Calculating the transition probabilities in R

r

Solution

In base R, you could use `prop.table` on a table object:

transMat <- prop.table(with(df, table(old, new)), 2)
transMat
   new
old          A          B          C          D
  A 0.26315789 0.27272727 0.18181818 0.22222222
  B 0.31578947 0.36363636 0.09090909 0.22222222
  C 0.21052632 0.27272727 0.45454545 0.33333333
  D 0.21052632 0.09090909 0.27272727 0.22222222

Here, the columns sum to 1:

colSums(transMat)
A B C D 
1 1 1 1

edit On further reflection, I think using margin=1 is actually the desired outcome since old (the conditioned variable) is in the rows and because p(A|A) + p(B|A) + p(C|A) + p(D|A) should equal 1. In this scenario,

transMat <- prop.table(with(df, table(old, new)), 1)
transMat
   new
old          A          B          C          D
  A 0.41666667 0.25000000 0.16666667 0.16666667
  B 0.46153846 0.30769231 0.07692308 0.15384615
  C 0.26666667 0.20000000 0.33333333 0.20000000
  D 0.40000000 0.10000000 0.30000000 0.20000000

will work. alternatively, the transpose `prop.table(with(df, table(new, old)), 2)`.

data

set.seed(1234)
df <- data.frame(old=sample(LETTERS[1:4], 50, replace=TRUE),
                 new=sample(LETTERS[1:4], 50, replace=TRUE))

Problem

Let's assume that we have the following 4 states: (A, B, C, D) The table I have has the following format ``` old new A B A A B C D B C D . . . . . . . . ``` I would like the calculate the following probabilities based on the data given in the table: ``` P(new=A | old=A) P(new=B | old=A) P(new=C | old=A) P(new=D | old=A) P(new=A | old=B) . . . . P(new=C | old=D) P(new=D | old=D) ``` I can do it in a manual way, summing up all the values when each transition happens and dividing by the number of rows, but I was wondering if there's a built-in function in R that calculates those probabilities or at least helps to fasten calculating those probabilities. Any help/input would be greatly appreciated. If there's no such function, oh well.

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