Bootstrap.Stage.2.NormTable {NormData}

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)

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.

Details

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

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.

Author(s)

Wim Van der Elst

References

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

See Also

Stage.2.NormTable

Examples

 # 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)