positive log likelihood and BIC values from mCLUST analysis
Barry Hall wrote:
My question is with respect to mCLUST and the values of BIC and log
likelihood. The relevant part of my R script is:
######################### BEGIN MDS ANALYSIS #########################
#load data
data <- read.table("Ecoli33_Barry.dis", header = TRUE, row.names = 1)
#perform MDS Scaling
mds <- metaMDS(data, k = Dimensions, trymax = 20, autotransform =TRUE,
noshare = 0.1, wascores = TRUE, expand = TRUE, trace = FALSE, plot = FALSE,
old.wa = FALSE)
######################### BEGIN EM ANALYSIS #########################
#Use the points determined by MDS to perform EM clustering.
#Allow only the unconstrained models. Sometimes, constrained models mess
things up!
EMclusters <- mclustBIC(mds$points, G=Clusterrange, modelNames= c("VII",
"VVI", "VVV"), prior=NULL, control=emControl(),
initialization=list(hcPairs=NULL, subset=NULL, noise=NULL),
Vinv=NULL, warn=FALSE, x=NULL)
The input data are in the form of an N X N matrix of pairwise genetic
distances between strains. Those distances can either be the total
number of differences over X characters, or can be normalized to the
fraction
of characters that differ by dividing the number of differences by X.
When the data are the total number of differences (over 5866 characters),
the optimal model is VVV for which BIC is -944.1225 and the likelihood
is -452.8305. Two clusters are found
When the data are normalized to the fraction of characters that differ,
the optimal model is VII for which the BIC is 202.3095 and the likelihood
is 127.3786 . Four clusters are found.
There are several things that I do not understand:
(1) How can log likelihood be a positive number?
Because likelihoods are densities.
(2) Why should simply scaling the data change the BIC and log likelihood values?
Because likelihoods are densities. And/or because it is not finding the same optimum.
(3) Perhaps most important, why should scaling the data change the optimum model and the number of clusters?
Hmm, well... I don't really know. I wouldn't expect it if you are scaling equally in all directions. Perhaps in theory, it shouldn't change, but clustering models are notoriously unstable and sensitive to starting values. So maybe you are just seeing the effect of slightly changed convergence paths?
To explore the effects of scaling the data I further scaled it by multiplying the normalized caluesby 10, by 1E4 and by 1E14. The larger the values the more negative were the BIC and log likelihood values, and the optimum model and number of clusters changed with each change to the scale of the data (though in no obvious pattern).
From my perspective the normalized values would be preferable because
when there are missing data they could be normalized to the number of characters or which there are daa in both members of the pair. Any help with this would be greatly appreciated. Barry Hall
O__ ---- Peter Dalgaard ?ster Farimagsgade 5, Entr.B c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907