gofglca: Goodness of Fit Tests for Fitted `glca` Model

Description

Provides AIC, 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".

Usage

gofglca(
  object,
  ...,
  test = NULL,
  nboot = 50,
  criteria = c("AIC", "BIC", "entropy"),
  maxiter = 500,
  eps = 1e-04,
  seed = NULL,
  verbose = FALSE
)

Value

gtable: a matrix with model goodneess-of-fit criteria
dtable: a matrix with deviance statistic and bootstrap p-value
boot: 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..

Arguments

object: an object of "glca", usually, a result of a call to glca.
...: an optional object of "glca" to be compared with object.
test: 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").
nboot: number of bootstrap samples, only used when test = "boot".
criteria: a character vector indicating criteria to be printed.
maxiter: an integer for maximum number of iteration for bootstrap sample.
eps: positive convergence tolerance for bootstrap sample.
seed: As the same value for seed guarantees the same datasets to be generated, this argument can be used for reproducibility of bootstrap results.
verbose: an logical value for whether or not to print the result of a function's execution.

References

Akaike, H. (1974) A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716–723. tools:::Rd_expr_doi("10.1109/tac.1974.1100705")

Schwarz, G. (1978) Estimating the dimensions of a model. The Annals of Statistics, 6, 461–464. tools:::Rd_expr_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. tools:::Rd_expr_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. tools:::Rd_expr_doi("10.1287/mksc.12.1.103")

Examples

Run this code

## 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)
class3 = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1,
              data = gss08, nclass = 3,  n.init = 1)
class4 = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1,
              data = gss08, nclass = 4,  n.init = 1)

gofglca(class2, class3, class4)
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)
cluster3 = glca(item(ECIGT, ECIGAR, ESLT, EELCIGT, EHOOKAH) ~ 1,
                group = SCH_ID, data = nyts18, nclass = 2, ncluster = 3, n.init = 1)

gofglca(cluster2, cluster3)
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)
measVar = glca(item(DEFECT, HLTH, RAPE, POOR, SINGLE, NOMORE) ~ 1,
               group = DEGREE, data = gss08, nclass = 3, n.init = 1, measure.inv = FALSE)

gofglca(measInv, measVar)