## Tuesday, February 9, 2010

### Variance inflation factors: What they are and what they contribute to SEM analyses

Note: This post refers to the use of variance inflation factors to identify "vertical", or classic, multicolinearity. For a broader discussion of variance inflation factors in the context of "lateral" and "full" collinearity tests, please see Kock & Lynn (2012). For a discussion in the context of common method bias tests, see the post linked here.

Variance inflation factors are provided in table format by WarpPLS for each latent variable that has two or more predictors. Each variance inflation factor is associated with one predictor, and relates to the link between that predictor and its latent variable criterion. (Or criteria, when one predictor latent variable points at two or more different latent variables in the model.)

A variance inflation factor is a measure of the degree of multicolinearity among the latent variables that are hypothesized to affect another latent variable. For example, let us assume that there is a block of latent variables in a model, with three latent variables A, B, and C (predictors) pointing at latent variable D. In this case, variance inflation factors are calculated for A, B, and C, and are estimates of the multicolinearity among these predictor latent variables.

Two criteria, one more conservative and one more relaxed, are traditionally recommended in connection with variance inflation factors. More conservatively, it is recommended that variance inflation factors be lower than 5; a more relaxed criterion is that they be lower than 10 (Hair et al., 1987; Kline, 1998). High variance inflation factors usually occur for pairs of predictor latent variables, and suggest that the latent variables measure the same thing. This problem can be solved through the removal of one of the offending latent variables from the block.

References:

Hair, J.F., Anderson, R.E., & Tatham, R.L. (1987). Multivariate data analysis. New York, NY: Macmillan.

Kline, R.B. (1998). Principles and practice of structural equation modeling. New York, NY: The Guilford Press.

Kock, N., & Lynn, G.S. (2012). Lateral collinearity and misleading results in variance-based SEM: An illustration and recommendations. Journal of the Association for Information Systems, 13(7), 546-580.

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