Now that the model is build, we can make prediction of the following states when we are confronted with new patterns. Note that the First-Order Markov Chain (mc)1 expects you to give 1 pattern sequence and mc2 expects 2 pattern sequences.
pattern1 <- new("Pattern", sequence = c("P8"))
resultPattern1 <- predict(mc1, startPattern = pattern1, dist = 1)
resultPattern1
Sequence: P5
Probability: 0.5
Absorbing Probabilities:
None
1 NaN
pattern2 <- new("Pattern", sequence = c("P9", "P2"))
resultPattern2 <- predict(mc2, startPattern = pattern2, dist = 1)
resultPattern2
Sequence: P1
Probability: 0.6666667
Absorbing Probabilities:
None
1 NaN
These results can also be calculated manually. Let’s calculate the latter step by step.
These probabilities are exactly the same probabilities that were shown in the previous exercise.
Q2 <- mc2@transitions[[2]]
Q1 <- mc2@transitions[[1]]
We extract the lambda for each lag and multiply it with the transition probabilities per lag.
L2 <- mc2@lambda[[2]]
L1 <- mc2@lambda[[1]]
lag1 <- L1 * Q1
lag2 <- L2 * Q2
Finally, we will try to calculate the next value for the sequence P9 and P2. To do so, add transition probability of P2 in lag1 and the transition probability of P9 in lag2 and select the state with the highest expected prob.
X <- lag1[,'P2'] + lag2[,'P9']
names(X) = names(mc2@transitions[[1]]) #Add names of our states to this object
X
Buy Defer P1 P10 P11 P12 P13 P2 P3 P4 P5 P6 P7
0.0000000 0.0000000 0.6666667 0.0000000 0.3333333 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
P8 P9
0.0000000 0.0000000
max(X) #The max probability is the next state
[1] 0.6666667
From this results we learn that the next state will be web page 1.
Calculate the next value for the sequence P5 and P11 by using the model and store it as
next_state. Manually calculate the probability that this state will be the
next state and store it as prob_next_state.