# Composite variable from Likert items

I have six 5-point Likert items (1-Strongly Disagree, 2-Disagree, 3-Neither agree or disagree, 4-Agree, 5-Strongly Agree) which are related to my dependent variable. I sum the six variables which gives the frequency as follows:

    Frequency
6.00    1
9.00    1
12.00   6
13.00   3
14.00   3
15.00   18
16.00   11
17.00   4
18.00   17
19.00   11
20.00   14
21.00   22
22.00   15
23.00   9
24.00   11
25.00   2
26.00   3
30.00   2
Total   153


Now I want to recode the sum variable again into a 5-point scale (1-5) to get a composite score of my dependent variable. I will use this composite dependent variable in further analysis of ordinal logistic regression. My question is this:

What is the best way to recode the sum again into 5-point scale? Or, please let me know if there exists any better way to create a composite scale from Likert items?

just to clarify my quesion: I have six variables that are related to my DV, all are on 5 point likert scale. and I could not find the best way to reduce these six variables into one. The composite score may be considered as one of the option.

Your decision appeares inconsistent. By virtue of summing up 6 rating items into the total score you discard your attitude to those six as ordinal level-of-measurement scales; instead, you treat them as interval ones. On the other hand, you disbelieve the total score to be interval - as seen in you wish to categorize it and input to ordinal regression. That means that you fully disregard your done action of summing up. Why then you chose just summing and not some other way of combining?

You seem to have made up your mind that you want to turn this 6-30 variable, which for all we know may communicate finely grained information, into a coarser 1-5 variable which figures to have lower reliability. Also that you want to conduct an ordinal logistic regression. To tell you the truth it's hard to see good reasons for these decisions.

Moreover --and backing up--it's not always obvious that 6 different rating items will yield a valid and reliable indicator if summed to create a composite. You'll see why if you browse through threads on this site related to the tags of scale, composite, psychometrics, and/or Likert.

I agree with @rolando2 and @ttnphns but would go further. Coarsening a scale invokes magical thinking. It says that something magic happens at the border between categories. And a different division could yield a different solution.

One possible reason for doing this is to look at nonlinearities, but you have eliminated that if you assume proportional odds. Instead, you could look at spline regression, or polynomial effects.

As to better ways of combining Likert items; one solution is to do a factor analysis and use the factor scores as the DV. However, this usually gives very similar results to just summing.

• yes categorical principle component analysis could be run (if i consider my data as categorical) or PCA (if I consider it as continuous )but in both cases then I have to use linear regression on the factors and my data do not completely fulfil the assumptions of linear regression – wxa Jan 17 '12 at 2:20
• If you create factors, then those factors are continuous. Other assumptions are about the error term, and you can't tell about that before doing the regression – Peter Flom - Reinstate Monica Jan 17 '12 at 10:45
• Do you suggest that using linear regression after obtaining factors from Categorical principle component analysis (CATPCA), is the best option? means is it right to convert categorical data into continuous by CATPCA and run linear regression (not logistic) to find relationships. – wxa Jan 17 '12 at 23:21
• I don't know if it's best, but it certainly seems reasonable. I don't know that you need CATPCA; you want something that captures the ordinality of the Likert items. Regular PCA may be better. – Peter Flom - Reinstate Monica Jan 19 '12 at 10:34