course_engagement: Student engagement across a sequence of courses
In latents: Multilevel Latent Profile, Class and Transition Models

course_engagement

R Documentation

Student engagement across a sequence of courses

Description

A simulated dataset with the structure this package exists for, and all of it in one place: enrolments nested in students, ordered within each student, with a covariate that predicts which pattern an enrolment follows.

Usage

course_engagement

Format

A data frame with 1422 rows (106 students, 32 courses, up to 15 enrolments each) and 11 columns:

student: Integer student identifier, 1 to 106. The nesting unit; pass it as id.
course: Integer course identifier, 1 to 32. Which course the enrolment was in.
sequence: Integer, the position of this course in the student's own order, 1 upwards. Pass it as time. Students who took fewer courses have shorter sequences, so the panel is ragged.
browse: Numeric, course page views on the log1p(events) scale, standardized within course.
lectures: Numeric, lecture videos viewed on the log1p(events) scale, standardized within course.
forum_read: Numeric, forum posts read on the log1p(events) scale, standardized within course.
forum_post: Numeric, forum posts written on the log1p(events) scale, standardized within course.
attendance: Numeric, days the student was active in the course as on the log1p(events) scale, standardized within course. It is generated from the four click measures and then blurred, because a student is recorded present on a day precisely because they clicked something, and a day is a coarse unit – one tick however much happened inside it. The indicators are therefore locally dependent on purpose: attendance correlates 0.51 to 0.67 with the click measures overall and 0.16 to 0.26 within a single profile, which is more association than a shared profile alone would produce. See the note on local dependence below.
previous_grade: Numeric, the grade the student earned in the course before this one, standardised across the cohort. At a student's first course an entry grade stands in its place. It is a predictor of engagement here, not an outcome of it: pass it as profile_covariates to multilpa(profile_covariates = ), or as the predictor to r3step().
engagement: Factor, "disengaged" or "engaged", the pattern the row was generated from. This is the truth behind the data, not something a study would observe; it is shipped so a fitted model can be checked against what produced it. It is deliberately not called profile: get_results(fit, "assignments") adds a column of that name, and a dataset already carrying it would make the verb refuse to join its own output.
student_type: Factor, "committed" or "wavering", the kind of student the row's student was generated as. The truth behind the group classes, shipped for the same reason.

Details

Each row is one student's enrolment in one course. A student takes up to fifteen courses, and sequence orders them, so the same rows support a cross-sectional two-level model (id = "student"), a latent transition model (time = "sequence"), and a membership-covariate model (profile_covariates = "previous_grade").

Two kinds of student were generated. Both contain both patterns of engagement; they differ in the mix, which is the two-level quantity this package estimates. A committed student is engaged in about four enrolments in five, a wavering student in about one in four. Pooled across the sample the engaged share describes neither kind, which is the point: recovering the split is what a two-level model does and a pooled one cannot.

Local independence does not hold here, on purpose

A latent profile model with a diagonal residual covariance assumes the indicators are independent given the profile. attendance is built from the click measures, so for these data that assumption is false, and the package finds it: get_results(fit, "residuals") reports a largest residual of 0.21 p = 1.7e-15, and covariance_model = "full" improves the log likelihood from -7618.5 to -7494.7 for twenty more parameters, which every information criterion prefers.

This is deliberate. A bundled dataset that satisfies local independence exactly can only ever show those verbs agreeing that nothing is wrong; here the diagnostic has a real violation to find, its cause is known, and the fix can be seen to work. One consequence is worth knowing before it surprises you: under a diagonal model enumerate_classes() keeps preferring more classes, because extra classes absorb residual association the model is not allowed to express directly.

The five activity indicators are standardized within course: each value is that enrolment's distance from its own course's mean, in that course's standard deviations. Every indicator therefore has mean zero and standard deviation one within every course, and a browse of 1.2 reads as "1.2 standard deviations more active than the average enrolment in that course". This is the scale a learning-analytics reader meets, because activity volume is not comparable across courses: a course with weekly quizzes generates more clicks than a seminar whatever its students are like, so an analyst compares a student with their coursemates rather than with the whole cohort.

In this simulation the courses do not in fact differ in activity volume, so the standardization sets the scale rather than removing a course effect. It is stated here rather than left implicit because a reader who assumed otherwise would misread what the course column does.

The indicators are simulated directly on the log1p(events) scale, the scale of a logged activity export; no raw counts are generated. They are standardized on that scale, not as counts. Standardizing is affine within a course, so it leaves the within-course skew exactly as it found it, and raw learning-analytics counts are strongly right-skewed: on an unlogged draft of these data the skew alone looked like an extra class, exactly as a floor or ceiling effect does. The log removes the skew; the standardization puts the courses on a common footing afterwards.

Source

Simulated by data-raw/course-engagement.R, seed 2026. The simulation is calibrated to the shape of a real learning-analytics export – its scales, its spreads, its correlations and how persistent engagement is across a student's courses – but only those aggregate constants were used. No row, identifier or value of any real student is present, and the source is not distributed.

Examples

fit <- multilpa(
  course_engagement,
  vars = c("browse", "lectures", "forum_read", "forum_post", "attendance"),
  id = "student", n_profiles = 2, n_group_classes = 2, n_starts = 4,
  seed = 1
)
as.data.frame(fit)
get_results(fit, what = "profile_probabilities")
# The generating truth ships alongside, so recovery can be checked directly.
get_results(fit, what = "assignments", data = course_engagement,
         truth = "engagement")

latents documentation built on Oct. 16, 2026, 5:09 p.m.