| Title: | Descriptive 3D Multidimensional Item Response Theory Modelling |
|---|---|
| Description: | For identifying, estimating, and plotting descriptive multidimensional item response theory models, restricted to 3D and dichotomous or polytomous data that fit the two-parameter logistic model or the graded response model. The method is foremost explorative and centered around the plot function that exposes item characteristics and constructs, represented by vector arrows, located in a three-dimensional interactive latent space. The results can be useful for item-level analysis as well as test development. |
| Authors: | Erik Forsberg [aut, cre, cph] |
| Maintainer: | Erik Forsberg <[email protected]> |
| License: | GPL (>= 3) |
| Version: | 2.0.4 |
| Built: | 2024-11-03 05:22:28 UTC |
| Source: | https://github.com/forsbergpyschometrics/d3mirt |
A subset of data (N = 1046, Mean age = 51.33, SD = 14.56, 57% Female) from the ANES 2008-2009 Panel Study Off Wave Questionnaires, December 2009 (DeBell et al., 2010), with complete responses on a pilot version of the Judgment subscale from what became the Moral Foundations Questionnaire (Graham et al., 2011). Demographic variables include age and gender (two levels), and Likert-items positively scored on a scale from 1 = Strongly Disagree to 6 = Strongly Agree.
anes0809offwavesanes0809offwaves
anes0809offwavesA data frame with 1046 rows and 22 columns:
Age
Gender (Male = 1, Female = 2)
When one of my loved ones needs my attention, I really try to slow down and give them the time and help they need
I am known by family and friends as someone who makes time to pay attention to others' problems
I’m the kind of person who is willing to go the “extra mile” to help take care of my friends, relatives, and acquaintances
When friends or family members experience something upsetting or discouraging I make a special point of being kind to them
When it comes to my personal relationships with others, I am a very generous person
It makes me very happy to give to other people in ways that meet their needs
It is just as important to me that other people around me are happy and thriving as it is that I am happy and thriving
My decisions are often based on concern for the welfare of others
I am usually willing to risk my own feelings being hurt in the process if I stand a chance of helping someone else in need
I make it a point to let my friends and family know how much I love and appreciate them
Compassion for those who are suffering is the most crucial virtue
One of the worst things a person could do is hurt a defenseless animal
When the government makes laws, the number one principle should be ensuring that everyone is treated fairly
Justice is the most important requirement for a society
I am proud of my country’s history
People should be loyal to their family members, even when they have done something wrong
Respect for authority is something all children need to learn
Men and women each have different roles to play in society
People should not do things that are disgusting, even if no one is harmed
I would call some acts wrong on the grounds that they are unnatural
...
https://electionstudies.org/data-center/2008-2009-panel-study/
DeBell, M., Krosnick, J. A., & Lupia, A. (2010). Methodology Report and User’s Guide for the 2008–2009 ANES Panel Study. Palo Alto, CA, and Ann Arbor, MI: Stanford University and the University of Michigan.
Graham, J., Nosek, B. A., Haidt, J., Iyer, R., Koleva, S., & Ditto, P. H. (2011). Mapping the moral domain. Journal of Personality and Social Psychology, 101(2), 366–385.
https://doi.org/10.1037/a0021847
data(anes0809offwaves)data(anes0809offwaves)
A test unit data frame consisting of 42 rows and 6 columns with standard angles in Cartesian coordinates as item loadings (columns denoted a1, a2, and a3) oriented in both positive and negative directions in a three-dimensional space.
The distance from the origin is set by d = 0,5 (4th column) on all rows, which refers to the parameter related to difficulty in the compensatory model.
The last two columns contain the angles converted to spherical coordinates with Theta representing the polar angle and Phi representing the azimuthal angle.
Running the data frame in D3mirt() converts the angles into spherical coordinates and can be used to check functionality in the package.
Note, Nan, i.e., "not-a-number", appears in the D3mirt() output because the function (used when changing to spherical coordinates) is not defined when cosine equals zero.
anglesangles
An object of class data.frame with 42 rows and 6 columns.
data(angles)data(angles)
Descriptive multidimensional item response theory model estimation (DMIRT; Reckase, 2009, 1985, Reckase and McKinley, 1991) for dichotomous and polytomous items restricted to three dimensions.
D3mirt( x, modid = NULL, model = NULL, con.items = NULL, con.sphe = NULL, itemtype = "graded", method.mirt = "QMCEM", method.fscores = "EAP", QMC = TRUE )D3mirt( x, modid = NULL, model = NULL, con.items = NULL, con.sphe = NULL, itemtype = "graded", method.mirt = "QMCEM", method.fscores = "EAP", QMC = TRUE )
x |
A data frame with items in rows and model parameters in columns containing raw response data as integer values or factor loadings. Input can also be an S4 object of class 'SingleGroupClass' exported from mirt::mirt (Chalmers, 2012). Regarding the data frame, the number of columns must be more than or equal to 4, i.e., three columns with (a) parameters and at least one column for difficulty (d) parameters. |
modid |
Use either the two model identification items from modid as a combined vector or use nested list of item indicators to fit an orthogonal model (see examples below).
The default is |
model |
The user has the option of imputing a model specification schema used in the call to mirt::mirt (Chalmers, 2012).
The default is |
con.items |
Optional. Nested lists with integer values as item indicators to identify constructs. The default is |
con.sphe |
Optional. Nested lists of spherical angles to identify constructs. The default is |
itemtype |
What item type to use in the function call. Available options are |
method.mirt |
Estimation algorithm for mirt::mirt (Chalmers, 2012) to fit the model. The default is |
method.fscores |
Factor estimation algorithm for mirt::fscores (Chalmers, 2012) for extracting respondent trait scores. The default is |
QMC |
Integration method for mirt::fscores (Chalmers, 2012). The default is |
The D3mirt() function takes in model parameters from a compensatory three-dimensional multidimensional two-parameter logistic model (M2PL) or a multidimensional graded
response model (MGRM), either in the form of a data frame with item data, or a data frame with factor loadings or an S4 object of class 'SingleGroupClass' exported from mirt::mirt (Chalmers, 2012) function fitted in accordance with descriptive item response theory model specifications (see package vignette).
The function returns DMIRT estimates that can be visualized with plot that graph vector arrows representing item response characteristics in a three-dimensional space.
Regarding the former, this includes visualization of the single multidimensional discrimination (MDISC) parameter and the multidimensional difficulty (MDIFF) parameters (Reckase, 2009, 1985; Reckase & McKinley, 1991).
The function also returns respondent trait scores that can be plotted with plot as spheres located in the three-dimensional latent space.
In turn, this allows for studying respondent profiles using the plot function (for more on profiles, see function documentation on plot).
There are two types of models available for D3mirt analysis. The default model is the basic DMIRT model (Reckase, 2009, 1985, Reckase & McKinley, 1991) that relaxes the assumption of unidimensionality in the items while restricting the latent space to be orthogonal.
To use the default option requires first selecting two items to identify the model. This can be done manually with the modid argument in the function call to D3mirt.
However, it is advisable to use the dedicated function modid included in the package for this purpose (for more on model identification see function documentation for modid).
In contrast, the optional orthogonal model constrains the items to be strictly parallel with the axes (see example section below).
Consequently, this option allows the user to investigate the model under the assumption that the items are strictly unidimensional and orthogonally oriented in the latent space.
In this context "orthogonal" refers to the perpendicular orientation of the item vectors the model specification creates.
Note that using the optional model will also affect respondent locations in the latent space accordingly.
It is also possible to specify a unique model with the help of the model argument in the function call to D3mirt if written in mirt (Chalmers, 2012) syntax (for an example, see the appendix in the package vignette).
The user also has the option of including constructs in the estimation. Constructs, in this context, refer to the assumption that a subset of items or a particular angle in the latent space holds some higher-order latent variable of interest. Constructs are visualized when plotting as solid black arrows running across the model space. In addition, if constructs are used, the output will also contain the directional discrimination (DDISC) parameters for all items assessed in the direction indicated by the construct vectors. This makes it possible to compare item discrimination under the assumption that the items are unidimensional, measuring the same latent variable indicated by the angle of the construct vector.
To include constructs, the user can create one or more nested lists that indicate what items belong to what construct (from one item to all items in the set; see the examples section below).
From this, the D3mirt() function calculates the average direction by adding and normalizing the direction cosines using the items in the nested lists.
Constructs can also be indicated using spherical coordinates stored in nested lists.
This allows the user to freely add any number of constructs at any angle in the latent space to study the item discrimination.
For more on theory and how to interpret statistical estimates, please see the package vignette.
A S3 object of class D3mirt with lists of a and d parameters from the M2PL or MGRM estimation, multidimensional difficulty (MDIFF), multidimensional discrimination (MDISC), direction cosines and degrees for vector angles, construct lists, vector coordinates, and respondent trait scores.
Erik Forsberg
Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29.
https://doi.org/10.18637/jss.v048.i06
Reckase, M. D. (2009). Multidimensional Item Response Theory. Springer.
Reckase, M. D. (1985). The Difficulty of Test Items That Measure More Than One Ability. Applied Psychological Measurement, 9(4), 401-412.
https://doi.org/10.1177/014662168500900409
Reckase, M. D., & McKinley, R. L. (1991). The Discriminating Power of Items That Measure More Than One Dimension. Applied Psychological Measurement, 15(4), 361-373.
https://doi.org/10.1177/014662169101500407
# Load data data("anes0809offwaves") x <- anes0809offwaves x <- x[, 3:22] # Remove columns for age and gender # Call to D3mirt(), including optional nested lists for three constructs # Item W7Q16 is not included in any construct because of model violations # Constructs can also be defined using interval notation, i.e., c(1:10) and so on. con <- list(c(1,2,3,4,5,6,7,8,9,10), c(11,12,13,14), c(15,17,18,19,20)) mod <- D3mirt(x, modid = c("W7Q3", "W7Q20"), con.items = con) # Show summary of results summary(mod) # Call to D3mirt(), including optional constructs with the help of spherical coordinates # Spherical coordinates are indicated using nested list structures with angles # First angle indicates the rotation in the xz-plane # The second angle is the angle away from the y-axis. # The specification below indicates three constructs located at a 45-degree angle # between the three axes in the positive orientation. # It is possible to assign factor loadings and difficulty parameters from mod to a new data frame # This skips fitting the compensatory model and makes fitting the model with D3mirt() instant # Note that trait scores will not be included in the exported S3 object when using this option y <- cbind(mod$loadings, mod$diff) con <- list(c(0, 45), c(45, 90), c(90, 45)) mod <- D3mirt(y, con.sphe = con) # Show summary of results summary(mod) # Call D3mirt() using the orthogonal optional model # often requires removing items with poor fit # In this example item W7Q16 is removed from the data frame y <- data.frame(x[,-16]) # Items are constrained to the x, y, and z-axes using # nested lists with positive integers as item indicators # Note that integers indicate where the items are located in the data frame mod <- D3mirt(y, modid = list(c(1:10), c(15:19), c(11:14))) # Show summary of results summary(mod)# Load data data("anes0809offwaves") x <- anes0809offwaves x <- x[, 3:22] # Remove columns for age and gender # Call to D3mirt(), including optional nested lists for three constructs # Item W7Q16 is not included in any construct because of model violations # Constructs can also be defined using interval notation, i.e., c(1:10) and so on. con <- list(c(1,2,3,4,5,6,7,8,9,10), c(11,12,13,14), c(15,17,18,19,20)) mod <- D3mirt(x, modid = c("W7Q3", "W7Q20"), con.items = con) # Show summary of results summary(mod) # Call to D3mirt(), including optional constructs with the help of spherical coordinates # Spherical coordinates are indicated using nested list structures with angles # First angle indicates the rotation in the xz-plane # The second angle is the angle away from the y-axis. # The specification below indicates three constructs located at a 45-degree angle # between the three axes in the positive orientation. # It is possible to assign factor loadings and difficulty parameters from mod to a new data frame # This skips fitting the compensatory model and makes fitting the model with D3mirt() instant # Note that trait scores will not be included in the exported S3 object when using this option y <- cbind(mod$loadings, mod$diff) con <- list(c(0, 45), c(45, 90), c(90, 45)) mod <- D3mirt(y, con.sphe = con) # Show summary of results summary(mod) # Call D3mirt() using the orthogonal optional model # often requires removing items with poor fit # In this example item W7Q16 is removed from the data frame y <- data.frame(x[,-16]) # Items are constrained to the x, y, and z-axes using # nested lists with positive integers as item indicators # Note that integers indicate where the items are located in the data frame mod <- D3mirt(y, modid = list(c(1:10), c(15:19), c(11:14))) # Show summary of results summary(mod)
modid() performs model identification for descriptive multidimensional item response theory (DMIRT) models by indicating what items, from a set or scale, to use to identify the DMIRT model.
modid( x, efa = TRUE, factors = 3, lower = 0.5, upper = 0.1, fac.order = NULL, itemtype = "graded", method = "EM", rotate = "oblimin", ... )modid( x, efa = TRUE, factors = 3, lower = 0.5, upper = 0.1, fac.order = NULL, itemtype = "graded", method = "EM", rotate = "oblimin", ... )
x |
A data frame with item data or item factor loadings that fit the multidimensional graded response model (MGRM) or the multidimensional 2-parameter logistic model (M2PL). |
efa |
Logical, if the data should be explored with exploratory factor analysis (EFA). The default is |
factors |
The number of factors for the exploratory factor analysis. The default is |
lower |
The lower bound for the item pool calculated using the standard deviation of scaled item factor loadings. The default is |
upper |
The upper bound for filtering absolute sum scores less than or equal to the indicated value. The default is |
fac.order |
Optional. Users can override the automatic sorting of factors by manually indicating factor order with integer values, e.g., |
itemtype |
The item model for the exploratory factor analysis. Note, only item type 'graded' (for the MGRM) or '2PL' (for the M2PL) are allowed. The default is |
method |
A string indicating what integration algorithm to use for the EFA. The default is |
rotate |
A string indicating what rotation method to use for the EFA. The default is |
... |
Any additional arguments passed to mirt(). |
Before performing DMIRT analysis, it is necessary to identify the compensatory model (Reckase, 2009). For a three-dimensional model, this implies that two items must be chosen and their loadings restricted as follows. The first item is fixed not to load on the second and third axes (y and z), while the second item is fixed not to load on the third axis (z). If this can be achieved, it is possible to create a three-dimensional DMIRT model that reflects the data correctly.
The modid() function can help by suggesting what items to use for the latter purpose.
The function does this by first performing an EFA on the data and then selecting the strongest loading items, following the order of strength of the factors and following the statistical assumptions described above.
This orders the entire model so that the strongest loading item, from the strongest factor, always aligns with the x-axis, and the other items follow thereon.
Note that the modid() function is not limited to three-dimensional analysis and can be used to identify a DMIRT model on any number of dimensions.
Because D3mirt analysis is based on the M2PL and the MGRM, it is recommended to use multidimensional item response theory EFA methods, such as the EFA option in mirt::mirt (Chalmers, 2012) with itemtype = 'graded' or '2PL', so that the EFA is performed with the proper item model.
For this reason, the mirt() function is integrated into modid() so that the user needs only to provide the data frame containing empirical item data in the first argument in the call to the function.
Accordingly, in the default mode (efa = TRUE), using raw item data, the function performs an EFA with three factors as default (factors = 3), and finishes with the model identification.
However, it is also possible to use the modid() function without performing the EFA by setting efa = FALSE if, for instance, a data frame with factor loadings is already available.
This allows the function to move directly to the model identification step.
Note, the EFA is only used to find model identification items that meet the necessary DMIRT model specification requirements. The EFA model itself is discarded after this step in the procedure and the user can, therefore, try different rotation methods and compare the results.
Running the function prints the number of items and factors together with the suggested model identification items to the console and the summary function is used to inspect the full results.
The latter includes data frames that hold all the model identification items (Item.1...Item.n) selected by modid() together with the items absolute sum score (ABS), one frame for the sum of squares for factors sorted in descending order, and one frame for item factor loadings.
The order of the factors follows the model identification items so that item 1 comes from the strongest factor, item 2 from the second strongest factor, and so on.
Model identification items should preferably (a) have an absolute sum score of less than or equal to .10 and (b) have the highest factor loading scores on the factor of interest. Of these two criteria, (a) should be given the strongest weight in the selection decision. If these conditions cannot be met, the user is advised to proceed with caution since the loading scores, therefore, imply that an adequate orthogonal structure may not be empirically attainable. For more details on the model identification process and troubleshooting, please see the package vignette.
A S3 object of class modid with lists of items and absolute sum scores, sorted by the latter, and sum of squared factor loadings and frame with raw factor loadings with columns ordered on explained variance (high to low) or according to user settings.
Erik Forsberg
Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29.
https://doi.org/10.18637/jss.v048.i06
Reckase, M. D. (2009). Multidimensional Item Response Theory. Springer.
# Load data data("anes0809offwaves") x <- anes0809offwaves x <- x[,3:22] # Remove columns for age and gender # Identify the DMIRT model using a three-factor EFA id <- modid(x) # Call to summary summary(id) # Call to modid with increased lower and upper bound # Assign loadings to a data frame and set efa to false x <- id$loadings id <- modid(x, efa = FALSE, lower = 1, upper = 1 ) summary(id) # Override factor order by reversing columns in the original data frame id <- modid(x, efa = FALSE, fac.order = c(3,2,1)) summary(id)# Load data data("anes0809offwaves") x <- anes0809offwaves x <- x[,3:22] # Remove columns for age and gender # Identify the DMIRT model using a three-factor EFA id <- modid(x) # Call to summary summary(id) # Call to modid with increased lower and upper bound # Assign loadings to a data frame and set efa to false x <- id$loadings id <- modid(x, efa = FALSE, lower = 1, upper = 1 ) summary(id) # Override factor order by reversing columns in the original data frame id <- modid(x, efa = FALSE, fac.order = c(3,2,1)) summary(id)
D3mirt
For graphing of objects of class D3mirt from the D3mirt() function using the rgl 3D visualization device system (Adler & Murdoch, 2022).
## S3 method for class 'D3mirt' plot( x, scale = FALSE, hide = FALSE, ind.scores = FALSE, diff.level = NULL, items = NULL, item.names = TRUE, item.lab = NULL, constructs = FALSE, construct.lab = NULL, adjust.lab = c(0.5, -0.8), x.lab = "X", y.lab = "Y", z.lab = "Z", title = "", line = -5, font = 1, cex = 1, font.col = "black", axis.scalar = 1.1, axis.length = NULL, axis.points = "black", axis.ticks = TRUE, nticks = 4, width.rgl.x = 1040, width.rgl.y = 1040, view = c(15, 20, 0.6), show.plane = TRUE, plane.col = "grey80", background = "white", type = "rotation", col = c("black", "grey20", "grey40", "grey60", "grey80"), arrow.width = 0.6, n = 20, theta = 0.2, barblen = 0.03, c.scalars = c(1, 1), c.type = "rotation", c.col = "black", c.arrow.width = 0.6, c.n = 20, c.theta = 0.2, c.barblen = 0.03, profiles = NULL, levels = NULL, sphere.col = c("black", "grey20", "grey40", "grey60", "grey80"), spheres.r = 0.05, ci = FALSE, ci.level = 0.95, ellipse.col = "grey80", ellipse.alpha = 0.2, ... )## S3 method for class 'D3mirt' plot( x, scale = FALSE, hide = FALSE, ind.scores = FALSE, diff.level = NULL, items = NULL, item.names = TRUE, item.lab = NULL, constructs = FALSE, construct.lab = NULL, adjust.lab = c(0.5, -0.8), x.lab = "X", y.lab = "Y", z.lab = "Z", title = "", line = -5, font = 1, cex = 1, font.col = "black", axis.scalar = 1.1, axis.length = NULL, axis.points = "black", axis.ticks = TRUE, nticks = 4, width.rgl.x = 1040, width.rgl.y = 1040, view = c(15, 20, 0.6), show.plane = TRUE, plane.col = "grey80", background = "white", type = "rotation", col = c("black", "grey20", "grey40", "grey60", "grey80"), arrow.width = 0.6, n = 20, theta = 0.2, barblen = 0.03, c.scalars = c(1, 1), c.type = "rotation", c.col = "black", c.arrow.width = 0.6, c.n = 20, c.theta = 0.2, c.barblen = 0.03, profiles = NULL, levels = NULL, sphere.col = c("black", "grey20", "grey40", "grey60", "grey80"), spheres.r = 0.05, ci = FALSE, ci.level = 0.95, ellipse.col = "grey80", ellipse.alpha = 0.2, ... )
x |
A S3 object of class |
scale |
Logical, if item vector arrow length should visualize the MDISC. If set to FALSE, the vector arrow length will be of one unit length. The default is |
hide |
Logical, if items should be plotted. The default is |
ind.scores |
Logical, should output plot respondents trait scores. The default is |
diff.level |
Optional. Plotting of a single level of difficulty indicated by an integer. |
items |
Optional. The user can input a list of integers indicating what item vector arrows will be visible while the remaining item vector arrows are hidden. |
item.names |
Logical, if item labels should be plotted. The default is |
item.lab |
Optional. String vector of item names that will override row names extracted from the data frame. Note that row names are not overwritten.
Instead, the string vector in |
constructs |
Logical, if construct vector arrows should be plotted. The default is |
construct.lab |
Optional. String vector of names for constructs, similar to |
adjust.lab |
Vector of parameters for the position of the item and construct labels for the |
x.lab |
Labels for x-axis, the default is |
y.lab |
Labels for y-axis, the default is |
z.lab |
Labels for y-axis, the default is |
title |
The main title for the graphical device, plotted with the |
line |
Title placement for |
font |
A numeric font number from 1 to 5, the default is |
cex |
A numeric character expansion value to adjust font size, the default is |
font.col |
Color of axes, numbers, and fonts. The default is |
axis.scalar |
Scalar multiple for adjusting the length of all axes (x, y, z) in the 3D model proportionally. The default is |
axis.length |
Optional. For adjusting the length of the axis manually by entering a numeric or a numeric vector.
For instance, c(3,2,4,3,3,2) indicate axis coordinates x = 3, -x = 3, y = 4, -y = 3, z = 3, -z = 2.
Note that a symmetric model can be created easily by adding a single numeric in the |
axis.points |
Color of axis points for the |
axis.ticks |
Logical, if axis ticks from the |
nticks |
Number of ticks for |
width.rgl.x |
Width in the x direction for |
width.rgl.y |
Width in the y direction for |
view |
Vector with polar coordinates and zoom factor for the |
show.plane |
Logical, if xz-plane should be visible in the graphical device. The default is |
plane.col |
Color of the plane, the default is |
background |
Set background color for the graphical device, the default is |
type |
Type of vector arrow for items, the default is |
col |
Vector of colors representing difficulty levels for item response functions used in |
arrow.width |
Width of vector arrows for |
n |
Number of barbs for the vector arrows from |
theta |
Opening angle of barbs for vector arrows from |
barblen |
The length of the barbs for vector arrows from |
c.scalars |
Set of scalars for adjusting construct arrow length proportionally.
The first numeric adjusts the length in the positive direction, and the second numeric the length in the negative direction. The default is |
c.type |
Type of vector arrow for constructs. See rgl::arrow3d for more options regarding arrow types. The default is |
c.col |
Color of construct vector arrows from |
c.arrow.width |
Width of construct vector arrows for |
c.n |
Number of barbs for the construct vector arrows from the |
c.theta |
Opening angle of barbs for construct vector arrows from |
c.barblen |
The length of the barbs for construct vector arrows from |
profiles |
Data frame with coordinates for spheres representing a subset of respondent scores. The default is |
levels |
Optional. A column with values indicating levels for sphere colors from the |
sphere.col |
Color vector for |
spheres.r |
Radius of the spheres for |
ci |
Logical, if spheres should include an ellipsoid outlining a confidence region returned from the |
ci.level |
Level of confidence for |
ellipse.col |
Color of the ellipse from |
ellipse.alpha |
Opacity for the confidence region from |
... |
Additional arguments passed to RGL or methods. |
The plotting function allows plotting of all items, a selection of items as well as plotting a single item.
Length of the vector arrows can be set to one unit length across all item vector arrows by setting scale = TRUE.
This removes the visualization of the MDISC parameter.
Note that when scaling items with scale = TRUE, the plot() function does not change the length of the model axes.
This often means that the axes of the model may need to be adjusted, which can be achieved proportionally with axis.scalar or manually with axis.length.
The user has the option of adding constructs to the graphical output with constructs = TRUE (see the documentation for D3mirt or the package vignette regarding constructs).
Other options include plotting one level of difficulty at a time with the diff.level argument if polytomous items are used in the model.
Item names are displayed by default, but the user has the option of adding new item labels for the items with item.lab, as well as labeling constructs with construct.lab.
Regarding the interpretation of results, the angle of the vector arrows indicates what traits, located along the orthogonal axes, an item can be said to describe (Reckase, 2009, 1985, Reckase & McKinley, 1991). For instance, an item located at 0 degrees seen from the x-axis, and 90 degrees as seen from the y and z-axis, only describes trait x. Such an item is unidimensional since its direction vector lies parallel and on the x-axis. In contrast, an item located at 45 degrees between all three axes in a three-dimensional model describes all three traits in the model equally well. Such an item is within-multidimensional with respect to all three latent traits used in the analysis because its direction vector points in a neutral direction in the model.
When plotting the D3mirt model with plot(), it is possible to visually observe statistical violations in the graphical output returned.
For instance, shorter vector arrows indicate weaker discrimination and, therefore, higher amounts of statistical violations.
Moreover, if a polytomous item struggles or even fails to describe any of the latent variables in the model, it can often lead to an extreme stretch of the MDIFF range.
This is comparable to trace lines turning horizontal in a unidimensional item response theory model.
The plot function can also display respondent scores in the three-dimensional model space, represented as spheres whose coordinates are derived from the respondent's factor scores.
This allows for a profile analysis in which respondent rows are separated or selected conditioned on some external criteria.
To do this, the user must first extract respondent factor scores with mirt::fscores (Chalmers, 2012) and then use some selection process to separate or subset respondent rows.
The resulting data frame is used in the profiles argument.
If desired, a confidence interval can be added to the spheres by setting ci = TRUE.
A general advice is to hide vector arrows with hide = TRUE when analyzing respondent profiles to avoid visual cluttering.
For more on profile analysis (e.g., preparation and examples), see package vignette.
The returned RGL device can, for example, be exported to the R console and saved as an interactive HTML file or as a still shoot (see examples below).
In the the latter case, the model perspective in the still shoot can be manually adjusted by changing the view argument for the function.
A RGL graphical device.
Erik Forsberg
Adler, D., & Murdoch, D. (2022). Rgl: 3d Visualization Using OpenGL Computer software.
Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29.
https://doi.org/10.18637/jss.v048.i06
Reckase, M. D. (2009). Multidimensional Item Response Theory. Springer.
Reckase, M. D. (1985). The Difficulty of Test Items That Measure More Than One Ability. Applied Psychological Measurement, 9(4), 401-412.
https://doi.org/10.1177/014662168500900409
Reckase, M. D., & McKinley, R. L. (1991). The Discriminating Power of Items That Measure More Than One Dimension. Applied Psychological Measurement, 15(4), 361-373.
https://doi.org/10.1177/014662169101500407
# Load data data("anes0809offwaves") x <- anes0809offwaves x <- x[, 3:22] # Remove columns for age and gender # Call D3mirt() with constructs assigned to con con <- list(c(1,2,3,4,5,6,7,8,9,10), c(11,12,13,14), c(15,17,18,19,20)) mod <- D3mirt(x, modid = c("W7Q3", "W7Q20"), con.items = con) # Plot RGL device with constructs invisible plot(mod) # Plot RGL device with constructs visible and named plot(mod, constructs = TRUE, construct.lab = c("Compassion", "Fairness", "Conformity")) plot(mod, constructs = TRUE, items = c(15, 17, 18, 19, 20), construct.lab = c("Compassion", "Fairness", "Conformity")) # Item W7Q16 has location 16 in the data set (gender and age excluded) # Below, the item is plotted together with construct to aid the visual interpretation plot(mod, constructs = TRUE, items = 16, construct.lab = c("Compassion", "Fairness", "Conformity")) # Plot RGL device on item difficulty level 5 plot(mod, diff.level = 5) # Plot RGL device with scaled items and constructs visible and named plot(mod, scale = TRUE, constructs = TRUE, construct.lab = c("Compassion", "Fairness", "Conformity")) # Profile Analysis # Plot respondents trait scores with item vectors hidden and no constructs plot(mod, hide = TRUE, ind.scores = TRUE) # Plot respondents separated on gender # Start by assigning the gender variable to a data frame # In this example, this is done by sub-setting the gender column x <- anes0809offwaves # Call plot() and use the gender variable column in the levels argument # Respondent data on gender is in column two, x[, 2] # In the function call below, both items and constructs are hidden # Score levels: 1 = Blue ("male") and 2 = Red ("female") plot(mod, hide = TRUE, ind.scores = TRUE, levels = x[, 2], sphere.col = c("blue", "red"), x.lab = "Compassion", y.lab="Conformity", z.lab="Fairness") # Add a 95% CI to respondent factor scores on <= 30 y.o. # Column bind trait scores with the age variable "W3Xage" z <- data.frame(cbind(mod$fscores, x[, 1])) # Subset data frame z conditioned on age <= 30 z1 <- subset(z, z[, 4] <= 30) # Use rep() to create a color vector to color groups based on the nlevels() output # z1 has 14 factor levels colvec <- c(rep("red", 14)) # Call plot() with profile data on age with item vector arrows hidden # Use the profiles argument for the data frame containing the subset to be plotted plot(mod, hide = TRUE, profiles = z1, levels = z1[, 4], sphere.col = colvec, x.lab = "Compassion", y.lab="Conformity", z.lab="Fairness", ci = TRUE, ci.level = 0.95, ellipse.col = "orange") ## Not run: # Export an open RGL device to the console to be saved as HTML or image file plot(mod, constructs = TRUE) s <- rgl::scene3d() rgl::rglwidget(s, width = 1040, height = 1040) # Export a snapshoot of an open RGL device directly to file plot(mod, constructs = TRUE) rgl::rgl.snapshot('RGLdevice.png', fmt = 'png') ## End(Not run)# Load data data("anes0809offwaves") x <- anes0809offwaves x <- x[, 3:22] # Remove columns for age and gender # Call D3mirt() with constructs assigned to con con <- list(c(1,2,3,4,5,6,7,8,9,10), c(11,12,13,14), c(15,17,18,19,20)) mod <- D3mirt(x, modid = c("W7Q3", "W7Q20"), con.items = con) # Plot RGL device with constructs invisible plot(mod) # Plot RGL device with constructs visible and named plot(mod, constructs = TRUE, construct.lab = c("Compassion", "Fairness", "Conformity")) plot(mod, constructs = TRUE, items = c(15, 17, 18, 19, 20), construct.lab = c("Compassion", "Fairness", "Conformity")) # Item W7Q16 has location 16 in the data set (gender and age excluded) # Below, the item is plotted together with construct to aid the visual interpretation plot(mod, constructs = TRUE, items = 16, construct.lab = c("Compassion", "Fairness", "Conformity")) # Plot RGL device on item difficulty level 5 plot(mod, diff.level = 5) # Plot RGL device with scaled items and constructs visible and named plot(mod, scale = TRUE, constructs = TRUE, construct.lab = c("Compassion", "Fairness", "Conformity")) # Profile Analysis # Plot respondents trait scores with item vectors hidden and no constructs plot(mod, hide = TRUE, ind.scores = TRUE) # Plot respondents separated on gender # Start by assigning the gender variable to a data frame # In this example, this is done by sub-setting the gender column x <- anes0809offwaves # Call plot() and use the gender variable column in the levels argument # Respondent data on gender is in column two, x[, 2] # In the function call below, both items and constructs are hidden # Score levels: 1 = Blue ("male") and 2 = Red ("female") plot(mod, hide = TRUE, ind.scores = TRUE, levels = x[, 2], sphere.col = c("blue", "red"), x.lab = "Compassion", y.lab="Conformity", z.lab="Fairness") # Add a 95% CI to respondent factor scores on <= 30 y.o. # Column bind trait scores with the age variable "W3Xage" z <- data.frame(cbind(mod$fscores, x[, 1])) # Subset data frame z conditioned on age <= 30 z1 <- subset(z, z[, 4] <= 30) # Use rep() to create a color vector to color groups based on the nlevels() output # z1 has 14 factor levels colvec <- c(rep("red", 14)) # Call plot() with profile data on age with item vector arrows hidden # Use the profiles argument for the data frame containing the subset to be plotted plot(mod, hide = TRUE, profiles = z1, levels = z1[, 4], sphere.col = colvec, x.lab = "Compassion", y.lab="Conformity", z.lab="Fairness", ci = TRUE, ci.level = 0.95, ellipse.col = "orange") ## Not run: # Export an open RGL device to the console to be saved as HTML or image file plot(mod, constructs = TRUE) s <- rgl::scene3d() rgl::rglwidget(s, width = 1040, height = 1040) # Export a snapshoot of an open RGL device directly to file plot(mod, constructs = TRUE) rgl::rgl.snapshot('RGLdevice.png', fmt = 'png') ## End(Not run)
D3mirt
The print method for the D3mirt() function.
## S3 method for class 'D3mirt' print(x, ...)## S3 method for class 'D3mirt' print(x, ...)
x |
A S3 object of class |
... |
Additional arguments. |
A printed message reporting the number of items, levels of difficulty, the number of construct vectors, and the names of the respective items contained in each construct.
Erik Forsberg
## Not run: # Load data data("anes0809offwaves") x <- anes0809offwaves x <- x[, 3:22] # Remove columns for age and gender # Call D3mirt() mod <- D3mirt(x, modid = c("W7Q3", "W7Q20")) # Print model summary print(mod) ## End(Not run)## Not run: # Load data data("anes0809offwaves") x <- anes0809offwaves x <- x[, 3:22] # Remove columns for age and gender # Call D3mirt() mod <- D3mirt(x, modid = c("W7Q3", "W7Q20")) # Print model summary print(mod) ## End(Not run)
modid
The print method for the modid() function.
## S3 method for class 'modid' print(x, ...)## S3 method for class 'modid' print(x, ...)
x |
A S3 object of class |
... |
Additional arguments. |
A printed message reporting the number of factors and the suggested model identification items.
## Not run: # Load data data("anes0809offwaves") x <- anes0809offwaves x <- x[,3:22] # Remove columns for age and gender # Identify the DMIRT model id <- modid(x) # Print model identification summary print(id) ## End(Not run)## Not run: # Load data data("anes0809offwaves") x <- anes0809offwaves x <- x[,3:22] # Remove columns for age and gender # Identify the DMIRT model id <- modid(x) # Print model identification summary print(id) ## End(Not run)
D3mirt
The summary method for the D3mirt() function.
## S3 method for class 'D3mirt' summary(object, ..., digits = 4)## S3 method for class 'D3mirt' summary(object, ..., digits = 4)
object |
A S3 object of class |
... |
Additional arguments. |
digits |
The number of digits shown per estimate. The default is |
Tables containing a and d parameters, multidimensional discrimination (MDISC), multidimensional item difficulty (MDIFF), direction cosines, and degrees for vector angles for items. If constructs were used in the estimation process, the summary function will also show tables for direction cosines, degrees for construct vectors, and directional discrimination (DDISC) parameters.
Erik Forsberg
## Not run: # Load data data("anes0809offwaves") x <- anes0809offwaves x <- x[, 3:22] # Remove columns for age and gender # Call D3mirt() with constructs con <- list(c(1,2,3,4,5,6,7,8,9,10), c(11,12,13,14), c(15,17,18,19,20)) mod <- D3mirt(x, modid = c("W7Q3", "W7Q20"), con.items = con) # Call to summary summary(mod) #' # Call to summary rounded off to 2 digits summary(mod, digits = 2) ## End(Not run)## Not run: # Load data data("anes0809offwaves") x <- anes0809offwaves x <- x[, 3:22] # Remove columns for age and gender # Call D3mirt() with constructs con <- list(c(1,2,3,4,5,6,7,8,9,10), c(11,12,13,14), c(15,17,18,19,20)) mod <- D3mirt(x, modid = c("W7Q3", "W7Q20"), con.items = con) # Call to summary summary(mod) #' # Call to summary rounded off to 2 digits summary(mod, digits = 2) ## End(Not run)
modid
The summary method for the modid() function.
## S3 method for class 'modid' summary(object, ..., digits = 4)## S3 method for class 'modid' summary(object, ..., digits = 4)
object |
A S3 object of class |
... |
Additional arguments. |
digits |
The number of digits shown per estimate. The default is |
Model identification items (one less than the number of factors), factor loadings and absolute sum score for model identification items, squared factor loadings, and factor loadings for all items.
Erik Forsberg
## Not run: # Load data data("anes0809offwaves") x <- anes0809offwaves x <- x[,3:22] # Remove columns for age and gender # Identify the DMIRT model id <- modid(x) # Call to summary summary(id) # Call to summary rounded off to 2 digits summary(id, digits = 2) ## End(Not run)## Not run: # Load data data("anes0809offwaves") x <- anes0809offwaves x <- x[,3:22] # Remove columns for age and gender # Identify the DMIRT model id <- modid(x) # Call to summary summary(id) # Call to summary rounded off to 2 digits summary(id, digits = 2) ## End(Not run)