stepcAIC {cAIC4}R Documentation

Function to stepwise select the (generalized) linear mixed model fitted via (g)lmer() or (generalized) additive (mixed) model fitted via gamm4() with the smallest cAIC.


The step function searches the space of possible models in a greedy manner, where the direction of the search is specified by the argument direction. If direction = "forward" / = "backward", the function adds / exludes random effects until the cAIC can't be improved further. In the case of forward-selection, either a new grouping structure, new slopes for the random effects or new covariates modeled nonparameterically must be supplied to the function call. If direction = "both", the greedy search is alternating between forward and backward steps, where the direction is changed after each step


  numberOfSavedModels = 1,
  groupCandidates = NULL,
  slopeCandidates = NULL,
  fixEfCandidates = NULL,
  numberOfPermissibleSlopes = 2,
  allowUseAcross = FALSE,
  allowCorrelationSel = FALSE,
  allowNoIntercept = FALSE,
  direction = "backward",
  trace = FALSE,
  steps = 50,
  keep = NULL,
  numCores = 1,
  data = NULL,
  returnResult = TRUE,
  calcNonOptimMod = TRUE,
  bsType = "tp",
  digits = 2,
  printValues = "caic",



object returned by [lme4]{lmer}, [lme4]{glmer} or [gamm4]{gamm4}


integer defining how many additional models to be saved during the step procedure. If 1 (DEFAULT), only the best model is returned. Any number k greater 1 will return the k best models. If 0, all models will be returned (not recommended for larger applications).


character vector containing names of possible grouping variables for new random effects. Group nesting must be specified manually, i.e. by listing up the string of the groups in the manner of lme4. For example groupCandidates = c("a", "b", "a/b").


character vector containing names of possible new random effects


character vector containing names of possible (non-)linear fixed effects in the GAMM; NULL for the (g)lmer-use case


how much slopes are permissible for one grouping variable


allow slopes to be used in other grouping variables


logical; FALSE does not allow correlations of random effects to be (de-)selected (default)


logical; FALSE does not allow random effects without random intercept


character vector indicating the direction ("both","backward","forward")


logical; should information be printed during the execution of stepcAIC?


maximum number of steps to be considered


list($fixed,$random) of formulae; which splines / fixed (fixed) or random effects (random) to be kept during selection; specified terms must be included in the original model


the number of cores to be used in calculations; parallelization is done by using parallel::mclapply


data.frame supplying the data used in object. data must also include variables, which are considered for forward updates.


logical; whether to return the result (best model and corresponding cAIC)


logical; if FALSE, models which failed to converge are not considered for cAIC calculation


type of splines to be used in forward gamm4 steps


number of digits used in printing the results


what values of c("cll", "df", "caic", "refit") to print in the table of comparisons


further options for cAIC call


if returnResult is TRUE, a list with the best model finalModel, additionalModels if numberOfSavedModels was specified and the corresponding cAIC bestCAIC is returned.

Note that if trace is set to FALSE and returnResult is also FALSE, the function call may not be meaningful


Note that the method can not handle mixed models with uncorrelated random effects and does NOT reduce models to such, i.e., the model with (1 + s | g) is either reduced to (1 | g) or (0 + s | g) but not to (1 + s || g).


David Ruegamer


(fm3 <- lmer(strength ~ 1 + (1|sample) + (1|batch), Pastes))

fm3_step <- stepcAIC(fm3, direction = "backward", trace = TRUE, data = Pastes)

fm3_min <- lm(strength ~ 1, data=Pastes)

fm3_min_step <- stepcAIC(fm3_min, groupCandidates = c("batch", "sample"), 
direction="forward", data=Pastes, trace=TRUE)
fm3_min_step <- stepcAIC(fm3_min, groupCandidates = c("batch", "sample"), 
direction="both", data=Pastes, trace=TRUE)
# try using a nested group effect which is actually not nested -> warning
fm3_min_step <- stepcAIC(fm3_min, groupCandidates = c("batch", "sample", "batch/sample"), 
                         direction="both", data=Pastes, trace=TRUE)

Pastes$time <- 1:dim(Pastes)[1]
fm3_slope <- lmer(data=Pastes, strength ~ 1 + (1 + time | cask))

fm3_slope_step <- stepcAIC(fm3_slope,direction="backward", trace=TRUE, data=Pastes)

fm3_min <- lm(strength ~ 1, data=Pastes)

fm3_min_step <- stepcAIC(fm3_min,groupCandidates=c("batch","sample"),
direction="forward", data=Pastes,trace=TRUE)

fm3_inta <- lmer(strength ~ 1 + (1|sample:batch), data=Pastes)

fm3_inta_step <- stepcAIC(fm3_inta,groupCandidates=c("batch","sample"),
direction="forward", data=Pastes,trace=TRUE)

fm3_min_step2 <- stepcAIC(fm3_min,groupCandidates=c("cask","batch","sample"),
direction="forward", data=Pastes,trace=TRUE)

fm3_min_step3 <- stepcAIC(fm3_min,groupCandidates=c("cask","batch","sample"),
direction="both", data=Pastes,trace=TRUE)

## Not run: 
fm3_inta_step2 <- stepcAIC(fm3_inta,direction="backward", 

## End(Not run)

##### create own example

na <- 20
nb <- 25
n <- 400
a <- sample(1:na,400,replace=TRUE)
b <- factor(sample(1:nb,400,replace=TRUE))
x <- runif(n)
y <- 2 + 3 * x + a*.02 + rnorm(n) * .4
a <- factor(a)
c <- interaction(a,b)
y <- y + as.numeric(as.character(c))*5
df <- data.frame(y=y,x=x,a=a,b=b,c=c)

smallMod <- lm(y ~ x)

## Not run: 
# throw error
stepcAIC(smallMod, groupCandidates=c("a","b","c"), data=df, trace=TRUE, returnResult=FALSE)

smallMod <- lm(y ~ x, data=df)

# throw error
stepcAIC(smallMod, groupCandidates=c("a","b","c"), data=df, trace=TRUE, returnResult=FALSE)

# get it all right
mod <- stepcAIC(smallMod, groupCandidates=c("a","b","c"), 
                data=df, trace=TRUE, 
                direction="forward", returnResult=TRUE)

# make some more steps...
stepcAIC(smallMod, groupCandidates=c("a","b","c"), data=df, trace=TRUE, 
         direction="both", returnResult=FALSE)

mod1 <- lmer(y ~ x + (1|a), data=df)

stepcAIC(mod1, groupCandidates=c("b","c"), data=df, trace=TRUE, direction="forward")
stepcAIC(mod1, groupCandidates=c("b","c"), data=df, trace=TRUE, direction="both")

mod2 <- lmer(y ~ x + (1|a) + (1|c), data=df)

stepcAIC(mod2, data=df, trace=TRUE, direction="backward")

mod3 <- lmer(y ~ x + (1|a) + (1|a:b), data=df)

stepcAIC(mod3, data=df, trace=TRUE, direction="backward")

## End(Not run)

[Package cAIC4 version 1.0 Index]