the techniques I have applied may not apply to your situation
@ Sarah mount, I indeed found your knowledge and advice very useful. I have different variables of different type and scale. Since you have sone the excercise on mixed of scales I could use your experiences more for my paper.
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