Can I use mean Likert Scores to measures a dependent variable numerically in simple linear regression?

Question

I'm using a 7-point frequency Likert scale in my paper to measure data on racism $(n>400)$. There is a total of 35 items on my survey and the dependent variable is "racism exposure" measured by the self-reported odds of experiencing daily racism. Each participant will receive a Likert score between 35 and 245 (35*7). The scale is as follows:

1 = never, 2 = rarely (in about 10% of the time), 3 = occasionally (in about 30% of the time), 4 = sometimes (in about 50% of the time), 5 = frequently (in about 70% of the time), 6 = usually (in about 90% of the time) and 7 = every time.

My supervisor said I can use a simple linear regression model for Likert score data when there is a 7 point numerical scale or higher. How would this be measured? That is, would my dependent variable be a mean likert score of racism exposure between 35 and 245 for a set of covariates? Interpreted as, say, for gender change "a female is expected to, on average, be 56.7 Likert-scores more likely to experience daily racism than a male"?

Answer 1

Treating Likert scores (usually ordinal categorical) as if interval numerical is ordinarily controversial. However, in the questionnaire the meanings of the various scores are specified as numerical, so there may be less controversy about treating the scores as numerical.

How subjects may interpret the questions is another matter. They may be very eager or very reluctant to give high scores on a question about racism.

Moreover, if you are using a kind of regression that expects normal data, you would need to check the Likert-7 data to see if they are nearly normally distributed.

Consider the fictitious Likert-7 data sampled in R below, which do not seem be be normally distributed:

set.seed(508)
x = replicate(400, sum(sample(1:7, 35, rep=T, p=(1:7)^2)))
summary(x)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  171.0   190.0   196.0   195.7   202.0   215.0 

The distance between the minimum and the median is greater than the distance between the median and the maximum, an indication of left-skewness that is not typical of normal data. The boxplot below also shows left-skewness.

boxplot(x, horizontal=T, col="skyblue2")

Furthermore a histogram of my Likert-7 scores has nothing like the shape of a normal distribution with the same mean and standard deviation as the data.

hist(x, prob=T, col="skyblue2")
 curve(dnorm(x, mean(x), sd(x)), add=T, col="red", lwd=2)

I am not saying your adviser is wrong. I am not saying that your real data will look anything like my fictitious data, but it is possible for Likert-7 data to be far from normal, and you'd need to check before using the Likert scores as an explanatory variable in a regression.