Hello Kanika,

The usual (and relevant) concern for single ratings given on Likert-type response scales is that the scale strength is ordinal, not interval or ratio. You could use percentile point adjustments to 'normalize' scores if: (a) you correctly identified the underlying population distribution for the single ratings--note that it might be inconsistent across variables; and (b) you correctly located the scale points on that distribution. As work by Theodore Micceri and Rand Wilcox demonstrate, the presumption of normality may be a hope more often than it is a reality, especially when applied to human judgments. For these reasons, I think that normalizing is not a dependable solution to the problem.

(If by normalizing, you mean standardizing, as in converting to z-scores, remember that arithmetic operations needed to generate values such as means, SDs, variances don't make sense with ordinal data.)

It might be simpler to apply methods which do not presume any specific distribution or scale strength beyond ordinal.

Here are some possibilities:

1. Polytomous item response theory models (where the ratings form the items);

2. Ordinal regression (if exploration of how a set of ordinal variables relate to some ordinal outcome);

3. Classification trees;

4. Non-parametric factor models Article Kelly's Non-Parametric Factor Analysis

5. Start with polychoric corrlations among the variables, then apply your chosen analysis (probably common factor analysis rather than principal components analysis).

Good luck with your work.

Thank you Dr. David.

Can we apply principal component analysis on polychoric correlations?

Yes, for PCA and PFA, you do not need to have the raw data, but it is sufficient to have the covariance or correlation matrix. If you want to use a polychoric approach (which is recommended for likert items, e.g.Holgado–Tello et al., 2010) you can calculate the polychoric correlation matrix in a first step and enter this into a EFA in a second step. PFA/CFA may be more useful than PCA as David Morse suggested.

Holgado–Tello, F. P., Chacón–Moscoso, S., Barbero–García, I., & Vila–Abad, E. (2010). Polychoric versus Pearson correlations in exploratory and confirmatory factor analysis of ordinal variables. Quality & Quantity, 44(1), 153-166.

Thank you Dr. Rainer.

Thanks for the nice discussion on PCA for Likert scale data....

I suggest a simple classification modeling approach for it as PCA is generally more recommended when you large number of data points on a few categories impossible to distinguish by my experience but as all the experts stated.

Such as David Morse Stated

"It might be simpler to apply methods which do not presume any specific distribution or scale strength beyond ordinal"

I would agree with it.