goodnessfit: Goodness of Fit results for Latent Budget Analysis

Description

The goodness of fit results assesses how well the model fits the data. It consists of measures of the resemblance between the observed and the expected data, and the parsimony of the model.

Usage

goodnessfit(object,...)
## S3 methods
# S3 method for default
goodnessfit(object, ...)
# S3 method for lba.ls
goodnessfit(object, ...)
    
# S3 method for lba.ls.fe
goodnessfit(object, ...)    
    
# S3 method for lba.ls.logit
goodnessfit(object, ...)
    
# S3 method for lba.mle
goodnessfit(object, ...)    
# S3 method for lba.mle.fe
goodnessfit(object, ...)    
 
# S3 method for lba.mle.logit
goodnessfit(object, ...)

Value

The goodnessfit function of the method lba.mle, lba.mle.fe and lba.mle.logit returns a list with the slots:

dfdb: Degrees of freedom of the base model
dfd: Degrees of freedom of the full model
G2b: Likelihood ratio statistic of the base model
G2: Likelihood ratio statistic of the full model
chi2b: Chi-square statistic of the base model
chi2: Chi-square statistic of the full model
proG1: P-value of likelihood ratio statistic of the base model
proG: P-value of likelihood ratio statistic of the full model
prochi1: P-value of chi-square statistic of the base model
prochi: P-value of chi-square statistic of the full model
AICb: AIC criteria of the base model
AICC: AIC criteria of the full model
BICb: BIC criteria of the base model
BICC: BIC criteria of the full model
CAICb: CAIC criteria of the base model
CAIC: CAIC criteria of the full model
delta1: Normed fit index
delta2: Normed fit index modified
rho1: Bollen index
rho2: Tucker-Lewis index
RSS1: Residual sum of square of the base model
RSS: Residual sum of square of the full model
impRSS: Improvement of RSS
impPB: Improvement per budget
impDF: Average improvement per degree of freedom
D1: Index of dissimilarity of the base model
D: Index of dissimilarity of the full model
pccb: Proportion of correctly classified data of the base model
pcc: Proportion of correctly classified data of the full model
impD: Improvement of proportion of correctly classified data
impPCCB: Improvement of Proportion of correctly classified data per budget
AimpPCCDF: Average improvement of Proportion of correctly classified data per degree of freedom
mad1: Mean angular deviation of the base model
madk: Mean angular deviation of the full model
impMad: Improvement mean angular deviation
impPBsat: Improvement mean angular deviation per budget
impDFsat: Average improvement mean angular deviation per degree of freedom

The goodnessfit function of the method lba.ls, lba.ls.fe and lba.ls.logit returns a list with the slots:

dfdb: Degrees of freedom of the base model
dfd: Degrees of freedom of the full model
RSS1: Residual sum of square of the base model
RSS: Residual sum of square of the full model
impRSS: Improvement of RSS
impPB: Improvement per budget
impDF: Average improvement per degree of freedom
D1: Index of dissimilarity of the base model
D: Index of dissimilarity of the full model
pccb: Proportion of correctly classified data of the base model
pcc: Proportion of correctly classified data of the full model
impD: Improvement of proportion of correctly classified data
impPCCB: Improvement of Proportion of correctly classified data per budget
AimpPCCDF: Average improvement of Proportion of correctly classified data per degree of freedom
mad1: Mean angular deviation of the base model
madk: Mean angular deviation of the full model
impMad: Improvement mean angular deviation
impPBsat: Improvement mean angular deviation per budget
impDFsat: Average improvement mean angular deviation per degree of freedom

Arguments

object: An object of one of following classes: lba.ls, lba.ls.fe, lba.ls.logit, lba.mle, lba.mle.fe, lba.mle.logit
...: Further arguments (required by generic).

References

Agresti, Alan. 2002. Categorical Data Analysis, second edition. Hoboken: John Wiley and Sons.

van der Ark, A. L. 1999. Contributions to Latent Budget Analysis, a tool for the analysis of compositional data. Ph.D. Thesis University of Utrecht.

Examples

Run this code

data('votB')

# Using LS method (default) without constraint
# K = 2
ex1 <- lba(parties ~ city,
           votB,
           K = 2)

gx1 <- goodnessfit(ex1)
gx1

# Using MLE method without constraint
# K = 2
exm <- lba(parties ~ city,
           votB,
           K = 2,
           method='mle')

gxm <- goodnessfit(exm)
gxm

# Using LS method (default) with LOGIT constrain
data('housing')

# Make cross-table to matrix design.
tbh <- xtabs(value ~ Influence + Housing, housing)

Xis <- model.matrix(~ Housing*Influence,
                    tbh,
                    contrasts=list(Housing='contr.sum',
                                   Influence='contr.sum'))

tby <- xtabs(value ~ Satisfaction + Contact, housing)

Yis <- model.matrix(~ Satisfaction*Contact,
                    tby,
                    contrasts=list(Satisfaction='contr.sum',
                                   Contact='contr.sum'))[,-1]

S <- 12
T <- 5

tabs <- xtabs(value ~ interaction(Housing,
                                  Influence) + interaction(Satisfaction,
                                  Contact),
              housing)
if (FALSE) {
ex2 <- lba(tabs,
           K = 2,
           logitA = Xis,
           logitB = Yis,
           S = S,
           T = T,
           trace.lba=FALSE) 

gex2 <- goodnessfit(ex2)
gex2
}