Marker-Variable Adjustment for Common Method Variance

The marker-variable technique of Lindell and Whitney (2001) estimates common method variance from the correlation of a marker variable that is theoretically unrelated to at least one of the substantive variables: any non-zero correlation it shows with that variable is attributed to shared method, and that amount is partialled out of the substantive correlations. When no a priori marker is available, the smallest positive correlation among the substantive items is used as a proxy, the common marker-free variant of the method. A correlation that remains statistically significant after the adjustment, by the paper's t test of the adjusted correlation with \(N - 3\) degrees of freedom (their Equation 5), is evidence that the relationship is not an artifact of method variance; the test is applied by the user, since this function works from the correlation matrix alone and does not take \(N\).

Usage

common_method_marker(R, marker_r = NULL)

Arguments

R

A correlation matrix among the substantive items.

marker_r

The marker variable's (CMV) correlation. When NULL (default) the smallest positive off-diagonal correlation in R is used as the proxy marker.

Value

A data.frame (class dmar_tbl) with rows marker_correlation, mean_abs_r_unadjusted, and mean_abs_r_adjusted in the value column. The full adjusted correlation matrix is the "adjusted" attribute.

Details

Writing \(r_M\) for the marker (or proxy) correlation, each substantive correlation is adjusted as \(r^{A}_{ij} = (r_{ij} - r_M) / (1 - r_M)\) (Lindell & Whitney, 2001, Equation 4). The CMV-adjusted correlation matrix is returned as the "adjusted" attribute; the reported table summarizes the marker correlation and the average absolute correlation before and after adjustment.

The method presumes the variables are reflected so that their intercorrelations are positive; a negative substantive correlation is pushed further from zero by the adjustment rather than attenuated, so reverse-code as needed before adjusting.

References

Lindell, M. K., & Whitney, D. J. (2001). Accounting for common method variance in cross-sectional research designs. Journal of Applied Psychology, 86(1), 114–121. doi:10.1037/0021-9010.86.1.114

See also

common_method_single_factor for the single-factor screen.

Other multivariate and latent variable methods: average_variance_extracted(), bifactor_indices(), cfa_1(), cfa_2(), cfa_k(), ci_eigenvalue(), common_method_single_factor(), dmacs(), ecvi(), htmt(), irt_grm(), irt_information(), measurement_alignment(), measurement_invariance(), procrustes_phi(), simple_structure()

Author

Ken Kelley kkelley@nd.edu

Examples

R <- matrix(c(1, .5, .4, .5, 1, .45, .4, .45, 1), 3, 3,
            dimnames = list(c("a", "b", "c"), c("a", "b", "c")))
res <- common_method_marker(R, marker_r = 0.10)
res
#>  term                  value
#>  marker_correlation    0.1  
#>  mean_abs_r_unadjusted 0.45 
#>  mean_abs_r_adjusted   0.389
attr(res, "adjusted")
#>           a         b         c
#> a 1.0000000 0.4444444 0.3333333
#> b 0.4444444 1.0000000 0.3888889
#> c 0.3333333 0.3888889 1.0000000