TNA Model Comparison: A Comprehensive Guide to Network Comparison

1 Introduction

Transition Network Analysis (TNA) has emerged as a methodologically rigorous framework for modeling behavioral processes as weighted directed networks, combining the temporal resolution of stochastic process mining with the structural analytic capacity of graph theory (Saqr, López-Pernas, Törmänen, et al., 2025). Since its introduction at LAK 2025, the framework has expanded rapidly: it now supports multiple model types—first-order Markov models, frequency-based transition models, co-occurrence.

This is the companion tutorial to the main TNA tutorial, focusing on pairwise model comparison using the compare() function. We assume you have already worked through the main tutorial and understand the basics of building a TNA model.

A single TNA model describes one set of transition dynamics. But most research questions involve two models — high vs. low achievers, pre vs. post intervention, treatment vs. control. Visual inspection can suggest differences, but cannot tell you whether a 3% weight gap is meaningful or which of two nearly-equal edges is actually stronger. compare() quantifies what changed, by how much, and where, so that you can report precise differences rather than eyeball them.

This tutorial works through comparison at three levels of resolution:

1. Network-level properties — are the two networks structurally different? One might be denser, more centralized, or more reciprocal, and these whole-network differences would be invisible if you only compared individual edges.
2. Edge-level differences — which specific transitions changed and by how much? This includes the raw difference matrix, 16 per-edge metrics, summary statistics that condense overall divergence into reportable numbers, and visualizations (heatmaps, scatterplots, density plots).
3. Centrality — did states change roles? A state that acts as a bridge in one group may be peripheral in the other, and centrality differences reveal these structural role shifts.

The compare() function returns seven components that map onto these levels:

Component	What It Contains
$network_metrics	13 network-level structural properties
$difference_matrix	Element-wise difference (x - y)
$edge_metrics	16 edge-level comparison metrics
$summary_metrics	22 aggregate divergence metrics across 5 categories
$matrices	The (optionally scaled) input matrices
$centrality_differences	Per-node centrality differences across 9 measures
$centrality_correlations	Cross-model centrality rank correlations

Companion tutorials:

• TNA Main Tutorial — building and analyzing a single TNA model
• TNA Group Analysis — group comparisons, permutation testing, and bootstrapping
• TNA Clustering — data-driven clustering of sequences
• Preparing Data for TNA — data import and preparation

1.1 Installation

The tna package is the only package required. Install from CRAN:

install.packages("tna")

Or install the development version from GitHub:

# install.packages("remotes")
remotes::install_github("sonsoleslp/tna")

2 Setup: Building Two Models to Compare

We use the built-in group_regulation_long dataset and build group-level TNA models for High and Low achievers. This gives us two models with different transition structures.

# Load the built-in collaborative regulation dataset
data("group_regulation_long")

# Convert to sequences, preserving the Achiever metadata column
prepared_data <- prepare_data(
  group_regulation_long,
  action = "Action",
  actor = "Actor",
  time = "Time"
)

# Build separate TNA models for High and Low achievers
gtna <- group_tna(prepared_data, group = "Achiever")

The simplest way to call compare() is to pass the group TNA object directly. If the object has more than two groups, it picks the first two by default. You can also specify which groups to compare with i and j (by name or index):

# Pass the group object directly; compares the first two groups
comp <- compare(gtna)

TipSelecting Specific Groups or Comparing Individual Models

# Pick specific groups by name or index
comp <- compare(gtna, i = "High", j = "Low")

# Compare two individual tna models directly
comp <- compare(gtna$High, gtna$Low)

3 Network Plots

Plotting the two networks side by side is the fastest way to get a sense of whether they look similar or different — before committing to any specific metric. Look for which transitions are strongest, which states are most active, and whether the two networks share the same dominant pathways. The minimum argument hides edges below a threshold, and cut fades edges below a second threshold, so the dominant structure stands out.

# Side-by-side network plots
plot(gtna, minimum = 0.05, cut = 0.1)

Figure 1: Transition networks for High and Low achievers

Figure 2: Transition networks for High and Low achievers

3.1 Difference Network

Side-by-side plots make it hard to compare specific edges because the eye has to jump between two layouts. plot_compare() solves this by overlaying both networks on the same node positions, coloring each edge by which group uses it more. This makes it immediately clear which behavioral pathways distinguish the groups.

# Overlay both networks; edge color shows direction of difference
plot_compare(gtna$High, gtna$Low, minimum = 0.01)

Figure 3: Network overlay: edges colored by direction of difference

4 Network Metrics

Before looking at individual edges, it is worth checking whether the two networks differ in overall structure. Two models can share similar average edge weights yet differ in how connections are distributed — one may route behavior through a few hub states (high centralization) while the other spreads transitions more evenly (high density, low centralization). $network_metrics reports 13 structural properties for each model, side by side, so you can spot these architectural differences early.

# 13 network-level properties, one value per model
comp$network_metrics

Metric	What It Tells You
Node Count	Whether both models have the same state space
Edge Count	Network complexity; more edges = more interconnected
Network Density	Proportion of possible edges that exist
Mean Distance	Average shortest path length between states
Mean/SD Out-Strength	Average and variability of outgoing transition weight per node
Mean/SD In-Strength	Average and variability of incoming transition weight per node
Mean/SD Out-Degree	Average and variability of outgoing connections per node
Centralization (Out/In-Degree)	Whether connections are dominated by a few hub nodes (higher = more hub-like)
Reciprocity	Proportion of mutual (bidirectional) edges

If two models differ on these properties, it tells you the groups have fundamentally different behavioral architectures — not just different strengths on the same pathways.

5 Edge-Level Comparisons

Network metrics tell you whether the two networks differ structurally, but not where. If density or centralization differs, you need to know which specific transitions drive that difference. The compare() output includes three edge-level components for this: a difference matrix, a table of 16 per-edge metrics, and 22 summary metrics that aggregate across all edges.

5.1 The Difference Matrix

The $difference_matrix is the starting point for edge-level comparison — it shows exactly which transitions are stronger in which group. The matrix is the element-wise subtraction (x_{ij} - y_{ij}), so positive values are transitions stronger in the first model and negative values are transitions stronger in the second. For example, if high achievers transition from Planning to Monitoring more often while low achievers cycle within Monitoring, those cells will have opposite signs. Rows are source states, columns are target states.

# Element-wise: High minus Low (positive = stronger in High)
comp$difference_matrix

              adapt cohesion consensus coregulate discuss emotion  monitor
adapt       0.00000 -0.01476   0.05577     -0.030  -0.032  0.0304 -0.00696
cohesion    0.00533  0.03711   0.08578     -0.085  -0.043  0.0061 -0.03578
consensus  -0.00132  0.01056   0.00308     -0.036   0.096  0.0187 -0.02421
coregulate  0.01122 -0.00045  -0.04763     -0.018  -0.071  0.0577  0.01813
discuss    -0.09616  0.02905   0.21028     -0.024  -0.052  0.0133 -0.01176
emotion     0.00167  0.00102   0.03465     -0.024   0.044 -0.0314 -0.01035
monitor    -0.00019 -0.01228   0.00081     -0.013  -0.010  0.0101  0.00146
plan        0.00077  0.01186   0.00662      0.013  -0.015  0.0668  0.00038
synthesis  -0.15825 -0.00866   0.19051     -0.052  -0.059 -0.0101 -0.02139
              plan synthesis
adapt      -0.0021   0.00000
cohesion    0.0232   0.00640
consensus  -0.0677   0.00081
coregulate  0.0497   0.00043
discuss     0.0017  -0.07025
emotion    -0.0208   0.00516
monitor     0.0184   0.00521
plan       -0.0875   0.00315
synthesis   0.1198   0.00000

5.2 Difference Heatmap

With many states, scanning a numeric matrix for patterns is slow. The heatmap makes structure visible: clusters of same-colored cells in a row mean one group has systematically stronger outgoing transitions from that state, which indicates the state plays a different role for each group. Isolated intense cells point to specific transitions that distinguish the groups.

# Difference heatmap
plot(comp, type = "heatmap", population = "difference")

Figure 4: Difference heatmap: blue = stronger in High, red = stronger in Low

5.3 Scatterplot

The heatmap and difference matrix show which edges differ, but not whether the two models agree on the overall pattern of transition weights. The scatterplot answers that: each point is one edge, plotted by its weight in both models, and the correlation coefficient printed on the plot quantifies overall linear agreement. A Pearson r above 0.9 indicates that both models prioritize the same transitions — they share the same structure at different intensities. A low r means the models disagree about which transitions matter. Points far from the diagonal are the specific edges driving any disagreement; these are candidates for closer inspection in the edge metrics table.

# Each point is one edge; diagonal = identical weights
plot(comp, type = "scatterplot", method = "pearson")

Figure 5: Edge weight scatterplot with Pearson correlation

TipScatterplot with Other Correlation Methods

The method argument can also be "spearman" (rank-based, robust to outliers), "kendall" (concordance-based), or "distance" (detects nonlinear relationships).

# Rank-based correlation, robust to outliers
plot(comp, type = "scatterplot", method = "spearman")

Figure 6: Edge weight scatterplot with Spearman rank correlation

5.4 Weight Density

The difference matrix and scatterplot compare individual edges, but two models can have similar edge-by-edge profiles yet distribute their total probability very differently. The density plot reveals this: if one group concentrates its weight on a few dominant transitions (peaked, long-tailed distribution) while the other spreads weight more evenly (flatter distribution), the groups differ in behavioral diversity even when their strongest edges agree. This connects directly to the CV Ratio in the summary metrics — a ratio far from 1.0 means unequal dispersion, and the density plot shows where that dispersion difference comes from.

# Overlay of weight distributions
plot(comp, type = "weight_density")

Figure 7: Distribution of edge weights in both models

TipSummary of All Plot Options

type	population options	method options	What It Shows
"heatmap"	"difference", "x", "y"	—	Edge weight matrices as color grids
"scatterplot"	—	"pearson", "spearman", "kendall", "distance"	Edge weights plotted against each other
"centrality_heatmap"	—	—	Centrality differences by state and measure
"weight_density"	—	—	Overlaid weight distributions

All plot types accept name_x and name_y to label the two models in the plot.

5.5 Edge Metrics Table

A raw difference of 0.05 between edges weighted 0.06 and 0.01 is a very different situation from the same 0.05 between edges weighted 0.50 and 0.45 — the first is a fivefold change, the second is a 10% shift. The $edge_metrics table (n^2 rows, 16 columns) provides multiple ways to quantify each edge’s difference so you can distinguish these cases. Sorting by absolute_difference identifies the transitions with the largest raw gaps; sorting by relative_difference or similarity_strength_index surfaces proportionally large changes that raw magnitude would miss. Here are the edges with the largest absolute differences:

# Edges sorted by largest absolute difference
edge_sorted <- comp$edge_metrics[order(-comp$edge_metrics$absolute_difference), ]
edge_sorted[, c("source", "target", "weight_x", "weight_y",
                        "raw_difference", "absolute_difference",
                        "relative_difference", "rank_difference")]

5.5.1 Which Edge Metric for Which Question?

Question	Best Metric	Why
Which direction is the difference?	raw_difference	Preserves sign
How large is the difference?	absolute_difference	Simple, interpretable
Is this edge proportionally different?	relative_difference	Normalizes by magnitude
How many times stronger?	similarity_strength_index	Multiplicative ratio
What % change from baseline?	difference_index	Percentage change from model y
Did the edge change in rank order?	rank_difference	Ordinal, robust to outliers
Is the edge at the same percentile?	percentile_difference	Distribution-based
Proportional comparison with zeros?	logarithmic_ratio	Handles zeros gracefully
Did relative position change?	standardized_score_inflation	Compares z-scores

NoteEdge Metric Definitions

raw_difference: w^x_{ij} - w^y_{ij} — the signed difference. Positive = stronger in model x.

absolute_difference: |w^x_{ij} - w^y_{ij}| — unsigned magnitude of difference.

squared_difference: (w^x_{ij} - w^y_{ij})^2 — penalizes large differences disproportionately.

relative_difference: \frac{|w^x_{ij} - w^y_{ij}|}{w^x_{ij} + w^y_{ij}} — normalized by combined magnitude. Range: [0, 1]. A difference of 0.01 between edges of weight 0.02 and 0.01 (relative = 0.33) is more meaningful than the same 0.01 between 0.50 and 0.49 (relative = 0.01).

similarity_strength_index: \frac{w^x_{ij}}{w^y_{ij}} — multiplicative ratio. Value of 2.0 = edge is twice as strong in model x.

difference_index: \frac{w^x_{ij} - w^y_{ij}}{w^y_{ij}} — percentage change from model y.

rank_difference: |\text{rank}(w^x_{ij}) - \text{rank}(w^y_{ij})| — ordinal comparison regardless of absolute values.

percentile_difference: |F_x(w^x_{ij}) - F_y(w^y_{ij})| — ECDF-based. Range: [0, 1].

logarithmic_ratio: \log(1+w^x_{ij}) - \log(1+w^y_{ij}) — proportional comparison that handles zeros.

standardized_weight_x / standardized_weight_y: Z-scores within each model: z^x_{ij} = (w^x_{ij} - \bar{w}^x) / \sigma_{w^x}.

standardized_score_inflation: z^x_{ij} / z^y_{ij} — ratio of standardized weights.

WarningNaN and Inf Values in Edge Metrics

Several metrics involve division and produce NaN or Inf when denominators are zero:

• similarity_strength_index and difference_index: Inf when w^y = 0
• standardized_score_inflation: Inf or NaN when z^y = 0
• relative_difference: NaN when both weights are zero

These occur for edges that exist in only one model. Filter before aggregation (e.g., dplyr::filter(is.finite(similarity_strength_index))).

5.6 Summary Metrics

Edge-level metrics tell you about specific transitions, but a paper or presentation often needs a single number: “how different are these two networks?” The $summary_metrics table condenses all edge-level differences into 22 aggregate measures across 5 categories. You can report MAD or Bray-Curtis for overall magnitude, Pearson or Spearman for pattern similarity, or Jaccard and Dice for distributional overlap — each captures a different aspect of divergence.

# 22 aggregate metrics across 5 categories
comp$summary_metrics

5.6.1 Which Summary Metric for Which Research Question?

Research Question	Recommended Metrics	Why
How different are the models overall?	MAD, RMSD, Bray-Curtis	Intuitive, interpretable magnitudes
Are differences concentrated or spread?	Compare MAD vs RMSD, Max Abs. Diff.	RMSD >> MAD = concentrated in few edges
Do models share the same pattern?	Pearson, Spearman, Cosine	Pattern similarity, scale-invariant
How similar are the weight distributions?	Jaccard, Dice, RV	Overlap-based, bounded [0,1]
Is there a nonlinear relationship?	Distance correlation	Detects nonlinear dependencies
As a percentage of baseline?	Rel. Mean Abs. Diff., Bray-Curtis	Normalized, percentage-like
Is one model more heterogeneous?	CV Ratio	Relative dispersion comparison
Do models agree on priority ordering?	Rank Agreement, Kendall	Ordinal, robust to outliers

NoteWeight Deviations — Formulas and Details (6 metrics)

These metrics quantify the typical magnitude of edge-level differences.

Mean Abs. Diff.: \text{MAD} = \frac{1}{n^2} \sum_{i,j} |w^x_{ij} - w^y_{ij}| The average absolute difference across all edges. Range: [0, \infty). Value of 0 means identical models.

Median Abs. Diff.: The median of |w^x_{ij} - w^y_{ij}|. More robust to outliers than the mean. If MAD \gg median, a few edges dominate the overall difference.

RMS Diff.: \text{RMSD} = \sqrt{\frac{1}{n^2} \sum_{i,j} (w^x_{ij} - w^y_{ij})^2} Penalizes large differences disproportionately. If RMSD \gg MAD, the difference is concentrated in a few edges.

Max Abs. Diff.: \max_{i,j} |w^x_{ij} - w^y_{ij}| The single largest edge difference — a quick worst-case check.

Rel. Mean Abs. Diff.: \frac{\text{MAD}}{\frac{1}{n^2} \sum_{i,j} |w^y_{ij}|} MAD as a proportion of the baseline weight magnitude. A value of 0.29 means the average edge differs by 29%.

CV Ratio: \frac{\text{CV}(w^x)}{\text{CV}(w^y)} = \frac{\sigma_{w^x} / \bar{w}^x}{\sigma_{w^y} / \bar{w}^y} Compares relative dispersion. Value of 1.0 = same spread; > 1 = model x more heterogeneous.

NoteCorrelations — Formulas and Details (4 metrics)

These assess whether both models agree on the pattern of edge weights, independent of absolute magnitudes.

Pearson: r = \frac{\sum (w^x_{ij} - \bar{w}^x)(w^y_{ij} - \bar{w}^y)}{\sqrt{\sum(w^x_{ij} - \bar{w}^x)^2 \cdot \sum(w^y_{ij} - \bar{w}^y)^2}} Linear correlation. Range: [-1, 1]. Sensitive to outliers.

Spearman: \rho = 1 - \frac{6 \sum d^2_{ij}}{n^2(n^4 - 1)} Rank-based correlation, robust to outliers. Answers: “Do the models agree on which edges are strongest?”

Kendall: \tau = \frac{C - D}{\binom{n^2}{2}} Concordance-based. More robust than Spearman for small samples and tied values.

Distance: The distance correlation of Székely et al. (2007). Detects nonlinear dependencies. Range: [0, 1]. A value of 0 implies statistical independence.

Important: Correlation \neq agreement. Two models can correlate at r = 0.99 yet differ systematically. A uniformly scaled version of model y gives perfect correlation but every edge weight is different. Always pair correlation metrics with deviation metrics (MAD, RMSD).

NoteDissimilarities — Formulas and Details (5 metrics)

These quantify the distance between two models. Larger = more different.

Euclidean: d_E = \sqrt{\sum_{i,j} (w^x_{ij} - w^y_{ij})^2} Straight-line distance. Sensitive to outlier edges.

Manhattan: d_M = \sum_{i,j} |w^x_{ij} - w^y_{ij}| Sum of absolute differences (L1 norm). Less sensitive to outliers. Manhattan = n^2 \times MAD.

Canberra: d_C = \sum_{i,j} \frac{|w^x_{ij} - w^y_{ij}|}{|w^x_{ij}| + |w^y_{ij}|} Per-edge normalization before summing. Range: [0, n^2].

Bray-Curtis: d_{BC} = \frac{\sum |w^x_{ij} - w^y_{ij}|}{\sum (w^x_{ij} + w^y_{ij})} Proportion of total weight that differs. Range: [0, 1]. A value of 0.14 = 14% of weight is allocated differently.

Frobenius: \|W^x - W^y\|_F = \sqrt{\sum_{i,j} (w^x_{ij} - w^y_{ij})^2} Matrix norm, divided by \sqrt{n/2} for normalization.

NoteSimilarities — Formulas and Details (5 metrics)

These quantify how alike two models are. Larger = more similar.

Cosine: \cos(\theta) = \frac{\sum w^x_{ij} \cdot w^y_{ij}}{\sqrt{\sum (w^x_{ij})^2} \cdot \sqrt{\sum (w^y_{ij})^2}} Directional alignment. Range: [-1, 1]. Value of 1 = identical patterns regardless of scale.

Jaccard (weighted): J = \frac{\sum \min(w^x_{ij}, w^y_{ij})}{\sum \max(w^x_{ij}, w^y_{ij})} Overlap relative to union. Range: [0, 1]. Sensitive to absolute differences.

Dice: D = \frac{2 \sum \min(w^x_{ij}, w^y_{ij})}{\sum w^x_{ij} + \sum w^y_{ij}} Emphasizes shared elements. Mathematically: D = 2J/(1+J).

Overlap: O = \frac{\sum \min(w^x_{ij}, w^y_{ij})}{\min(\sum w^x_{ij}, \sum w^y_{ij})} Normalizes by the smaller total. Useful when models have very different total weight.

RV Coefficient: Multivariate generalization of squared Pearson correlation for matrices (Robert & Escoufier, 1976). Range: [0, 1]. Considers full matrix structure.

NotePattern Similarities — Details (2 metrics)

Rank Agreement: Proportion of edge pairs where both models agree on relative ordering. Range: [0, 1]. Value of 1 = identical priority structure.

Sign Agreement: Proportion of edges where the sign relative to the mean is the same. Range: [0, 1]. Value of 0.94 = 94% of edges are on the same side of their respective means.

6 Centrality

Network and edge metrics compare the connections between states. Centrality shifts the focus to the states themselves: did any state change its structural role between groups? A state that acts as a bridge (high betweenness) in one group may be peripheral in the other — meaning the groups route their behavior through different hubs. A state that gains outstrength has become a more dominant launching point. compare() provides three centrality-related outputs: a table of per-node differences, a heatmap visualization, and cross-model correlations.

6.1 Centrality Differences

To identify which states changed roles and how, check $centrality_differences. Each row is one state–measure combination, with columns for each model’s value and their difference. A positive difference means the state has higher centrality in the first model; negative means higher in the second.

# Centrality values and differences: 9 measures × 9 states = 81 rows
comp$centrality_differences

The 9 centrality measures:

Measure	What It Captures
OutStrength	Total outgoing transition probability. Higher = stronger outgoing transitions
InStrength	Total incoming transition probability. Higher = more frequently transitioned to
ClosenessIn	How quickly a state can be reached from all others. Higher = more accessible
ClosenessOut	How quickly all others can be reached from this state. Higher = better launching point
Closeness	Combined in/out closeness. Higher = more central overall
Betweenness	Shortest paths passing through the state. Higher = more of a bridge
BetweennessRSP	Randomized shortest-path betweenness. Considers near-optimal paths too
Diffusion	How broadly influence spreads from this state. Higher = more influential
Clustering	Local clustering coefficient. Higher = neighbors tend to connect to each other

6.2 Centrality Heatmap

The heatmap maps all centrality differences at once. Rows (states) with consistently strong colors have changed roles across the board; isolated bright cells point to specific state–measure shifts. Each cell is one state–measure combination; the color intensity shows how large the difference is.

# Heatmap of centrality differences across all states and measures
plot(comp, type = "centrality_heatmap")

Figure 8: Centrality differences: positive = higher in first model, negative = higher in second

6.3 Centrality Correlations

The per-state differences show individual shifts, but you may also want to know whether the overall hierarchy of states is preserved. $centrality_correlations reports, for each centrality measure, the Pearson correlation of its values across states between the two models. High correlation means both groups agree on which states are important — the same hierarchy at different magnitudes. Low correlation means the groups organize around different states entirely.

# How consistently do states maintain their centrality rankings?
comp$centrality_correlations

• High correlation (e.g., OutStrength at 0.99) — states keep similar structural roles in both models.
• Low correlation (e.g., Betweenness at 0.46) — structural roles are reshuffled. A state that acts as a bridge in one model may be peripheral in the other.

When correlations are low, check $centrality_differences to see which states changed roles and how.

7 Scaling Options

The scaling argument in compare() transforms both matrices before comparison. This matters when comparing different types of TNA models that live on different scales — for example, a relative (probability) TNA versus a frequency-based model, or an absolute TNA versus a fitted TNA. Raw values are not directly comparable in those cases, and scaling puts both matrices on a common footing.

# Compare raw vs minmax-scaled summary metrics side by side
comp_raw <- compare(gtna, i = "High", j = "Low", scaling = "none")
comp_minmax <- compare(gtna, i = "High", j = "Low", scaling = "minmax")

# Merge for comparison
merged <- merge(
  comp_raw$summary_metrics,
  comp_minmax$summary_metrics,
  by = c("category", "metric"),
  suffixes = c("_raw", "_minmax")
)
merged

The available scaling methods:

Method	Formula	Best For
"none"	No transformation (default)	Comparing models on the same scale (e.g., two relative TNA models)
"minmax"	\frac{w - \min(w)}{\max(w) - \min(w)}	Normalizing to [0, 1]; comparing models with different weight ranges (e.g., frequency vs. probability)
"rank"	Min-max normalization of ranks	Ordinal comparison; robust to outliers and nonlinear relationships
"zscore"	\frac{w - \bar{w}}{\sigma_w}	Standardizing to mean 0, SD 1; comparing relative positions
"log"	\log(w)	Skewed distributions with strictly positive weights
"log1p"	\log(1 + w)	Skewed distributions that may include zeros (e.g., frequency models)
"softmax"	\frac{e^{w_i}}{\sum_j e^{w_j}}	Converting to probability-like scale; useful for frequency or absolute TNA models
"quantile"	Empirical CDF via stats::ecdf()	Purely distributional comparison; fully nonparametric

TipWhen to Use Scaling

Use "none" (default) when: Both models are on the same scale — the most common scenario (e.g., comparing two relative TNA models from different groups or time periods).

Use scaling when: You are comparing models of different types (e.g., a frequency TNA vs. a relative TNA, or an absolute TNA vs. a fitted TNA), where raw weights are on fundamentally different scales.

WarningScaling Caveats

• "zscore" produces negative values, which can cause errors in centrality computations that require non-negative weights.
• "log" requires strictly positive weights (no zeros). Use "log1p" instead if your matrix contains zeros.
• Scaling changes the magnitude of all downstream metrics. Summary metrics from scaled matrices are not directly comparable to those from unscaled matrices.

8 From Comparison to Significance

compare() tells you how much two models differ, but not whether those differences are statistically significant. A difference of 0.05 in a transition probability could be real or could be sampling noise. The permutation_test() function tests this by randomly reassigning group labels thousands of times to build a null distribution.

set.seed(265)
# Permutation test: which differences exceed chance?
perm <- permutation_test(gtna, iter = 500)

# Significant edges
perm_results <- perm[[1]]
sig_edges <- perm_results$edges$stats[perm_results$edges$stats$p_value < 0.05, ]
sig_edges[order(-abs(sig_edges$effect_size)), ]

The recommended workflow: use compare() to find where and how much models differ, then permutation_test() to check which differences are statistically reliable. See the Group Analysis tutorial for full treatment of permutation testing and bootstrapping.

NoteMagnitude ≠ Significance

A large difference may not be significant if it falls within the range of chance variation. A small difference can be significant if the null distribution is tight. Always pair compare() with permutation_test() for inferential claims.

9 Quick Reference

9.1 Summary Metrics

Category	Metric	Range	Value When Identical
Weight Deviations	Mean Abs. Diff.	[0, \infty)	0
Weight Deviations	Median Abs. Diff.	[0, \infty)	0
Weight Deviations	RMS Diff.	[0, \infty)	0
Weight Deviations	Max Abs. Diff.	[0, \infty)	0
Weight Deviations	Rel. Mean Abs. Diff.	[0, \infty)	0
Weight Deviations	CV Ratio	(0, \infty)	1
Correlations	Pearson	[-1, 1]	1
Correlations	Spearman	[-1, 1]	1
Correlations	Kendall	[-1, 1]	1
Correlations	Distance	[0, 1]	1
Dissimilarities	Euclidean	[0, \infty)	0
Dissimilarities	Manhattan	[0, \infty)	0
Dissimilarities	Canberra	[0, n^2]	0
Dissimilarities	Bray-Curtis	[0, 1]	0
Dissimilarities	Frobenius	[0, \infty)	0
Similarities	Cosine	[-1, 1]	1
Similarities	Jaccard	[0, 1]	1
Similarities	Dice	[0, 1]	1
Similarities	Overlap	[0, 1]	1
Similarities	RV	[0, 1]	1
Pattern Similarities	Rank Agreement	[0, 1]	1
Pattern Similarities	Sign Agreement	[0, 1]	1

9.2 Edge Metrics

Metric	Range	Handles Zeros?	Preserves Sign?
raw_difference	(-\infty, \infty)	Yes	Yes
absolute_difference	[0, \infty)	Yes	No
squared_difference	[0, \infty)	Yes	No
relative_difference	[0, 1]	NaN if both 0	No
similarity_strength_index	(0, \infty)	Inf if y = 0	No (ratio)
difference_index	(-\infty, \infty)	Inf if y = 0	Yes
rank_difference	[0, n^2 - 1]	Yes	No
percentile_difference	[0, 1]	Yes	No
logarithmic_ratio	(-\infty, \infty)	Yes (via log1p)	Yes
standardized_weight_x	(-\infty, \infty)	Yes	Yes
standardized_weight_y	(-\infty, \infty)	Yes	Yes
standardized_score_inflation	(-\infty, \infty)	Inf/NaN if z_y = 0	Yes

9.3 Decision Guide

Goal	Metric(s) to Use
Quick overall similarity check	Pearson, Cosine, Bray-Curtis
Identify the most different edges	Sort edge_metrics by absolute_difference
Compare edge importance orderings	Spearman, Rank Agreement, rank_difference
Check if structural roles changed	centrality_correlations, centrality_differences
Assess global network structure	network_metrics (density, reciprocity, centralization)
Statistical significance of differences	Pair with permutation_test()

References

• Tikka, S., López-Pernas, S., & Saqr, M. (2025). tna: An R Package for Transition Network Analysis. Applied Psychological Measurement. https://doi.org/10.1177/01466216251348840
• Robert, P., & Escoufier, Y. (1976). A unifying tool for linear multivariate statistical methods: The RV-coefficient. Journal of the Royal Statistical Society: Series C, 25(3), 257–265.
• Székely, G. J., Rizzo, M. L., & Bakirov, N. K. (2007). Measuring and testing dependence by correlation of distances. The Annals of Statistics, 35(6), 2769–2794.
• Package website: https://sonsoles.me/tna/