Parametric forward selection of explanatory variables in regression and RDA

If Y is univariate, this function implements FS in regression. If Y is multivariate, this function implements FS using the F-test described by Miller and Farr (1971). This test requires that (i) the Y variables be standardized, and (ii) the error in the response variables be normally distributed (to be verified by the user).

forward.sel.par(
  Y,
  X,
  alpha = 0.05,
  K = nrow(X) - 1,
  R2thresh = 0.99,
  R2more = 0.001,
  adjR2thresh = 0.99,
  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
alpha: Significance level. Stop the forward selection procedure if the p-value of a variable is higher than alpha. The default is 0.05
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
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
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
Yscale: Standardize the variables in table Y to variance 1. The default setting is FALSE. The setting is automatically changed to TRUE if Y contains more than one variable. This is a validity condition for the parametric test of significance (Miller and Farr 1971)
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.

References

Miller, J. K. & S. D. Farr. 1971. Bimultivariate redundancy: a comprehensive measure of interbattery relationship. Multivariate Behavioral Research, 6, 313–324.

Author

Pierre Legendre pierre.legendre@umontreal.ca and Guillaume Blanchet

Examples


x <- matrix(rnorm(30),10,3)
y <- matrix(rnorm(50),10,5)
    
forward.sel.par(y,x, alpha = 0.5)
#> The variables in response matrix Y have been standardized 
#> Procedure stopped (alpha criterion): pvalue for variable  2  is  1 
#> Procedure stopped (R2more criterion): delta for variable  2  is  -0.419663 
#>   variable order        R2     R2cum   AdjR2Cum        F      pval
#> 1       V1     1 0.1710138 0.1710138 0.06739051 1.650341 0.1690767
#> 2       V3     3 0.1453721 0.3163859 0.12106760 1.488566 0.2185444
#> 3       V2     2 0.1032770 0.4196630 0.12949444 1.067763 0.3976949