Bootstrap.Stage.2.NormTable: Bootstraps confidence intervals for a normative table

Description

The function Stage.2.NormTable() is used to derive a normative table that shows the percentile ranks \(\hat{\pi}_0\) that correspond to a wide range of raw test scores \(Y_0\) (stratified by the relevant independent variables). The function Bootstrap.Stage.2.NormTable() can be used to obtain confidence intervals (CIs) around the point estimates of the percentile ranks \(\hat{\pi}_0\) in the normative table. A non-parametric bootstrap is used to compute these CIs (for details, see Chapter 8 in Van der Elst, 2023).

Usage

Bootstrap.Stage.2.NormTable(Stage.2.NormTable,
CI=.99, Number.Bootstraps=2000, Seed=123, 
Rounded=FALSE, Show.Fitted.Boot=FALSE, verbose=TRUE)

Value

An object of class Stage.2.NormTable with components,

NormTable.With.CI: The normative table with the bootstrapped CI.
CI: The CI used.
Assume.Homoscedasticity: Logical. Was homoscedasticity assumed in the normative conversion? For details, see Stage.2.NormTable.
Assume.Normality: Logical. Was normality assumed in the in the normative conversion? For details, see Stage.2.NormTable.
NormTable.With.CI.Min: A table with the lower bounds of the CIs.
NormTable.With.CI.Max: A table with the upper bounds of the CIs.

Arguments

Stage.2.NormTable: A fitted object of class Stage.2.NormTable.
CI: The desired CI around the percentile ranks. Default CI=.99.
Number.Bootstraps: The number of bootstrap samples that are taken. Default Number.Bootstraps=2000.
Seed: The seed to be used in the bootstrap (for repoducibility). Default Seed = 123.
Rounded: Logical. Should the percentile ranks that are shown in the normative table be rounded to a whole number? Default Rounded=FALSE.
Show.Fitted.Boot: Logical. Should the fitted Stage 1 models for the bootstrap samples be printed? Default Show.Fitted.Boot=FALSE.
verbose: A logical value indicating whether verbose output should be generated.

Author

Wim Van der Elst

Details

For details, see Chapter 8 in Van der Elst (2023).

References

Van der Elst, W. (2024). Regression-based normative data for psychological assessment: A hands-on approach using R. Springer Nature.

Examples

Run this code

 # Time-intensive part
# Replicate the bootstrap results that were obtained in 
# Case study 1 of Chapter 8 in Van der Elst (2023)
# -----------------------------------------------------
library(NormData) # load the NormData package
data(GCSE)        # load the GCSE dataset

# Fit the Stage 1 model
Model.1.GCSE <- Stage.1(Dataset=GCSE, 
  Model=Science.Exam~Gender)

# Normative table with CIs
NormTable.GCSE <- Stage.2.NormTable(
  Stage.1.Model=Model.1.GCSE, 
  Test.Scores=seq(from=10, to=85, by=5),
  Grid.Norm.Table=data.frame(Gender=c("F", "M")), 
  Rounded = FALSE)
summary(NormTable.GCSE)

# Bootstrap the CIs
Bootstrap_NormTable.GCSE <- Bootstrap.Stage.2.NormTable(
  Stage.2.NormTable = NormTable.GCSE)
summary(Bootstrap_NormTable.GCSE)


# Replicate the bootstrap results that were obtained in 
# Case study 2 of Chapter 8 in Van der Elst (2023)
# ------------------------------------------------
library(NormData)   # load the NormData package
data(Substitution)  # load the Substitution dataset

# Make the new variable Age.C (= Age centered) that is 
# needed to fit the final Stage 1 model, 
# and add it to the Substitution dataset
Substitution$Age.C <- Substitution$Age - 50

# Fit the final Stage 1 model
Substitution.Model.9 <- Stage.1(Dataset=Substitution, 
  Alpha=0.005, Model=LDST~Age.C+LE, Order.Poly.Var=1) 

summary(Substitution.Model.9)

# Make the normative table
NormTable.LDST <- Stage.2.NormTable(
Stage.1.Model=Substitution.Model.9, 
  Test.Scores=seq(from=25, to=40, by=5),
  Grid.Norm.Table=expand.grid(
  Age.C=seq(from=-30, to=30, by = 1), 
  LE=c("Low", "Average", "High")), Rounded = FALSE)

# Bootstrap the CIs
Bootstrap_NormTable.LDST <- Bootstrap.Stage.2.NormTable(
  Stage.2.NormTable = NormTable.LDST)

summary(Bootstrap_NormTable.LDST)

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