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Summary Statistics for rho Distribution

Source: R/09_weights_rho.R
summary_rho.Rd

Computes comprehensive summary statistics for the co-clustering probability rho under the hierarchical prior alpha ~ Gamma(a, b).

Usage

summary_rho(a, b, M = .QUAD_NODES_DEFAULT)

Arguments

a

Numeric; shape parameter of the Gamma prior on alpha (a > 0).

b

Numeric; rate parameter of the Gamma prior on alpha (b > 0).

M

Integer; number of quadrature nodes. Default is 80.

Value

A list of class "rho_summary" containing:

mean

E(rho | a, b)

var

Var(rho | a, b)

sd

SD(rho | a, b) = sqrt(Var)

cv

Coefficient of variation SD/mean

interpretation

Qualitative interpretation of co-clustering level

params

List of input parameters (a, b)

alpha_prior

Summary of the alpha prior (mean, sd, cv)

conditional_at_alpha_mean

Conditional moments evaluated at E(alpha)

Details

The co-clustering probability rho indicates how likely two randomly chosen observations are to belong to the same cluster a priori.

Interpretation guidelines:

  • E(rho) > 0.5: High co-clustering; most pairs expected in same cluster

  • E(rho) in (0.2, 0.5): Moderate co-clustering

  • E(rho) < 0.2: Low co-clustering; fragmented prior

The conditional_at_alpha_mean component provides a "plug-in" estimate for comparison: what the moments would be if alpha were fixed at its prior mean.

See also

mean_rho, var_rho, summary_w1

Examples

summary_rho(a = 2, b = 1)
#> Co-Clustering Probability (rho) Summary
#> ================================================== 
#> 
#> Gamma prior: alpha ~ Gamma(2.0000, 1.0000)
#> E[alpha] = 2.0000, SD(alpha) = 1.4142, CV(alpha) = 70.7%
#> 
#> Marginal distribution of rho:
#> ----------------------------------- 
#>   Mean:   0.4037
#>   SD:     0.2397
#>   CV:     59.4%
#> 
#> Conditional at E[alpha] = 2.0000 (plug-in):
#> ----------------------------------- 
#>   E[rho | E[alpha]]:   0.3333
#>   Var(rho | E[alpha]): 0.0222
#> 
#> Interpretation:
#> ----------------------------------- 
#>   Moderate co-clustering
summary_rho(a = 1.6, b = 1.22)
#> Co-Clustering Probability (rho) Summary
#> ================================================== 
#> 
#> Gamma prior: alpha ~ Gamma(1.6000, 1.2200)
#> E[alpha] = 1.3115, SD(alpha) = 1.0368, CV(alpha) = 79.1%
#> 
#> Marginal distribution of rho:
#> ----------------------------------- 
#>   Mean:   0.5084
#>   SD:     0.2664
#>   CV:     52.4%
#> 
#> Conditional at E[alpha] = 1.3115 (plug-in):
#> ----------------------------------- 
#>   E[rho | E[alpha]]:   0.4326
#>   Var(rho | E[alpha]): 0.0344
#> 
#> Interpretation:
#> ----------------------------------- 
#>   High co-clustering: most pairs expected in same cluster