This is my humble answer based on my literature review. The use of five-point scale is acceptable for most instruments (Hinkin, 1995) which is the minimum scale at least. This would be the advantage for ordinal data (five and more categories) to be treated as its continuous scale counterpart (Byrne, 2010). At this point, descriptive or inferential is not an issue. Thus, any multivariate statistics including Confirmatory Factor Analysis (CFA) and Structural Equation Modeling could be applied.

For a Likert Scale to be interval/continuous, the answer options must have certain characteristics including that

- they must form a “continuum” – so that the answer options flow uniformly from each option as the intensity of response increases (or decreases);

- they must be balanced (i.e. there is a mid-point and an equal number of positive and negative options) – think of a see-saw as the metaphor;

- all answer options should be “behaviorally” or “verbally” “anchored (i.e. each option should have an explanation of what it means);

- the conceptual difference between any two points on the scale should be identical (i.e. the difference in intensity of opinion between a “1” and a “2” should be equal to that between a “4” and a “5” or any other two contiguous points on the scale).

The structure responses for a research question, for example: strongly disagree, disagree, neither agree nor disagree, agree & strongly agree are categorical on a Likert scale. These categories can serve to a purpose up to determining proportion frequency or or percentage of respondents in each categories, and not for making any statistical inferences. Hence, there arises a need to quantitate the qualitative likert responses as strongly disagree = 1, disagree = 2, neither agree nor disagree = 3, agree = 4, strongly agree = 5 to facilitate statistical analysis. Once the responses are converted to numerical values using the accepted procedures, the responses become interval data. Two references are:

1. Sullivan G and Artino A. Analyzing and Interpreting Data From Likert-Type Scales. Journal of graduate medical education. 2013; 5: 541-542, 10.4300/JGME-5-4-18.

2. Joshi A, Kale S, Chandel S and Pal D. Likert Scale: Explored and Explained. British Journal of Applied Science & Technology. 2015;7:396-403, 10.9734/BJAST/2015/14975.

The Likert scale is ordinal but if we assume that the distance between each option is equal, we can consider it as interval scale.

We can consider the data is ordinal and can apply CFA or SEQ foranalysis

It is important to clarify the difference between the item scale and the total score scale. The item scales are ordinal as they represent distinct ordered categories. While a number is typically assigned to these categories, the numbers represent the first, second, third, etc., ordered categories.

The Likert scale represents the range of all possible total scores, with the total score itself comprised of the sum of the item scores. The Likert scale can be treated as an interval scale, under certain conditions. This was an important element of Likert's contribution. While these total scores are discrete and not continuous, under the Likert perspective, these total scores are treated as adhering to an interval scale.

To recap: Likert item scores, ordinal. Likert scale as the sum of Likert item scores, interval.

Likert is ordinal until there are 7 steps. From there it can be used as an interval scale. (check Tabachnik & Fidell)

I see it the same way:

The Likert scale is ordinal but if we sum up the item responses for a scale (e.g. psychological trait extravsion is measured by 5 items), then we have interval scaled values

Article Can Likert Scales be Treated as Interval Scales?—A Simulation Study

Individual Likert-type questions are generally considered ordinal data because the items have clear rank order but don’t have an even distribution. Overall Likert scale scores are sometimes treated as interval data. These scores are considered to have directionality and even spacing between them .