Forward selection with multivariate Y using permutation under reducel model

Performs a forward selection by permutation of residuals under reduced model. Y can be multivariate.

forward.sel(
  Y,
  X,
  K = nrow(X) - 1,
  R2thresh = 0.99,
  adjR2thresh = 0.99,
  nperm = 999,
  R2more = 0.001,
  alpha = 0.05,
  Xscale = TRUE,
  Ycenter = TRUE,
  Yscale = FALSE,
  verbose = TRUE
)

Arguments

Y: Response data matrix with n rows and m columns containing quantitative variables
X: Explanatory data matrix with n rows and p columns containing quantitative variables
K: Maximum number of variables to be selected. The default is one minus the number of rows
R2thresh: Stop the forward selection procedure if the R-square of the model exceeds the stated value. This parameter can vary from 0.001 to 1
adjR2thresh: Stop the forward selection procedure if the adjusted R-square of the model exceeds the stated value. This parameter can take any value (positive or negative) smaller than 1
nperm: The number of permutation to be used.The default setting is 999 permutation.
R2more: Stop the forward selection procedure if the difference in model R-square with the previous step is lower than R2more. The default setting is 0.001
alpha: Significance level. Stop the forward selection procedure if the p-value of a variable is higher than alpha. The default is 0.05 is TRUE
Xscale: Standardize the variables in table X to variance 1. The default setting is TRUE
Ycenter: Center the variables in table Y. The default setting is TRUE
Yscale: Standardize the variables in table Y to variance 1. The default setting is FALSE.
verbose: If 'TRUE' more diagnostics are printed. The default setting is TRUE

Value

A dataframe with:

variables: The names of the variables
order: The order of the selection of the variables
R2: The R2 of the variable selected
R2Cum: The cumulative R2 of the variables selected
AdjR2Cum: The cumulative adjusted R2 of the variables selected
F: The F statistic
pval: The P-value statistic

Details

The forward selection will stop when either K, R2tresh, adjR2tresh, alpha and R2more has its parameter reached.

Note

Not yet implemented for CCA (weighted regression) and with covariables.

References

Canoco manual p.49

Author

Stephane Dray stephane.dray@univ-lyon1.fr

Examples


x <- matrix(rnorm(30),10,3)
y <- matrix(rnorm(50),10,5)
    
forward.sel(y,x,nperm=99, alpha = 0.5)
#> Testing variable 1
#> Testing variable 2
#> Testing variable 3
#> Procedure stopped (alpha criteria): pvalue for variable 3 is 0.770000 (> 0.500000)
#>   variables order        R2     R2Cum   AdjR2Cum        F pvalue
#> 1        V3     3 0.1540777 0.1540777 0.04833738 1.457133   0.21
#> 2        V2     2 0.2005871 0.3546648 0.17028326 2.175783   0.06