qpcR (version 1.4-1)

mselect: Sigmoidal model selection by different criteria

Description

Model selection by comparison of different models using

1) the maximum log likelihood value, 2) Akaike's Information Criterion (AIC), 3) bias-corrected Akaike's Information Criterion (AICc), 4) the estimated residual variance, 5) the p-value from a nested F-test on the residual variance, 6) the p-value from the likelihood ratio, 7) the Akaike weights based on AIC, 8) the Akaike weights based on AICc, and 9) the reduced chi-square, \(\chi_\nu^2\), if replicates exist.

The best model is chosen by 5), 6), 8) or 9) and returned as a new model.

Usage

mselect(object, fctList = NULL, sig.level = 0.05, verbose = TRUE, 
        crit = c("ftest", "ratio", "weights", "chisq"), do.all = FALSE, ...)

Arguments

object

an object of class 'pcrfit' or 'replist'.

fctList

a list of functions to be analyzed, i.e. for a non-nested regime. Should also contain the original model.

sig.level

the significance level for the nested F-test.

verbose

logical. If TRUE, the result matrix is displayed in the console.

crit

the criterium for model selection. Either "ftest"/"ratio" for nested models or "weights"/"fitprob" for nested and non-nested models.

do.all

if TRUE, all available sigmoidal models are tested and the best one is selected based on AICc weights.

...

other parameters to be passed to fitchisq.

Value

A model of the best fit selected by one of the criteria above. The new model has an additional list item 'retMat' with a result matrix of the criterion tests.

Details

Criteria 5) and 6) cannot be used for comparison unless the models are nested. Criterion 8), Akaike weights, can be used for nested and non-nested regimes, which also accounts for the reduced \(\chi_\nu^2\). For criterion 1) the larger the better. For criteria 2), 3) and 4): the smaller the better. The best model is chosen either from the nested F-test (anova), likelihood ratio (llratio), corrected Akaike weights (akaike.weights) or reduced \(\chi_\nu^2\) (fitchisq) and returned as a new model. When using "ftest"/"ratio" the corresponding nested functions are analyzed automatically, i.e. b3/b4/b5/b6/b7; l3/l4/l5/l6/l7. If supplying nested models, please do this with ascending number of parameters.

See Also

llratio, akaike.weights and fitchisq.

Examples

# NOT RUN {
## Choose best model based on F-tests 
## on the corresponding nested models.
m1 <- pcrfit(reps, 1, 2, l4)
m2 <- mselect(m1)
summary(m2)  ## Converted to l7 model!

## Use Akaike weights on non-nested models
## compare to original model.
m2 <- mselect(m1, fctList = list(l4, b5, cm3), crit = "weights")
summary(m2) ## Converted to b5 model!

## Try all sigmoidal models.
m3 <- pcrfit(reps, 1, 20, l4)
mselect(m3, do.all = TRUE) ## l7 wins by far!

## On replicated data using reduced chi-square.
ml1 <- modlist(reps, fluo = 2:5, model = l4)
rl1 <- replist(ml1, group = c(1, 1, 1, 1))
mselect(rl1, crit = "chisq")  ## converted to l6!
# }