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library(imaginarycss)

Perceptual Error Analysis

When people report how they see a social network, their perceptions systematically deviate from the true structure. The imaginarycss package classifies these deviations using two complementary tools:

• count_recip_errors() – counts reciprocity-related misperceptions.
• count_imaginary_census() – performs the full 10-category imaginary census introduced in Tanaka & Vega Yon (2023).

Setup: A Small Example Network

We use a four-node network with one perceiver to illustrate the key ideas.

# Build a true network and one perceiver's view
source_ <- c(1, 2, 3, 1, c(1, 2, 3) + 4)
target_ <- c(2, 1, 4, 4, c(2, 1, 4) + 4)

adjmat <- matrix(0L, nrow = 8, ncol = 8)
adjmat[cbind(source_, target_)] <- 1L
graph <- new_barry_graph(adjmat, n = 4)

Printing the graph shows some information:

print(graph)

A barry_graph with 2 networks of size 4
.    .  1.00     .  1.00 
 1.00     .     .     . 
    .     .     .  1.00 
    .     .     .     . 
Skipping 4 rows. Skipping 4 columns. 

Reciprocity Errors

Reciprocity errors capture how often a perceiver incorrectly sees a directed tie as mutual (or vice versa). Higher counts indicate a stronger tendency to assume reciprocity where none exists.

recip_errors <- count_recip_errors(graph)
barplot(
  recip_errors$value,
  names.arg = recip_errors$name,
  horiz = TRUE, las = 1,
  col = "steelblue",
  xlab = "Count",
  main = "Reciprocity Errors by Type"
)

Imaginary Census

The imaginary census classifies every perceiver–dyad combination into one of ten categories that capture the full spectrum from accurate perception to complete misperception (see ?count_imaginary_census for definitions).

census <- count_imaginary_census(graph)

# Aggregate by motif type using the summary method
agg <- summary(census)
agg <- sort(agg)

par(mar = c(4, 12, 3, 1))
barplot(
  agg,
  horiz = TRUE, las = 1,
  col = "steelblue",
  xlab = "Count",
  main = "Imaginary Census Distribution"
)

Individual Accuracy

The function tie_level_accuracy() decomposes each perceiver’s accuracy into four probabilities:

These rates are then used by sample_css_network() to generate null distributions for hypothesis testing.

accuracy <- tie_level_accuracy(graph)
acc_mat <- as.matrix(accuracy[, c("p_0_ego", "p_1_ego", "p_0_alter", "p_1_alter")])

boxplot(
  acc_mat,
  names = c("TN (Ego)", "TP (Ego)", "TN (Alter)", "TP (Alter)"),
  ylab = "Probability",
  main = "Individual-Level Accuracy Rates",
  col = c("#3498db", "#2980b9", "#e74c3c", "#c0392b"),
  border = "gray30"
)

Null Model Testing

Using the individual accuracy rates, sample_css_network() generates synthetic CSS data that preserves each perceiver’s overall error rates but randomises which dyads are misperceived. Repeating this many times yields a null distribution for any network statistic.

set.seed(123)
n_samples <- 100

null_densities <- replicate(n_samples, {
  nets <- sample_css_network(graph, keep_baseline = FALSE)
  sum(nets[[1]]) / (4 * 3)
})

sampled <- sample_css_network(graph, keep_baseline = TRUE)
observed_density <- sum(sampled[[2]]) / (4 * 3)

hist(
  null_densities,
  breaks = 15,
  col = "steelblue",
  border = "white",
  main = "Null Distribution of Network Density",
  xlab = "Density"
)
abline(v = observed_density, col = "red", lwd = 2, lty = 2)
legend("topright",
  legend = paste("Observed =", round(observed_density, 3)),
  col = "red", lty = 2, lwd = 2, bty = "n"
)

Key Takeaways

• Reciprocity errors quantify how people misperceive mutual relationships.
• The imaginary census provides a fine-grained, 10-category taxonomy of perceptual errors.
• Individual accuracy rates separate ego-involved from alter-only dyads and true positives from true negatives.
• Null models based on these rates let us test whether observed motif counts are more extreme than expected by chance.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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