Fornell-Larcker discriminant validity

Formula: sqrt(AVE_i) > correlation(F_i, F_j)

Usage

Divgvs(AVE, factor_correlations)

Arguments

AVE

Average variance extracted, one entry per construct.

factor_correlations

k x k matrix of inter-construct correlations.

Value

List with estimate (minimum margin), sqrt_ave, pass_factor, n_violations, discriminant, k, method.

Details

A construct passes when the square root of its average variance extracted exceeds its correlation with every other construct, i.e. it shares more variance with its own indicators than with any other factor. The reported margin is the smallest sqrt(AVE_i) - |r_ij| over all off-diagonal pairs: positive means the whole model passes.

References

Fornell & Larcker (1981), J. Marketing Research 18(1):39-50.

Examples

AVE <- c(0.6, 0.7)
factor_correlations <- matrix(c(1, 0.4, 0.4, 1), 2, 2)
Divgvs(AVE, factor_correlations)
#> $estimate
#> [1] 0.3745967
#> 
#> $sqrt_ave
#> [1] 0.7745967 0.8366600
#> 
#> $pass_factor
#> [1] 1 1
#> 
#> $n_violations
#> [1] 0
#> 
#> $discriminant
#> [1] 1
#> 
#> $k
#> [1] 2
#> 
#> $method
#> [1] "Fornell-Larcker discriminant validity"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"