efdm (version 0.2.2)

estimatetransprobs: Estimate Transition Probabilities from Pairdata

Description

Estimate Transition Probabilities from Pairdata

Usage

estimatetransprobs(
  dynamicvariables,
  pairdata,
  statespace,
  factors = character(),
  by = character(),
  prior = "nochange"
)

Value

Transition probabilities as a data.frame

Arguments

dynamicvariables

The names of the dynamic variables, character vector

pairdata

data.frame Observed transitions

statespace

data.frame or a list of two data.frames if the state space changes as a result of the activity

factors

character Variables used by the activity

by

character Variables that split the state space

prior

function or character

Details

Transition probabilities 'move' the forest areas allocated in the cells of state matrix from the initial states in the beginning of a EFDM run step to the end position. This end position will be the initial state of the next EFDM step. Length of a step (=time) in the EFDM run is typically determined by the pairdata. It is the time difference of tree observations. Note that the pairdata can be also constructed from single observation, if the other (pair) observation is estimated or modelled.

Each activity needs to have a transition probability. If no pairdata is available, transition probability matrices can be based entirely on a prior defined with expert knowledge.

The estimation uses an iterative Bayesian algorithm that is explained in https://github.com/ec-jrc/efdm/blob/master/documents/EFDMinstructions/Seija_Mathematics_behind_EFDM.pdf. The transition probability estimate is the proportion of observed transitions divided by the number of all transitions from the same starting state. prior gives the number of prior transitions. For each factor variable the transitions are counted in classes of all factors before the current factor. The "most important" observations (having all classes right) is counted length(factors) times, the second most important observations are counted length(factors)-1 times and so on.

If pairdata is NULL prior is used by itself.

Observations should have 'factor' and 'by' variables and statepairs with 0 and 1 suffixes to indicate before and after observations.

The estimation algorithm uses information across 'factor' variables, but not across 'by' variables.

prior can either character or function.

• "nochange" implies that there is one observation where state doesn't change

• "uninformative" when no observations are given all states are as likely

• function(A, dynvar1, dynvar0) where A is an array of zeros with dimnames(A) <- c(dynvar1, dynvar0). The function should fill A with the number of prior transitions and return it.

The statespace is used to fill in the transitions where there are no observations. In special cases the statespace may change as a result of the activity. For example changing the tree species might lead to change in the volume classification used.

This function assumes that the dynamic variables are coded as integers starting with 1. Other variables are not restricted.

Examples

# Estimation can use observed transitions with different levels of factors.
statespace <- expand.grid(a=1:2, b=1:2, vol=1:5)
pairdata <- data.frame(a=c(1,1,2,2), b=c(1,2,1,2), vol0=c(1,1,1,1), vol1=c(2,3,4,5))
state0 <- statespace
actprob <- statespace
actprob$test <- 1
state0$area <- 0
state0$area[1] <- 1

# With by=c("a", "b") there are two observations: one from prior and the other
# from the exact combination of class levels.
probs <- estimatetransprobs("vol", pairdata, statespace, by=c("a", "b"), prior="nochange")
act1 <- define_activity("test", c("vol"), probs)
runEFDM(state0, actprob, list(act1), 1)

probs <- estimatetransprobs("vol", pairdata, statespace, factors="a", by="b", prior="nochange")
act2 <- define_activity("test", c("vol"), probs)
runEFDM(state0, actprob, list(act2), 1)

probs <- estimatetransprobs("vol", pairdata, statespace, factors="b", by="a", prior="nochange")
act3 <- define_activity("test", c("vol"), probs)
runEFDM(state0, actprob, list(act3), 1)

# The order of variables in factors argument specifies the order of importance.
# Observation that differ in the first variable are counted more times.
probs <- estimatetransprobs("vol", pairdata, statespace, factors=c("a", "b"), prior="nochange")
act4 <- define_activity("test", c("vol"), probs)
runEFDM(state0, actprob, list(act4), 1)

probs <- estimatetransprobs("vol", pairdata, statespace, factors=c("b", "a"), prior="nochange")
act5 <- define_activity("test", c("vol"), probs)
runEFDM(state0, actprob, list(act5), 1)