Compare Regression Coefficiente between Nested Models

Comparing regression coefficients between models when one model is nested within another for clustered data.

compCoef(fit0, fit1)

Arguments

fit0

a fitted object of class geese

fit1

another fitted object of class geese

Value

a list of two components:

delta

estimated difference in the coefficients of common covariates from fit0 and fit1

variance

estimated variance matrix of delta

References

Allison, P. D. (1995). The impact of random predictors on comparisons of coefficients between models: Comment on Clogg, Petkova, and Haritou. American Journal of Sociology, 100(5), 1294–1305.

Clogg, C. C., Petkova, E., and Haritou, A. (1995). Statistical methods for comparing regression coefficients between models. American Journal of Sociology, 100(5), 1261–1293.

Yan, J., Aseltine, R., and Harel, O. (2011). Comparing Regression Coefficients Between Nested Linear Models for Clustered Data with Generalized Estimating Equations. Journal of Educational and Behaviorial Statistics, Forthcoming.

Author

Jun Yan jyan.stat@gmail.com

Examples

## generate clustered data
gendat <- function(ncl, clsz) {
## ncl: number of clusters
## clsz: cluster size (all equal)
  id <- rep(1:ncl, each = clsz)
  visit <- rep(1:clsz, ncl)
  n <- ncl * clsz
  x1 <- rbinom(n, 1, 0.5) ## within cluster varying binary covariate
  x2 <- runif(n, 0, 1)   ## within cluster varying continuous covariate
  ## the true correlation coefficient rho for an ar(1)
  ## correlation structure is 2/3
  rho <- 2/3
  rhomat <- rho ^ outer(1:4, 1:4, function(x, y) abs(x - y))
  chol.u <- chol(rhomat)
  noise <- as.vector(sapply(1:ncl, function(x) chol.u %*% rnorm(clsz)))
  y <- 1 + 3 * x1 - 2 * x2 + noise
  dat <- data.frame(y, id, visit, x1, x2)
  dat
}

simdat <- gendat(100, 4)
fit0 <- geese(y ~ x1, id = id, data = simdat, corstr = "un")
fit1 <- geese(y ~ x1 + x2, id = id, data = simdat, corstr = "un")
compCoef(fit0, fit1)
#> $delta
#> (Intercept)          x1 
#> -1.02293803  0.04506944 
#> 
#> $variance
#>                  beta_(Intercept)      beta_x1
#> beta_(Intercept)      0.010715045 -0.002740304
#> beta_x1              -0.002740304  0.005926041
#>