# A Composing Likert "Subvariables" into a Single Variable

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1. Jul 25, 2017

### WWGD

Hi All,
I have many Likert variables regarding a single item issue. Specifically, I am dealing with several measures of
IT Dept Quality, like % of budget devoted to IT department, Number of External Audits, etc ; each is measured on a Likert scale. I ultimately want to regress EDIT against a( single-valued) IV Likert. For this , I need to transform all the individual "submeasures" of IT Dept quality into a single measure. I did FA ( Factor Analysis) and I was able to select 4 items explaining some 79% of variability, so that I may dispose of the other items. Still, I want to make a single variable out of these 4 reduced ones. Are there standard ways of going about this? Would a single variable as the mean to all of these work? Should I maybe do a weighted sum with each subvariable given a weight proportional to the variance it explains, e.g., if I am given X,Y,Z ( after FA) , explaining, say, 60%, 25% and 15% of total variance respectively, would it make sense to transform a triple (x,y,z) of values in (X,Y,Z) into a single value w=12x+5y+3z ? How would this compare to just averaging out into w'=(x+y+z)/3 Any other Ideas?

Last edited: Jul 25, 2017
2. Jul 25, 2017

### FactChecker

What would be the advantage of making another single combined variable versus just doing a multiple linear regression using the four factors?

3. Jul 25, 2017

### WWGD

Because I want the Likert to be the DV, so I need to have it as a single variable to regress against a group of IVs.

4. Jul 25, 2017

### FactChecker

Oh. I see. Sorry, I can't help you. I have no ideas. It seems as though the FA indicates that the 4 factors would be hard (and maybe counter-productive) to combine.

5. Jul 25, 2017

### WWGD

No problem, actually I think it is my fault, I think I did not explain why I wanted to combine them or at least not very clearly. Common, FactChecker, cant you read my mind ;) ?

6. Jul 25, 2017

### FactChecker

You stated it in the OP, but I overlooked the significance.

7. Jul 25, 2017

### Staff: Mentor

This is the topic of item response theory, but I am not familiar with the details

8. Jul 26, 2017

### FactChecker

I would have thought that the single factor that combines them all the best would be the top factor in the SPSS FA "Total Variance Explained" table. The Item Response Theory that @Dale mentions does seem like the right subject. I never heard of it before.

9. Jul 26, 2017

### Staff: Mentor

IRT may not apply. Or, more likely, I should be quiet on the subject.

From wikipedia:
So, are we violating basic assumptions here by extending Likert scaling results to IRT?

Edit:
source -- https://en.wikipedia.org/wiki/Item_response_theory

10. Jul 26, 2017