This review exercises every VaSSTra plot on the longitudinal
engagement data from Chapter
11 of Learning Analytics Methods and Tutorials: the state,
sequence, and trajectory views (base graphics, no ggplot2
dependency), the combined per-trajectory grid, the
evaluate() panels, and the cograph-rendered
flow and transition networks. Every view shares one state palette and
one state order, both of which can be pinned on the fit with
state_colors and state_order.
The whole analysis in one call
vasstra(engagement) needs nothing else. Roles come from
the attached metadata, and the state and trajectory counts are selected
by comparing two through six candidates. Here BIC favours five states,
so the fully automatic fit reports five; the chapter analysis below
fixes three for interpretability. Each decision is reported as a message
and recorded in the fit.
library(VaSSTra)
data("engagement", package = "VaSSTra")
fit_auto <- vasstra(engagement)
#> Selected n_states = 5 (lpa, bic = 19008.964); see `diagnostics$selection`.
#> Registered S3 method overwritten by 'Nestimate':
#> method from
#> print.mcml cograph
#> Selected n_trajectories = 3 (hamming + pam, silhouette = 0.222); see `diagnostics$selection`.
fit_auto
#> VaSSTra Analysis
#> 142 subjects | 8 times | 5 states | 3 trajectories
#> hamming + pam | silhouette 0.222Evaluate the automatic clustering
evaluate() returns the candidate comparison with
best and fitted markers plus per-cluster
silhouette quality; its plot shows the selection curve, the per-group
silhouette widths, and the group sizes for both clustering steps. The
state and trajectory rows use distinct palettes, so the two groupings
are not read as corresponding.
evaluation <- evaluate(fit_auto)
evaluation
#> VaSSTra clustering evaluation: states (lpa)
#> Fitted: 5 states | silhouette 0.197
#> Candidates:
#> n_states method lpa_model silhouette bic aic classification_entropy
#> 2 lpa EEI 0.351 21679.00 21553.12 0.903
#> 3 lpa EEI 0.260 20120.13 19948.93 0.894
#> 4 lpa EEI 0.203 19362.24 19145.73 0.893
#> 5 lpa EEI 0.197 19008.96 18747.13 0.871
#> 6 lpa EEI 0.181 18600.79 18293.64 0.887
#> min_size max_size size_ratio eligible best fitted
#> 509 627 1.232 TRUE FALSE FALSE
#> 266 551 2.071 TRUE FALSE FALSE
#> 152 414 2.724 TRUE FALSE FALSE
#> 155 367 2.368 TRUE TRUE TRUE
#> 33 350 10.606 FALSE FALSE FALSE
#> Fitted states:
#> state n proportion silhouette
#> State 1 155 0.136 0.300
#> State 2 367 0.323 0.172
#> State 3 230 0.202 0.219
#> State 4 228 0.201 0.164
#> State 5 156 0.137 0.167
#>
#> VaSSTra clustering evaluation: trajectories (hamming + pam)
#> Fitted: 3 trajectories | silhouette 0.222
#> Candidates:
#> n_trajectories dissimilarity method silhouette mean_within_distance min_size
#> 2 hamming pam 0.221 5.491 49
#> 3 hamming pam 0.222 5.138 24
#> 4 hamming pam 0.199 4.817 18
#> 5 hamming pam 0.210 4.490 17
#> 6 hamming pam 0.202 4.345 16
#> max_size size_ratio eligible best fitted
#> 93 1.898 TRUE FALSE FALSE
#> 85 3.542 TRUE TRUE TRUE
#> 68 3.778 TRUE FALSE FALSE
#> 53 3.118 TRUE FALSE FALSE
#> 43 2.688 TRUE FALSE FALSE
#> Fitted trajectories:
#> trajectory n proportion mean_within_distance silhouette
#> Trajectory 1 85 0.599 5.353 0.219
#> Trajectory 2 33 0.232 4.830 0.213
#> Trajectory 3 24 0.169 4.801 0.246
plot(evaluation)
The chapter analysis, explicit where it matters
The chapter’s substantive choices stay in one readable call. The
state method defaults to LPA with the chapter’s "EEI"
model, and the three labels fix the three profiles used from here on;
automation only fills what is omitted.
fit <- vasstra(
engagement,
state_labels = c("Disengaged", "Average", "Active"),
dissimilarity = "lcs",
cluster_method = "ward.D2",
trajectory_labels = c(
"Mostly active",
"Mostly average",
"Mostly disengaged"
),
positive_states = "Active",
negative_states = "Disengaged",
seed = 22294
)
#> Using n_states = 3 to match the supplied labels.
#> Using n_trajectories = 3 to match the supplied labels.
fit
#> VaSSTra Analysis
#> 142 subjects | 8 times | 3 states | 3 trajectories
#> lcs + ward.D2 | silhouette 0.514
Tidy fit indices
The fitted LPA solution as one tidy row with the complete information-criterion family, then the comparison against all candidate counts, then the trajectory clustering.
fit_indices(fit)
#> VaSSTra fit indices: states (lpa)
#> n_states method lpa_model log_likelihood n_parameters aic bic
#> 3 lpa EEI -9940.47 34 19948.93 20120.13
#> sabic caic awe clc kic icl entropy prob_min
#> 20012.14 20154.13 20461.33 20144.89 19985.93 20384.09 0.894 0.945
#> prob_max silhouette min_size max_size size_ratio
#> 0.956 0.26 266 551 2.07
fit_indices(fit, compare = TRUE)
#> VaSSTra fit indices: states (lpa)
#> n_states method lpa_model log_likelihood n_parameters aic bic
#> 2 lpa EEI -10751.56 25 21553.12 21679.00
#> 3 lpa EEI -9940.47 34 19948.93 20120.13
#> 4 lpa EEI -9529.86 43 19145.73 19362.25
#> 5 lpa EEI -9321.57 52 18747.13 19008.96
#> 6 lpa EEI -9085.82 61 18293.64 18600.79
#> sabic caic awe clc kic icl entropy prob_min
#> 21599.59 21704.00 21929.88 21655.20 21581.12 21831.08 0.903 0.973
#> 20012.14 20154.13 20461.33 20144.89 19985.93 20384.09 0.894 0.945
#> 19225.66 19405.25 19793.76 19397.81 19191.73 19700.33 0.893 0.928
#> 18843.80 19060.96 19530.80 19113.95 18802.13 19479.79 0.871 0.873
#> 18407.04 18661.79 19212.95 18633.20 18357.64 19062.35 0.887 0.876
#> prob_max silhouette min_size max_size size_ratio eligible best fitted
#> 0.975 0.351 509 627 1.23 TRUE FALSE FALSE
#> 0.956 0.260 266 551 2.07 TRUE FALSE TRUE
#> 0.969 0.203 152 414 2.72 TRUE FALSE FALSE
#> 0.964 0.197 155 367 2.37 TRUE TRUE FALSE
#> 0.973 0.181 33 350 10.61 FALSE FALSE FALSE
fit_indices(fit, step = "trajectories", compare = TRUE)
#> VaSSTra fit indices: trajectories (lcs + ward.D2)
#> n_trajectories dissimilarity method silhouette mean_within_distance min_size
#> 2 lcs ward.D2 0.440 6.35 41
#> 3 lcs ward.D2 0.514 4.54 28
#> 4 lcs ward.D2 0.400 4.17 28
#> 5 lcs ward.D2 0.370 3.92 8
#> 6 lcs ward.D2 0.350 3.59 8
#> max_size size_ratio eligible best fitted
#> 101 2.46 TRUE FALSE FALSE
#> 73 2.61 TRUE TRUE TRUE
#> 43 1.54 TRUE FALSE FALSE
#> 43 5.38 TRUE FALSE FALSE
#> 43 5.38 TRUE FALSE FALSERelabel after inspection
set_labels() renames groups in place — full vectors or
partial named renames — and every downstream table follows.
fit_renamed <- set_labels(
fit,
states = c("Average" = "Moderate"),
trajectories = c("Thriving", "Coasting", "Struggling")
)
as.data.frame(fit_renamed, unit = "trajectory")
#> trajectory n proportion mean_within_distance n_observed unique_states
#> 1 Thriving 41 0.2887324 4.258537 8 1.878049
#> 2 Coasting 73 0.5140845 4.961187 8 1.986301
#> 3 Struggling 28 0.1971831 3.857143 8 1.821429
#> transitions entropy complexity volatility integrative_potential
#> 1 1.829268 0.4189906 0.3251220 0.4436702 0.7696477
#> 2 2.328767 0.4736884 0.3865300 0.4973907 0.1149163
#> 3 1.892857 0.3978570 0.3246998 0.4387755 0.0000000
#> negative_exposure
#> 1 0.009485095
#> 2 0.131659056
#> 3 0.820436508Tidy outputs
head(as.data.frame(fit, unit = "subject"))
#> user_id trajectory n_observed unique_states transitions entropy
#> 1 D2C5F64E Mostly active 8 3 3 0.9850568
#> 2 D7E3D0DC Mostly active 8 3 4 0.8194484
#> 3 2926CF64 Mostly disengaged 8 1 0 0.0000000
#> 4 985AFF35 Mostly disengaged 8 2 2 0.6021808
#> 5 F89100C7 Mostly active 8 3 4 0.8868595
#> 6 AB944042 Mostly disengaged 8 2 2 0.3429510
#> complexity volatility integrative_potential negative_exposure
#> 1 0.6497440 0.7142857 0.4166667 0.08333333
#> 2 0.6842925 0.7857143 0.5833333 0.08333333
#> 3 0.0000000 0.1666667 0.0000000 1.00000000
#> 4 0.4147911 0.4761905 0.0000000 0.55555556
#> 5 0.7118826 0.7857143 0.3888889 0.19444444
#> 6 0.3130271 0.4761905 0.0000000 0.88888889
head(as.data.frame(fit, unit = "observation"))
#> user_id sequence_position state position trajectory
#> 1 D2C5F64E 1 Disengaged 1 Mostly active
#> 2 D2C5F64E 2 Disengaged 2 Mostly active
#> 3 D2C5F64E 3 Average 3 Mostly active
#> 4 D2C5F64E 4 Active 4 Mostly active
#> 5 D2C5F64E 5 Active 5 Mostly active
#> 6 D2C5F64E 6 Active 6 Mostly active
head(as.data.frame(fit, unit = "state_profile"))
#> state variable mean sd n
#> 1 Disengaged course_view_count_z -1.13211349 0.5755714 266
#> 2 Average course_view_count_z -0.07877558 0.5387538 551
#> 3 Active course_view_count_z 1.07947227 0.6503939 319
#> 4 Disengaged forum_consume_count_z -1.08450800 0.6669212 266
#> 5 Average forum_consume_count_z -0.01863047 0.6225600 551
#> 6 Active forum_consume_count_z 0.93670820 0.7397460 319
as.data.frame(fit, unit = "trajectory")
#> trajectory n proportion mean_within_distance n_observed unique_states
#> 1 Mostly active 41 0.2887324 4.258537 8 1.878049
#> 2 Mostly average 73 0.5140845 4.961187 8 1.986301
#> 3 Mostly disengaged 28 0.1971831 3.857143 8 1.821429
#> transitions entropy complexity volatility integrative_potential
#> 1 1.829268 0.4189906 0.3251220 0.4436702 0.7696477
#> 2 2.328767 0.4736884 0.3865300 0.4973907 0.1149163
#> 3 1.892857 0.3978570 0.3246998 0.4387755 0.0000000
#> negative_exposure
#> 1 0.009485095
#> 2 0.131659056
#> 3 0.820436508State overview: profile + bars + heatmap + sizes
type = "all" draws the four state views together on the
shared palette; the profile heatmap reads with the first state as its
top row, matching the bars, sizes, and legends.
plot(fit, which = "states", type = "all")
Each view is also available alone:
plot(fit, which = "states", type = "profile")
plot(fit, which = "states", type = "bars")
plot(fit, which = "states", type = "heatmap")
plot(fit, which = "states", type = "sizes")
Palette and state order
colors recolours a single plot; the states are coloured
by position, so supply one colour per state in state order.
To reuse a palette everywhere without repeating colors,
pin it on the fit with state_colors (a named vector is
matched by state and survives reordering and set_labels()).
state_order fixes the order the states read in every plot —
stacking, legends, transition and flow nodes — independent of the order
the clusters were discovered in.
fit_styled <- vasstra(
engagement,
state_labels = c("Disengaged", "Average", "Active"),
state_order = c("Active", "Average", "Disengaged"),
state_colors = c(Disengaged = "#D55E00", Average = "#0072B2", Active = "#009E73"),
dissimilarity = "lcs",
cluster_method = "ward.D2"
)
#> Using n_states = 3 to match the supplied labels.
#> Selected n_trajectories = 3 (lcs + ward.D2, silhouette = 0.514); see `diagnostics$selection`.
plot(fit_styled, type = "distribution")
Choice comparisons across methods
The explicit comparison draws a metric-aware plot, on the shared palette with light gridlines.
state_options <- state_choices(
engagement,
n_states = 2:5,
method = c("kmeans", "pam", "ward.D2", "lpa"),
lpa_model = "EEI",
seed = 22294
)
state_options
#> VaSSTra state choices
#> 16 candidates | 16 successful | 4 recommended
#> candidate_id n_states method lpa_model recommendation_criterion silhouette
#> 1 2 kmeans <NA> silhouette 0.3519794
#> 5 2 pam <NA> silhouette 0.3497139
#> 9 2 ward.D2 <NA> silhouette 0.3312179
#> 16 5 lpa EEI bic 0.1966979
#> bic min_size eligible
#> NA 519 TRUE
#> NA 543 TRUE
#> NA 483 TRUE
#> 19008.96 155 TRUE
plot(state_options, metric = "silhouette")
plot(state_options, metric = "bic", groups = "lpa/EEI")
All sequences: heatmap (default), distribution, index
Every plot containing state sequences is rendered by
Nestimate::sequence_plot(). The heatmap is the default view
for the complete sequence set.
plot(fit, which = "sequences")
plot(fit, which = "sequences", type = "distribution")
plot(fit, which = "sequences", type = "index")
Flow plots (cograph)
flow_plot() renders state movement between consecutive
time points through cograph, on the same palette and state order as
every other plot, and returns a ggplot object rather than
drawing base graphics. Aggregated bands and individual lines are the two
views:
flow_plot(fit)
flow_plot(fit, type = "individual")
The vignette("flow-plots") article covers the rest —
colouring by destination or by first/last state, restricting to one
trajectory, line bundling, thresholding negligible flows, and tuning a
figure for a manuscript.
Transition network (Nestimate builds, cograph draws)
Node size is a transition-network centrality from
Nestimate::net_centrality(); the network comes from
Nestimate::build_tna(). Drawn by
cograph::splot(); returns the tidy node table invisibly.
The paired form places the sequences beside the network on one shared
palette.
transition_plot(fit)
transition_plot(fit, sequences = TRUE)
The centralities are also available as a tidy table:
transition_centrality(fit)
#> state InStrength OutStrength
#> 1 Active 0.1713675 0.2678571
#> 2 Average 0.5726801 0.3020833
#> 3 Disengaged 0.1592262 0.3333333See vignette("flow-plots") for the centrality-driven
node sizing (size, weights,
loops), the per-trajectory networks, and the other paired
views.
Trajectories: distribution, index, heatmap
plot(fit, type = "distribution")
plot(fit, type = "index")
plot(fit, type = "heatmap")
The combined per-trajectory grid
Passing several views in type composes them into one
figure with one row per trajectory and one column per
view, in the order requested — the standard per-cluster VaSSTra
display, drawn in a single call with a shared ordered legend. The
transition column needs the suggested cograph package.
