Agfdhyk

I have been presented with a problem, regarding the minimization of the absolute error, the problem know as LAD(Least absolute deviation) but, being each regressor the result of expensive test with an associated cost, one should refrain from using regressors that don't explain variance to a high degree. It takes the following equations:

Where N is the total number of observations, E the deviation associated with observation i, S the number of independant variables, lambda a penalty coefficient for the cost, and C the cost associated with performing the test.

So far, I have oriented as usual. To make it lineal, I transformed the absolute value in two errors, e^+ and e^-, where e= y_i-(B_0+sum(B_j*X_ij) and the following constraints:

• z_j ={0,1}, binary value about whether the regressor enters my model.




• B_i<=M_zj; B_i>=-M_zj



• E^+, E^- >=0

A toy subset of data I'm working has the following structure:
For y

 quality

1       5

2       5

3       5

4       6

5       7

6       5

For the regressors

fixed.acidity volatile.acidity citric.acid

1           7.5            0.610        0.26

2           5.6            0.540        0.04

3           7.4            0.965        0.00

4           6.7            0.460        0.24

5           6.1            0.400        0.16

6           9.7            0.690        0.32

And for the cost

fixed.acidity volatile.acidity citric.acid

1          0.26              0.6        0.52

So far, my code looks like this:

# loading the matrixes

y <- read.csv(file="PATH\y.csv", header = TRUE, sep = ",") #dim=100*11

regresores <- read.csv(file="PATH\regressors.csv", header = TRUE, sep = ",")#dim=100*1

cost <- read.csv(file="PATH\cost.csv", header = TRUE, sep = ",")#dim=1*11



for  (i in seq(0, 1, by = 0.1)){#so as to have a collection of models with          different penalties

  obj.fun <- c(1,1,i*coste)

  constr <- matrix(

    c(y,regresores,-regresores),

    c(-y,-regresores,regresores),

    sum(regresores),ncol = ,byrow = TRUE)

  constr.dir <- c("<=",">=","<=","==")

  rhs<-c(regresores,-regresores,1,binary)

  sol<- lp("min", obj.fun, constr, constr.tr, rhs)

  sol$objval

  sol$solution}

I know theres is a LAD function in R, but for consistence sake with my colleagues, as well as a pretty annoying phD tutor, I have to perform this using lpSolve in R. I have just started with R for the project and I don't know exactly why this won't run. Is there something wrong with the syntax or my formulation of the model. Right know, the main problem I have is:

"Error in matrix(c(y, regressors, -regressors), c(-y, -regressors, regressors), : non-numeric matrix extent".

Mainly, I intended for it to create said weighted LAD model and have it return the different values of lambda, from 0 to 1 in a 0.1 step.

Thanks in advance and sorry for any inconvenience, neither English nor R are my native languages.