bias_correction: GEE Bias Correction testing
In donaldRwilliams/litterEffects: Investigation of Litter Effects

Description Usage Arguments Details References Examples

This function allows the user to determine the "correct" bias correction for generalized estimating equations. The corrections are to ensure the standard error of the estimates is not underestimated in small sample situations. When uncorrected, GEE's can have error rates that exceed nominal levels (alpha = 0.05). It should also be noted that this function is for a specific design, that has observations completely nested within a higher level unit. For example, litter mates (rodents from same mother) are all categorized one way. In reference to educational settings, this would be equivalent to entire schools receiving an intervention and the students were the observational units.

1	bias_correction(nsim = 500, icc, v_overall, n_litters, pups_litter)

`nsim`	Number of simulations. Default is set to 500
`icc`	Intra-class correlation coefficient for the litter effect (between 0.05 to 0.95 of the total variance)
`v_overall`	total variance (litter + residual variance)
`n_litters`	Number of litters in the study (or number of schools)
`pups_litter`	Number observations per litter (or student from a given school)

n_litters must be even. Returned value closest to pretermined alpha level should be used as correction

Fay and Graubard (2001). Small-Sample Adjustments for Wald-Type Tests Using Sandwich Estimators. Biometrics 57: 1198-1206.

Gunsolley, J. C., Getchell, C., & Chinchilli, V. M. (1995). Small sample characteristics of generalized estimating equations. Communications in Statistics-simulation and Computation, 24: 869-878.

Williams, D.R., Burkner, P.C., Carlsson, R. (2017). Between-litter variation in developmental studies of hormones and behavior: effects on false positives and statistical power. https://osf.io/wydmc/

bias_correction()

# for loop to investigate type I according to litter number

# number of litters
n_lit <- seq(5, 20, 5)

# matrix to store results
mat <- matrix(ncol = 6, nrow = length(n_lit))
 
# simulaton

for(j in 1:length(n_lit)){
      lit <- n_lit[j] 
      mat[j, 1:6] <- bias_correction(nsim = 500, 
      icc = 0.5, v_overall = 10, n_litters = lit , 
      pups_litter = 4)[1:6]
}
   
res_df <- as.data.table(cbind(n_lit, mat))
colnames(res_df) <- c("n_litters", "d1", "d2", 
                       "d3", "d4", "d5", "dm")
res_df