Doubt about Likert scale

Question

I know from a previous question that I can use zero in a Likert scale, e.g., 0, 1, 2, 3.

I was wondering, is there any reason I should not use a scale like: 0, 1, 2, 4.

Answer 1

I was wondering, is there any reason I should not use a scale like: 0, 1, 2, 4.

From a modelling perspective, no, there is no reason why you shouldn't use such a scale, because, as mentioned in comments, the numbers themselves have no meaning, because a likert scale is ordinal. That is to say, a "value" of 4 does not mean that whatever is being measured is twice as big as for a "value" of 2. It just means that is higher.

We can readily see that this is the case with a simple example in R using the clm function in the ordinal package to fit a cumulative link model:

> library(ordinal)
> library(plyr)  # used for changing the scale

> # create a new ordinal variable with 10 instead of 5
> wine$newrating <- mapvalues(wine$rating, from = "5", to = "10")

> table(wine$rating)

 1  2  3  4  5 
 5 22 26 12  7 

> table(wine$newrating)

 1  2  3  4  10 
 5 22 26 12  7 

Now we fit 2 models, one using the 1,2,3,4,5 scale and then one using the 1,2,3,4,10 scale:

> m0 <- clm(rating ~ 1 , data = wine)
> m1 <- clm(newrating ~ 1 , data = wine)
> summary(m0)

 link  threshold nobs logLik  AIC    niter max.grad cond.H 
 logit flexible  72   -103.72 215.44 5(0)  7.23e-08 8.4e+00

Threshold coefficients:
    Estimate Std. Error z value
1|2  -2.5953     0.4636  -5.598
2|3  -0.5108     0.2434  -2.098
3|4   1.0259     0.2674   3.836
4|5   2.2285     0.3978   5.602

> summary(m1)

 link  threshold nobs logLik  AIC    niter max.grad cond.H 
 logit flexible  72   -103.72 215.44 5(0)  7.23e-08 8.4e+00

Threshold coefficients:
     Estimate Std. Error z value
1|2   -2.5953     0.4636  -5.598
2|3   -0.5108     0.2434  -2.098
3|4    1.0259     0.2674   3.836
4|10   2.2285     0.3978   5.602

It is clear that the two models are identical.

However a little care should be exercised if other analyses are to be carried out, such as computing the mean or standard deviation of such variables - which is a highly questionable thing to do - see here for a discussion on this: Calculate mean of ordinal variable

It should also be borne in mind that choosing a scale such as 0,1,2,4 may introduce bias, for example, if it is a questionnaire, an analyst should know that an answer of 4 does not mean twice that of 2, or four times that of 1, but the participant may not understand this and could therefore answer differently depending on the scale chosen (if shown to the participant, obviously)

So, while there may not be a statistical reason to do so, it may not make sense to do it, and whether or not this is the case will be dependent on the domain you are working in.