Technically, both are data reduction techniques, used to extract maximum variance from the data set with each component thus reducing a large number of variables into smaller number of components (PCA) or factors (for PCF).

Principal Axis Factoring (for PCF) — which is based on the 'notion that all variables belong to the first group and when the factor is extracted, a residual matrix is calculated -- is usually considered when the data violate the assumption of multivariate normality.'

Read this self-explanatory paper: http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=F79BF84CB915D64A481ABBA5EA53F3F5?doi=10.1.1.666.1050&rep=rep1&type=pdf

And yes, you can run PCA in Stata -- https://www.stata.com/features/overview/principal-components/

Technically, both are data reduction techniques, used to extract maximum variance from the data set with each component thus reducing a large number of variables into smaller number of components (PCA) or factors (for PCF).

Principal Axis Factoring (for PCF) — which is based on the 'notion that all variables belong to the first group and when the factor is extracted, a residual matrix is calculated -- is usually considered when the data violate the assumption of multivariate normality.'

Read this self-explanatory paper: http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=F79BF84CB915D64A481ABBA5EA53F3F5?doi=10.1.1.666.1050&rep=rep1&type=pdf

And yes, you can run PCA in Stata -- https://www.stata.com/features/overview/principal-components/

I agree

They are both data dimension reduction techniques. However, PCA peforms that by finding a linear set of sources which help observations' reconstruction, under the constraints of orthogonality and maximum variance (which decreases from the first to the last PC extracted). Factor analysis identifies a cause-relation relation between a latent variable (which cannot be measured) and the observed ones. Both techniques are included in most of the commercial statistical softwares.

Hello Asheek,

PCA and Common factor analysis (CFA) make very different assumptions about reality. PCA asserts that all variance in a data set is common variance and no unique variance (e.g., specific to an individual variable or error variance, as in measurement error) exists. Hence, all of the variance is considered common/shared and is repartitioned into 1,2,...,k components (for k variables). CFA only attempts to partition the variance that is common, and allows for unique variance. Functionally, they differ by starting with the original correlation matrix (PCA) or an adjusted correlation matrix with values less than 1 on the main diagonal (CFA).

If you're working with a small to moderate number of variables, you'll find that PCA tends to yield somewhat stronger loading estimates than does CFA (for a given number of extracted components/factors). If the number of variables is large, there is often little appreciable difference in the final factor solution and pattern/structure matrices.

Here's a nice resource that addresses the differences: http://www2.sas.com/proceedings/sugi30/203-30.pdf

Good luck with your work!

I think Marianna Meo has rightly defined.