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Re: st: 1-4 scale

From   Richard Williams <>
Subject   Re: st: 1-4 scale
Date   Sun, 05 Aug 2012 12:52:00 -0500

At 10:57 AM 8/5/2012, David Hoaglin wrote:
Dear Ebru,

People often analyze data from Likert scales as equally spaced, so you
can use each of the eight items in your model as a numerical variable,
with values 1 to 4.  You simply need to be aware that you are treating
the four categories as equally spaced.

It is a debatable practice though. Consider the following (warm has 4 values):

use "";, clear
reg warm yr89 male white age ed prst

According to the reference manual discussion of rvfplot, "In a well-fitted model, there should be no pattern to the residuals plotted against the fitted values...Any pattern whatsoever indicates a violation of the least-squares assumptions."

Clearly, there is a pattern in the above rvfplot, i.e. you get 4 parallel straight lines. Further, it isn't unique to this example; any 4 category dependent variable will show the same thing.

In fairness, if your dependent variable had 17 possible values, you would have 17 straight lines -- but your eye probably wouldn't detect that because everything would seem so cluttered. There is probably some point where there are enough possible values that violations of OLS assumptions aren't important, but I would be hesitant to say that point is met with a DV that only has 4 categories.

Earlier you asked about centering those variables.  Centering will do
no harm.  As far as the model is concerned, it affects only the
definition of the intercept.  If you do decide to "center" the
variables, you may want to use one of the four values.  If the data on
an item are not concentrated at one end, you could use 2 or 3 or
perhaps 2.5 as the centering constant.  (In a 5-point Likert scale
with a neutral category at 3, using 3 would often be a reasonable

When you have the results from the model with the eight separate
items, you may want to see whether the coefficients for the four items
within a heading are similar.  If they are, and it makes sense, you
could consider replacing those four items with their sum (or average)
--- a composite score.

David Hoaglin

On Sun, Aug 5, 2012 at 2:35 AM, Ebru Ozturk <> wrote:
> Dear David,
> I use tobit estimation. If I enter each item (8) in the question (objectives of innovation) into the model without changing their values, leaving them as they are (1 to 4), does it work? Because sometimes tobit can create problems if it has many variables in the model.

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