7 Basic mirt Commands: A Reference Guide

Author

Derek C. Briggs and Claude Code (Opus 4.6 & 4.7)

7.1 Introduction

This document is a reference guide for using the mirt package in R to fit IRT models to dichotomously scored item response data. It covers the essential workflow from classical item analysis through model fitting, parameter extraction, and plotting. Use this as a resource when working with different data sets to complete class assignments.

7.1.1 Required Packages

Code

library(mirt)

7.1.2 Loading Data

For this guide we use a 15-item data set (pset1_formA.csv). When working with your own data, update the file path accordingly.

Code

data_path <- "../IRT Models for Dichotomously Scored Items/Data/"
forma <- read.csv(paste0(data_path, "pset1_formA.csv"))
forma <- forma[, 1:15]  # Use first 15 items
head(forma)

  V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15
1  0  0  0  0  1  1  0  0  1   0   0   0   0   0   1
2  0  0  0  1  1  1  1  1  1   1   0   0   1   0   0
3  0  0  0  0  0  0  0  0  1   0   0   0   0   0   1
4  0  0  0  1  1  1  1  0  0   0   0   0   0   1   0
5  1  1  1  1  1  1  1  1  1   1   1   1   1   1   1
6  0  0  0  1  1  1  1  0  0   0   0   0   0   0   0

7.2 Part 1: Classical Item Analysis

Always start with descriptive statistics before doing anything fancy. In this context, descriptive stats are classical item statistics.

7.2.1 Item Statistics using `mirt:itemstats`

Code

itemstats(forma)

$overall
    N mean_total.score sd_total.score ave.r  sd.r alpha SEM.alpha
 1958            5.652          4.061 0.304 0.112 0.866     1.487

$itemstats
       N K  mean    sd total.r total.r_if_rm alpha_if_rm
V1  1958 2 0.278 0.448   0.608         0.531       0.857
V2  1958 2 0.261 0.440   0.606         0.530       0.857
V3  1958 2 0.208 0.406   0.584         0.513       0.858
V4  1958 2 0.601 0.490   0.606         0.520       0.857
V5  1958 2 0.554 0.497   0.651         0.572       0.854
V6  1958 2 0.380 0.486   0.600         0.515       0.857
V7  1958 2 0.630 0.483   0.594         0.508       0.858
V8  1958 2 0.202 0.402   0.577         0.505       0.858
V9  1958 2 0.455 0.498   0.613         0.527       0.857
V10 1958 2 0.368 0.482   0.672         0.598       0.853
V11 1958 2 0.138 0.345   0.532         0.467       0.860
V12 1958 2 0.172 0.378   0.542         0.471       0.860
V13 1958 2 0.448 0.497   0.475         0.372       0.865
V14 1958 2 0.515 0.500   0.615         0.530       0.857
V15 1958 2 0.440 0.497   0.591         0.502       0.858

$proportions
        0     1
V1  0.722 0.278
V2  0.739 0.261
V3  0.792 0.208
V4  0.399 0.601
V5  0.446 0.554
V6  0.620 0.380
V7  0.370 0.630
V8  0.798 0.202
V9  0.545 0.455
V10 0.632 0.368
V11 0.862 0.138
V12 0.828 0.172
V13 0.552 0.448
V14 0.485 0.515
V15 0.560 0.440

7.3 Part 2: Fitting IRT Models with `mirt`

7.3.1 Estimating the 1PL, 2PL, and 3PL Models

The mirt function is used to fit unidimensional IRT models. The key arguments are:

model = 1 specifies a unidimensional model
itemtype specifies the model type: "Rasch", "2PL", or "3PL"
method = "EM" specifies the EM algorithm for estimation (this is the default)

Code

mirt_1pl <- mirt(forma, model = 1, itemtype = "Rasch", method = "EM")
mirt_2pl <- mirt(forma, model = 1, itemtype = "2PL", method = "EM")
mirt_3pl <- mirt(forma, model = 1, itemtype = "3PL", method = "EM")

7.3.2 Extracting Item Parameter Estimates

By default, mirt parameterizes models in slope-intercept form: $a_i(\theta_p + d_i)$. To get the traditional IRT parameterization $a_i(\theta_p - b_i)$, use IRTpars = TRUE.

Code

# Slope-intercept form (default)
coef(mirt_2pl, simplify = TRUE)

$items
       a1      d g u
V1  2.223 -1.707 0 1
V2  2.285 -1.877 0 1
V3  2.371 -2.413 0 1
V4  1.833  0.599 0 1
V5  2.152  0.311 0 1
V6  1.641 -0.756 0 1
V7  1.595  0.741 0 1
V8  2.057 -2.258 0 1
V9  1.580 -0.299 0 1
V10 2.338 -1.052 0 1
V11 2.353 -3.177 0 1
V12 2.018 -2.520 0 1
V13 0.956 -0.262 0 1
V14 1.566  0.052 0 1
V15 1.468 -0.368 0 1

$means
F1 
 0 

$cov
   F1
F1  1

Code

# Traditional IRT form
coef(mirt_2pl, simplify = TRUE, IRTpars = TRUE)

$items
        a      b g u
V1  2.223  0.768 0 1
V2  2.285  0.821 0 1
V3  2.371  1.018 0 1
V4  1.833 -0.327 0 1
V5  2.152 -0.144 0 1
V6  1.641  0.461 0 1
V7  1.595 -0.465 0 1
V8  2.057  1.098 0 1
V9  1.580  0.189 0 1
V10 2.338  0.450 0 1
V11 2.353  1.350 0 1
V12 2.018  1.249 0 1
V13 0.956  0.274 0 1
V14 1.566 -0.033 0 1
V15 1.468  0.251 0 1

$means
F1 
 0 

$cov
   F1
F1  1

Note the relationship between the two parameterizations: $b = -d/a$.

7.3.3 Saving and Working with Parameter Estimates

Code

coef_1pl <- coef(mirt_1pl, simplify = TRUE, IRTpars = TRUE)
coef_2pl <- coef(mirt_2pl, simplify = TRUE, IRTpars = TRUE)
coef_3pl <- coef(mirt_3pl, simplify = TRUE, IRTpars = TRUE)

# Extract just the a and b columns for the 2PL
coef_2pl$items[, 1:2]

            a           b
V1  2.2229042  0.76796594
V2  2.2852959  0.82116507
V3  2.3709157  1.01792382
V4  1.8331464 -0.32676666
V5  2.1519449 -0.14432116
V6  1.6413947  0.46051170
V7  1.5948384 -0.46481011
V8  2.0568636  1.09772715
V9  1.5795863  0.18920500
V10 2.3383711  0.44967213
V11 2.3534503  1.35010342
V12 2.0179700  1.24898596
V13 0.9564336  0.27361200
V14 1.5655666 -0.03331578
V15 1.4678540  0.25067126

The g and u columns in the output represent the lower asymptote (guessing) and upper asymptote parameters. These are only estimated in the 3PL (and a hypothetical 4PL) model.

7.3.4 Comparing Parameters Across Models

Code

round(data.frame(
  coef_1pl$items[, 1:2],
  coef_2pl$items[, 1:2],
  coef_3pl$items[, 1:3]
), 3)

    a      b   a.1    b.1    a.2    b.2     g
V1  1  1.469 2.223  0.768 48.255  0.936 0.080
V2  1  1.590 2.285  0.821 47.597  0.950 0.064
V3  1  2.013 2.371  1.018 11.356  1.007 0.044
V4  1 -0.604 1.833 -0.327  1.747 -0.290 0.000
V5  1 -0.306 2.152 -0.144  2.048 -0.095 0.000
V6  1  0.774 1.641  0.461  1.545  0.532 0.000
V7  1 -0.791 1.595 -0.465  1.537 -0.433 0.000
V8  1  2.066 2.057  1.098  1.903  1.186 0.000
V9  1  0.306 1.580  0.189  1.531  0.248 0.000
V10 1  0.853 2.338  0.450  2.139  0.532 0.000
V11 1  2.697 2.353  1.350  2.027  1.470 0.000
V12 1  2.342 2.018  1.249  1.838  1.347 0.000
V13 1  0.351 0.956  0.274  0.932  0.324 0.000
V14 1 -0.065 1.566 -0.033  1.476  0.016 0.000
V15 1  0.398 1.468  0.251  1.412  0.310 0.000

Note that the 1PL estimates are on a different scale than the 2PL and 3PL estimates (see the companion document on scale constraints for details). But the $b$-values are highly correlated across models—the differences are up to a linear transformation due to scale.

Code

plot(coef_2pl$items[, 2], coef_1pl$items[, 2],
     pch = 19, xlab = "b (2PL)", ylab = "b (1PL)",
     main = "Difficulty Estimates: 1PL vs. 2PL")
abline(lm(coef_1pl$items[, 2] ~ coef_2pl$items[, 2]), col = "red", lty = 2)

7.4 Part 3: Plotting with `mirt`

The mirt package has a powerful built-in plot function with many options. Use help('plot-method') to see all available plot types.

7.4.1 Item Response Functions (ICCs)

Code

# All items
plot(mirt_2pl, type = 'trace',theta_lim = c(-3, 3))

Code

# Specific items
plot(mirt_2pl, which.items = c(1, 3, 8), type = 'trace',theta_lim = c(-3, 3))

Code

# Overlay specific ICCs on a single plot
plot(mirt_2pl,
     type = "trace",
     which.items = c(1, 3, 8),
     theta_lim = c(-3, 3),
     facet_items = FALSE)

7.4.2 Observed vs. Predicted (Item Fit)

The itemfit function with empirical.plot overlays observed response proportions on the model-implied ICC. This is useful for diagnosing item misfit.

Code

itemfit(mirt_2pl, group.bins = 15, empirical.plot = 1,theta_lim = c(-3, 3))

7.5 Part 4: Test Characteristic Curve and Information Functions

7.5.1 Test Characteristic Curve (TCC)

The TCC shows the expected number of correct answers (out of 15) at each ability level.

Code

plot(mirt_2pl,theta_lim = c(-3, 3))

7.5.2 Item Information Functions

Each item provides a certain amount of “information” about ability at different points on the theta scale.

Code

plot(mirt_2pl, type = 'infotrace', which.items = c(1:3),theta_lim = c(-3, 3))

7.5.3 Test Information Function

The test information function is the sum of all item information functions.

Code

plot(mirt_2pl, type = 'info',theta_lim = c(-3, 3))

7.5.4 Test Information and Standard Error of Measurement

This combined plot shows both the test information function and the SEM on the same graph. The SEM is the inverse of the square root of the information: $SEM(\theta) = 1/\sqrt{I(\theta)}$.

Code

plot(mirt_2pl, type = 'infoSE', theta_lim = c(-3, 3))

7.5.5 Comparing Custom Test Information Functions

Say we create two test forms, form A with items 1-7, and form B with items 8-14. Let’s compare test info by form

Code

A<-c(1:7)
B<-c(8:14)
A.info <- testinfo(mirt_2pl, which.items = A, Theta = matrix(seq(-3,3,by=0.1)))
B.info <- testinfo(mirt_2pl, which.items = B, Theta = matrix(seq(-3,3,by=0.1)))
ymax <- round(max(max(A.info), max(B.info)), 0) + 1  # Top end of y-axis
# Plotting information without using the mirt plot function
Theta <- seq(-3, 3, by = 0.1)
plot(Theta, A.info, type = "l", ylim = c(0, ymax), col = "blue",
     ylab = "Information", main = "Blue = Form A, Black = Form B")
lines(Theta, B.info, col = "black")

7.6 Quick Reference Summary

7.6.1 Classical Item Analysis

Task	Command
Classical item stats	`itemstats(data)`

7.6.2 Model Fitting

Task	Command
Fit Rasch model	`mirt(data, 1, itemtype = "Rasch")`
Fit 2PL model	`mirt(data, 1, itemtype = "2PL")`
Fit 3PL model	`mirt(data, 1, itemtype = "3PL")`

7.6.3 Extracting Parameters

Task	Command
Get IRT parameters	`coef(mod, simplify = TRUE, IRTpars = TRUE)`
Get slope-intercept form	`coef(mod, simplify = TRUE)`
EAP ability estimates	`fscores(mod, method = "EAP")`

7.6.4 Plotting

Task	Command
Plot all ICCs (faceted)	`plot(mod, type = 'trace', theta_lim = c(-3, 3))`
Plot specific item ICCs	`plot(mod, which.items = c(1, 3), type = 'trace', theta_lim = c(-3, 3))`
Overlay ICCs on one plot	`plot(mod, which.items = c(1, 3), type = 'trace', facet_items = FALSE)`
Plot TCC	`plot(mod, theta_lim = c(-3, 3))`
Plot item information	`plot(mod, type = 'infotrace', which.items = 1:3, theta_lim = c(-3, 3))`
Plot test information	`plot(mod, type = 'info', theta_lim = c(-3, 3))`
Plot info + SEM	`plot(mod, type = 'infoSE', theta_lim = c(-3, 3))`
Custom test info by form	`testinfo(mod, which.items = c(1:7), Theta = matrix(seq(-3, 3, by = 0.1)))`
Check item fit	`itemfit(mod, group.bins = 15, empirical.plot = 1, theta_lim = c(-3, 3))`

--- title: "Basic mirt Commands: A Reference Guide" author: "Derek C. Briggs and Claude Code (Opus 4.6 & 4.7)" output: html_document: toc: true toc_float: true code_folding: show pdf_document: toc: true latex_engine: xelatex --- ```{r inject-rootdir, include=FALSE} knitr::opts_knit$set(root.dir = "/Users/briggsd/Library/CloudStorage/Dropbox/Github/Measurement and Psychometrics/Using the mirt package") ``` ```{r setup, include=FALSE} knitr::opts_chunk$set(echo = TRUE, message = FALSE, warning = FALSE) ``` ## Introduction This document is a reference guide for using the `mirt` package in R to fit IRT models to dichotomously scored item response data. It covers the essential workflow from classical item analysis through model fitting, parameter extraction, and plotting. Use this as a resource when working with different data sets to complete class assignments. ### Required Packages ```{r load-packages} library(mirt) ``` ### Loading Data For this guide we use a 15-item data set (`pset1_formA.csv`). When working with your own data, update the file path accordingly. ```{r load-data} data_path <- "../IRT Models for Dichotomously Scored Items/Data/" forma <- read.csv(paste0(data_path, "pset1_formA.csv")) forma <- forma[, 1:15] # Use first 15 items head(forma) ``` --- ## Part 1: Classical Item Analysis Always start with descriptive statistics before doing anything fancy. In this context, descriptive stats are classical item statistics. ### Item Statistics using `mirt:itemstats` ```{r alpha-stats} itemstats(forma) ``` ## Part 2: Fitting IRT Models with `mirt` ### Estimating the 1PL, 2PL, and 3PL Models The `mirt` function is used to fit unidimensional IRT models. The key arguments are: - `model = 1` specifies a unidimensional model - `itemtype` specifies the model type: `"Rasch"`, `"2PL"`, or `"3PL"` - `method = "EM"` specifies the EM algorithm for estimation (this is the default) ```{r fit-models, results='hide'} mirt_1pl <- mirt(forma, model = 1, itemtype = "Rasch", method = "EM") mirt_2pl <- mirt(forma, model = 1, itemtype = "2PL", method = "EM") mirt_3pl <- mirt(forma, model = 1, itemtype = "3PL", method = "EM") ``` ### Extracting Item Parameter Estimates By default, `mirt` parameterizes models in **slope-intercept form**: $a_i(\theta_p + d_i)$. To get the traditional IRT parameterization $a_i(\theta_p - b_i)$, use `IRTpars = TRUE`. ```{r coef-default} # Slope-intercept form (default) coef(mirt_2pl, simplify = TRUE) ``` ```{r coef-irt} # Traditional IRT form coef(mirt_2pl, simplify = TRUE, IRTpars = TRUE) ``` Note the relationship between the two parameterizations: $b = -d/a$. ### Saving and Working with Parameter Estimates ```{r extract-params} coef_1pl <- coef(mirt_1pl, simplify = TRUE, IRTpars = TRUE) coef_2pl <- coef(mirt_2pl, simplify = TRUE, IRTpars = TRUE) coef_3pl <- coef(mirt_3pl, simplify = TRUE, IRTpars = TRUE) # Extract just the a and b columns for the 2PL coef_2pl$items[, 1:2] ``` The `g` and `u` columns in the output represent the lower asymptote (guessing) and upper asymptote parameters. These are only estimated in the 3PL (and a hypothetical 4PL) model. ### Comparing Parameters Across Models ```{r compare-models} round(data.frame( coef_1pl$items[, 1:2], coef_2pl$items[, 1:2], coef_3pl$items[, 1:3] ), 3) ``` Note that the 1PL estimates are on a **different scale** than the 2PL and 3PL estimates (see the companion document on scale constraints for details). But the $b$-values are highly correlated across models---the differences are up to a linear transformation due to scale. ```{r compare-b-values, fig.width=6, fig.height=5} plot(coef_2pl$items[, 2], coef_1pl$items[, 2], pch = 19, xlab = "b (2PL)", ylab = "b (1PL)", main = "Difficulty Estimates: 1PL vs. 2PL") abline(lm(coef_1pl$items[, 2] ~ coef_2pl$items[, 2]), col = "red", lty = 2) ``` --- ## Part 3: Plotting with `mirt` The `mirt` package has a powerful built-in `plot` function with many options. Use `help('plot-method')` to see all available plot types. ### Item Response Functions (ICCs) ```{r plot-iccs, fig.width=10, fig.height=8} # All items plot(mirt_2pl, type = 'trace',theta_lim = c(-3, 3)) ``` ```{r plot-iccs-select, fig.width=10, fig.height=4} # Specific items plot(mirt_2pl, which.items = c(1, 3, 8), type = 'trace',theta_lim = c(-3, 3)) ``` ```{r one-plot, fig.width=10, fig.height=5} # Overlay specific ICCs on a single plot plot(mirt_2pl, type = "trace", which.items = c(1, 3, 8), theta_lim = c(-3, 3), facet_items = FALSE) ``` ### Observed vs. Predicted (Item Fit) The `itemfit` function with `empirical.plot` overlays observed response proportions on the model-implied ICC. This is useful for diagnosing item misfit. ```{r item-fit, fig.width=6, fig.height=5} itemfit(mirt_2pl, group.bins = 15, empirical.plot = 1,theta_lim = c(-3, 3)) ``` --- ## Part 4: Test Characteristic Curve and Information Functions ### Test Characteristic Curve (TCC) The TCC shows the expected number of correct answers (out of 15) at each ability level. ```{r tcc, fig.width=8, fig.height=5} plot(mirt_2pl,theta_lim = c(-3, 3)) ``` ### Item Information Functions Each item provides a certain amount of "information" about ability at different points on the theta scale. ```{r item-info, fig.width=10, fig.height=4} plot(mirt_2pl, type = 'infotrace', which.items = c(1:3),theta_lim = c(-3, 3)) ``` ### Test Information Function The test information function is the sum of all item information functions. ```{r test-info, fig.width=8, fig.height=5} plot(mirt_2pl, type = 'info',theta_lim = c(-3, 3)) ``` ### Test Information and Standard Error of Measurement This combined plot shows both the test information function and the SEM on the same graph. The SEM is the inverse of the square root of the information: $SEM(\theta) = 1/\sqrt{I(\theta)}$. ```{r info-sem, fig.width=8, fig.height=5} plot(mirt_2pl, type = 'infoSE', theta_lim = c(-3, 3)) ``` ### Comparing Custom Test Information Functions Say we create two test forms, form A with items 1-7, and form B with items 8-14. Let's compare test info by form ```{r custom-info, fig.width=8, fig.height=5} A<-c(1:7) B<-c(8:14) A.info <- testinfo(mirt_2pl, which.items = A, Theta = matrix(seq(-3,3,by=0.1))) B.info <- testinfo(mirt_2pl, which.items = B, Theta = matrix(seq(-3,3,by=0.1))) ymax <- round(max(max(A.info), max(B.info)), 0) + 1 # Top end of y-axis # Plotting information without using the mirt plot function Theta <- seq(-3, 3, by = 0.1) plot(Theta, A.info, type = "l", ylim = c(0, ymax), col = "blue", ylab = "Information", main = "Blue = Form A, Black = Form B") lines(Theta, B.info, col = "black") ``` --- ## Quick Reference Summary ### Classical Item Analysis | Task | Command | |:-----|:--------| | Classical item stats | `itemstats(data)` | ### Model Fitting | Task | Command | |:-----|:--------| | Fit Rasch model | `mirt(data, 1, itemtype = "Rasch")` | | Fit 2PL model | `mirt(data, 1, itemtype = "2PL")` | | Fit 3PL model | `mirt(data, 1, itemtype = "3PL")` | ### Extracting Parameters | Task | Command | |:-----|:--------| | Get IRT parameters | `coef(mod, simplify = TRUE, IRTpars = TRUE)` | | Get slope-intercept form | `coef(mod, simplify = TRUE)` | | EAP ability estimates | `fscores(mod, method = "EAP")` | ### Plotting | Task | Command | |:-----|:--------| | Plot all ICCs (faceted) | `plot(mod, type = 'trace', theta_lim = c(-3, 3))` | | Plot specific item ICCs | `plot(mod, which.items = c(1, 3), type = 'trace', theta_lim = c(-3, 3))` | | Overlay ICCs on one plot | `plot(mod, which.items = c(1, 3), type = 'trace', facet_items = FALSE)` | | Plot TCC | `plot(mod, theta_lim = c(-3, 3))` | | Plot item information | `plot(mod, type = 'infotrace', which.items = 1:3, theta_lim = c(-3, 3))` | | Plot test information | `plot(mod, type = 'info', theta_lim = c(-3, 3))` | | Plot info + SEM | `plot(mod, type = 'infoSE', theta_lim = c(-3, 3))` | | Custom test info by form | `testinfo(mod, which.items = c(1:7), Theta = matrix(seq(-3, 3, by = 0.1)))` | | Check item fit | `itemfit(mod, group.bins = 15, empirical.plot = 1, theta_lim = c(-3, 3))` |

7.1 Introduction

7.1.1 Required Packages

7.1.2 Loading Data

7.2 Part 1: Classical Item Analysis

7.2.1 Item Statistics using mirt:itemstats

7.3 Part 2: Fitting IRT Models with mirt

7.3.1 Estimating the 1PL, 2PL, and 3PL Models

7.3.2 Extracting Item Parameter Estimates

7.3.3 Saving and Working with Parameter Estimates

7.3.4 Comparing Parameters Across Models

7.4 Part 3: Plotting with mirt

7.4.1 Item Response Functions (ICCs)

7.4.2 Observed vs. Predicted (Item Fit)

7.5 Part 4: Test Characteristic Curve and Information Functions

7.5.1 Test Characteristic Curve (TCC)

7.5.2 Item Information Functions

7.5.3 Test Information Function

7.5.4 Test Information and Standard Error of Measurement

7.5.5 Comparing Custom Test Information Functions

7.6 Quick Reference Summary

7.6.1 Classical Item Analysis

7.6.2 Model Fitting

7.6.3 Extracting Parameters

7.6.4 Plotting

7.2.1 Item Statistics using `mirt:itemstats`

7.3 Part 2: Fitting IRT Models with `mirt`

7.4 Part 3: Plotting with `mirt`