# Factor Analysis: Choosing Your Variables

by Maike Rahn, PhD

In previous posts in this series, we discussed factors and factor loadings and rotations. In this post, I would like to address another important detail for a successful factor analysis, the type of variables that you include in your analysis.

### What type of variable?

Ideally, factor analysis is conducted with continuous variables that are normally distributed since factor analysis is based on a correlation matrix.

However, you will undoubtedly find many factor analyses that include ordinal variables, particularly Likert scale items.

While technically, Likert items don’t meet the assumptions of Factor Analysis, at least in some situations the  results have been found to be quite reasonable.  For example,  Lubke & Muthen, (2004) found that Confirmatory Factor Analysis on a single homogenous group worked, as long as items have at least seven values.

Some researchers include variables with fewer than seven values into their factor analysis.  Sometimes this cannot be avoided, if you are using an already published scale.

Last, there is an interesting discussion about including binary variables in a factor analysis in the Sage Publications booklet “Factor analysis. Statistical methods and practical issues” (Kim and Mueller, 1978; page 75).

### Correct coding of variables

It is important to prepare your variables in advance. For example, if you anticipate finding a socioeconomic factor, create your ordinal variable occupation with levels from lowest to highest to make sure that you have a positive factor loading with your factor.

 Occupational categories Levels of occupation variable Nurse’s Aid 1 Administrative assistant 2 Nurse 3 Nurse manager 4 Physician 5 Department chair 6 Director 7

The reason for this preparation is that you will wind up with factor solutions that are easily interpretable, because variables that are coded in the same direction as the factor will always have a positive factor loading. On the other hand, variables that have an inverse association with the factor will always have a negative factor loading.

Kim, Jae-On and Mueller, Charles W (1978) Factor analysis. Statistical methods and practical issues. Series: Quantitative Applications in the Social Sciences. Sage Publications: Beverly Hills, CA.

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