Compare Two Fitted slca Models

Conducts a relative model fit test between two fitted SLCM models using the deviance statistic.

Usage

compare(
  model1,
  model2,
  test = c("none", "chisq", "boot"),
  nboot = 50,
  method = c("hybrid", "em", "nlm"),
  plot = FALSE,
  maxiter = 1000,
  tol = 1e-08,
  verbose = FALSE,
  nrep = 3
)

Arguments

model1

an object of class slcafit.

model2

another object of class slcafit to be compared with model1.

test

a character string specifying the type of test to be conducted. If "chisq", a chi-squared test is conducted. If "boot", a bootstrap test is conducted.

nboot

a positive number specifying the number of bootstrap iterations to perform (used only when test = "boot"). Non-integer values are rounded up. The default is 50.

method

a character string specifying the estimation method for bootstrapping.

plot

a logical value indicating whether to display a histogram of G-squared statistics for the bootstrap samples (applicable only for test = "boot"). The default is FALSE.

maxiter

an integer specifying the maximum number of iterations allowed during each bootstrap estimation round. The default is 1000.

tol

numeric value setting the convergence tolerance for each bootstrap iteration. The default is 1e-8.

verbose

a logical value indicating whether to print progress updates on completed bootstrap iterations. The default is FALSE.

nrep

a positive number specifying the number of starting values used for each model in a bootstrap iteration. The fitted-model parameters are used first and additional starting values are generated randomly. The default is 3.

Value

A data.frame containing the number of parameters (Df), loglikelihood, AIC, BIC, G-squared statistics, and the residual degree of freedom for each object. If a statistical test is conducted (via test), the resulting p-value for the comparison is also included. For test = "boot", failed bootstrap replicates are omitted from the p-value calculation and recorded in the bootFail, boot.fail.msgs, and boot.all.msgs attributes.

Bootstrap samples retain the fitted data's missing-value pattern. Nonconverged refits and negative bootstrap likelihood ratios are counted as failures. Hybrid refits must converge in their final nlm stage. With \(B\) successful replicates and \(b\) statistics at least as large as observed, the p-value is \((b + 1)/(B + 1)\). When the observed likelihood ratio is effectively zero, the p-value is one; no bootstrap samples or histogram are generated.

See also

gof

Examples

library(magrittr)
set.seed(20261017)
data <- gss7677[gss7677$COHORT == "YOUNG", ]
stat2 <- slca(status(2) ~ PAPRES + PADEG + MADEG) %>%
   estimate(data = data, control = list(verbose = FALSE))
stat3 <- slca(status(3) ~ PAPRES + PADEG + MADEG) %>%
   estimate(data = data, control = list(verbose = FALSE))
stat4 <- slca(status(4) ~ PAPRES + PADEG + MADEG) %>%
   estimate(data = data, control = list(verbose = FALSE))

gof(stat2, stat3, stat4)
#> Analysis of Goodness of Fit Table
#> 
#>       Df  logLik    AIC    BIC     Gsq Res. Df
#> stat2 21 -1179.2 2400.4 2489.0 115.980      53
#> stat3 32 -1139.3 2342.6 2477.7  36.204      42
#> stat4 43 -1135.4 2356.8 2538.3  28.424      31
gof(stat2, stat3, stat4, test = "chisq")
#> Analysis of Goodness of Fit Table
#> 
#>       Df  logLik    AIC    BIC     Gsq Res. Df Pr(>Chi)    
#> stat2 21 -1179.2 2400.4 2489.0 115.980      53 1.34e-06 ***
#> stat3 32 -1139.3 2342.6 2477.7  36.204      42   0.7225    
#> stat4 43 -1135.4 2356.8 2538.3  28.424      31   0.5992    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# \donttest{
# Five replicates illustrate the interface only; use more for inference.
absolute_boot <- gof(stat2, stat3, stat4, test = "boot",
                     nboot = 5, maxiter = 5000, tol = 1e-6)
absolute_boot
#> Analysis of Goodness of Fit Table
#> 
#>       Df  logLik    AIC    BIC     Gsq Res. Df Pr(Boot)
#> stat2 21 -1179.2 2400.4 2489.0 115.980      53   0.1667
#> stat3 32 -1139.3 2342.6 2477.7  36.204      42   0.1667
#> stat4 43 -1135.4 2356.8 2538.3  28.424      31   0.5000
attr(absolute_boot, "bootFail")
#> stat2 stat3 stat4 
#>     0     0     0 
# }

compare(stat3, stat4)
#> Analysis of Relative Model Fit
#> 
#> Model H0: stat3
#> Model H1: stat4
#>       Df  logLik    AIC    BIC    Gsq Res. Df
#> stat3 32 -1139.3 2342.6 2477.7               
#> stat4 43 -1135.4 2356.8 2538.3 7.7805      11
compare(stat3, stat4, test = "chisq")
#> Analysis of Relative Model Fit
#> 
#> Model H0: stat3
#> Model H1: stat4
#>       Df  logLik    AIC    BIC    Gsq Res. Df Pr(>Chi)
#> stat3 32 -1139.3 2342.6 2477.7                        
#> stat4 43 -1135.4 2356.8 2538.3 7.7805      11   0.7328
# \donttest{
# Use EM refits here; always inspect convergence failures.
relative_boot <- compare(stat3, stat4, test = "boot", method = "em",
                         nboot = 5, maxiter = 5000, tol = 1e-6)
relative_boot
#> Analysis of Relative Model Fit
#> 
#> Model H0: stat3
#> Model H1: stat4
#>       Df  logLik    AIC    BIC    Gsq Res. Df Pr(Boot)
#> stat3 32 -1139.3 2342.6 2477.7                        
#> stat4 43 -1135.4 2356.8 2538.3 7.7805      11      0.5
attr(relative_boot, "bootFail")
#> [1] 0
# }