npEMindrep: Nonparametric EM-like Algorithm for Mixtures of Independent Repeated Measurements

Description

Returns nonparametric EM algorithm output (Benaglia et al, 2007) for mixtures of multivariate (repeated measures) data where the coordinates of a row (case) in the data matrix are assumed to be independent, conditional on the mixture component (subpopulation) from which they are drawn.

Usage

npEMindrep(x, mu0, blockid = 1:ncol(x), bw=bw.nrd0(as.matrix(x)), h=bw,
           eps=1e-8, maxiter = 100, stochastic = FALSE, verb = TRUE)

Arguments

An $n\times r$ matrix of data. Each of the $n$ rows is a case, and each case has $r$ repeated measurements. These measurements are assumed to be conditionally independent, conditional on the mixture component (subpopulation) from which the case i

mu0

Either an $m\times r$ matrix specifying the initial centers for the kmeans function, or an integer $m$ specifying the number of initial centers, which are then choosen randomly in

blockid

A vector of length $r$ identifying coordinates (columns of x) that are assumed to be identically distributed (i.e., in the same block). For instance, the default has all distinct elements, indicating that no two coordinates are ass

Bandwidth for density estimation, equal to the standard deviation of the kernel density.

Alternative way to specify the bandwidth, to provide backward compatibility.

eps

Tolerance limit for declaring algorithm convergence. Convergence is declared whenever the maximum change in any coordinate of the lambda vector (of mixing proportion estimates) does not exceed eps.

maxiter

The maximum number of iterations allowed, for both stochastic and non-stochastic versions; for non-stochastic algorithms (stochastic = FALSE), convergence may be declared before maxiter iterations (see eps ab

stochastic

Flag, if FALSE (the default), runs the non-stochastic version of the npEM algorithm, as in Benaglia et al (2007). Set to TRUE to run a stochastic version which simulates the posteriors at each iteration, and runs for maxiter

verb

If TRUE, print updates for every iteration of the algorithm as it runs

Value

npEMindrep returns a list of class npEM with the following items:
dataThe raw data (an $n\times r$ matrix).
posteriorsAn $n\times m$ matrix of posterior probabilities for observation. If stochastic = TRUE, this matrix is computed from an average over the maxiter iterations.
bandwidthSame as the bw input argument, returned because this information is needed by any method that produces density estimates from the output.
blockidSame as the blockid input argument, but recoded to have positive integer values. Also needed by any method that produces density estimates from the output.
lambdaThe sequence of mixing proportions over iterations.
lambdahatThe final mixing proportions if stochastic = FALSE, or the average mixing proportions if stochastic = TRUE.

References

\itemBordes, L., Chauveau, D., and Vandekerkhove, P. (2007), An EM algorithm for a semiparametric mixture model, Computational Statistics and Data Analysis, 51: 5429-5443.

\itemBenaglia, T., Chauveau, D., and Hunter, D. R. (2007), An EM-like algorithm for semi- and non-parametric estimation in multivariate mixtures, Penn State Department of Statistics Technical Report 07-01.

Examples

Run this code

## Examine and plot water-level task data set.

## First, try a 3-component solution where no two coordinates are
## assumed i.d.
data(Waterdata)
a <- npEMindrep(Waterdata, mu0=3, bw=4) # Assume indep but not iid
plot(a) # This produces 8 plots, one for each coordinate

## Next, same thing but pairing clock angles that are directly opposite one
## another (1:00 with 7:00, 2:00 with 8:00, etc.)
b <- npEMindrep(Waterdata, mu0=3, blockid=c(4,3,2,1,3,4,1,2), bw=4) # iid in pairs
plot(b) # Now only 4 plots, one for each block

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