Compare Log-Linear Models for Mobility Tables

Compares multiple log-linear model fits for a mobility table, producing a summary table with fit statistics and likelihood-ratio tests between nested models.

Usage

compare_mobility_models(..., mx = NULL, level = NULL, include_topology = TRUE)

Arguments

...

One or more moneca_loglinear objects to compare.

mx

Optional. A mobility matrix with margins or a moneca object. If provided, fits all standard models automatically for comparison.

level

Integer specifying the hierarchical level for the MONECA topology model. Used when mx is a moneca object.

include_topology

Logical. Whether to include the MONECA topology model when fitting all models via mx. Default is TRUE. Set to FALSE if mx is a plain matrix without segment information.

Value

An object of class "moneca_model_comparison" containing:

table

Data frame with columns: model, deviance, df, aic, bic, p_value, dissimilarity

lr_tests

Data frame of pairwise likelihood-ratio tests between nested models, with columns: model_1, model_2, delta_deviance, delta_df, p_value

models

Named list of the fitted model objects

Details

When mx is provided, the function fits independence, quasi-independence, quasi-symmetry, and uniform association models automatically. If mx is a moneca object and include_topology = TRUE, a MONECA topology model is also fit.

Likelihood-ratio tests are computed for known nesting relationships:

• Independence is nested in quasi-independence

• Independence is nested in uniform association

• Quasi-independence is nested in quasi-symmetry

• Quasi-independence is nested in MONECA topology

Models passed via ... are combined with any automatically fitted models. Duplicate model types are resolved by keeping the explicitly passed version.

See also

fit_mobility_model for fitting individual models

Examples

mx <- generate_mobility_data(n_classes = 5, seed = 42)
seg <- moneca_fast(mx, segment.levels = 3)
#> 
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#> 
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# Compare all standard models
comp <- compare_mobility_models(mx = seg, level = 2)
print(comp)
#> Log-Linear Model Comparison
#> ===========================
#> 
#>                model deviance df      aic      bic   p_value dissimilarity
#>       quasi_symmetry   12.256  6  225.218  248.377  5.65e-02         0.006
#>      moneca_topology  364.959  9  571.921  591.423  4.05e-73         0.046
#>   quasi_independence 1244.431 11 1447.393 1464.457 4.29e-260         0.077
#>  uniform_association 1432.361 15 1627.323 1639.511 1.80e-296         0.133
#>         independence 9126.035 16 9318.997 9329.967  0.00e+00         0.392
#> 
#> Likelihood-Ratio Tests:
#>             model_1             model_2 delta_deviance delta_df   p_value
#>        independence  quasi_independence       7881.604        5  0.00e+00
#>        independence uniform_association       7693.675        1  0.00e+00
#>  quasi_independence      quasi_symmetry       1232.174        5 3.15e-264
#>  quasi_independence     moneca_topology        879.472        2 1.06e-191

# Compare specific models
m1 <- fit_mobility_model(mx, type = "independence")
m2 <- fit_mobility_model(mx, type = "quasi_independence")
compare_mobility_models(m1, m2)
#> Log-Linear Model Comparison
#> ===========================
#> 
#>               model deviance df      aic      bic   p_value dissimilarity
#>  quasi_independence 1244.431 11 1447.393 1464.457 4.29e-260         0.077
#>        independence 9126.035 16 9318.997 9329.967  0.00e+00         0.392
#> 
#> Likelihood-Ratio Tests:
#>       model_1            model_2 delta_deviance delta_df p_value
#>  independence quasi_independence       7881.604        5       0