Cross-Validate Mixed-Effects Model

cv() methods for mixed-effect models of class "merMod", fit by the lmer() and glmer() functions in the lme4 package; for models of class "lme" fit by the lme() function in the nlme package; and for models of class "glmmTMB" fit by the glmmTMB() function in the glmmTMB package.

Usage

# S3 method for class 'merMod'
cv(
  model,
  data = insight::get_data(model),
  criterion = mse,
  k = NULL,
  reps = 1L,
  seed,
  details = NULL,
  ncores = 1L,
  clusterVariables,
  ...
)

# S3 method for class 'lme'
cv(
  model,
  data = insight::get_data(model),
  criterion = mse,
  k = NULL,
  reps = 1L,
  seed,
  details = NULL,
  ncores = 1L,
  clusterVariables,
  ...
)

# S3 method for class 'glmmTMB'
cv(
  model,
  data = insight::get_data(model),
  criterion = mse,
  k = NULL,
  reps = 1L,
  seed,
  details = NULL,
  ncores = 1L,
  clusterVariables,
  ...
)

Arguments

model: a mixed-effects model object for which a cv() method is available.
data: data frame to which the model was fit (not usually necessary).
criterion: cross-validation ("cost" or lack-of-fit) criterion function of form f(y, yhat) where y is the observed values of the response and yhat the predicted values; the default is mse (the mean-squared error).
k: perform k-fold cross-validation; k may be a number or "loo" or "n" for n-fold (leave-one-out) cross-validation; the default is 10 if cross-validating individual cases and "loo" if cross-validating clusters.
reps: number of times to replicate k-fold CV (default is 1), or greater), compute a confidence interval for the bias-corrected CV criterion, if the criterion is the average of casewise components.
seed: for R's random number generator; optional, if not supplied a random seed will be selected and saved; not needed for n-fold cross-validation.
details: if TRUE (the default if the number of folds k <= 10), save detailed information about the value of the CV criterion for the cases in each fold and the regression coefficients with that fold deleted.
ncores: number of cores to use for parallel computations (default is 1, i.e., computations aren't done in parallel).
clusterVariables: a character vector of names of the variables defining clusters for a mixed model with nested or crossed random effects; if missing, cross-validation is performed for individual cases rather than for clusters.
...: for cv() methods, to match generic, and for cvMixed(), arguments to be passed to update().

Value

The methods cv.merMod(), cv.lme(), and cv.glmmTMB(), return objects of class "cv", or, if reps > 1, of class "cvList" (see cv()).

Details

For mixed-effects models, cross-validation can be done by "clusters" or by individual observations. If the former, predictions are based only on fixed effects; if the latter, predictions include the random effects (i.e., are the best linear unbiased predictors or "BLUPS").

Functions

cv(merMod): cv() method for lmer() and glmer() models from the lme4 package.
cv(lme): cv() method for lme() models from the nlme package.
cv(glmmTMB): cv() method for glmmTMB() models from the glmmTMB package.

Examples

library("lme4")
# from ?lmer:
(fm1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy))
#> Linear mixed model fit by REML ['lmerMod']
#> Formula: Reaction ~ Days + (Days | Subject)
#>    Data: sleepstudy
#> REML criterion at convergence: 1743.628
#> Random effects:
#>  Groups   Name        Std.Dev. Corr
#>  Subject  (Intercept) 24.741       
#>           Days         5.922   0.07
#>  Residual             25.592       
#> Number of obs: 180, groups:  Subject, 18
#> Fixed Effects:
#> (Intercept)         Days  
#>      251.41        10.47  
summary(cv(fm1, clusterVariables="Subject")) # LOO CV of clusters
#> n-Fold Cross Validation based on 18 {Subject} clusters
#> criterion: mse
#> cross-validation criterion = 2460.604
#> bias-adjusted cross-validation criterion = 2454.627
#> full-sample criterion = 2251.398
summary(cv(fm1, seed=447)) # 10-fold CV of cases
#> R RNG seed set to 447
#> 10-Fold Cross Validation
#> criterion: mse
#> cross-validation criterion = 869.533
#> bias-adjusted cross-validation criterion = 847.5586
#> full-sample criterion = 549.342
summary(cv(fm1, clusterVariables="Subject", k=5,
   seed=834, reps=3)) # 5-fold CV of clusters, repeated 3 times
#> R RNG seed set to 834
#> R RNG seed set to 448690
#> R RNG seed set to 916534
#> 
#> Replicate 1:
#> 5-Fold Cross Validation based on 18 {Subject} clusters
#> criterion: mse
#> cross-validation criterion = 2458.192
#> bias-adjusted cross-validation criterion = 2434.117
#> full-sample criterion = 2251.398
#> 
#> Replicate 2:
#> 5-Fold Cross Validation based on 18 {Subject} clusters
#> criterion: mse
#> cross-validation criterion = 2511.651
#> bias-adjusted cross-validation criterion = 2479.989
#> full-sample criterion = 2251.398
#> 
#> Replicate 3:
#> 5-Fold Cross Validation based on 18 {Subject} clusters
#> criterion: mse
#> cross-validation criterion = 2403.755
#> bias-adjusted cross-validation criterion = 2387.049
#> full-sample criterion = 2251.398
#> 
#> Average:
#> 5-Fold Cross Validation based on 18 {Subject} clusters
#> criterion: mse
#> cross-validation criterion = 2457.947 (44.04918)
#> bias-adjusted cross-validation criterion = 2433.818 (37.94423)
#> full-sample criterion = 2251.398

library("nlme")
#> 
#> Attaching package: ‘nlme’
#> The following object is masked from ‘package:lme4’:
#> 
#>     lmList
# from ?lme
(fm2 <- lme(distance ~ age + Sex, data = Orthodont,
            random = ~ 1))
#> Linear mixed-effects model fit by REML
#>   Data: Orthodont 
#>   Log-restricted-likelihood: -218.7563
#>   Fixed: distance ~ age + Sex 
#> (Intercept)         age   SexFemale 
#>  17.7067130   0.6601852  -2.3210227 
#> 
#> Random effects:
#>  Formula: ~1 | Subject
#>         (Intercept) Residual
#> StdDev:    1.807425 1.431592
#> 
#> Number of Observations: 108
#> Number of Groups: 27 
summary(cv(fm2)) # LOO CV of cases
#> R RNG seed set to 765199
#> 10-Fold Cross Validation
#> criterion: mse
#> cross-validation criterion = 2.666103
#> bias-adjusted cross-validation criterion = 2.589541
#> full-sample criterion = 1.582435
summary(cv(fm2, clusterVariables="Subject",
        k=5, seed=321)) # 5-fold CV of clusters
#> R RNG seed set to 321
#> 5-Fold Cross Validation based on 27 {Subject} clusters
#> criterion: mse
#> cross-validation criterion = 5.875411
#> bias-adjusted cross-validation criterion = 5.780695
#> full-sample criterion = 5.017326

library("glmmTMB")
# from ?glmmTMB
(m1 <- glmmTMB(count ~ mined + (1|site),
               zi=~mined,
               family=poisson, data=Salamanders))
#> Formula:          count ~ mined + (1 | site)
#> Zero inflation:         ~mined
#> Data: Salamanders
#>       AIC       BIC    logLik  df.resid 
#> 1908.4695 1930.8080 -949.2348       639 
#> Random-effects (co)variances:
#> 
#> Conditional model:
#>  Groups Name        Std.Dev.
#>  site   (Intercept) 0.28    
#> 
#> Number of obs: 644 / Conditional model: site, 23
#> 
#> Fixed Effects:
#> 
#> Conditional model:
#> (Intercept)      minedno  
#>      0.0879       1.1419  
#> 
#> Zero-inflation model:
#> (Intercept)      minedno  
#>       1.139       -1.736  
summary(cv(m1, seed=97816, k=5,
          clusterVariables="site")) # 5-fold CV of clusters
#> R RNG seed set to 97816
#> 5-Fold Cross Validation based on 23 {site} clusters
#> criterion: mse
#> cross-validation criterion = 6.006117
#> bias-adjusted cross-validation criterion = 6.002191
#> 95% CI for bias-adjusted CV criterion = (2.385452, 9.61893)
#> full-sample criterion = 5.970489
summary(cv(m1, seed=34506, k=5)) # 5-fold CV of cases
#> R RNG seed set to 34506
#> 5-Fold Cross Validation
#> criterion: mse
#> cross-validation criterion = 6.058988
#> bias-adjusted cross-validation criterion = 6.032337
#> 95% CI for bias-adjusted CV criterion = (2.483579, 9.581094)
#> full-sample criterion = 5.79783