cprob: Empirical conditional probability distributions of order 'L'
In PST: Probabilistic Suffix Trees and Variable Length Markov Chains
Description
Usage
Arguments
Details
Value
Author(s)
References
Examples
Description
Compute the empirical conditional probability distributions of order L from a set of sequences
Usage
1
2
3
Arguments
object
a sequence object, that is an object of class stslist as created by TraMineR seqdef function.
L
integer. Context length.
cdata
under development
context
character. An optional subsequence (a character string where symbols are separated by '-') for which the conditional probability distribution is to be computed.
stationary
logical. If FALSE probability distributions are computed for each sequence position L+1 ... l where l is the maximum sequence length. If TRUE the probability distributions are stationary that is time homogenous.
nmin
integer. Minimal frequency of a context. See details.
prob
logical. If TRUE the probability distributions are returned. If FALSE the function returns the empirical counts on which the probability distributions are computed.
weighted
logical. If TRUE case weights attached to the sequence object are used in the computation of the probabilities.
with.missing
logical. If FALSE only contexts contining no missing status are considered.
to.list
logical. If TRUE and stationary=TRUE, a list instead of a matrix is returned. See value.
Details
The empirical conditional probability \hat{P}(σ | c) of observing a symbol σ \in A after the subsequence c=c_{1}, …, c_{k} of length k=L is computed as
\hat{P}(σ | c) = \frac{N(cσ)}{∑_{α \in A} N(cα)}
where
N(c)=∑_{i=1}^{\ell} 1 ≤ft[x_{i}, …, x_{i+|c|-1}=c \right], \; x=x_{1}, …, x_{\ell}, \; c=c_{1}, …, c_{k}
is the number of occurrences of the subsequence c in the sequence x and cσ is the concatenation of the subsequence c and the symbol σ.
Considering a - possibly weighted - sample of m sequences having weights w^{j}, \; j=1 … m, the function N(c) is replaced by
N(c)=∑_{j=1}^{m} w^{j} ∑_{i=1}^{\ell} 1 ≤ft[x_{i}^{j}, …, x_{i+|c|-1}^{j}=c \right], \; c=c_{1}, …, c_{k}
where x^{j}=x_{1}^{j}, …, x_{\ell}^{j} is the jth sequence in the sample. For more details, see Gabadinho 2016.
Value
If stationary=TRUE a matrix with one row for each subsequence of length L and minimal frequency nmin appearing in object. If stationary=FALSE a list where each element corresponds to one subsequence and contains a matrix whith the probability distribution at each position p where a state is preceded by the subsequence.
Author(s)
Alexis Gabadinho
References
Gabadinho, A. & Ritschard, G. (2016). Analyzing State Sequences with Probabilistic Suffix Trees: The PST R Package. Journal of Statistical Software, 72(3), pp. 1-39.
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
## Example with the single sequence s1
data(s1)
s1 <- seqdef(s1)
cprob(s1, L=0, prob=FALSE)
cprob(s1, L=1, prob=TRUE)
## Preparing a sequence object with the SRH data set
data(SRH)
state.list <- levels(SRH$p99c01)
## sequential color palette
mycol5 <- rev(brewer.pal(5, "RdYlGn"))
SRH.seq <- seqdef(SRH, 5:15, alphabet=state.list, states=c("G1", "G2", "M", "B2", "B1"),
labels=state.list, weights=SRH$wp09lp1s, right=NA, cpal=mycol5)
names(SRH.seq) <- 1999:2009
## Example 1: 0th order: weighted and unweigthed counts
cprob(SRH.seq, L=0, prob=FALSE, weighted=FALSE)
cprob(SRH.seq, L=0, prob=FALSE, weighted=TRUE)
## Example 2: 2th order: weighted and unweigthed probability distrib.
cprob(SRH.seq, L=2, prob=TRUE, weighted=FALSE)
cprob(SRH.seq, L=2, prob=TRUE, weighted=TRUE)
Example output
Loading required package: TraMineR
TraMineR stable version 2.0-7 (Built: "Sat,)
Website: http://traminer.unige.ch
Please type 'citation("TraMineR")' for citation information.
Loading required package: RColorBrewer
PST version 0.94 (Built: 2017-09-22)
Website: http://r-forge.r-project.org/projects/pst
[>] 2 distinct states appear in the data:
1 = a
2 = b
[>] state coding:
[alphabet] [label] [long label]
1 a a a
2 b b b
[>] 1 sequences in the data set
[>] min/max sequence length: 27/27
[>] 1 sequences, min/max length: 27/27
[>] computing prob., L=0, 1 distinct context(s)
[>] total time: 0.007 secs
a b [n]
e 13 14 27
[>] 1 sequences, min/max length: 27/27
[>] computing prob., L=1, 2 distinct context(s)
[>] total time: 0.004 secs
a b [n]
a 0.3846154 0.6153846 13
b 0.5384615 0.4615385 13
[>] found missing values ('NA') in sequence data
[>] preparing 2612 sequences
[>] coding void elements with '%' and missing values with '*'
[>] state coding:
[alphabet] [label] [long label]
1 very well G1 very well
2 well G2 well
3 so, so (average) M so, so (average)
4 not very well B2 not very well
5 not well at all B1 not well at all
[>] sum of weights: 2653.77 - min/max: 0.232673704624176/4.55576086044312
[>] 2612 sequences in the data set
[>] min/max sequence length: 11/11
[>] 2612 sequences, min/max length: 11/11
[>] computing prob., L=0, 1 distinct context(s)
[>] total time: 0.26 secs
G1 G2 M B2 B1 [n]
e 6224 17616 3591 371 52 27854
[>] 2612 sequences, min/max length: 11/11
[>] computing prob., L=0, 1 distinct context(s)
[>] total time: 0.036 secs
G1 G2 M B2 B1 [n]
e 6201.074 17830.85 3758.909 368.4725 51.10312 27854
[>] 2612 sequences, min/max length: 11/11
[>] computing prob., L=2, 35 distinct context(s)
[>] removing 11 context(s) containing missing values
[>] total time: 0.024 secs
G1 G2 M B2 B1 [n]
B1-B1 0.00000000 0.00000000 0.14285714 0.285714286 0.5714285714 7
B1-B2 0.00000000 0.12500000 0.00000000 0.625000000 0.2500000000 8
B1-G1 1.00000000 0.00000000 0.00000000 0.000000000 0.0000000000 1
B1-G2 0.00000000 1.00000000 0.00000000 0.000000000 0.0000000000 5
B1-M 0.00000000 0.11111111 0.55555556 0.333333333 0.0000000000 9
B2-B1 0.00000000 0.00000000 0.16666667 0.416666667 0.4166666667 12
B2-B2 0.00000000 0.09756098 0.43902439 0.317073171 0.1463414634 41
B2-G1 0.22222222 0.55555556 0.22222222 0.000000000 0.0000000000 9
B2-G2 0.06666667 0.53333333 0.34444444 0.055555556 0.0000000000 90
B2-M 0.02702703 0.24324324 0.56756757 0.135135135 0.0270270270 111
G1-B2 0.21428571 0.35714286 0.35714286 0.071428571 0.0000000000 14
G1-G1 0.58900634 0.38266385 0.02663848 0.001691332 0.0000000000 2365
G1-G2 0.29896497 0.64888535 0.04936306 0.002786624 0.0000000000 2512
G1-M 0.25000000 0.52450980 0.20588235 0.014705882 0.0049019608 204
G2-B1 0.10000000 0.30000000 0.50000000 0.000000000 0.1000000000 10
G2-B2 0.06741573 0.58426966 0.30337079 0.044943820 0.0000000000 89
G2-G1 0.34759867 0.60294817 0.04660010 0.002853067 0.0000000000 2103
G2-G2 0.12129573 0.77948089 0.09298999 0.005518087 0.0007153076 9786
G2-M 0.06004289 0.63187991 0.28162974 0.024303074 0.0021443888 1399
M-B1 0.00000000 0.33333333 0.33333333 0.222222222 0.1111111111 9
M-B2 0.00000000 0.23364486 0.52336449 0.214953271 0.0280373832 107
M-G1 0.31428571 0.54857143 0.13142857 0.005714286 0.0000000000 175
M-G2 0.06699929 0.65146115 0.25944405 0.019957234 0.0021382751 1403
M-M 0.02576336 0.36832061 0.53625954 0.065839695 0.0038167939 1048
[>] 2612 sequences, min/max length: 11/11
[>] computing prob., L=2, 35 distinct context(s)
[>] removing 11 context(s) containing missing values
[>] total time: 0.032 secs
G1 G2 M B2 B1 [n]
B1-B1 0.00000000 0.00000000 0.09818135 0.335028651 0.5667899946 7
B1-B2 0.00000000 0.12965429 0.00000000 0.553821776 0.3165239369 8
B1-G1 1.00000000 0.00000000 0.00000000 0.000000000 0.0000000000 1
B1-G2 0.00000000 1.00000000 0.00000000 0.000000000 0.0000000000 5
B1-M 0.00000000 0.20500861 0.53019242 0.264798970 0.0000000000 9
B2-B1 0.00000000 0.00000000 0.18658460 0.408762718 0.4046526865 12
B2-B2 0.00000000 0.08762715 0.49743688 0.304345521 0.1105904504 41
B2-G1 0.15269255 0.56929607 0.27801138 0.000000000 0.0000000000 9
B2-G2 0.06736504 0.50905666 0.35812437 0.065453926 0.0000000000 90
B2-M 0.02400026 0.24139846 0.58999910 0.119801242 0.0248009471 111
G1-B2 0.19126499 0.37109769 0.35074171 0.086895609 0.0000000000 14
G1-G1 0.58674034 0.38404366 0.02747219 0.001743816 0.0000000000 2365
G1-G2 0.29732333 0.65016030 0.04976264 0.002753734 0.0000000000 2512
G1-M 0.24415949 0.51633832 0.21334358 0.020040363 0.0061182509 204
G2-B1 0.04016650 0.30014000 0.61271478 0.000000000 0.0469787227 10
G2-B2 0.06616120 0.53516824 0.33857735 0.060093210 0.0000000000 89
G2-G1 0.34300931 0.60359596 0.05129085 0.002103880 0.0000000000 2103
G2-G2 0.11902674 0.77887958 0.09646083 0.004992888 0.0006399592 9786
G2-M 0.05424277 0.63001545 0.28661320 0.026701475 0.0024271068 1399
M-B1 0.00000000 0.32258387 0.26163294 0.262630848 0.1531523341 9
M-B2 0.00000000 0.21069475 0.54266810 0.214763222 0.0318739189 107
M-G1 0.35606381 0.51180852 0.12949028 0.002637382 0.0000000000 175
M-G2 0.06042470 0.65290600 0.26436511 0.019544672 0.0027595167 1403
M-M 0.02771553 0.36685274 0.53683261 0.064524580 0.0040745414 1048
PST documentation built on May 2, 2019, 3:43 a.m.
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Description Usage Arguments Details Value Author(s) References Examples
Description
Compute the empirical conditional probability distributions of order L from a set of sequences
Usage
1 2 3 |
Arguments
object |
a sequence object, that is an object of class stslist as created by TraMineR |
L |
integer. Context length. |
cdata |
under development |
context |
character. An optional subsequence (a character string where symbols are separated by '-') for which the conditional probability distribution is to be computed. |
stationary |
logical. If |
nmin |
integer. Minimal frequency of a context. See details. |
prob |
logical. If |
weighted |
logical. If |
with.missing |
logical. If |
to.list |
logical. If |
Details
The empirical conditional probability \hat{P}(σ | c) of observing a symbol σ \in A after the subsequence c=c_{1}, …, c_{k} of length k=L is computed as
\hat{P}(σ | c) = \frac{N(cσ)}{∑_{α \in A} N(cα)}
where
N(c)=∑_{i=1}^{\ell} 1 ≤ft[x_{i}, …, x_{i+|c|-1}=c \right], \; x=x_{1}, …, x_{\ell}, \; c=c_{1}, …, c_{k}
is the number of occurrences of the subsequence c in the sequence x and cσ is the concatenation of the subsequence c and the symbol σ.
Considering a - possibly weighted - sample of m sequences having weights w^{j}, \; j=1 … m, the function N(c) is replaced by
N(c)=∑_{j=1}^{m} w^{j} ∑_{i=1}^{\ell} 1 ≤ft[x_{i}^{j}, …, x_{i+|c|-1}^{j}=c \right], \; c=c_{1}, …, c_{k}
where x^{j}=x_{1}^{j}, …, x_{\ell}^{j} is the jth sequence in the sample. For more details, see Gabadinho 2016.
Value
If stationary=TRUE a matrix with one row for each subsequence of length L and minimal frequency nmin appearing in object. If stationary=FALSE a list where each element corresponds to one subsequence and contains a matrix whith the probability distribution at each position p where a state is preceded by the subsequence.
Author(s)
Alexis Gabadinho
References
Gabadinho, A. & Ritschard, G. (2016). Analyzing State Sequences with Probabilistic Suffix Trees: The PST R Package. Journal of Statistical Software, 72(3), pp. 1-39.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ## Example with the single sequence s1
data(s1)
s1 <- seqdef(s1)
cprob(s1, L=0, prob=FALSE)
cprob(s1, L=1, prob=TRUE)
## Preparing a sequence object with the SRH data set
data(SRH)
state.list <- levels(SRH$p99c01)
## sequential color palette
mycol5 <- rev(brewer.pal(5, "RdYlGn"))
SRH.seq <- seqdef(SRH, 5:15, alphabet=state.list, states=c("G1", "G2", "M", "B2", "B1"),
labels=state.list, weights=SRH$wp09lp1s, right=NA, cpal=mycol5)
names(SRH.seq) <- 1999:2009
## Example 1: 0th order: weighted and unweigthed counts
cprob(SRH.seq, L=0, prob=FALSE, weighted=FALSE)
cprob(SRH.seq, L=0, prob=FALSE, weighted=TRUE)
## Example 2: 2th order: weighted and unweigthed probability distrib.
cprob(SRH.seq, L=2, prob=TRUE, weighted=FALSE)
cprob(SRH.seq, L=2, prob=TRUE, weighted=TRUE)
|
Example output
Loading required package: TraMineR
TraMineR stable version 2.0-7 (Built: "Sat,)
Website: http://traminer.unige.ch
Please type 'citation("TraMineR")' for citation information.
Loading required package: RColorBrewer
PST version 0.94 (Built: 2017-09-22)
Website: http://r-forge.r-project.org/projects/pst
[>] 2 distinct states appear in the data:
1 = a
2 = b
[>] state coding:
[alphabet] [label] [long label]
1 a a a
2 b b b
[>] 1 sequences in the data set
[>] min/max sequence length: 27/27
[>] 1 sequences, min/max length: 27/27
[>] computing prob., L=0, 1 distinct context(s)
[>] total time: 0.007 secs
a b [n]
e 13 14 27
[>] 1 sequences, min/max length: 27/27
[>] computing prob., L=1, 2 distinct context(s)
[>] total time: 0.004 secs
a b [n]
a 0.3846154 0.6153846 13
b 0.5384615 0.4615385 13
[>] found missing values ('NA') in sequence data
[>] preparing 2612 sequences
[>] coding void elements with '%' and missing values with '*'
[>] state coding:
[alphabet] [label] [long label]
1 very well G1 very well
2 well G2 well
3 so, so (average) M so, so (average)
4 not very well B2 not very well
5 not well at all B1 not well at all
[>] sum of weights: 2653.77 - min/max: 0.232673704624176/4.55576086044312
[>] 2612 sequences in the data set
[>] min/max sequence length: 11/11
[>] 2612 sequences, min/max length: 11/11
[>] computing prob., L=0, 1 distinct context(s)
[>] total time: 0.26 secs
G1 G2 M B2 B1 [n]
e 6224 17616 3591 371 52 27854
[>] 2612 sequences, min/max length: 11/11
[>] computing prob., L=0, 1 distinct context(s)
[>] total time: 0.036 secs
G1 G2 M B2 B1 [n]
e 6201.074 17830.85 3758.909 368.4725 51.10312 27854
[>] 2612 sequences, min/max length: 11/11
[>] computing prob., L=2, 35 distinct context(s)
[>] removing 11 context(s) containing missing values
[>] total time: 0.024 secs
G1 G2 M B2 B1 [n]
B1-B1 0.00000000 0.00000000 0.14285714 0.285714286 0.5714285714 7
B1-B2 0.00000000 0.12500000 0.00000000 0.625000000 0.2500000000 8
B1-G1 1.00000000 0.00000000 0.00000000 0.000000000 0.0000000000 1
B1-G2 0.00000000 1.00000000 0.00000000 0.000000000 0.0000000000 5
B1-M 0.00000000 0.11111111 0.55555556 0.333333333 0.0000000000 9
B2-B1 0.00000000 0.00000000 0.16666667 0.416666667 0.4166666667 12
B2-B2 0.00000000 0.09756098 0.43902439 0.317073171 0.1463414634 41
B2-G1 0.22222222 0.55555556 0.22222222 0.000000000 0.0000000000 9
B2-G2 0.06666667 0.53333333 0.34444444 0.055555556 0.0000000000 90
B2-M 0.02702703 0.24324324 0.56756757 0.135135135 0.0270270270 111
G1-B2 0.21428571 0.35714286 0.35714286 0.071428571 0.0000000000 14
G1-G1 0.58900634 0.38266385 0.02663848 0.001691332 0.0000000000 2365
G1-G2 0.29896497 0.64888535 0.04936306 0.002786624 0.0000000000 2512
G1-M 0.25000000 0.52450980 0.20588235 0.014705882 0.0049019608 204
G2-B1 0.10000000 0.30000000 0.50000000 0.000000000 0.1000000000 10
G2-B2 0.06741573 0.58426966 0.30337079 0.044943820 0.0000000000 89
G2-G1 0.34759867 0.60294817 0.04660010 0.002853067 0.0000000000 2103
G2-G2 0.12129573 0.77948089 0.09298999 0.005518087 0.0007153076 9786
G2-M 0.06004289 0.63187991 0.28162974 0.024303074 0.0021443888 1399
M-B1 0.00000000 0.33333333 0.33333333 0.222222222 0.1111111111 9
M-B2 0.00000000 0.23364486 0.52336449 0.214953271 0.0280373832 107
M-G1 0.31428571 0.54857143 0.13142857 0.005714286 0.0000000000 175
M-G2 0.06699929 0.65146115 0.25944405 0.019957234 0.0021382751 1403
M-M 0.02576336 0.36832061 0.53625954 0.065839695 0.0038167939 1048
[>] 2612 sequences, min/max length: 11/11
[>] computing prob., L=2, 35 distinct context(s)
[>] removing 11 context(s) containing missing values
[>] total time: 0.032 secs
G1 G2 M B2 B1 [n]
B1-B1 0.00000000 0.00000000 0.09818135 0.335028651 0.5667899946 7
B1-B2 0.00000000 0.12965429 0.00000000 0.553821776 0.3165239369 8
B1-G1 1.00000000 0.00000000 0.00000000 0.000000000 0.0000000000 1
B1-G2 0.00000000 1.00000000 0.00000000 0.000000000 0.0000000000 5
B1-M 0.00000000 0.20500861 0.53019242 0.264798970 0.0000000000 9
B2-B1 0.00000000 0.00000000 0.18658460 0.408762718 0.4046526865 12
B2-B2 0.00000000 0.08762715 0.49743688 0.304345521 0.1105904504 41
B2-G1 0.15269255 0.56929607 0.27801138 0.000000000 0.0000000000 9
B2-G2 0.06736504 0.50905666 0.35812437 0.065453926 0.0000000000 90
B2-M 0.02400026 0.24139846 0.58999910 0.119801242 0.0248009471 111
G1-B2 0.19126499 0.37109769 0.35074171 0.086895609 0.0000000000 14
G1-G1 0.58674034 0.38404366 0.02747219 0.001743816 0.0000000000 2365
G1-G2 0.29732333 0.65016030 0.04976264 0.002753734 0.0000000000 2512
G1-M 0.24415949 0.51633832 0.21334358 0.020040363 0.0061182509 204
G2-B1 0.04016650 0.30014000 0.61271478 0.000000000 0.0469787227 10
G2-B2 0.06616120 0.53516824 0.33857735 0.060093210 0.0000000000 89
G2-G1 0.34300931 0.60359596 0.05129085 0.002103880 0.0000000000 2103
G2-G2 0.11902674 0.77887958 0.09646083 0.004992888 0.0006399592 9786
G2-M 0.05424277 0.63001545 0.28661320 0.026701475 0.0024271068 1399
M-B1 0.00000000 0.32258387 0.26163294 0.262630848 0.1531523341 9
M-B2 0.00000000 0.21069475 0.54266810 0.214763222 0.0318739189 107
M-G1 0.35606381 0.51180852 0.12949028 0.002637382 0.0000000000 175
M-G2 0.06042470 0.65290600 0.26436511 0.019544672 0.0027595167 1403
M-M 0.02771553 0.36685274 0.53683261 0.064524580 0.0040745414 1048
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