Provides AIC, CAIC, BIC, entropy and deviance statitistic for goodness of fit test for the fitted model. Given object2, the function computes the log-likelihood ratio (LRT) statisic for comparing the goodness of fit for two models. The bootstrap p-value can be obtained from the empirical distribution of LRT statistic by choosing test = "boot".
gofglca(
object,
...,
test = NULL,
nboot = 50,
criteria = c("logLik", "AIC", "CAIC", "BIC", "entropy"),
maxiter = 500,
eps = 1e-04,
seed = NULL,
verbose = FALSE
)an object of "glca", usually, a result of a call to glca.
an optional object of "glca" to be compared with object.
a character string indicating type of test (chi-square test or bootstrap) to obtain the p-value for goodness of fit test ("chisq" or "boot").
number of bootstrap samples, only used when test = "boot".
a character vector indicating criteria to be printed.
an integer for maximum number of iteration for bootstrap sample.
positive convergence tolerance for bootstrap sample.
As the same value for seed guarantees the same datasets to be generated, this argument can be used for reproducibility of bootstrap results.
an logical value for whether or not to print the result of a function's execution.
a matrix with model goodneess-of-fit criteria
a matrix with deviance statistic and bootstrap p-value
a list of LRT statistics from each bootstrap sample
gtable, which is always included in output of this function, includes goodness-of-fit criteria which are indicated criteria arguments for the object(s). dtable are contained when the objects are competing models. (when used items of the models are identical) dtable prints deviance and p-value. (bootstrap or chi-square) Lastly, when the boostrap sample is used, the G^2-statistics for each bootstrap samples will be included in return object..
Akaike, H. (1974) A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716–723. doi:10.1109/tac.1974.1100705
Schwarz, G. (1978) Estimating the dimensions of a model. The Annals of Statistics, 6, 461–464. doi:10.1214/aos/1176344136
Langeheine, R., Pannekoek, J., and van de Pol, F. (1996) Bootstrapping goodness-of-fit measures in categorical data analysis. Sociological Methods and Research. 24. 492-516. doi:10.1177/0049124196024004004
Ramaswamy, V., Desarbo, W., Reibstein, D., & Robinson, W. (1993). An Empirical Pooling Approach for Estimating Marketing Mix Elasticities with PIMS Data. Marketing Science, 12(1), 103-124. doi:10.1287/mksc.12.1.103
## Example 1.
## Model selection between two LCA models with different number of latent classes.
data(gss08)
class2 = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1,
data = gss08, nclass = 2, n.init = 1)
#> Manifest items :
#> DEFECT HLTH RAPE POOR SINGLE NOMORE
#>
#> Deleted observation(s) :
#> 3 observation(s) for missing all manifest items
#> 0 observation(s) for missing at least 1 covariates
#>
#> Latent class analysis Fitting...
#>
#> 38 iteration
#>
#> Converged at 38 iteration (loglik :-740.1018)
class3 = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1,
data = gss08, nclass = 3, n.init = 1)
#> Manifest items :
#> DEFECT HLTH RAPE POOR SINGLE NOMORE
#>
#> Deleted observation(s) :
#> 3 observation(s) for missing all manifest items
#> 0 observation(s) for missing at least 1 covariates
#>
#> Latent class analysis Fitting...
#>
#> 48 iteration
#>
#> Converged at 48 iteration (loglik :-687.4486)
class4 = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1,
data = gss08, nclass = 4, n.init = 1)
#> Manifest items :
#> DEFECT HLTH RAPE POOR SINGLE NOMORE
#>
#> Deleted observation(s) :
#> 3 observation(s) for missing all manifest items
#> 0 observation(s) for missing at least 1 covariates
#>
#> Latent class analysis Fitting...
#>
#> .. 259 iteration
#>
#> Converged at 259 iteration (loglik :-684.7354)
gofglca(class2, class3, class4)
#> Model 1: item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1
#> nclass: 2
#> Model 2: item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1
#> nclass: 3
#> Model 3: item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1
#> nclass: 4
#>
#> Goodness of Fit Table :
#> loglik AIC BIC entropy df Gsq
#> 1 -740.10 1506.20 1556.43 0.95 50 135.13
#> 2 -687.45 1414.90 1492.17 0.88 43 29.83
#> 3 -684.74 1423.47 1527.79 0.87 36 24.40
#>
#> Analysis of Deviance Table :
#> npar loglik Df Deviance
#> 1 13 -740.10
#> 2 20 -687.45 7 105.31
#> 3 27 -684.74 7 5.43
if (FALSE) gofglca(class2, class3, class4, test = "boot")
## Example 2.
## Model selection between two MLCA models with different number of latent clusters.
cluster2 = glca(item(ECIGT, ECIGAR, ESLT, EELCIGT, EHOOKAH) ~ 1,
group = SCH_ID, data = nyts18, nclass = 2, ncluster = 2, n.init = 1)
#> Manifest items :
#> ECIGT ECIGAR ESLT EELCIGT EHOOKAH
#> Grouping variable : SCH_ID
#>
#> Deleted observation(s) :
#> 0 observation(s) for missing all manifest items
#> 0 observation(s) for missing at least 1 covariates
#>
#> Nonparametric multilevel latent class analysis Fitting...
#>
#> 30 iteration
#>
#> Converged at 30 iteration (loglik :-2017.808)
cluster3 = glca(item(ECIGT, ECIGAR, ESLT, EELCIGT, EHOOKAH) ~ 1,
group = SCH_ID, data = nyts18, nclass = 2, ncluster = 3, n.init = 1)
#> Manifest items :
#> ECIGT ECIGAR ESLT EELCIGT EHOOKAH
#> Grouping variable : SCH_ID
#>
#> Deleted observation(s) :
#> 0 observation(s) for missing all manifest items
#> 0 observation(s) for missing at least 1 covariates
#>
#> Nonparametric multilevel latent class analysis Fitting...
#>
#> 77 iteration
#>
#> Converged at 77 iteration (loglik :-2008.164)
gofglca(cluster2, cluster3)
#> Model 1: item(ECIGT, ECIGAR, ESLT, EELCIGT, EHOOKAH) ~ 1
#> Group: SCH_ID, nclass: 2, ncluster: 2
#> Model 2: item(ECIGT, ECIGAR, ESLT, EELCIGT, EHOOKAH) ~ 1
#> Group: SCH_ID, nclass: 2, ncluster: 3
#>
#> Goodness of Fit Table :
#> loglik AIC BIC entropy df Gsq
#> 1 -2017.81 4061.62 4132.57 0.91 1426 893.15
#> 2 -2008.16 4046.33 4128.20 0.90 1424 873.86
#>
#> Analysis of Deviance Table :
#> npar loglik Df Deviance
#> 1 13 -2017.81
#> 2 15 -2008.16 2 19.29
if (FALSE) gofglca(cluster2, cluster3, test = "boot")
## Example 3.
## MGLCA model selection under the measurement (invariance) assumption across groups.
measInv = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1,
group = DEGREE, data = gss08, nclass = 3, n.init = 1)
#> Manifest items :
#> DEFECT HLTH RAPE POOR SINGLE NOMORE
#> Grouping variable : DEGREE
#>
#> Deleted observation(s) :
#> 3 observation(s) for missing all manifest items
#> 0 observation(s) for missing at least 1 covariates
#>
#> Multiple-group latent class analysis Fitting...
#>
#> .. 261 iteration
#>
#> Converged at 261 iteration (loglik :-672.4138)
measVar = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1,
group = DEGREE, data = gss08, nclass = 3, n.init = 1, measure.inv = FALSE)
#> Manifest items :
#> DEFECT HLTH RAPE POOR SINGLE NOMORE
#> Grouping variable : DEGREE
#>
#> Deleted observation(s) :
#> 3 observation(s) for missing all manifest items
#> 0 observation(s) for missing at least 1 covariates
#>
#> Multiple-group latent class analysis Fitting...
#>
#> .. 291 iteration
#>
#> Converged at 291 iteration (loglik :-666.3987)
gofglca(measInv, measVar)
#> Model 1: item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1
#> Group: DEGREE, nclass: 3, measure.inv: TRUE
#> Model 2: item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1
#> Group: DEGREE, nclass: 3, measure.inv: FALSE
#>
#> Goodness of Fit Table :
#> loglik AIC BIC entropy df Gsq
#> 1 -672.41 1396.83 1497.28 0.88 229 87.85
#> 2 -666.40 1492.80 1801.89 0.88 175 75.82
#>
#> Analysis of Deviance Table :
#> npar loglik Df Deviance
#> 1 26 -672.41
#> 2 80 -666.40 54 12.03