creating a transitions matrix for markov Model in R

Question

I need help on a topic related to markov chains and preprocessing of data. Suppose I have the following matrix relating individuals to states over time:

     ID Time1 Time2
1 14021     A     A
2 15031     B     A
3 16452     A     C

I would like to obtain, for this matrix, the state transition matrix: Hence, what is required is

  A  B  C
A 1  0  1
B 1  0  0
C 0  0  0

and the same thing, but now weighted by the toal number of transitions from that state, ie,

  A    B   C
A 0.5  0  0.5
B 1    0   0
C 0    0   0

(as there are two transitions leaving from state A). I know that the markovchain package has a functionality for doing this if one has a sequence, say AAABBAAABBCC, but not if data is set up like I have. Ideally a direct procedure would be great, but if there is some way of turning the data into a set of sequences that would work as well.

Any ideas?

Thanks in advance

Answer 1

Here is another base R solution.

df <- data.frame(Time1 = c("A","B","A"), Time2 = c("A","A","C"), stringsAsFactors = FALSE)

myStates <- sort(unique(c(df$Time1, df$Time2)))
lenSt <- length(myStates)

currState <- match(df$Time1, myStates)
nextState <- match(df$Time2, myStates)
transMat <- matrix(0L, lenSt, lenSt)

transMat[cbind(currState, nextState)] <- 1L
transMat <- transMat/rowSums(transMat)
transMat[is.na(transMat)] <- 0

transMat
     [,1] [,2] [,3]
[1,]  0.5    0  0.5
[2,]  1.0    0  0.0
[3,]  0.0    0  0.0

Answer 2

An igraph approach, so using df from Joseph's answer:

library(igraph)

g <- graph_from_data_frame(df)

E(g)$weight = 1/degree(g, mode="out")[df$Time1] # get counts

as_adj(g, attr = "weight", sparse=FALSE) # output weighted adjacency matrix

    A B   C
A 0.5 0 0.5
B 1.0 0 0.0
C 0.0 0 0.0

Answer 3

Definitely there's a better way. This is me doodling with loops on a lame Friday afternoon.

lvls <- sort(unique(unlist(df[,-1])))

dat <- matrix(0, nrow= length(lvls), ncol= length(lvls))

colnames(dat) <- lvls
rownames(dat) <- lvls

concat <- paste0(df[,2], df[,3])

for (i in 1:length(lvls)) {
  for (j in 1:length(lvls)) {
    dat[i,j] <- paste0(rownames(dat)[i], colnames(dat)[j])
  }
}

dat <- matrix(sapply(dat, function(x) length(grep(x, concat))), 
       nrow= length(lvls), ncol= length(lvls))

colnames(dat) <- lvls
rownames(dat) <- lvls

dat

##   A B C
## A 1 0 1
## B 1 0 0
## C 0 0 0

dat <- dat / rowSums(dat)
dat[is.na(dat)] <- 0

dat

##    A B   C
##A 0.5 0 0.5
##B 1.0 0 0.0
##C 0.0 0 0.0