Provides functions to fit speed-accuracy psychometric models
for binomial count outcome data. The models jointly represent accuracy
and response time and can be used for model-based calibration and scoring
of oral reading fluency (ORF) assessment data. The methods are based on
Potgieter, Kamata and Kara (2017)
bspam is an R package that contains functions to fit the
speed-accuracy psychometric model for repeatedly measured count outcome
data (Potgieter, Kamata & Kara, 2017; Kara, Kamata, Potgieter & Nese,
2020), where the accuracy and speed are modeled by a binomial count and
a log-normal latent variable models, respectively.
For example, the use of this modeling technique allows model-based
calibration and scoring for oral reading fluency (ORF) assessment data.
This document demonstrates some uses of the bspam package by using an
ORF assessment data set.
| Function | Purpose |
|---|---|
prep() |
Prepare passage- or sentence-level data for analysis |
fit.model() |
Estimate task parameters by MCEM or Bayesian estimation |
scoring() |
Estimate latent factor scores and model-based WCPM scores |
get.cases() |
Generate person-by-occasion case identifiers |
summary() |
Summarize calibration and scoring results |
plot.task() |
Visualize task parameter estimates |
plot.person() |
Visualize person-level score estimates |
plot.information() |
Visualize calibration information |
Advanced users can also access lower-level functions such as
run.mcem(), run.scoring(), bayes(), and bayes.wcpm(). See the
package help pages for details.
To install the bspam package, follow the steps below.
remotes package, by running the following R code.if(!requireNamespace("remotes", quietly = TRUE)) install.packages("remotes")
bspam by running the following R code.remotes::install_github("kamataak/bspam")
bspam can implement a fully Bayesian approach for the calibration of
model parameters and scoring by using JAGS or Stan. If you desire to use
the fully Bayesian estimation, please download JAGS and Stan software on
your computer.
To download and install JAGS, download the installation file from
https://sourceforge.net/projects/mcmc-jags/files/JAGS/ as per
operating system requirements and follow the installation steps. bspam
internally uses runjags package as an interface to JAGS. runjags
package needs to be installed separately once JAGS is installed.
Stan can be installed by following the steps explained here:
https://github.com/stan-dev/rstan/wiki/RStan-Getting-Started. Note
that these steps show the installation of RStan, which bspam uses as
an internal package to run Stan code. Please follow the installation
steps carefully along with recommended versions of R and RStudio to
prevent any issues releated to running Stan with bspam.
It is required that the data are prepared as a long-format data, where each row is data for a unique case, namely, a specific task from a specific person in a specific testing occasion. In the context of ORF assessment, each row is data for a specific passage from a specific student in a specific testing occasion. A data file can be prepared in any file format that is readable into R.
For example, a CSV formatted data can be read into R by using the
read.csv() function that is part of the base packages. Also, data
files in some statistical software formats can be read in to R with
functions in packages, such as the haven package. For example,
read_spss() function can be used to read in an SPSS formatted data
file into R.
The data set should minimally contain the following 5 variables: (1)
individual ID, (2) task ID, (3)
the maximum number of attempts in the task, (4) the number of successes
in the task, and (5) the time took to complete the task. Two optional variables, group ID and testing occasion ID,
can also be included. However, note if the
data are coming from only one testing occasion and one group, these two
variables should contain an
arbitrary constant value, such as all 1’s.
Note: The occasion and group variables are optional when using the bspam prep() functions. If the data do not contain an occasion variable, bspam internally assigns all observations to a default occasion (occasion = 1). Similarly, if the data do not contain a group variable, all observations are assigned to a default group (group = 1). Therefore, users do not need to manually create these columns when their data contain only one occasion or when group information is not available.
Variable names and the order of the variables can be flexible in the data frame. When running functions in this package, variable names for required variables need to be specified, as shown in examples below.
Then, the data need to be read into R as a data frame.
The bspam package comes with several example data sets in the ORF
assessment context. To demonstrate some basic usage of key functions in
the package, a sample ORF assessment data set is used here. In the
context of an ORF assessment, a task is a passage given to the student
to read aloud, and an attempt is student’s reading on a word in the
passage, which is scored correct (i.e., success) or not. Accordingly,
the number of successes in the task is the number of words correctly
read in the passage.
The data set passage2 is a passage-level student data and consisted of
reading accuracy and time data for 12 passages from 85 students.
Although the 85 students were assigned to all 12 passages, the number of
passages read by the 85 students varied from 2 to 12 passages. The
number of students per passage were between 59 to 79. This is a small
subset of the data collected by Nese and Kamata (2014-2018).
The package also includes the following example data sets and output objects:
| Object | Purpose |
|---|---|
passage2 |
Passage-level ORF example data |
sentence.level.data |
Sentence-level/testlet ORF example data |
sentence.cens.low |
Sentence-level example data with low censoring |
sentence.cens.high |
Sentence-level example data with high censoring |
passage.calib.mcem |
Example MCEM calibration output |
passage.calib.bayes |
Example Bayesian calibration output |
Load required packages, and view the example data set passage2.
library(tidyverse)
library(bspam)
View(passage2)
Calibrate the passages using the fit.model() function by implementing
the Monte Carlo EM algorithm described in Potgieter et al. (2017).
MCEM_run <- fit.model(data = passage2,
person.id = "id.student",
task.id = "id.passage",
max.counts = "numwords.pass",
obs.counts = "wrc",
time = "sec",
k.in = 5,
reps.in = 50,
est = "mcem")
MCEM_run
The fit.model() function supports two calibration modes:
testlet = TRUE and providing a sub.task.id, which models local
dependence among sub-tasks (e.g., sentences within a passage).For Bayesian calibration (est = "bayes"), bspam automatically
selects the estimation engine: Stan is used when the data are complete,
and JAGS is used when missing observations are present.
By default, the standard errors for the model parameters are not
estimated. This will allow one to increase the number of Monte-Carlo
iterations reps.in to improve the quality of the model parameter
estimates, while minimizing the computation time. The number of
reps.in should be 50 to 100 in realistic calibrations. Also note that
k.in is the number of imputations for the MCEM algorithm, where the
default is 5. Note that SE’s for model parameters are not required for
running the scoring() function to estimate latent factor scores and
WCPM scores in the next step. If standard errors for model parameters
are desired, an additional argument se = "analytic" or
se = "bootstrap" needs to be added to the fit.model() function.
Passage calibration can also be done by using the est = "bayes"
option, which implements a fully Bayesian approach through Gibbs
sampling or Hamiltonian Monte Carlo with JAGS and Stan, respectively.
Currently, Stan will be used with complete data, that is, if all
students have data on all passages. Otherwise, JAGS will be used as it
provides faster computations with missing observations. Note that
bspam runs JAGS in the auto mode, which does not require the user to
supply any specifications for Bayesian estimation (e.g., number of the
iterations) or monitor convergence. The standard deviations of the
posterior distributions are reported as the standard errors. A
specification for the fit.model() function can look like as follows.
Bayes_run <- fit.model(data = passage2,
person.id = "id.student",
task.id = "id.passage",
max.counts = "numwords.pass",
obs.counts = "wrc",
time = "sec",
est = "bayes",
verbose=TRUE)
Bayes_run
In order to estimate latent factor scores and/or WCPM scores, the
scoring() function needs to be run.
Note that we use the output object MCEM_run from the previous passage
calibration phase. By default (type = "general"), only factor scores
($\theta$ and $\tau$) and their standard errors are reported. By
providing an argument type = "orf", WCPM scores and their standard
errors are also reported. Also, WCPM scores and/or factor scores, and
their standard errors will be estimated for all cases in the data by
default.
There are several estimator options for scoring: maximum likelihood
("mle"), maximum a posteriori ("map"), expected a posteriori
("eap"), and a fully Bayesian approach ("bayes"). Standard errors
can be estimated analytically or via bootstrap, except when
est = "bayes", in which case posterior standard deviations are
reported.
When se = "bootstrap" is used, the number of bootstrap replications
can be controlled with the bootstrap argument (default = 100). The
failsafe argument can be used to specify the number of retry attempts
for failed bootstrap samples.
In addition to standard scoring, the scoring() function supports
censored (truncated) response data by setting censoring = TRUE and
supplying a censoring indicator via the cens argument. Sentence-level
testlet scoring also uses the censoring framework internally.
To estimate WCPM scores for all observations in the data set passage2,
we use the scoring() function as follows.
WCPM_all <- scoring(calib.data=MCEM_run,
data = passage2,
person.id = "id.student",
occasion = "occasion",
group = "grade",
task.id = "id.passage",
max.counts = "numwords.pass",
obs.counts = "wrc",
time = "sec",
est = "map",
se = "analytic",
type="general")
summary(WCPM_all)
If the computations of WCPM scores and/or factor scores for only
selected cases are desired, a list of cases needs to be provided by the
cases = argument. The list of cases has to be a one-variable data
frame with a variable name cases. The format of case values should be:
personid_occasion. This one-variable data frame can be created
manually, just like shown below. Also, it can be generated by the
get.cases() function, which will be shown later in this document.
A case is identified by the combination of the person ID and testing occasion, separated by an underscore (for example, 2033_Fall). The group variable is not part of the case identifier. It is treated as descriptive information associated with the person-occasion case and is retained in the scoring output.
If no occasion variable is supplied, bspam internally creates a single default occasion with the value 1. Thus, all observations for a person belong to the same occasion.
sample.cases <- data.frame(cases = c("2033_fall", "2043_fall", "2089_fall"))
WCPM_sample <- scoring(calib.data = MCEM_run,
data = passage2,
person.id = "id.student",
occasion = "occasion",
group = "grade",
task.id = "id.passage",
max.counts = "numwords.pass",
obs.counts = "wrc",
time = "sec",
cases = sample.cases,
est = "eap",
se = "analytic",
type = "orf")
summary(WCPM_sample)
Also, we can specify a set of tasks (i.e., passages) to scale the WCPM scores. If WCPM scores are scaled with a set of passages that is different from the set of passages the student read, the set of passages is referred to as an external passage set for the ORF assessment context, or external task set in general.
The use of an external passage set is particularly important in the context of ORF assessment to make the estimated WCPM scores to be comparable between students who read different sets of passages, as well as within students for longitudinal data, where a student is likely to read different sets of passages.
WCPM_sample_ext1 <- scoring(calib.data = MCEM_run,
data = passage2,
person.id = "id.student",
occasion = "occasion",
group = "grade",
task.id = "id.passage",
max.counts = "numwords.pass",
obs.counts = "wrc",
time = "sec",
cases = sample.cases,
external = c("32004","32010","32015","32016","33003","33037"),
est = "eap",
se = "analytic",
type = "orf")
summary(WCPM_sample_ext1)
A fully Bayesian approach can also be used as an estimator in the
scoring() function. Note that if est="bayes" is specified, there is
no need to use the se= argument. By default, the standard deviations
of the posterior distributions are reported as the standard errors,
along with 95% high density intervals, which is analogous to 95%
confidence intervals. Here is an example of using the fully Bayesian
approach for estimating WCPM scores from the same external passages used
in the previous example.
WCPM_sample_ext1_bayes <- scoring(calib.data=MCEM_run,
data = passage2,
person.id = "id.student",
occasion = "occasion",
group = "grade",
task.id = "id.passage",
max.counts = "numwords.pass",
obs.counts = "wrc",
time = "sec",
cases = sample.cases,
external = c("32004","32010","32015","32016","33003","33037"),
est = "bayes",
type = "orf")
summary(WCPM_sample_ext1_bayes)
Alternatively, we can run the scoring() in two steps.
Step 1: Prepare the data using the prep() function. The function
standardizes variable names, computes the natural logarithm of time, and
creates analysis-ready long and wide data structures.
For passage-level data, use the default setting
(sentence_level = FALSE).
For sentence-level data, set sentence_level = TRUE and provide a
sub.task.id.
If occasion or group variables are not provided, prep() will
create default constant values automatically.
The automatically created values are occasion = 1 and group = 1, so users should leave these arguments unspecified rather than manually adding dummy columns when the corresponding information is not present in their data.
The output from the prep() function is a list of two components. The
data.long component is a data frame, which is a long format of student
response data, and the data.wide is list that contains four
components, including a wide format of the data, as well as other
information such as the number of passages and the number of words for
each passage.
One benefit of this two-step approach is that we can use another utility
function get.cases() to generate a list of unique cases with the
output of the prep() function. This list can be useful when our
interest is to estimate WCPM scores only for selected cases.
data <- prep(data = passage2,
person.id = "id.student",
occasion = "occasion",
group = "grade",
task.id = "id.passage",
max.counts = "numwords.pass",
obs.counts = "wrc",
time = "sec")
Generate a list of unique cases:
all.cases <- get.cases(data$data.long)
all.cases
Step 2: Run the scoring() function to estimate WCPM scores. Note
that we pass the output object MCEM_run from the passage calibration
phase, as well as the manipulated data data.long from Step 1. By
default, WCPM scores will be estimated for all cases in the data.
Additionally, there are several estimator options and standard error
estimation options. In this example, maximum a priori (MAP) estimators
for model parameter estimation and analytic approach to estimate
standard errors are used.
WCPM_all <- scoring(calib.data=MCEM_run,
data = data$data.long,
est = "map",
se = "analytic",
type = "orf")
summary(WCPM_all)
WCPM_sample_ext2 <- scoring(calib.data=MCEM_run,
data = data$data.long,
cases = sample.cases,
external = c("32004","32010","32015","32016","33003","33037"),
est = "map",
se = "analytic",
type = "orf")
summary(WCPM_sample_ext2)
When ORF data are collected at the sentence level, sentences are nested
within passages and may exhibit local dependence. In this case, a
testlet-version of the model can be fitted and scored using bspam.
The example data set sentence.level.data is a sentence-level student
data and consisted of reading accuracy and time data for 4 passages from
58 students. The 4 passages were consisted of 4 to 8 sentences,
totalling 23 sentences. All 58 students read all 4 passages completely.
This is a small subset of the data collected by Nese and Kamata
(2014-2018).
Testlet_run <- fit.model(
data = sentence.level.data,
person.id = "id.student",
task.id = "id.passage",
sub.task.id = "id.sentence",
max.counts = "numwords.sent",
obs.counts = "wrc",
time = "sec",
testlet = TRUE,
verbose = TRUE
)
The estimated testlet parameter is reported as part of the hyper-parameters.
Testlet_run$hyper.param
Task- and sentence-level parameters can be extracted by:
Testlet_run$task.param
The scoring by the MAP can be done for this data set by:
Testlet_scoring <-
scoring(calib.data = Testlet_run,
data = sentence.level.data,
person.id = "id.student",
task.id = "id.passage",
sub.task.id = "id.sentence",
obs.counts = "wrc",
max.counts = "numwords.sent",
time = "sec",
type = "orf",
testlet = TRUE,
censoring = TRUE)
In some circumstances, a test may be designed as a speeded test, such
that many examinees do not complete all the tasks in the test. For
example, the traditional administration of the ORF test only gives the
student 60 seconds to read aloud the given passage, which is typically
consisted of 250 words. In this case, many students do not finish
reading the entire passage. The bspam R package can score such a data
set by the censored model both for the regular and the testlet models.
For example, the package includes sentence.cens.low and
sentence.cens.high for demonstrating sentence-level scoring with
censored observations. A censored testlet scoring analysis can be run
as follows:
Testlet_scoring_cens <-
scoring(calib.data = Testlet_run,
data = sentence.cens.low,
person.id = "id.student",
task.id = "id.passage",
sub.task.id = "id.sentence",
obs.counts = "wrc",
max.counts = "numwords.sent",
time = "sec",
cens = "cens",
type = "orf",
testlet = TRUE,
censoring = TRUE)
Please see the package website for more detailed usage of the package.
plot.task(MCEM_run, parameter = "a", sort = TRUE)
plot.person(WCPM_all, parameter = "wcpm", show.se = TRUE)
Additional plotting functions documented in the package include
plot.information() for calibration information and plot.wcpm() for
comparing observed and model-based WCPM scores.
plot.information(MCEM_run)
plot.wcpm(WCPM_all)
You can use citation("bspam") to get the following information. The current version is 1.2.5.
To cite package ‘bspam’ in publications use:
Wang K, Kamata A, Potgieter C, Nese J, Kara Y, Somsong S, Qiao X (2023). bspam: Speed-Accuracy Psychometric Modeling for Binomial Count Outcome Data with R. R package version 1.2.5, https://github.com/kamataak/bspam
A BibTeX entry for LaTeX users is
@Manual{, title = {bspam: Speed-Accuracy Psychometric Modeling for Binomial Count Outcome Data with R}, author = {Kuo Wang and Akihito Kamata and Cornelis J. Potgieter and Joseph F. T. Nese and Yusuf Kara and Sarunya Somsong and Xin Qiao}, year = {2023}, note = {R package version 1.2.6}, url = {https://github.com/kamataak/bspam}, }
Kara, Y., Kamata, A., Potgieter, C., & Nese, J. F. (2020). Estimating model-based oral reading fluency: A bayesian approach with a binomial-lognormal joint latent model. Educational and Psychological Measurement, 1–25.
Nese, J. F. T. & Kamata, A. (2014-2018). Measuring Oral Reading Fluency: Computerized Oral Reading Evaluation (Project No. R305A140203) $$Grant$$. Institute of Education Sciences, U.S. Department of Education.
Potgieter, N., Kamata, A., & Kara, Y. (2017). An EM algorithm for estimating an oral reading speed and accuracy model. Manuscript submitted for publication.
Qiao, X, Potgieter, N., & Kamata, A. (2023). Likelihood Estimation of Model-based Oral Reading Fluency. Manuscript submitted for publication.
Copyright (C) 2022-2026 The ORF Project Team
The bspam package is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or any later version.
The bspam package is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this package. If not, see http://www.gnu.org/licenses/.