A Composing Likert "Subvariables" into a Single Variable

[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?

 

[FactChecker]

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

 

[WWGD]

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

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.

 

[FactChecker]

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.

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.

 

[WWGD]

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.

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, can't you read my mind ;) ?

 

[FactChecker]

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, can't you read my mind ;) ?

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

 

[Dale]

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

 

[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.

 

[jim mcnamara]

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

From wikipedia:

This distinguishes IRT from, for instance, the assumption in Likert scaling that "All items are assumed to be replications of each other or in other words items are considered to be parallel instruments"

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

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

 

[jim mcnamara]

Hmm. @DiracPool may know more about this as it is a tool to evaluate psychometrics results.

 

[WWGD]

Thank you all. What if I considered FactChecker's suggestion ( If I understood correctly) to regress each Likert subvariable that contributes, say, at least 20% of total variability ( as DVs, of course) separately against the IVs?