This function estimates the intercept and slope coefficients in a meta-regression model where the dependent variable is a log-complement Cronbach reliablity. The estimates are OLS estimates with robust standard errors that accommodate residual heteroscedasticity. The exponentiated slope estimate for a predictor variable describes a multiplicative change in non-reliability associated with a 1-unit increase in that predictor variable, controlling for all other predictor variables in the model.
meta.lm.cronbach(alpha, n, rel, r, X)alpha level for 1-alpha confidence
vector of sample sizes
vector of estimated reliabilities
number of measurements (e.g., items)
matrix of predictor values
Returns a matrix. The first row is for the intercept with one additional row per predictor. The matrix has the following columns:
Estimate - exponentiated OLS estimate
SE - standard error
z - z-value
p - p-value
LL - lower limit of the exponentiated confidence interval
UL - upper limit of the exponentiated confidence interval
Bonett DG (2010). “Varying coefficient meta-analytic methods for alpha reliability.” Psychological Methods, 15(4), 368--385. ISSN 1939-1463, doi:10.1037/a0020142 .
n <- c(583, 470, 546, 680)
rel <- c(.91, .89, .90, .89)
x1 <- c(1, 0, 0, 0)
X <- matrix(x1, 4, 1)
meta.lm.cronbach(.05, n, rel, 10, X)
#> Estimate SE z p LL UL
#> b0 -2.2408328 0.03675883 -60.960391 0.000 -2.3128788 -2.16878684
#> b1 -0.1689006 0.07204625 -2.344336 0.019 -0.3101087 -0.02769259
# Should return:
# Estimate SE z p LL UL
# b0 -2.2408328 0.03675883 -60.960391 0.000 -2.3128788 -2.16878684
# b1 -0.1689006 0.07204625 -2.344336 0.019 -0.3101087 -0.02769259