boot_predict: Compute prediction estimates for the replication size using...

In SimDesign: Structure for Organizing Monte Carlo Simulation Designs

Compute prediction estimates for the replication size using bootstrap MSE estimates

Description

This function computes bootstrap mean-square error estimates to approximate the sampling behavior of the meta-statistics in SimDesign's summarise functions. A single design condition is supplied, and a simulation with max(Rstar) replications is performed whereby the generate-analyse results are collected. After obtaining these replication values, the replications are further drawn from (with replacement) using the differing sizes in Rstar to approximate the bootstrap MSE behavior given different replication sizes. Finally, given these bootstrap estimates linear regression models are fitted using the predictor term one_sqrtR = 1 / sqrt(Rstar) to allow extrapolation to replication sizes not observed in Rstar. For more information about the method and subsequent bootstrap MSE plots, refer to Koehler, Brown, and Haneuse (2009).

Usage

boot_predict(
  condition,
  generate,
  analyse,
  summarise,
  fixed_objects = NULL,
  ...,
  Rstar = seq(100, 500, by = 100),
  boot_draws = 1000
)

Arguments

condition	a data.frame consisting of one row from the original design input object used within runSimulation
generate	see runSimulation
analyse	see runSimulation
summarise	see runSimulation
fixed_objects	see runSimulation
...	additional arguments to be passed to runSimulation
Rstar	a vector containing the size of the bootstrap subsets to obtain. Default investigates the vector [100, 200, 300, 400, 500] to compute the respective MSE terms
boot_draws	number of bootstrap replications to draw. Default is 1000

Value

returns a list of linear model objects (via lm) for each meta-statistics returned by the summarise() function

Author(s)

Phil Chalmers [e-mail]

References

Chalmers, R. P., & Adkins, M. C. (2020). Writing Effective and Reliable Monte Carlo Simulations with the SimDesign Package. The Quantitative Methods for Psychology, 16(4), 248-280. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.20982/tqmp.16.4.p248")}

Koehler, E., Brown, E., & Haneuse, S. J.-P. A. (2009). On the Assessment of Monte Carlo Error in Simulation-Based Statistical Analyses. The American Statistician, 63, 155-162.

Sigal, M. J., & Chalmers, R. P. (2016). Play it again: Teaching statistics with Monte Carlo simulation. Journal of Statistics Education, 24(3), 136-156. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/10691898.2016.1246953")}

Examples

set.seed(4321)
Design <- createDesign(sigma = c(1, 2))

#-------------------------------------------------------------------

Generate <- function(condition, fixed_objects = NULL) {
    dat <- rnorm(100, 0, condition$sigma)
    dat
}

Analyse <- function(condition, dat, fixed_objects = NULL) {
    CIs <- t.test(dat)$conf.int
    names(CIs) <- c('lower', 'upper')
    ret <- c(mean = mean(dat), CIs)
    ret
}

Summarise <- function(condition, results, fixed_objects = NULL) {
    ret <- c(mu_bias = bias(results[,1], 0),
             mu_coverage = ECR(results[,2:3], parameter = 0))
    ret
}

## Not run: 
# boot_predict supports only one condition at a time
out <- boot_predict(condition=Design[1L, , drop=FALSE],
    generate=Generate, analyse=Analyse, summarise=Summarise)
out # list of fitted linear model(s)

# extract first meta-statistic
mu_bias <- out$mu_bias

dat <- model.frame(mu_bias)
print(dat)

# original R metric plot
R <- 1 / dat$one_sqrtR^2
plot(R, dat$MSE, type = 'b', ylab = 'MSE', main = "Replications by MSE")

plot(MSE ~ one_sqrtR, dat, main = "Bootstrap prediction plot", xlim = c(0, max(one_sqrtR)),
     ylim = c(0, max(MSE)), ylab = 'MSE', xlab = expression(1/sqrt(R)))
beta <- coef(mu_bias)
abline(a = 0, b = beta, lty = 2, col='red')

# what is the replication value when x-axis = .02? What's its associated expected MSE?
1 / .02^2 # number of replications
predict(mu_bias, data.frame(one_sqrtR = .02)) # y-axis value

# approximately how many replications to obtain MSE = .001?
(beta / .001)^2

## End(Not run)

SimDesign documentation built on Oct. 17, 2023, 5:07 p.m.