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Analyze Orbits for Leunbach Model

Source: R/orbits.R
analyze_orbits.Rd

Performs orbit analysis for the Leunbach model. For each total score (orbit), computes the expected distribution of (Test1, Test2) score pairs and cumulative probabilities for assessing person fit.

Usage

analyze_orbits(fit, alpha = 0.05, verbose = FALSE)

Arguments

fit

A leunbach_ipf object from leunbach_ipf()

alpha

Significance level for critical values (default 0.05)

verbose

Print detailed output

Value

A list of class "leunbach_orbits" containing:

  • orbits: Matrix of expected percentages within each total score

  • left_right: Cumulative probabilities P(X ≤ x | S = s)

  • right_left: Cumulative probabilities P(X ≥ x | S = s)

  • crit_left: Critical values for left tail by total score

  • crit_right: Critical values for right tail by total score

  • crit_values: Combined critical values (two-tailed)

  • expected_critical: Expected number of persons with significant differences

  • variance_expected: Variance of expected critical count

  • n_significant: Number of observed persons with significant differences

  • orbit_df: Degrees of freedom for each orbit

Details

For each total score S = X + Y, the orbit consists of all valid (X, Y) pairs. The expected probability of each cell within an orbit is: P(X = x | S = s) = (gamma_x * delta_y) / sigma_s

Cumulative probabilities are computed in both directions:

  • Left-to-right: P(X ≤ x | S = s) - tests if Test1 score is unusually low

  • Right-to-left: P(X ≥ x | S = s) - tests if Test1 score is unusually high