# Whether to use original or reverse coded items in factor analysis?

I am currently analyzing data from a 34-item Likert scale. I already recoded the negatively stated variables in SPSS as different variables. I'm about to do a factor analysis.

Should I use the original variables or the recoded variables in the factor analysis?

• – chl Aug 10 '12 at 8:27

It doesn't matter which you use. The signs on the factor loadings will simply flip. For example, let's say that item 1 and item 2 should load on the same factor, but item 2 is reverse scored. The factor loading for item 1 might be .53, and the factor loading for item 2 might be -.41, but if you had used the recoded variable instead, it would have been .41. Just don't put both in!

• is right. But it may be that one coding or the other is more intuitively appealing. Your factor should be measuring some latent variable. For many of these, one direction will be "more" and the other "less". In these cases, it's usually easier to have higher factor scores relate to "more" of the latent variable – Peter Flom Aug 10 '12 at 14:36
• @PeterFlom, good point (+1). – gung - Reinstate Monica Aug 10 '12 at 14:48

As gung said, recoding reverse-scored variables will only reverse the sign of their factor loadings, so the decision is only important because you will have to keep track of (and specify in anything you write about it) which variables are reverse-scored, or whether you recoded them.

An unrelated concern arises with factor analysis of Likert scale ratings. Likert scales produce ordinal (i.e., polytomous, ordered, categorical) data, not continuous data. Factor analysis generally assumes any raw data input are continuous. Here's a quote from Reise, Moore, and Haviland (2010):

Ordinary confirmatory factor analytic techniques do not apply to dichotomous or polytomous data (Byrne, 2006). Instead, special estimation procedures are required (Wirth & Edwards, 2007). There basically are three options for working with polytomous item response data. The first is to compute a polychoric matrix and then apply standard factor analytic methods (see Knol & Berger, 1991). A second option is to use full-information item factor analysis (Gibbons & Hedeker, 1992). The third is to use limited information estimation procedures designed specifically for ordered data such as weighted least squares with mean and variance adjustment (MPLUS; Muthén & Muthén, 2009).

I would recommend combining both the first and third approaches (i.e., use diagonally weighted least squares estimation on a polychoric correlation matrix), based on Wang and Cunningham's (2005) discussion of the problems with typical alternatives:

When confirmatory factor analysis was conducted with nonnormal ordinal data using maximum likelihood and based on Pearson product-moment correlations, the downward parameter estimates produced in this study were consistent with Olsson's (1979) findings. In other words, the magnitude of nonnormality in the observed ordinal variables is a major determinant of the accuracy of parameter estimates.

The results also support the findings of Babakus, et al. (1987). When maximum likelihood estimation is used with a polychoric correlation input matrix in confirmatory factor analyses, the solutions tend to result in unacceptable and therefore significant chi-square values together with poor fit statistics.

SPSS has some solutions for exploratory factor analysis of Likert scale ratings. The second solution for producing polychoric correlations should work with confirmatory factor analysis too. It seems you can use generalized (weighted) least squares estimation in SPSS, but not diagonally weighted least squares ($DWLS$). Another precaution from Wang and Cunningham (2005):

Because weighted least squares estimation is based on fourth-order moments, this approach frequently leads to practical problems and is very computationally demanding. This means that weighted least squares estimation may lack robustness when used to evaluate models of medium, i.e., with 10 indicators, to large size and small to moderate sample sizes.

It isn't clear to me whether the same concern applies to $DWLS$ estimation; regardless, the authors recommend that estimator. In case you're willing to switch programs to use $DWLS$:

• R (R Core Team, 2012) is free. You'll need an old version (e.g., 2.15.2) for these packages:
• The psych package (Revelle, 2013) contains the polychoric function.
• The fa.parallel function can help identify the number of factors to extract.
• The lavaan package (Rosseel, 2012) offers $DWLS$ estimation for latent variable analysis.
• The semTools package contains the efaUnrotate, orthRotate, and oblqRotate functions.

I imagine Mplus (Muthén & Muthén, 1998-2011) would work too, but the free demo version won't accommodate more than six measurements, and the licensed version isn't cheap. It may be worth it if you can afford it though; people love Mplus, and the Muthéns' customer service via their forums is incredible!

P.S. If one headache for the sake of psychometric validity isn't too many, you may want to consider analyzing problems with extreme response style as well, given the subjective nature of Likert scale ratings.

References

Babakus, E., Ferguson, J. C. E., & Jöreskog, K. G. (1987). The sensitivity of confirmatory maximum likelihood factor analysis to violations of measurement scale and distributional assumptions. Journal of Marketing Research, 24, 222–228.

Byrne, B. M. (2006). Structural Equation Modeling with EQS. Mahwah, NJ: Lawrence Erlbaum.

Gibbons, R. D., & Hedeker, D. R. (1992). Full-information item bi-factor analysis. Psychometrika, 57, 423–436.

Knol, D. L., & Berger, M. P. F. (1991). Empirical comparison between factor analysis and multidimensional item response models. Multivariate Behavioral Research, 26, 457–477.

Muthén, L. K., & Muthén, B. O. (1998-2011). Mplus user's guide (6th ed.). Los Angeles, CA: Muthén & Muthén.

Muthén, L. K., & Muthén, B. O. (2009). Mplus (Version 4.00). [Computer software]. Los Angeles, CA: Author. URL: http://www.statmodel.com.

Olsson, U. (1979). Maximum likelihood estimates for the polychoric correlation coefficient. Psychometrika, 44, 443–460.

R Core Team. (2012). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL: http://www.R-project.org/.

Reise, S. P., Moore, T. M., & Haviland, M. G. (2010). Bifactor models and rotations: Exploring the extent to which multidimensional data yield univocal scale scores. Journal of Personality Assessment, 92(6), 544–559. Retrieved November 21, 2013. Freely available online, URL: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2981404/.

Revelle, W. (2013). psych: Procedures for Personality and Psychological Research. Northwestern University, Evanston, Illinois, USA. URL: http://CRAN.R-project.org/package=psych. Version = 1.3.2.

Rosseel, Y. (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1–36. URL: http://www.jstatsoft.org/v48/i02/.

Wirth, R. J., & Edwards, M. C. (2007). Item factor analysis: Current approaches and future directions. Psychological Methods, 12, 58–79. Retrieved November 21, 2013. Freely available online, URL: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3162326/.

• This is a great & very authoritative contribution, thanks. I hope we'll see more like it in the future. – gung - Reinstate Monica Nov 22 '13 at 1:30