# 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 ```r stepcAIC( object, 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", ... ) ``` ## Arguments - `object`: object returned by `[lme4]{lmer}`, `[lme4]{glmer}` or `[gamm4]{gamm4}` - `numberOfSavedModels`: 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). - `groupCandidates`: 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")`. - `slopeCandidates`: character vector containing names of possible new random effects - `fixEfCandidates`: character vector containing names of possible (non-)linear fixed effects in the GAMM; NULL for the (g)lmer-use case - `numberOfPermissibleSlopes`: how much slopes are permissible for one grouping variable - `allowUseAcross`: allow slopes to be used in other grouping variables - `allowCorrelationSel`: logical; FALSE does not allow correlations of random effects to be (de-)selected (default) - `allowNoIntercept`: logical; FALSE does not allow random effects without random intercept - `direction`: character vector indicating the direction ("both","backward","forward") - `trace`: logical; should information be printed during the execution of stepcAIC? - `steps`: maximum number of steps to be considered - `keep`: 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 - `numCores`: the number of cores to be used in calculations; parallelization is done by using `parallel::mclapply` - `data`: data.frame supplying the data used in `object`. `data` must also include variables, which are considered for forward updates. - `returnResult`: logical; whether to return the result (best model and corresponding cAIC) - `calcNonOptimMod`: logical; if FALSE, models which failed to converge are not considered for cAIC calculation - `bsType`: type of splines to be used in forward gamm4 steps - `digits`: number of digits used in printing the results - `printValues`: what values of `c("cll", "df", "caic", "refit")` to print in the table of comparisons - `...`: further options for cAIC call ## Returns 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 ## Details 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)`. ## Examples ```r (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", data=Pastes,trace=TRUE) ## 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) ``` ## Author(s) David Ruegamer

stepcAIC function