Allow for multiple tau in DKQS

[a-torgovitsky]

Same as #25 with lambda for fsst.

Currently I get rather strange behavior:

rdkqs <- dkqs(data = data,
              lpmodel = lpm,
              beta.tgt = .3,
              R = 100,
              tau = c(.2, .5),
              solver = "gurobi",
              cores = 1,
              progress = TRUE)
print(rdkqs)
Test statistic: 99.35703.             
p-value: 0.32.
Value of tau used: 0.2.
 Value of tau used: 0.5.
Solver used: gurobi.
Number of cores used: 1.
Warning messages:
1: In temp[1] <- coeff.tau :
  number of items to replace is not a multiple of replacement length
2: In temp[1] <- coeff.tau :
  number of items to replace is not a multiple of replacement length
3: In temp[1] <- coeff.tau :
  number of items to replace is not a multiple of replacement length
4: In temp[1] <- coeff.tau :
  number of items to replace is not a multiple of replacement length
5: In temp[1] <- coeff.tau :
  number of items to replace is not a multiple of replacement length
6: In temp[1] <- coeff.tau :
  number of items to replace is not a multiple of replacement length
7: In temp[1] <- coeff.tau :
  number of items to replace is not a multiple of replacement length
8: In temp[1] <- coeff.tau :
  number of items to replace is not a multiple of replacement length
9: In if (tau > tau.return$objval) { :
  the condition has length > 1 and only the first element will be used
10: In if (tau <= tau.return$objval) { :
  the condition has length > 1 and only the first element will be used

[conroylau]

I am updating the code for multiple tau and I am thinking what would be the best output in the following hypothetical example:

• The list of taus provided by the user is {0.1, 0.2, 0.5, 0.9}.
• The value of $\tau^\star$ (the maximum value of tau so that the main QP is feasible) is 0.4 (calculated from problem (6) in the DKQS notes).
• In the current procedure, the tau used in the module is $\tau^\star$ if it is smaller than the tau passed by the user. Otherwise, the tau provided by the user is used.

Hence, in the case of having multiple taus in dkqs, should the code only run and print the results with tau = 0.1, 0.2 and 0.4, and then add a remark saying that tau = 0.5 and 0.9 are infeasible?

Thanks!

[a-torgovitsky]

That sounds like a good solution to me!

[conroylau]

Done! The code now allows for multiple taus. The following is a sample output with multiple taus:

Input (following the example file earlier)

rdkqs <- dkqs(data = data,
              lpmodel = lpm,
              beta.tgt = .3,
              R = 100,
              tau = c(.2, .5, 2, 10),
              solver = "gurobi",
              cores = 2,
              progress = TRUE)

Output for print(rdkqs):

p-values:
 tau p-value
 0.2    0.29
 0.5    0.31
 1.0    0.39
The following taus from the input are infeasible: 2, 10

Output for summary(rdkqs):

p-values:
 tau p-value
 0.2    0.29
 0.5    0.31
 1.0    0.39
Test statistic: 99.35703
Solver used: gurobi
Number of cores used: 2
Maximum feasible tau: 1
The following taus from the input are infeasible: 2, 10

Thanks!

[a-torgovitsky]

Looks good, but maybe to keep it more coherent, it would be better to add the infeasible ones also to the table with p-value listed as infeasible Also, I don't think there is any need for the first p-values: in the top line

[conroylau]

Done! The updated messages look like the followings:

Print:

 tau    p-value
 0.2       0.29
 0.5       0.31
   1       0.39
   2 infeasible
  10 infeasible

Summary:

 tau    p-value
 0.2       0.29
 0.5       0.31
   1       0.39
   2 infeasible
  10 infeasible
 Maximum feasible tau: 1
 Test statistic: 99.35703
 Solver used: gurobi
 Number of cores used: 2

[a-torgovitsky]

Looks good!