The naive multilevel analogue of R-squared can go negative when
predictors are added, because the separate variance components are not
each individually reduced. Snijders and Bosker define explained
variance on the total residual variance of an individual observation,
sigma2_e + sigma2_u, comparing the fitted model against the empty
model; so defined it does not go negative for a useless predictor.
Usage
Snr2(sigma2_e1, sigma2_u1, sigma2_e0, sigma2_u0)
Arguments
- sigma2_e1
Level-1 residual variance of the fitted model.
- sigma2_u1
Level-2 intercept variance of the fitted model.
- sigma2_e0
Level-1 residual variance of the empty model.
- sigma2_u0
Level-2 intercept variance of the empty model.
Value
List with estimate, total1, total0,
icc0, icc1, reduction, method.
Details
Formula: R2_1 = 1 - (sigma2_e1 + sigma2_u1) / (sigma2_e0 + sigma2_u0).
References
Snijders, T. A. B. and Bosker, R. J. (1994). Modeled
variance in two-level models. Sociological Methods and Research
22(3):342-363. doi:10.1177/0049124194022003004
Examples
Snr2(1, 0.5, 4, 1)
#> $estimate
#> [1] 0.7
#>
#> $total1
#> [1] 1.5
#>
#> $total0
#> [1] 5
#>
#> $icc0
#> [1] 0.2
#>
#> $icc1
#> [1] 0.3333333
#>
#> $reduction
#> [1] 3.5
#>
#> $method
#> [1] "R2_1 = 1 - (s2_e1+s2_u1)/(s2_e0+s2_u0) [Snijders & Bosker 1994]"
#>
