What thresholds should I use for factor loading cut-offs?
Hair et al (1998) give rules of thumb for assessing the practical significance of standardised factor loadings as denoted by either the component coefficients in the case of principal components, the factor matrix (in a single factor model or an uncorrelated multiple factor model) or the pattern matrix (in a correlated multiple factor model).
On the other hand Field (2005) advocates the suggestion of Guadagnoli & Velicer (1988) to regard a factor as reliable if it has four or more loadings of at least 0.6 regardless of sample size. Stevens (1992) suggests using a cut-off of 0.4, irrespective of sample size, for interpretative purposes. When the items have different frequency distributions Tabachnick and Fidell (2007) follow Comrey and Lee (1992) in suggesting using more stringent cut-offs going from 0.32 (poor), 0.45 (fair), 0.55 (good), 0.63 (very good) or 0.71 (excellent).
MacCallum et al. (1999, 2001) advocate that all items in a factor model should have communalities of over 0.60 or an average communality of 0.7 to justify performing a factor analysis with small sample sizes.
Hair et al. (p112) Table of Loadings for Practical Significance
Factor Loading |
Sample Size needed for significance |
|
0.30 |
350 |
|
0.35 |
250 |
|
0.40 |
200 |
|
0.45 |
150 |
|
0.50 |
120 |
|
0.55 |
100 |
|
0.60 |
85 |
|
0.65 |
70 |
|
0.70 |
60 |
|
0.75 |
50 |
|
References
Comrey AL and Lee HB (1992) A first course in factor analysis (2nd edition). Hillsdale,NJ: Lawrence Erlbaum Associates.
Guadagnoli E and Velicer W (1988) Relation of sample size to the stability of component patterns. Psychological Bulletin 103 265-275.
Hair JF, Tatham RL, Anderson RE and Black W (1998) Multivariate data analysis. (Fifth Ed.) Prentice-Hall:London.
Field A (2005) Discovering statistics using SPSS. Second edition. Sage.
MacCallum RC, Widaman KF, Zhang S and Hong S. (1999) Sample size in factor analysis. Psychological Methods 4(1) 84-99.
MacCallum RC, Widaman KF, Preacher KJ and Hong S (2001) Sample size in factor analysis: The role of model error. Multivariate Behavioral Research 36 611-637.
Stevens JP (1992) Applied multivariate statistics for the social sciences (2nd edition). Hillsdale, NJ:Erlbaum.
Tabachnick BG and Fidell LS (2007) Using multivariate statistics. Fifth Edition. Pearson Education Inc.