Introducing Person Probability Plots

Using the ppPlot Function

Introduction

In this tutorial, we’re going to dive into a cool new feature introduced in WrightMap version 1.2: the Person Probability Plot (PP plot). This plot is designed to represent model information for specific proficiencies, giving us a neat way to visualize the uncertainty surrounding a person’s estimate and to see the probabilities that the person will answer different items correctly.

Let’s get started by loading an example ConQuest output:

fpath <- system.file("extdata", package="WrightMap")
model1 <- CQmodel(p.est = file.path(fpath,"ex2.eap"), show = file.path(fpath,"ex2.shw"))

Creating a Basic Person Probability Plot

Now, let’s create the default version of the PP plot. There are three key things we need to provide:

1. A model object (in this case, model1 from ConQuest)
2. The person’s proficiency estimate (let’s set it at 0 logits)
3. The standard error associated with the estimate (we’ll use 1 logit as the standard error)

Here’s the code to generate the plot:

ppPlot(model1, est = 0, SE = 1)

Using GIN table for threshold parameters

Basic Person Probability Plot

Understanding the Plot

In this basic version, we’re using the ConQuest item and person information stored in model1. The person being represented has a proficiency estimate of 0 logits and a standard error of 1 logit.

• Person Side (Histogram): The darkest bar represents the group in which the person’s proficiency estimate falls. The light gray bars on either side show the range of the standard error.
• Item Side (Probability Lines): For each item, the lines mark the probabilities that a person with this proficiency would answer correctly. The plot draws lines at 80%, 60%, 50%, 40%, and 20% probability thresholds.

Modifying the Plot: Adding Density and Classic Item Styles

What if you want to change things up? Let’s try using a density plot on the person side instead of a histogram and switch to a classic style for the item side. Here’s how:

ppPlot(model1, est = 0, SE = 1, person.side = personDens, item.side = itemClassic)

Using GIN table for threshold parameters

Person Probability Plot with Density and Classic Item Style

In this version: - Person Side (Density): We’re using a density curve instead of the histogram to show where the proficiency estimate falls. - Item Side (Classic): We’re switching to a “classic” item representation, giving us a more traditional look for the probability lines.

Conclusion

The Person Probability Plot is a great tool for visualizing the relationship between person proficiencies and item difficulties, especially when you want to show how likely it is for a person to answer specific items correctly. You can easily customize these plots by switching between histogram or density views on the person side, and by using different styles for the item side.

Hopefully, this new addition to WrightMap will make it easier to communicate the results of a model for specific respondents. Play around with the options and see how the PP plot can enhance your analysis!