goodnessfit: Goodness of Fit results for Latent Budget Analysis

In ivanalaman/lba: Latent Budget Analysis for Compositional Data

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
## Default S3 method:
goodnessfit(object, ...)

## S3 method for class 'lba.ls'
goodnessfit(object, ...)
    
## S3 method for class 'lba.ls.fe'
goodnessfit(object, ...)    
    
## S3 method for class 'lba.ls.logit'
goodnessfit(object, ...)
    
## S3 method for class 'lba.mle'
goodnessfit(object, ...)    

## S3 method for class 'lba.mle.fe'
goodnessfit(object, ...)    
 
## S3 method for class 'lba.mle.logit'
goodnessfit(object, ...) 

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).

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

Note

For a detailed and complete discussion about goodness of fit results for latent budget analysis, see van der Ark 1999.

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.

See Also

summary.goodnessfit.lba.ls, summary.goodnessfit.lba.mle,lba

Examples

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)
## Not run: 
ex2 <- lba(tabs,
           K = 2,
           logitA = Xis,
           logitB = Yis,
           S = S,
           T = T,
           trace.lba=FALSE) 

gex2 <- goodnessfit(ex2)
gex2

## End(Not run)

ivanalaman/lba documentation built on Sept. 9, 2023, 11:31 a.m.