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Saturday, January 30, 2010

Reflective and formative latent variable measurement in WarpPLS


A reflective latent variable is one in which all the indicators are expected to be highly correlated with the latent variable score. For example, the answers to certain question-statements by a group of people, measured on a 1 to 7 scale (1=strongly disagree; 7 strongly agree) and answered after a meal, are expected to be highly correlated with the latent variable “satisfaction with a meal”. The question-statements are: “I am satisfied with this meal”, and “After this meal, I feel good”. Therefore, the latent variable “satisfaction with a meal”, can be said to be reflectively measured through two indicators. Those indicators store answers to the two question-statements. This latent variable could be represented in a model graph as “Satisf”, and the indicators as “Satisf1” and “Satisf2”.

A formative latent variable is one in which the indicators are expected to measure certain attributes of the latent variable, but the indicators are not expected to be highly correlated with the latent variable score, because they (i.e., the indicators) are not expected to be correlated with one other. For example, let us assume that the latent variable “Satisf” (“satisfaction with a meal”) is now measured using the two following question-statements: “I am satisfied with the main course” and “I am satisfied with the dessert”. Here, the meal comprises the main course, say, filet mignon; and a dessert, a fruit salad. Both main course and dessert make up the meal (i.e., they are part of the same meal) but their satistisfaction indicators are not expected to be highly correlated with each other. The reason is that some people may like the main course very much, and not like the dessert. Conversely, other people may be vegetarians and hate the main course, but may like the dessert very much.

If the indicators are not expected to be highly correlated with each other, they cannot be expected to be highly correlated with their latent variable’s score. So here is a general rule of thumb that can be used to decide if a latent variable is reflectively or formatively measured. If the indicators are expected to be highly correlated, then the measurement model should be set as reflective in WarpPLS. If the indicators are not expected to be highly correlated, even though they clearly refer to the same latent variable, then the measurement model should be set as formative.

9 comments:

Anonymous said...

Congrats on the software! Is there a *complete* list of available features and fit statistics for this program?

Anyway, I recommend you read this article which also has a 'comparison chart' about reflective and formative indicators:

Jarvis, C.B., MacKenzie, S.B. & Podsakoff, P.M., 2003. A Critical Review of Construct Indicators and Measurement Model Misspecification in Marketing and Consumer Research. , 30(2), p.199-218

Ned Kock said...

Hi Anon, thanks.

The User Manual has a complete description of all features, plus even some discussions on how to interpret various outputs.

C. Carr said...

Great explanation! I am a new Doctoral student with a limited Statistics background. Thanks for the assist.

Ned Kock said...

I am glad to know it was useful. Having said that, I should also say that this post is only a very basic intro. There is a whole literature out there on formative LV measurement.

Ned Kock said...

Answering the following questions from "Anonymous":

"Is WarpPLS computing a EFA or CFA? I have both formative and reflective variables in my model and i hate being constrained to change my formative latent contructs into reflective in order to use amos :("

WarpPLS conducts a CFA.

Anonymous said...

"A reflective latent variable is one in which all the indicators are expected to be highly correlated with the latent variable score."

That is not the defining aspect of a reflective variable. The indicators of a reflective variable (say items in a psychometric test) may correlate lowly with the reflective latent variable. That is why tests often contain many items.

Ned Kock said...

Anon, tests for reflective measurement quality specifically require high correlations. One example is the expectation that loadings will be greater than a threshold, such as .5, in reflective measurement. Loadings are correlations between LVs and indicators.

Dave said...

Hi Ned,

Is a formative variable analogous to an index of related (but perhaps not highly correlated) variables? For instance, if I wanted to compile an index of strenuous exercise, could I use the three or four variables which form it (e.g., gym frequency, attendance time, exertion) as indicators of a formative construct which I could call 'strenuous exercise'?

If so, can I use reflective latent variables to predict such a formative variable?

Hope this makes sense.

Thanks,
Dave

Ned Kock said...

Hi Dave. Often 2nd level LVs are formative, and they are made up of 1st level reflective LVs. This clip may be useful:

http://youtu.be/bkO6YoRK8Zg