Speed-Accuracy Psychometric Modeling for Binomial Count Outcome Data with R
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.
Main Functions
| 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.
Installation:
To install the bspam package, follow the steps below.
- Install
remotespackage, by running the following R code.
if(!requireNamespace("remotes", quietly = TRUE)) install.packages("remotes")- Install
bspamby running the following R code.
remotes::install_github("kamataak/bspam")Optional:
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.
Basic Usage: Task-level Data Analysis
Data Preparation
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.
Data Set For the Demonstration
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 |
Task (i.e., Passage) Calibration
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_runThe fit.model() function supports two calibration modes:
- Task-level (passage-level) calibration (default), where each task is modeled independently.
-
Testlet (sentence-level) calibration, enabled by setting
testlet = TRUEand providing asub.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_runScoring: Estimating Latent Factor Scores and WCPM Scores 1
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 ( and ) 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.
Scoring for All Cases
To estimate WCPM scores for all observations in the data set passage2, we use the scoring() function as follows.
Scoring for Selected Cases
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)Scoring with External Task Set
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)Scoring: Estimating Latent Factor Scores and WCPM Scores 2
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$data.long)
all.casesStep 2: Run the scoring() function to estimate WCPM scores. Note that we pass the output object MCEM_run from the passage calibration phase, as well as the manipulated data data.long from Step 1. By default, WCPM scores will be estimated for all cases in the data. Additionally, there are several estimator options and standard error estimation options. In this example, maximum a priori (MAP) estimators for model parameter estimation and analytic approach to estimate standard errors are used.
Other Features
Fitting and Scoring by the Testlet Model (Sentence-level)
When ORF data are collected at the sentence level, sentences are nested within passages and may exhibit local dependence. In this case, a testlet-version of the model can be fitted and scored using bspam.
The example data set sentence.level.data is a sentence-level student data and consisted of reading accuracy and time data for 4 passages from 58 students. The 4 passages were consisted of 4 to 8 sentences, totalling 23 sentences. All 58 students read all 4 passages completely. This is a small subset of the data collected by Nese and Kamata (2014-2018).
Testlet Calibration
Testlet_run <- fit.model(
data = sentence.level.data,
person.id = "id.student",
task.id = "id.passage",
sub.task.id = "id.sentence",
max.counts = "numwords.sent",
obs.counts = "wrc",
time = "sec",
testlet = TRUE,
verbose = TRUE
)The estimated testlet parameter is reported as part of the hyper-parameters.
Testlet_run$hyper.paramTask- and sentence-level parameters can be extracted by:
Testlet_run$task.paramTestlet Scoring
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)Scoring for Truncated Response Data
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.
Plotting
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)Cite this software as:
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 1.2.5}, url = {https://github.com/kamataak/bspam}, }
References
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) . Institute of Education Sciences, U.S. Department of Education. https://ies.ed.gov/funding/grantsearch/details.asp?ID=1492
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 Statement
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/.