seqCompare {TraMineRextras}

BIC and Likelihood ratio test for comparing two sequence data

Description

The function seqCompare computes the likelihood ratio test (LRT) and Bayesian Information Criterion (BIC) for comparing two groups within each of a series of set. The functions seqBIC and seqLRT are aliases that return only the BIC or the LRT.

Usage

seqCompare(seqdata, seqdata2=NULL, group=NULL, set=NULL,
    s=100, seed=36963, stat="all", squared="LRTonly",
    weighted=TRUE, opt=NULL, BFopt=NULL, method, ...)

seqLRT(seqdata, seqdata2=NULL, group=NULL, set=NULL, s=100,
    seed=36963, squared="LRTonly", weighted=TRUE, opt=NULL,
    BFopt=NULL, method, ...)

seqBIC(seqdata, seqdata2=NULL, group=NULL, set=NULL, s=100,
    seed=36963, squared="LRTonly", weighted=TRUE, opt=NULL,
    BFopt=NULL, method, ...)

Arguments

seqdata

Either a state sequence object (stslist created with seqdef) or a list of state sequence objects, e.g., list(cohort1.seq,cohort2.seq,cohort3.seq).

seqdata2

Either a state sequence object (stslist or a list of state sequence objects. Must be NULL when group is not NULL. If not NULL, must be of same type than seqdata. See details.

group

Vector of length equal to number of sequences in seqdata. A dichotomous grouping variable. See details.

set

Vector of length equal to number of sequences in seqdata. Variable defining the sets. See details.

s

Integer. Default 100. The size of random samples of sequences. When 0, no sampling is done.

seed

Integer. Default 36963. Using the same seed number guarantees the same results each time. Set s=NULL if you don't want to set a seed. The random generator can be chosen with RNGkind.

stat

String. The requested statistics. One of "LRT", "BIC", or "all"

squared

Logical. Should squared distances be used? Can also be "LRTonly", in which case the distances to the centers are computed using non-squared distances and LRT is computed with squared distances.

weighted

Logical or String. Should weights be taken into account when available? Can also be "by.group", in which case weights are used and normalized to respect group sizes.

opt

Integer or NULL. Either 1 or 2. Computation option. When 1, the distance matrix is computed successively for each pair of samples of size s. When 2, the distances are computed only once for each pair of sets of observed sequences and the distances for the samples are extracted from that matrix. When NULL (default), 1 is chosen when the sum of sizes of the two groups is larger than 2*s and 2 otherwise.

BFopt

Integer or NULL. Either 1 or 2. Applies only when BIC is computed on multiple samples. When 1 the displayed Bayes Factor (BF) is the averaged BF. When 2, the displayed BF is obtained from the averaged BIC. When NULL both BFs are displayed.

method

String. Method for computing sequence distances. See documentation for seqdist. Additional arguments may be required depending on the method chosen.

...

Additional arguments passed to seqdist.

Details

The group and set arguments can only be used when seqdata is an stslist object (a state sequence object).

When seqdata and seqdata2 are both provided, the LRT and BIC statistics are computed for comparing these two sets. In that case both group and set should be left at their default NULL value.

When seqdata is a list of stslist objects, seqdata2 must be a list of the same number of stslist objects.

The default option squared="LRTonly" corresponds to the initial proposition of Liao and Fasang (2021). With that option, the distances to the virtual center are obtained from the pairwise non-squared dissimilarities and the resulting distances to the virtual center are squared when computing the LRT (which is in turn used to compute the BIC). With squared=FALSE, non-squared distances are used in both cases, and with squared=TRUE, squared distances are used in both cases.

The computation is based on the pairwise distances between the sequences. The opt argument permits to choose between two strategies. With opt=1, the matrix of distances is computed successively for each pair of samples of size s. When opt=2, the matrix of distances is computed once for the observed sequences and the distances for the samples are extracted from that matrix. Option 2 is often more efficient, especially for distances based on spells. It may be slower for methods such as OM or LCS when the number of observed sequences becomes large.

Value

The function seqLRT (and seqCompare with the default "LRT" stat value) outputs two variables, LRT and p.LRT.

LRT

This is the likelihood ratio test statistic for comparing the two groups.

p.LRT

This is the upper tail probability associated with the LRT.

The function seqBIC (and seqLRT with the "BIC" stat value) outputs two variables, BIC and BF.

BIC

This is the difference between two BICs for comparing the two groups.

BF

This is the Bayes factor associated with the BIC difference.

seqCompare with stat="all" outputs all four indicators.

Author(s)

Tim Liao and Gilbert Ritschard

References

Tim F. Liao & Anette E. Fasang (2021). "Comparing Groups of Life Course Sequences Using the Bayesian Information Criterion and the Likelihood Ratio Test.” Sociological Methodology, 55 (1), 44-85. doi:10.1177/0081175020959401.

Examples

## biofam data set
data(biofam)
biofam.lab <- c("Parent", "Left", "Married", "Left+Marr",
                "Child", "Left+Child", "Left+Marr+Child", "Divorced")
alph <- seqstatl(biofam[10:25])
## To illustrate, we use only a sample of 150 cases
set.seed(10)
biofam <- biofam[sample(nrow(biofam),150),]
biofam.seq <- seqdef(biofam, 10:25, alphabet=alph, labels=biofam.lab)

## Defining the grouping variable
lang <- as.vector(biofam[["plingu02"]])
lang[is.na(lang)] <- "unknown"
lang <- factor(lang)

## Chronogram by language group
seqdplot(biofam.seq, group=lang)

## Extracting the sequence subsets by language
lev <- levels(lang)
l <- length(lev)
seq.list <- list()
for (i in 1:l){
  seq.list[[i]] <- biofam.seq[lang==lev[i],]
}

seqCompare(list(seq.list[[1]]),list(seq.list[[2]]), stat="all", method="OM", sm="CONSTANT")
seqBIC(biofam.seq, group=biofam$sex, method="HAM")
seqLRT(biofam.seq, group=biofam$sex, set=lang, s=80, method="HAM")