latent_trait_analysis {airt}

Performs the latent trait analysis

Description

This function performs the latent trait analysis of the datasets/problems after fitting a continuous IRT model. It fits a smoothing spline to the points to compute the latent trait. The autoplot function plots the latent trait and the performance.

Usage

latent_trait_analysis(
  df,
  paras,
  min_item = NULL,
  max_item = NULL,
  epsilon = 0.01
)

## S3 method for class 'latenttrait'
autoplot(
  object,
  xlab = "Problem Difficulty",
  ylab = "Performance",
  plottype = 1,
  nrow = 2,
  se = TRUE,
  ratio = 3,
  ...
)

Arguments

df

The performance data in a matrix or dataframe.

paras

The parameters from fitting cirtmodel.

min_item

A vector with the minimum performance value for each algorithm.

max_item

A vector with the maximum performance value for each algorithm.

epsilon

A value defining good algorithm performance. If epsilon = 0, then only the best algorithm is considered. A default

object

For autoplot: the output of the function latent_trait_analysis.

xlab

For autoplot: the xlabel.

ylab

For autoplot: the ylabel.

plottype

For autoplot: plottype = 1 for all algorithm performances in a single plot, plottype = 2 for using facet_wrap to plot individual algorithms, plottype = 3 to plot the smoothing splines and plottype = 4 to plot strengths and weaknesses.

nrow

For autoplot: If plottype = 2, the number of rows for facet_wrap.

se

For autoplot: for plotting splines with standard errors.

ratio

For autoplot: for plotting strengths and weaknesses, ratio between x and y axis.

...

Other arguments currently ignored.

Value

A list with the following components:

crmtheta

The problem trait output computed from the R package EstCRM.

strengths

The strengths of each algorithm and positions on the latent trait that they performs well.

longdf

The dataset in long format of latent trait occupancy.

plt

The ggplot object showing the fitted smoothing splines.

widedf

The dataset in wide format with latent trait.

thetas

The easiness of the problem set instances.

weakness

The weaknesses of each algorithm and positions on the latent trait that they performs poorly.

Examples

# This is a dummy example.
set.seed(1)
x1 <- runif(200)
x2 <- 2*x1 + rnorm(200, mean=0, sd=0.1)
x3 <- 1 - x1 + rnorm(200, mean=0, sd=0.1)
X <- cbind.data.frame(x1, x2, x3)
max_item <- rep(max(x1, x2, x3),3)
min_item <- rep(min(x1, x2, x3),3)
mod <- cirtmodel(X, max.item=max_item, min.item=min_item)
out <- latent_trait_analysis(X, mod$model$param, min_item= min_item, max_item = max_item)
out
# To plot performance against the problem difficulty
autoplot(out)
# To plot individual panels
autoplot(out, plottype = 2)
# To plot smoothing splines
autoplot(out, plottype = 3)
# To plot strengths and weaknesses
autoplot(out, plottype = 4)