plot CheckFit {NormData}

Evaluate the fit of the mean structure of a fitted Stage 1 model.

Description

The function CheckFit() allows for evaluating the fit of the mean structure of a regression model by comparing sample means and model-predicted means. This function plots the sample means (with CIs) and the means of the model-predicted values. If the model fits the data well, there should be a good agreement between the sample means and the predicted mean test scores in the relevant subgroups. When the model only contains (binary and/or non-binary) qualitative independent variables, the subgroups correspond to all possible combinations of the different levels of the qualitative variables. When there are quantitative independent variables in the model, these have to be discretized first.

Usage

## S3 method for class 'CheckFit'
plot(x, Color, pch, lty, 
Width.CI.Lines=.125, Size.symbol = 1, 
No.Overlap.X.Axis=TRUE, xlab, ylab="Test score", 
main = " ", Legend.text.size=1, Connect.Means, 
cex.axis=1, cex.main=1.5, cex.lab=1.5, ...)

Arguments

x

A fitted object of class CheckFit.

Color

The colors to be used for the means. If not specified, the default colors are used.

pch

The symbols to be used for the means. If not specified, dots are used.

lty

The line types to be used for the means. If not specified, solid lines are used.

Width.CI.Lines

The width of the horizontal lines that are used to depict the CI around the mean. Default Width.CI.Lines=0.125.

Size.symbol

The size of the symbol used to depict the mean test score. Default Size.symbol=1.

No.Overlap.X.Axis

Logical. When a plot is constructed using two IVs (i.e., 2 or more lines of the mean and CIs in the plot), it is possible that the plot is unclear because the different means and CIs can no longer be distinguished. To avoid this, the levels of IV1 (plotted on the X-axis) can be assigned slightly different values for each level of IV2. For example, the mean for the subcategory males in age range [20; 40] will be shown at value X=0.9 (rather than 1) and the mean for the subcategory females in age range [20; 40] will be shown at value X=1.1 (rather than 1). In this way, the different means and CIs can be more clearly distinguished. Default No.Overlap.X.Axis=TRUE.

xlab

The label that should be added to the X-axis.

ylab

The label that should be added to the Y-axis. Default ylab="Test score".

main

The title of the plot. Default main=" ".

Legend.text.size

The size of the text of the label for IV2. Default Legend.text.size=1.

Connect.Means

Logical. Should the symbols depicting the mean test scores be connected? If not specified, Connect.Means = TRUE is used if the model contains numeric independent variables and Connect.Means = FALSE otherwise.

cex.axis

The size of the labels on the X- and Y-axis. Default cex.axis=1.

cex.main

The magnification to be used for the main label.

cex.lab

The magnification to be used for X and Y labels.

...

Extra graphical parameters to be passed to plot().

Value

No return value, called for side effects.

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.1, plot.CheckFit

Examples

# Replicate the fit plot that was obtained in 
# Case study 1 of Chapter 7 in Van der Elst (2023)
# ------------------------------------------------
library(NormData)   # load the NormData package
data(Substitution)  # load the Substitution dataset
head(Substitution)  # have a look at the first datalines in
# the Substitution dataset

# Final Stage 1 model 
Substitution$Age.C <- Substitution$Age - 50
  # Add Age_Group (that discretizes the quantitative variable Age 
  # into 6 groups with a span of 10 years in the dataset for use 
  # by the CheckFit() function later on)
Substitution$Age_Group <- cut(Substitution$Age, 
   breaks=seq(from=20, to=80, by=10)) 
Substitution.Model.9 <- Stage.1(Dataset=Substitution, 
   Alpha=0.005, Model=LDST~Age.C+LE, Order.Poly.Var=1) 

# Examine fit 
Fit.LDST <- CheckFit(Stage.1.Model=Substitution.Model.9, 
  Means=LDST~Age_Group+LE)
summary(Fit.LDST) 
plot(Fit.LDST)


# Replicate the fit plot that was obtained in 
# Case study 2 of Chapter 7 in Van der Elst (2023)
# ------------------------------------------------
library(NormData)   # load the NormData package
data(VLT)           # load the VLT dataset
head(VLT)           # have a look at the first datalines in 
                    # the VLT dataset

# Fit the final Stage 1 model
VLT$Age.C <- VLT$Age - 50
VLT$Age.C2 <- (VLT$Age - 50)**2
  # Add Age_Group (that discretizes the quantitative variable Age 
  # into 6 groups with a span of 10 years in the dataset for use 
  # by the CheckFit() function later on)
VLT$Age_Group <- cut(VLT$Age, breaks=seq(from=20, to=80, by=10)) 

VLT.Model.4 <- Stage.1(Dataset = VLT, Alpha = .005, 
  Model = Total.Recall ~ Age.C+Age.C2+Gender+LE+Age.C:Gender)

# Examine fit using fit plots for the Age Group by 
# LE by Gender subgroups
Fit.Means.Total.Recall <- CheckFit(Stage.1.Model=VLT.Model.4, 
  Means=Total.Recall~Age_Group+LE+Gender)

summary(Fit.Means.Total.Recall)
plot(Fit.Means.Total.Recall)