How to combine single Likert items into one scale? (Time-sensitiv)

#1
Hello,

I have a very time-sensitive question:

I am replicating a theory that uses 12 Likert items to measure three latent variables (4 items per latent variable).

Also in my study I use these 12 likert items that measure three latent variables. Every latent variables is measured by 4 Likert items. For my research, I have to combine/sum these variables into one measurement. So hat I have three variables as a result.

My question/problem is: How can I combine these 4 Likert items into one scale, so that I have one number for each latent variable that I can use for my analysis?

Some extra information:
All the Likert item are measured on a 5-point-Likert scale.

I have already run Cronbach's Alpha in SPSS and the 4 items have a very high Alpha. Also, the "corrected item- total correlation" is high enough.

I want to use the three variables in a ordinal log regression analysis.

Your help is greatly appreciated!
 

spunky

Doesn't actually exist
#2
My question/problem is: How can I combine these 4 Likert items into one scale, so that I have one number for each latent variable that I can use for my analysis?
hello there... could you maybe elaborate a little bit more on this one or give me an example? the thing is i'm not exactly sure as whether you dont to have do anything or if you need to do a hierarchical factor analysis with oblique rotations... if you have 3 well-defined dimensions in your scale (and 4 items tap into each one) then what you actually have are 3 "sub-scales" so to speak and you can get a factor score on each one of them and, therefore, have a single number the represents each latent variable... or do you need to combine each of those sub-scales into high-order factors to get total composite scores?

i'm confused by the way you phrased your question...:)

thanks!
 
#3
Hello Spunky,

Thank you so much for your answer.

In my research, I have three independent variables. Each variable is measured by four 5-point Likert items. For my future analysis, I need to "combine" these 4 Likert items into one single score. So that I have one single score for the variable.

One example would be the independent variable social influence: four 5-point Likert items ask about social influence. Therefore, they all measure social influence. I need to combine these four Likert items into one single score for my variable social influence. I have two other independent variables with 4 Likert items each.

I hope this helps.
 
#4
Can I just simply sum the 4 likert items and calculate the mean/mode and then use this score as the score for my variable? (I have tested reliability, etc.)
 

spunky

Doesn't actually exist
#5
Can I just simply sum the 4 likert items and calculate the mean/mode and then use this score as the score for my variable?
well... the short answer would be "yes" but there's a minor caveat i would just like you to be aware of. if you say the 12 items can be sub-divided among 3 factors and you have good-enough evidence for that, then what i would advise you to do is to get the factor score (the weighed score from factor loadings) and use that as your total score (that would be the most correct way of doing it) or you wouldn't be too off by just doing what you said, adding them together and calculating means, modes, etc... one thing you cannot do is to add accross scales and get a general total score for everything (you'd need evidence for unidimensionality there and you dont have that, you have 3 latent variables).

here's the minor caveat: recent research has brought to light that a lot of factor analyses that substantiate the dimensionality of tests developed from particularly older, well-estabilished theories (like the Big 5 personality traits) were not done correctly because they used principal components analysis as their method of choice and when they tried to test the theory via confirmatory factor analysis they didnt find those 5 big factors. from a methodological standpoint i would try and bring forth evidence of those three dimensions by doing confirmatory factor analysis, especially if you happen to see that the people who developed the theory you're using based their analysis on principal components. but anyways, that's just me being OCD about things... :)
 
#6
then what i would advise you to do is to get the factor score (the weighed score from factor loadings) and use that as your total score (that would be the most correct way of doing it)
Thank you, spunky. That was very helpful. Just to clarify this:

I would run a factor analysis for the 4 items for each latent variable separately to get a general total score for this particular variable? And then for next set of 4 Likert items for the next variable? And then again separately for the next for the set of 4 Likert items for the last variable?

(Both the theory and the PCA suggests that there are three factors as theorized and the single items also load on these three factors as expected. Cronbach's Alpha is alos high enough for all the factors)
 

spunky

Doesn't actually exist
#7
uhmm... have you ran a factor analysis before? you run the factor anlysis on thecomplete scale... to the necessary rotations until you get whatever is closest to thurstone's paradigmatic simple structure... from there you'll see those 3 distinct factors, with their respective loadings which you can later use to get your scores....

well... problem with that is that PCA is NOT factor analysis. it's a data reduction technique and lumps together common and error variance so that maybe, if you were to do a factor analysis, you'd find out that one of those factors is actually just error variance (error variance usually gets subsumed under common variance which would make you either over- or under- identify factors)

i'd be very cautious to make inferences about a scale's dimensionality if it's only based on PCA... although, given the current state of affairs, you might be able to get away with it (almost everybody uses it) but i would just like to give you my 2-cents in saying that there are more appropriate ways to do this...