datana (version 1.0.9)

lrt: Performs a likelihood ratio test between two models being fitted by maximum likelihood.

Description

Function to perform a likelihood ratio test (LRT) between a reduced model (modA) versus a more complex model (modB), provided both models were fitted by maximum likelihood. The function requires to be filled with the needed values used to perform a LRT.

Usage

lrt(
  llma = llma,
  llmb = llmb,
  qa = qa,
  qb = qb,
  nfit = nfit,
  modA = "modA",
  modB = "modB",
  alpha = 0.05
)

Value

This function wraps two outputs: (i) a table that computes the AIC, BIC and AICc goodness-of-fit statistics for both models, and (ii) the result of the likelihood ratio test, such as the value of the statistic being computed, its respective p-value, and the tabulated value of the statistics using the a defined alpha significance of level.

Arguments

llma

maximized log-likelihood of the reduced model (or modA).

llmb

maximized log-likelihood of the more-complex model (or modB).

qa

the number of parameters of the reduced model.

qb

the number of parameters of the more-complex model.

nfit

the sample size used for fitted both models.

modA

is a character with a name to be assigned to object modA.

modB

is a character with a name to be assigned to object modB.

alpha

is the level of sifnificance to used for computing as a reference only, the tabulated value of the respective Chi-Squared statistic. By the defaul is set to 0.05.

Author

Christian Salas-Eljatib.

Details

The resulting output offers statistical inference estimates of the LRT, as well as other maximum likelihood-based statistics. Notice that the function only works if the number of parameters for modA is lower than the ones of modB.

References

Salas-Eljatib, C. 2025. Estadística Aplicada e Inferencial. Borrador de libro, Universidad de Chile, Santiago, Chile. https://eljatib.com/rlibro

Examples

#Maximized values for two probability mass functions
max.ll.pois<- -39.86337; max.ll.bneg<--33.823003
c(max.ll.pois,max.ll.bneg)
sample.size<-26
#Number of parameters
num.para.pois<- 1; num.para.bneg<- 3
c(num.para.pois, num.para.bneg)
#Names to be used for each model
 modA="Poisson"; modB="hiper"
outall<-lrt(llma=max.ll.pois,llmb=max.ll.bneg,qa=num.para.pois,
qb=num.para.bneg,nfit = sample.size,modA = "Poisson",
modB = "Hipergeometrico")
#Output1: A comparative table 
tab.out<-outall$tab.models
tab.out
#Output2: the results of the LRT
out<-outall$lrt.out
out$r.tab
out$Ldif