R help - Apr 2004 - Probability(Markov chain transition matrix)

Hello, My name is Maria, MBA student in Sanfransisco, USA.
In my credit scoring class, I have hard time making "transition
matrix",
which explains probability especially in relation to "Markov chain
model".
It is regarding people's monthly credit payment behavior. Does R have 
function to caculate it? I am actually a novice in using 'R'. Please
help
me!!!

Maria Gu

On 29 Apr 2004 at 20:27, Maria Gu wrote:
> Hello, My name is Maria, MBA student in Sanfransisco, USA.
> In my credit scoring class, I have hard time making "transition
> matrix", which explains probability especially in relation to
"Markov
> chain model". It is regarding people's monthly credit payment
> behavior. Does R have function to caculate it? I am actually a novice
> in using 'R'. Please help me!!!
> 
> Maria Gu
> 
Hola Maria, 

you need to be more specific in what you want. Do you want to 
estimate a markov transistion matrix from data? Do you want to 
simulate from a Markoc chain model? Whatever you want, it is 
likely possible in R, but we need more information.

If you want to simulate from a model, maybe something like:
> P <- matrix(c(0.1, 0.4, 0.5, 
+               0.9, 0.05, 0.05, 
+               0.3, 0.6, 0.1),3,3, byrow=TRUE)
> simMarkov <- function(P, init, n) {
+    p <- dim(P)[1]
+    chain <- numeric(length=n)
+    chain[1] <- init
+    for (i in 2:n) {
+      chain[i] <- sample(1:p, 1, prob=P[chain[i-1],])
+    }
+    return(chain)
+ }
> simMarkov(P,1,20)
 [1] 1 2 1 3 2 2 2 1 2 1 2 1 3 1 2 1 3 2 1 1
> 
Kjetil Halvorsen
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide!
> http://www.R-project.org/posting-guide.html
>

Hi all, thank you for the response of my inquiry.
Let me explain more specifically about what I want from R.
It is about estimating bad debt related to people's credit card payment 
behavior.
Here we go!


Status of a credit account {NC, 0,1,2,.....M} where NC is no-credit 
status(account has no balance), 0 is where the account has a credit balance 
but the payment are up to date, 1 is where the account is one payment 
overdue, and M payment overdue is classified as default.

So we come up with Transition matrix stating probabilities of each state

FromTo NC   0       1     2     3
NC      0.79  0.21  0      0    0
0          0.09  0.73 0.18 0    0
1          0.09  0.51  0   0.40  0
2          0.09  0.38  0      0   0.55
3          0.06  0.32  0      0   0.62


Thus if one starts with all the accounts having no credit ?0 =(1,0,0,0,0), 
after one period the distribution of account is ?1=(0.79, 0.21, 0, 0, 0)  
after subsequent periods, it becomes

佇2=(0.64, 0.32, 0.04, 0, 0),
佇3= (0.540, 0.387, 0.058, 0.015, 0)
佇4=(0.468,0.431, 0.070, 0.023, 0.008)
佇5=(0.417, 0.460, 0.077, 0.028, 0.018)
and ++++
佇10=(0.315, 0.512, 0.091, 0.036, 0.046)

This proves a way for estimating the amount of bad debt will appear the 
future periods. After 10 periods, it estimates that 4.6%(0.046) of the 
accounts will be bad.

I am sure R can solve this, please help me!

Maria Gu
510-418-1240

_________________________________________________________________

At 17:25 30/04/2004, you wrote:
>So we come up with Transition matrix stating probabilities of each state
>
>FromTo NC   0       1     2     3
>NC      0.79  0.21  0      0    0
>0          0.09  0.73 0.18 0    0
>1          0.09  0.51  0   0.40  0
>2          0.09  0.38  0      0   0.55
>3          0.06  0.32  0      0   0.62
>
>
>Thus if one starts with all the accounts having no credit ?0 =(1,0,0,0,0),
after one period the distribution of account is ?1=(0.79, 0.21, 0, 0, 0)
>after subsequent periods, it becomes
>
>?2=(0.64, 0.32, 0.04, 0, 0),
>?3= (0.540, 0.387, 0.058, 0.015, 0)
>?4=(0.468,0.431, 0.070, 0.023, 0.008)
>?5=(0.417, 0.460, 0.077, 0.028, 0.018)
>and ++++
>?10=(0.315, 0.512, 0.091, 0.036, 0.046)
Hi 


I create a rotine for a problem like this, I hope this is useful for you
------------
#############################################
##            MARKOV CHAIN                 ## 
##                                         ##
## ini- initial state                      ## 
## trans- transition matrix                ##
## n - number of transitions               ##
## f - ini%*%trans                         ##  
## fase - f consolidate                    ##
##                                         ## 
#############################################



#          initial state

ini<-matrix(c(10,0,0,0,0,0,0,0,0),nrow=3,ncol=3)

#          transition matrix
#
#      [,1] [,2] [,3]
# [1,] 0.85  0.1  0.05
# [2,] 0.00  0.7  0.3
# [3,] 0.00  0.0  1.0
#
# In R the command is

trans<-matrix(c(.85,0,0,.1,.7,0,0.05,0.3,1),ncol=3)

markov<-function(ini,trans,n){
  l<-ncol(ini)
  fase<-matrix(0,nrow=l,ncol=l)
  fases<-array(0,dim=c(nrow(ini),ncol(ini),n))
  for (i in 1:n){
    f<-ini%*%trans
    for (w in 1:l){fase[w,w]<-sum(f[,w])}
  ini<-fase
  fases[,,i]<-fase
# print(fase)
# 
# Fase allow calcule de value for transition:
# If sate 1 value 0,95, state 2 value 0,3 and  state 3
# value 0 QALY. 
# I?m calculate de value of any transition if
#  print(sum(fase%*%c(.95,.3,0)))
#
# 

  }
  return(fases)
}

a<-markov(ini,trans,5)

For your case:

ini<-matrix(c(1,rep(0,24)),ncol=5)
trans<-matrix(c(0.79,0.21,0,0,0,0.09,0.73,0.18,0,0,0.09,0.51,0,0.40,0,0.09,0.38,0,0,0.55,0.06,0.32,0,0,0.62),ncol=5)
solv<-markov(ini,trans,10)
> solv[,,10]
          [,1]      [,2]      [,3]      [,4]      [,5]
[1,] 0.3173366 0.0000000 0.0000000 0.0000000 0.0000000
[2,] 0.0000000 0.2876792 0.0000000 0.0000000 0.0000000
[3,] 0.0000000 0.0000000 0.2875772 0.0000000 0.0000000
[4,] 0.0000000 0.0000000 0.0000000 0.2886571 0.0000000
[5,] 0.0000000 0.0000000 0.0000000 0.0000000 0.2810951








Bernardo Rangel Tura, MD, MSc
National Institute of Cardiology Laranjeiras
Rio de Janeiro Brazil