Creating a transition matrix for markov chain

Question

I have a dataset with monthly frequency of observations that fall in each category, Cat. I would like to construct a transition matrix from this, i.e., from Cat11 to Cat2, Cat1 to Cat3, to all the combinations of Cat. The goal would be to use the markovchain package in R for predicting the future months frequency based on the original data. My questions are:

1. Is it possible to construct a transition matrix based on this data?
2. Is it the correct approach?

I looked at the examples in library(markovchain) / library(etm), but I am confused. For example,

library(etm)
head(sir.cont)
   id from to time      age sex
1   41    0  2    4 75.34153   F
2  395    0  2   24 19.17380   M
3  710    1  0   33 61.56568   M
4  710    0  2   37 61.56568   M
5 3138    0  2    8 57.88038   F
6 3154    0  2    3 39.00639   M

have the 'from', 'to' columns.

and my dataset is

df1 <- structure(list(Cat = 1:10, JUL_2013 = c(19L, 10L, 1L, 18L, 2L, 
    15L, 3L, 5L, 4L, 12L), AUG_2013 = c(1L, 16L, 18L, 17L, 11L, 9L, 
    NA, 2L, 4L, 19L), SEP_2013 = c(8L, 7L, 2L, 1L, 5L, 18L, 19L, 
    15L, NA, 4L), OCT_2013 = c(16L, NA, 3L, 18L, 10L, 17L, 2L, 15L, 
    19L, 5L), NOV_2013 = c(8L, 5L, 12L, 3L, 13L, 9L, 16L, 18L, 14L, 
    2L), DEC_2013 = c(NA, 18L, 5L, 20L, 1L, 11L, 9L, 16L, 2L, 3L), 
    JAN_2014 = c(19L, 16L, 6L, 4L, 20L, 2L, 18L, 7L, 5L, 8L), 
    FEB_2014 = c(2L, 8L, 14L, NA, 17L, 15L, 5L, 3L, 4L, 13L), 
    MAR_2014 = c(16L, 8L, 5L, 2L, 7L, 17L, 14L, 11L, 3L, 1L), 
    APR_2014 = c(15L, 10L, 18L, 11L, NA, 1L, 4L, 7L, 12L, 13L
    ), MAY_2014 = c(10L, 8L, 17L, 5L, 1L, 19L, 11L, 16L, 7L, 
    NA), JUN_2014 = c(10L, 17L, 15L, 18L, 11L, 12L, 1L, 8L, 19L, 
    NA), JUL_2014 = c(9L, 20L, 17L, 1L, 3L, 6L, 18L, 14L, 11L, 
    7L), AUG_2014 = c(16L, 19L, NA, 3L, 8L, 14L, 12L, 9L, 13L, 
    4L), SEP_2014 = c(19L, 5L, 16L, 15L, NA, 10L, 13L, 11L, 9L, 
    18L), OCT_2014 = c(NA, 11L, 7L, 17L, 18L, 14L, 3L, 13L, 8L, 
    1L), NOV_2014 = c(18L, 17L, 10L, 5L, 14L, 6L, 20L, 19L, 11L, 
    9L), DEC_2014 = c(14L, 19L, 2L, 18L, 15L, 7L, 5L, 10L, 16L, 
    20L), JAN_2015 = c(4L, 7L, 19L, 18L, 6L, 13L, 9L, 10L, 14L, 
    2L), FEB_2015 = c(4L, 17L, 7L, 18L, 2L, 3L, 5L, 14L, 11L, 
    6L), MAR_2015 = c(18L, 19L, NA, 12L, 11L, 6L, 20L, 15L, 8L, 
    1L), APR_2015 = c(1L, 11L, 16L, 17L, 9L, 10L, 18L, 20L, 6L, 
    2L), MAY_2015 = c(9L, 13L, 4L, 16L, 20L, 17L, 6L, NA, 2L, 
    5L), JUN_2015 = c(7L, 3L, 10L, 19L, NA, 2L, 20L, 16L, 1L, 
    14L), JUL_2015 = c(5L, 6L, 18L, 1L, 20L, 9L, 2L, 4L, 16L, 
    11L)), .Names = c("Cat", "JUL_2013", "AUG_2013", "SEP_2013", 
    "OCT_2013", "NOV_2013", "DEC_2013", "JAN_2014", "FEB_2014", "MAR_2014", 
    "APR_2014", "MAY_2014", "JUN_2014", "JUL_2014", "AUG_2014", "SEP_2014", 
    "OCT_2014", "NOV_2014", "DEC_2014", "JAN_2015", "FEB_2015", "MAR_2015", 
    "APR_2015", "MAY_2015", "JUN_2015", "JUL_2015"), row.names = c(NA, 
    -10L), class = "data.frame")

Answer 1

For a transition matrix you need to know how many persons went from state A to state B and from state A to state C and from state B to state A etc. Knowing how many were in each state at any given point in time is not enough. You need to know the movements between states.

So, no your data does not contain the necessary information to compute a transition matrix.