LEGIT (version 1.3)

IMLEGIT_cv: Cross-validation for the IMLEGIT model

Description

Uses cross-validation on the IMLEGIT model. Note that this is not a very fast implementation since it was written in R.

Usage

IMLEGIT_cv(data, latent_var, formula, cv_iter = 5, cv_folds = 10,
  folds = NULL, Huber_p = 1.345, classification = FALSE,
  start_latent_var = NULL, eps = 0.001, maxiter = 100,
  family = gaussian, ylim = NULL, seed = NULL, id = NULL)

Arguments

data

data.frame of the dataset to be used.

latent_var

list of data.frame. The elements of the list are the datasets used to construct each latent variable. For interpretability and proper convergence, not using the same variable in more than one latent variable is highly recommended. It is recommended to set names to the list elements to prevent confusion because otherwise, the latent variables will be named L1, L2, ...

formula

Model formula. The names of latent_var can be used in the formula to represent the latent variables. If names(latent_var) is NULL, then L1, L2, ... can be used in the formula to represent the latent variables. Do not manually code interactions, write them in the formula instead (ex: G*E1*E2 or G:E1:E2).

cv_iter

Number of cross-validation iterations (Default = 5).

cv_folds

Number of cross-validation folds (Default = 10). Using cv_folds=NROW(data) will lead to leave-one-out cross-validation.

folds

Optional list of vectors containing the fold number for each observation. Bypass cv_iter and cv_folds. Setting your own folds could be important for certain data types like time series or longitudinal data.

Huber_p

Parameter controlling the Huber cross-validation error (Default = 1.345).

classification

Set to TRUE if you are doing classification (binary outcome).

start_latent_var

Optional list of starting points for each latent variable (The list must have the same length as the number of latent variables and each element of the list must have the same length as the number of variables of the corresponding latent variable).

eps

Threshold for convergence (.01 for quick batch simulations, .0001 for accurate results).

maxiter

Maximum number of iterations.

family

Outcome distribution and link function (Default = gaussian).

ylim

Optional vector containing the known min and max of the outcome variable. Even if your outcome is known to be in [a,b], if you assume a Gaussian distribution, predict() could return values outside this range. This parameter ensures that this never happens. This is not necessary with a distribution that already assumes the proper range (ex: [0,1] with binomial distribution).

seed

Seed for cross-validation folds.

id

Optional id of observations, can be a vector or data.frame (only used when returning list of possible outliers).

Value

If classification = FALSE, returns a list containing, in the following order: a vector of the cross-validated \(R^2\) at each iteration, a vector of the Huber cross-validation error at each iteration, a vector of the L1-norm cross-validation error at each iteration, a matrix of the possible outliers (standardized residuals > 2.5 or < -2.5) and their corresponding standardized residuals and standardized pearson residuals. If classification = TRUE, returns a list containing, in the following order: a vector of the cross-validated \(R^2\) at each iteration, a vector of the Huber cross-validation error at each iteration, a vector of the L1-norm cross-validation error at each iteration, a vector of the AUC at each iteration, a matrix of the best choice of threshold (based on Youden index) and the corresponding specificity and sensitivity at each iteration, and a list of objects of class "roc" (to be able to make roc curve plots) at each iteration. The Huber and L1-norm cross-validation errors are alternatives to the usual cross-validation L2-norm error (which the \(R^2\) is based on) that are more resistant to outliers, the lower the values the better.

References

Denis Heng-Yan Leung. Cross-validation in nonparametric regression with outliers. Annals of Statistics (2005): 2291-2310.

Examples

# NOT RUN {
train = example_3way_3latent(250, 1, seed=777)
# Cross-validation 4 times with 5 Folds
cv_5folds = IMLEGIT_cv(train$data, train$latent_var, y ~ G*E*Z, cv_iter=4, cv_folds=5)
cv_5folds
# Leave-one-out cross-validation (Note: very slow)
cv_loo = IMLEGIT_cv(train$data, train$latent_var, y ~ G*E*Z, cv_iter=1, cv_folds=250)
cv_loo
# Cross-validation 4 times with 5 Folds (binary outcome)
train_bin = example_2way(500, 2.5, logit=TRUE, seed=777)
cv_5folds_bin = IMLEGIT_cv(train_bin$data, list(G=train_bin$G, E=train_bin$E), y ~ G*E, 
cv_iter=4, cv_folds=5, classification=TRUE, family=binomial)
cv_5folds_bin
par(mfrow=c(2,2))
pROC::plot.roc(cv_5folds_bin$roc_curve[[1]])
pROC::plot.roc(cv_5folds_bin$roc_curve[[2]])
pROC::plot.roc(cv_5folds_bin$roc_curve[[3]])
pROC::plot.roc(cv_5folds_bin$roc_curve[[4]])
# }