| Title: | Analysis of Multiple Time Course Data |
|---|---|
| Description: | Contains general data structures and functions for longitudinal data with multiple variables, repeated measurements, and irregularly spaced time points. Also implements a shrinkage estimator of dynamical correlation and dynamical covariance. |
| Authors: | Rainer Opgen-Rhein and Korbinian Strimmer. |
| Maintainer: | Korbinian Strimmer <[email protected]> |
| License: | GPL (>= 3) |
| Version: | 1.1.13 |
| Built: | 2024-11-27 06:28:10 UTC |
| Source: | CRAN |
This package contains general data structures and functions for longitudinal data with multiple variables, repeated measurements, and irregularly spaced time points. It also implements a shrinkage estimator of dynamical correlation and dynamical covariance.
Rainer Opgen-Rhein and Korbinian Strimmer (https://strimmerlab.github.io/)
See website: https://strimmerlab.github.io/software/longitudinal/
The functions estimate dynamical correlation and covariance, and related quantities.
dyn.cor(x, lambda, verbose=TRUE) dyn.var(x, lambda.var, verbose=TRUE) dyn.cov(x, lambda, lambda.var, verbose=TRUE) dyn.invcor(x, lambda, verbose=TRUE) dyn.invcov(x, lambda, lambda.var, verbose=TRUE) dyn.pvar(x, lambda, lambda.var, verbose=TRUE) dyn.pcor(x, lambda, verbose=TRUE)dyn.cor(x, lambda, verbose=TRUE) dyn.var(x, lambda.var, verbose=TRUE) dyn.cov(x, lambda, lambda.var, verbose=TRUE) dyn.invcor(x, lambda, verbose=TRUE) dyn.invcov(x, lambda, lambda.var, verbose=TRUE) dyn.pvar(x, lambda, lambda.var, verbose=TRUE) dyn.pcor(x, lambda, verbose=TRUE)
x |
a data matrix |
lambda |
the correlation shrinkage intensity (range 0-1). If |
lambda.var |
the variance shrinkage intensity (range 0-1). If |
verbose |
report progress while computing (default: TRUE) |
The dynamical correlation and related quantities implemented here follow the definition of Opgen-Rhein and Strimmer (2006a,b). This approach is derived from a FDA perspective. Essentially, it takes account of the distances between the various time points by assigning weights to samples. If these weights are all equal the usual iid estimators are obtained.
For details about the analytic shrinkage procedure consult
Opgen-Rhein and Strimmer (2006b) and Sch\"afer and Strimmer (2005)
as well as the help page of cov.shrink.
dyn.cor returns the dynamical correlation matrix.
dyn.var returns the vector of dynamical variances.
dyn.cov returns the dynamical covariance matrix.
dyn.invcor returns the inverse dynamical correlation matrix.
dyn.invcov returns the inverse dynamical covariance matrix.
dyn.pvar returns the vector of partial dynamical variances.
dyn.pcor returns the partial dynamical correlation matrix.
Rainer Opgen-Rhein and Korbinian Strimmer (https://strimmerlab.github.io).
Opgen-Rhein, R., and K. Strimmer. 2006a. Inferring gene dependency networks from genomic longitudinal data: a functional data approach. REVSTAT 4:53-65.
Opgen-Rhein, R., and K. Strimmer. 2006b. Using regularized dynamic correlation to infer gene dependency networks from time-series microarray data. The 4th International Workshop on Computational Systems Biology, WCSB 2006 (June 12-13, 2006, Tampere, Finland).
Schaefer, J., and Strimmer, K. (2005). A shrinkage approach to large-scale covariance estimation and implications for functional genomics. Statist. Appl. Genet. Mol. Biol. 4:32. <DOI:10.2202/1544-6115.1175>
dyn.weights, cov.shrink, pcor.shrink
# load "longitudinal" library library("longitudinal") # load tcell data data(tcell) get.time.repeats(tcell.34) # dynamical partial correlation # (this takes into account of the unequal spacings between time points) dynpc <- dyn.pcor(tcell.34, lambda=0) # static partial correlation statpc <- pcor.shrink(tcell.34, lambda=0) # this is NOT the same sum((dynpc - statpc)^2)# load "longitudinal" library library("longitudinal") # load tcell data data(tcell) get.time.repeats(tcell.34) # dynamical partial correlation # (this takes into account of the unequal spacings between time points) dynpc <- dyn.pcor(tcell.34, lambda=0) # static partial correlation statpc <- pcor.shrink(tcell.34, lambda=0) # this is NOT the same sum((dynpc - statpc)^2)
time2weights computes weights corresponding to time points
dyn.weights computes these weights for a given longitudinal matrix.
dyn.moments computes means and variances for the variables in
a longitudinal object.
dyn.scale centers and standardizes a longitudinal matrix.
time2weights(t) dyn.weights(x) dyn.moments(x) dyn.scale(x, center=TRUE, scale=TRUE)time2weights(t) dyn.weights(x) dyn.moments(x) dyn.scale(x, center=TRUE, scale=TRUE)
t |
a vector with time points |
x |
a |
center |
logical value |
scale |
logical value |
The dynamical weights are computed assuming a linear spline - see Opgen-Rhein and Strimmer (2006a,b). The dynamical mean and variance etc. are then simply weighted versions of the usual empirical estimators.
A vector with weights (time2weights and dyn.weights),
a list containing the column means and variances (dyn.moments),
or a rescaled longitudinal matrix (dyn.scale).
Rainer Opgen-Rhein and Korbinian Strimmer (https://strimmerlab.github.io).
Opgen-Rhein, R., and K. Strimmer. 2006a. Inferring gene dependency networks from genomic longitudinal data: a functional data approach. REVSTAT 4:53-65.
Opgen-Rhein, R., and K. Strimmer. 2006b. Using regularized dynamic correlation to infer gene dependency networks from time-series microarray data. The 4th International Workshop on Computational Systems Biology, WCSB 2006 (June 12-13, 2006, Tampere, Finland).
# load "longitudinal" library library("longitudinal") # weights of for the data points in tcell data data(tcell) dyn.weights(tcell.34) # dynamical moments dyn.moments(tcell.34)# load "longitudinal" library library("longitudinal") # weights of for the data points in tcell data data(tcell) dyn.weights(tcell.34) # dynamical moments dyn.moments(tcell.34)
The data type longitudinal stores multiple time series data. It allows repeated
measurements, irregular sampling, and unequal temporal spacing of the time points.
as.longitudinal converts a matrix into a longitudinal object. The columns of the
input matrix are considered as individual variables (time series). The rows contain the
measurements in temporal order (for instance, rows 1-10 could contain 10 repeated measurements taken at
time point 1, rows 11-20 further 10 measurements taken at time point 2, and so on).
The dates for the time points can be specified with the argument times and need not
be equally spaced. With the argument repeats it is possible to specify the number
of measurements per time point (this may be different from time point to time point). In the resulting
longitudinal matrix object the row names will indicate both the time points and the
repetition number (e.g., "10-1", "10-2", "10-3", ..., "20-1", "20-2", "20-3", etc.).
is.longitudinal checks whether a matrix has the longitudinal attributes.
The functions summary, print, plot are the standard generic functions
adapted to longitudinal objects.
as.longitudinal(x, repeats=1, time) is.longitudinal(x) ## S3 method for class 'longitudinal' summary(object, ...) ## S3 method for class 'longitudinal' print(x, ...) ## S3 method for class 'longitudinal' plot(x, series=1, type=c("median", "mean"), autolayout=TRUE, ...)as.longitudinal(x, repeats=1, time) is.longitudinal(x) ## S3 method for class 'longitudinal' summary(object, ...) ## S3 method for class 'longitudinal' print(x, ...) ## S3 method for class 'longitudinal' plot(x, series=1, type=c("median", "mean"), autolayout=TRUE, ...)
x, object
|
Time series data, contained in a |
repeats |
Integer, or a vector of integers, that specifies the number of available measurements per time point. If only one number is given then it is assumed the time series is regularly sampled. If instead a vector is specified, then each time point may have a different number of samples. |
time |
A vector with the dates for the time points. If not specified, equally spaced time points 1, 2, 3, ... are assumed. |
series |
Number, or a vector of numbers, that indicates which time series (=variables and columns of x) are plotted. |
type |
Determines whether the plotted line corresponds to the mean or median value of the samples per time point (default: "median"). |
autolayout |
determine the number of columns and rows in the plot automatically in the display of multiple time series (default: TRUE). |
... |
Additional optional parameters |
as.longitudinal returns a longitudinal object.
is.longitudinal returns TRUE or false.
Korbinian Strimmer (https://strimmerlab.github.io).
# load "longitudinal" library library("longitudinal") # load data set data(tcell) is.longitudinal(tcell.34) attributes(tcell.34) tcell.34[,1:3] # how many samples and how many genes? dim(tcell.34) summary(tcell.34) # plot first nine time series plot(tcell.34, 1:9) ##### # an artificial example with repeated measurements, irregular sampling, and unequal spacing m <- matrix(rnorm(200), 50, 4) z <- as.longitudinal(m, repeats=c(10,5,5,10,20), time=c(2,8,9,15,16)) plot(z, 1:4)# load "longitudinal" library library("longitudinal") # load data set data(tcell) is.longitudinal(tcell.34) attributes(tcell.34) tcell.34[,1:3] # how many samples and how many genes? dim(tcell.34) summary(tcell.34) # plot first nine time series plot(tcell.34, 1:9) ##### # an artificial example with repeated measurements, irregular sampling, and unequal spacing m <- matrix(rnorm(200), 50, 4) z <- as.longitudinal(m, repeats=c(10,5,5,10,20), time=c(2,8,9,15,16)) plot(z, 1:4)
The above functions are all utility functions for longitudinal objects.
get.time.repeats returns the measurement design, i.e. the time points
and the number of repeats per time point.
is.equally.spaced checks whether the distances between subsequent time points
are all equal.
is.regularly.sampled checks whether the number of measurements are identical
across time points.
has.repeated.measurements checks whether any time point as been measured more
than once.
combine.longitudinal combines the measurements of two longitudinal objects.
These objects must have the same (number of) variables.
condense.longitudinal condenses the multiple measurements per time point using
an arbitrary function (e.g., mean, median, var).
get.time.repeats(x) is.equally.spaced(x) is.regularly.sampled(x) has.repeated.measurements(x) combine.longitudinal(x1, x2) condense.longitudinal(x, s, func=median)get.time.repeats(x) is.equally.spaced(x) is.regularly.sampled(x) has.repeated.measurements(x) combine.longitudinal(x1, x2) condense.longitudinal(x, s, func=median)
x, x1, x2
|
|
s |
An integer, or a vector of integers, that designate the set of time series (variables) to condense. |
func |
Univariate function used to summarize the multiple measurements per time point. |
get.time.repeats returns a list containing two vectors (time and repeats).
is.equally.spaced, is.regularly.sampled, and has.repeated.measurements
return either TRUE or FALSE.
combine.longitudinal returns a longitudinal object.
condense.longitudinal returns a matrix.
Korbinian Strimmer (https://strimmerlab.github.io).
# load "longitudinal" library library("longitudinal") # load tcell data set data(tcell) dim(tcell.34) is.longitudinal(tcell.34) summary(tcell.34) # information get.time.repeats(tcell.34) is.equally.spaced(tcell.34) is.regularly.sampled(tcell.34) has.repeated.measurements(tcell.34) # compute the mean value at each time point for the first two gene condense.longitudinal(tcell.34, 1:2, mean) # combine two time series m1 <- matrix(rnorm(100), 50, 2) m2 <- matrix(rnorm(100), 50, 2) z1 <- as.longitudinal(m1, repeats=c(10,5,5,10,20), time=c(2,8,9,15,16)) z2 <- as.longitudinal(m2, repeats=c(10,5,5,10,20), time=c(1,8,9,15,20)) z3 <- combine.longitudinal(z1,z2) summary(z3) get.time.repeats(z3) # compare with z1 and z2# load "longitudinal" library library("longitudinal") # load tcell data set data(tcell) dim(tcell.34) is.longitudinal(tcell.34) summary(tcell.34) # information get.time.repeats(tcell.34) is.equally.spaced(tcell.34) is.regularly.sampled(tcell.34) has.repeated.measurements(tcell.34) # compute the mean value at each time point for the first two gene condense.longitudinal(tcell.34, 1:2, mean) # combine two time series m1 <- matrix(rnorm(100), 50, 2) m2 <- matrix(rnorm(100), 50, 2) z1 <- as.longitudinal(m1, repeats=c(10,5,5,10,20), time=c(2,8,9,15,16)) z2 <- as.longitudinal(m2, repeats=c(10,5,5,10,20), time=c(1,8,9,15,20)) z3 <- combine.longitudinal(z1,z2) summary(z3) get.time.repeats(z3) # compare with z1 and z2
The data result from two experiments investigating the expression response of human T cells to PMA and ionomicin treatment.
The first data set (tcell.34) contains the temporal expression levels of 58 genes
for 10 unequally spaced time points. At each time point there are 34
separate measurements. The second data set (tcell.10) stems from
a related experiment considering
the same genes and identical time points, and contains
10 further measurements per time point. See Rangel et al. (2004) for more details.
data(tcell)data(tcell)
tcell.10 and tcell.34 are longitudinal objects,
i.e. matrices with 58 colums each and a number of extra attributes
(see longitudinal and longitudinal.util).
The vector tcell.gene.descriptions contains the
description of the functions of the 58 investigated genes.
This data is described in Rangel et al. (2004).
Rangel, C., Angus, J., Ghahramani, Z., Lioumi, M., Sotheran, E., Gaiba, A., Wild, D. L., and Falciani, F. (2004) Modeling T-cell activation using gene expression profiling and state-space models. Bioinformatics, 20, 1361–1372.
# load "longitudinal" library library("longitudinal") # load data sets data(tcell) # data set with 10 repeats dim(tcell.10) summary(tcell.10) is.longitudinal(tcell.10) is.regularly.sampled(tcell.10) is.equally.spaced(tcell.10) get.time.repeats(tcell.10) # data set with 34 repeats dim(tcell.34) summary(tcell.34) is.longitudinal(tcell.34) is.regularly.sampled(tcell.34) is.equally.spaced(tcell.34) get.time.repeats(tcell.34) # descriptions of the first nine genes tcell.gene.description[1:9] # plot the first nine time series plot(tcell.10, 1:9) plot(tcell.34, 1:9) # Rangel et al. use the combined data set tcell.44 <- combine.longitudinal(tcell.34, tcell.10) plot(tcell.44, 1:9)# load "longitudinal" library library("longitudinal") # load data sets data(tcell) # data set with 10 repeats dim(tcell.10) summary(tcell.10) is.longitudinal(tcell.10) is.regularly.sampled(tcell.10) is.equally.spaced(tcell.10) get.time.repeats(tcell.10) # data set with 34 repeats dim(tcell.34) summary(tcell.34) is.longitudinal(tcell.34) is.regularly.sampled(tcell.34) is.equally.spaced(tcell.34) get.time.repeats(tcell.34) # descriptions of the first nine genes tcell.gene.description[1:9] # plot the first nine time series plot(tcell.10, 1:9) plot(tcell.34, 1:9) # Rangel et al. use the combined data set tcell.44 <- combine.longitudinal(tcell.34, tcell.10) plot(tcell.44, 1:9)