coinflibs: Conditional Inference after Likelihood-based Selection

This is a wrapper and convenience function for several functions included in this package. Please see calculate_selinf for more details and how to calculate inference when several model selection procedures are combined. When more than one list is supplied, the best model in the first listOfModels is used to perform inference.

1 2	selinf(listOfModels, ..., response = NULL, what, REML = FALSE, df = 1, sd, alpha = 0.05, gridpts = 500, griddepth = 3, range = 100)

`listOfModels`	a `list` of models representing one comparison
`...`	optionally more `list`s of models representing further comparisons
`response`	response vector
`what`	`character` describing the method, on the basis of which variable selection was performed. Supported variable selection procedures are AIC (`"aic"`), BIC (`"bic"`), likelihood-based selection (`"llonly"`) and significance tests based on the likelihood-ratio or the F-statistic (`"lrt"`, `"Ftest"`). If different selection procedures have been used, please supply the corresponding character for each list of models.
`REML`	`logical`; whether scale estimates should be calculated via `REML` or not. Default is `FALSE` since the log-likelihood is calculated with `REML=FALSE` by the `logLik` function.
`df`	positive integer; defines the degree of freedom when using the likelihood ratio test for model selection. Defaults to `1` (testing one parameter at a time).
`sd`	standard deviation of error used for the p-value calculation (see details)
`alpha`	value for `(1-alpha)`-confidence interval construction. Defaults to `0.05`.
`gridpts, griddepth, range`	options for the calculation of confidence intervals. See `ci_tnorm` for more details.

library(MASS)
data("cpus")
# Fit initial model
cpus$perf <- log10(cpus$perf)
cpus$cach <- as.factor(cpus$cach)
mod <- lm(perf ~ .-name, data = cpus)

# use the stepAIC function to find the best model in a backward 
# stepwise search
cpus.lm <- stepAIC(mod, trace = FALSE, direction = "backward", steps = 3)
# check model selection
cpus.lm$anova$Step

# recalculate all visited models in the first step
lom1 <- c(lapply(attr(mod$terms, "term.labels"), function(x) 
update(mod, as.formula(paste0("perf ~ .-", x)))), list(mod))

# perform likelihood ratio test at level 
alpha = 0.001

# check for non-significant variables
coefTable <- anova(cpus.lm)
drop <- rownames(coefTable)[alpha < coefTable[-nrow(coefTable),5]]

# drop non-significant variable
cpus.lm2 <- update(cpus.lm, as.formula(paste0(".~.-",drop)))

# compute selective inference
selinf(list(cpus.lm, cpus.lm2), lom1, 
response = cpus$perf,
what = c("Ftest", "aic"),
sd = summary(cpus.lm2)$sigma)