IRT explains why items correlate with a single latent trait; network psychometrics explains it with a graph of direct partial-correlation edges between items, no latent variable required. Under a strong single common cause, the two should agree: a network’s node centrality should track IRT discrimination, and the network should look densely and uniformly connected. We test this across real IRW instruments and check whether the relationship tracks tables already flagged as multidimensional or locally dependent elsewhere on this site.
Every other vignette on this site treats item covariation the same way IRT does: responses correlate because they all depend, more or less, on one latent trait. Network psychometrics proposes a different account. Instead of a shared cause behind the correlations, it models items as nodes in a graph and estimates direct, partial-correlation edges between them — an Ising model for binary items, a Gaussian graphical model (EBICglasso) for polytomous ones. No latent variable is fit at all; the graph is the model.
These two accounts aren’t just philosophically different — they make a shared, testable prediction. Van der Maas et al. (2006) (Maas et al. 2006) and Epskamp, Maris, van Borkulo, & Borsboom (2018) (Epskamp et al. 2018) show that if a single dominant common cause really does explain a set of items, the two descriptions should coincide. This isn’t just an informal observation: Marsman et al. (2018) (Marsman et al. 2018) prove a formal statistical equivalence between the Ising model and the 2PL for binary items, and Marsman, van den Bergh, & Haslbeck (2025) (Marsman et al. 2025) extend that equivalence to ordinal items – with a wrinkle noted in Data and methods below. Under that equivalence, a node’s centrality (how strongly and directly it connects to every other node) should track that item’s IRT discrimination, and the estimated network should look densely and fairly uniformly connected — not clustered into visibly separate sub-groups. This vignette tests that prediction across real IRW instruments, and asks whether it holds up better or worse for tables this site’s other diagnostics already flag as multidimensional (dimensionality vignette) or locally dependent (local-dependence vignette).
binary_tables <- irw_filter(n_items = c(5, 30), n_participants = c(300, Inf),
n_categories = 2)
poly_tables <- irw_filter(n_items = c(5, 30), n_participants = c(300, Inf),
n_categories = c(3, 7))Items are capped at 30 (lower than the dimensionality vignette’s 40) and polytomous tables are restricted to 3-7 response categories, mainly for compute reasons: EBIC-regularized network estimation scales worse than a single IRT fit or eigen-decomposition. 660 tables met this criterion as of July 2026 (125 binary, 535 polytomous). This pass analyzes all 660 of them.
For each candidate table, fit_network():
bootnet::estimateNetwork(): IsingFit for binary items, EBICglasso for polytomous items. The polytomous correlations are computed via qgraph::cor_auto() (corMethod = "cor_auto", corArgs = list(forcePD = TRUE)), which estimates polychoric correlations for ordinal data and projects to the nearest valid correlation matrix when the polychoric estimate isn’t positive-definite — this still treats the graph estimation step as Gaussian, an approximation relative to an exact ordinal network model, but does not additionally treat Likert categories as literally continuous integers (see Limitations for why both of those still fall short of the ordinal Markov random field with a proven IRT equivalence).qgraph::centrality_auto(). In a genuinely weighted network this returns a Strength column (each item’s summed edge weight); a fully empty regularized network — every edge shrunk to zero — gets auto-detected as unweighted and falls back to Degree instead. That’s still a real, informative result (kept in the data below), just not one with a meaningful strength-discrimination correlation, so that comparison is left NA for those tables.construct_type/ item_format from IRW’s tags.fit_network <- function(table_name) {
resp <- fetch_wide(table_name) # irw_fetch() + irw_long2resp(), cleaned
net <- if (n_categories == 2) {
estimateNetwork(resp, default = "IsingFit")
} else {
estimateNetwork(resp, default = "EBICglasso", corMethod = "cor_auto")
}
cent <- centrality_auto(net$graph)
fit <- mirt(resp, 1, itemtype = if (n_categories == 2) "2PL" else "gpcm")
a <- coef(fit, simplify = TRUE)$items[, "a1"]
cor(cent$node.centrality$Strength, a) # the core comparison
}Of the 660 candidate tables in this pass, 609 produced usable results (the rest were dropped for too few usable items, an unsupported column type on fetch, a network/IRT model that failed to fit, or too few remaining response categories). This pass matched a dimensionality-vignette entry for 581 of those tables and a local-dependence-vignette entry for 572 — both caches were built on an overlapping but not identical candidate pool, so coverage is high but not total.
example_candidates <- summary_df %>%
filter(!is.na(strength_a_cor), network_density > 0) %>%
rowwise() %>%
# Exclude numerically degenerate IRT fits -- e.g. a near-duplicate item
# pair can drive discrimination to an implausible boundary value (a ~ 50),
# which makes for a misleading rather than illustrative example.
mutate(max_abs_a = max(abs(discriminations_list[[table]]), na.rm = TRUE)) %>%
ungroup() %>%
filter(max_abs_a < 5)
hi_table <- example_candidates %>% slice_max(strength_a_cor, n = 1, with_ties = FALSE) %>% pull(table)
lo_table <- example_candidates %>% slice_min(strength_a_cor, n = 1, with_ties = FALSE) %>% pull(table)
hi_cor <- summary_df$strength_a_cor[summary_df$table == hi_table]
lo_cor <- summary_df$strength_a_cor[summary_df$table == lo_table]
plot_example_pair <- function(table_name, label) {
g <- graphs_list[[table_name]]
s <- strengths_list[[table_name]]
a <- discriminations_list[[table_name]]
par(mar = c(4, 1, 4, 1))
qgraph::qgraph(g, layout = "spring", labels = names(s),
label.cex = 0.9, vsize = 11, posCol = irw_blue, negCol = irw_red,
title = paste0(label, ": ", table_name, "\nestimated network"),
title.cex = 1)
par(mar = c(4, 10, 4, 2))
ord <- order(a)
barplot(a[ord], names.arg = names(a)[ord], horiz = TRUE, las = 1,
cex.names = 0.8, col = irw_blue, border = NA,
xlab = "IRT discrimination (a)",
main = paste0(label, ": ", table_name, "\ndiscrimination"), cex.main = 1)
}
par(mfrow = c(2, 2))
plot_example_pair(hi_table, "Highest correlation")
plot_example_pair(lo_table, "Lowest correlation")
ALSECYPIAMH_WU_2022_SWEMWBS has a strength-discrimination correlation of 1 — about as clean a confirmation of the theory as this sample produces. florida_twins_class sits at the opposite end, at -0.7: the two descriptions of the same items agree much less about which ones matter most, to the point of actively disagreeing about direction.
What makes the contrast worth dwelling on is what doesn’t differ much between them: both networks are comparably dense (density 0.95 and 0.76 respectively). Density and uniformity, the other half of Epskamp et al.’s prediction, don’t distinguish these two cases well; only the strength-discrimination correlation reveals that one table matches the single-common-cause story and the other doesn’t. A network that merely looks dense and uniform is not, on its own, evidence that IRT and network psychometrics agree about the items — this pair is a direct counterexample.
The disagreement in florida_twins_class isn’t subtle, either: 4 of its 10 items get a negative IRT discrimination, meaning the graded response model estimates them as running opposite the trait it fit from the rest. The network still connects those items to every other about as strongly as any pair in hi_table, despite the sign disagreement in the IRT fit. Practically, that matters most for anyone using either statistic to pick or drop items — shortening a scale by discrimination, or by network centrality, is not a neutral choice, and a table like this one is exactly where the two selections would part ways. Compare both examples to the aggregate picture below: most tables fall somewhere between these two extremes, but not always close to the middle.
ranked_df <- summary_df %>%
filter(!is.na(strength_a_cor)) %>%
arrange(strength_a_cor) %>%
mutate(
rank = row_number(),
tooltip = paste0(
"Table: ", table,
"<br>Strength-a correlation: ", round(strength_a_cor, 2),
"<br>Network method: ", network_method,
"<br>Network density: ", round(network_density, 2),
"<br>n_items: ", n_items
)
)
p <- ggplot(ranked_df, aes(x = strength_a_cor, y = rank, text = tooltip)) +
geom_point(colour = irw_blue, size = 1.6, alpha = 0.7) +
geom_vline(xintercept = 0, linetype = "dashed", colour = irw_grey) +
labs(x = "Correlation: node strength vs. IRT discrimination",
y = "Rank (spreads points out only -- carries no meaning of its own)") +
theme(axis.text.y = element_blank(), axis.ticks.y = element_blank())
ggplotly(p, tooltip = "text") |> layout(margin = list(t = 60))The median strength-discrimination correlation across 602 tables with a usable comparison is 0.68, and 48% of tables exceed 0.7. 7 table(s) are excluded here because their regularized network had no edges at all – an empty network, not a low correlation. The relationship is real and often strong, but — as the two comparisons below make concrete — it is not universal.
join_dim_df <- summary_df %>%
filter(!is.na(strength_a_cor), !is.na(dim_ratio_12)) %>%
mutate(tooltip = paste0(
"Table: ", table,
"<br>Strength-a cor: ", round(strength_a_cor, 2),
"<br>Eigenvalue ratio: ", round(dim_ratio_12, 2),
"<br>PA unidimensional: ", dim_unidimensional
))
p <- ggplot(join_dim_df, aes(x = pmin(dim_ratio_12, 15), y = strength_a_cor, text = tooltip)) +
geom_point(colour = irw_blue, size = 2, alpha = 0.7) +
geom_smooth(method = "loess", se = FALSE, colour = irw_red, linewidth = 0.8) +
scale_x_log10() +
labs(x = "Eigenvalue ratio (dimensionality vignette, log scale, capped at 15)",
y = "Strength-discrimination correlation")
ggplotly(p, tooltip = "text") |> layout(margin = list(t = 60))Across the 575 tables with a match in both this vignette and the dimensionality vignette, the two diagnostics move together weakly but reliably (r = 0.26 between strength-discrimination correlation and log eigenvalue ratio) — real signal in the direction the theory predicts, not a tight relationship. The theory’s prediction shows up more clearly when split by the dimensionality vignette’s own parallel-analysis call: the 14 tables it flags as unidimensional have a median strength-discrimination correlation of 0.95, versus 0.69 for the 561 tables it flags as multidimensional (Wilcoxon p < 0.001). Parallel analysis is strict — only a small fraction of tables clear its bar for “unidimensional” — but among the ones that do, network centrality and IRT discrimination agree noticeably better.
join_ld_df <- summary_df %>%
filter(!is.na(network_density), !is.na(ld_prop_flagged)) %>%
mutate(tooltip = paste0(
"Table: ", table,
"<br>Network density: ", round(network_density, 2),
"<br>Prop. Q3-flagged: ", round(ld_prop_flagged, 2)
))
p <- ggplot(join_ld_df, aes(x = ld_prop_flagged, y = network_density, text = tooltip)) +
geom_point(colour = irw_blue, size = 2, alpha = 0.7) +
labs(x = "Proportion of pairs Q3-flagged (local-dependence vignette)",
y = "Network density")
ggplotly(p, tooltip = "text") |> layout(margin = list(t = 60))Across the 572 tables with a match in both this vignette and the local-dependence vignette, network density and the proportion of Q3-flagged pairs correlate at r = 0.42 (p < 0.001) — the expected sign (more flagged pairs, denser network), and with 572 tables behind it, a reliable one. Density alone doesn’t distinguish a uniformly dense network from one with a few tightly-connected clusters sitting inside an otherwise sparse graph — the latter is the more specific testlet signature, and it’s exactly what the local-dependence vignette’s Q3 heatmaps are built to catch directly. Detecting that cluster structure from the network side properly needs community-detection tools this pass didn’t run at batch scale (see Limitations); density is the coarser proxy available here.
Where the strength-discrimination correlation is high and the network is dense and uniform, network psychometrics and IRT are, practically speaking, telling the same story about the same items — using either framework to identify the “best” items should agree. Where it breaks down, that’s a signal worth taking seriously in its own right, independent of which framework you prefer: it means the two ways of describing item covariation actually disagree about which items matter most, and a table flagged as multidimensional or locally dependent elsewhere on this site is a reasonable place to expect exactly that disagreement.
bootnet::estimateNetwork()’s EBICglasso preset does not call qgraph::cor_auto() by default — as of bootnet 1.4, the EBICglasso default set switched from corMethod = "cor_auto" to plain Pearson correlations (cor). Neither bootnet nor qgraph was pinned in renv.lock at the time (now fixed — see below), so an earlier pass of this vignette likely ran on whatever version was on the machine at the time and may have silently treated 7-point Likert integers as literally continuous. This pass instead passes corMethod = "cor_auto" explicitly (polychoric/polyserial correlations for ordinal items) with corArgs = list(forcePD = TRUE), since a polychoric correlation matrix over several ordinal items is not always positive-definite and bootnet errors out by default rather than correcting it; forcePD projects to the nearest valid correlation matrix instead. The impact was real and sometimes large: clifford_2018_police_blame, the lowest strength-discrimination correlation table in an earlier pass of this vignette (r = −0.69), moved to r = 0.09 once the network side used polychoric correlations and the IRT side used GPCM instead of GRM (next point) — a different table is now the lowest-correlation example (see the worked-case callout above). Separately, and regardless of that fix: even an exact polychoric-correlation Gaussian graphical model is still not the network model with a proven equivalence to an ordinal IRT model. Marsman, van den Bergh, & Haslbeck (2025) (Marsman et al. 2025) derive that equivalence for the ordinal Markov random field, and show it corresponds to the generalized partial credit model (GPCM), not the graded response model most applied network-IRT comparisons use for polytomous items — this vignette now fits GPCM for that reason (see Data and methods), but an exact ordinal-MRF network fit (rather than a Gaussian approximation on polychoric correlations) is still not implemented here.bootnet’s case-dropping bootstrap (the standard way to check whether an estimated network’s edges and centrality ordering are stable) was not run at full-batch scale for compute reasons. A natural follow-up: run it for a handful of the most interesting example tables from the full batch (the strongest confirmation, the sharpest breakdown) rather than all of them.bootnet and qgraph were not pinned in renv.lock when this pass was run. This pass ran against whatever versions of these two packages happened to be installed, which is how the cor_auto default-behavior change above went unnoticed. Both are now pinned in renv.lock, which prevents a silent version drift like this going forward but doesn’t retroactively confirm which version produced the results above.# 1. Re-run the prerequisite compute scripts first (from the project root)
Rscript vignettes/dimensionality_compute.R
Rscript vignettes/local_dependence_compute.R
# 2. Re-run this vignette's compute script
Rscript vignettes/network_psych_compute.R
# 3. Re-render this page
quarto render vignettes/network_psych.qmdSession info from the compute run: R R version 4.6.1 (2026-06-24), run on July 21, 2026.