Description Usage Arguments Details Value References Examples
fitFMM()
is used to fit FMM models. The only required argument to fit FMM models is the input data. By default it is assumed that time points, corresponding to a single time period, are equally spaced from 0 to 2*pi.
1 2 3 4 5 
vData 
A numeric vector containing the data to be fitted a FMM model. 
nPeriods 
A numeric value specifying the number of periods at which 
timePoints 
A numeric vector containing the time points at which each data of one single period is observed.
The default value is 
nback 
Number of FMM components to be fitted. Its default value is 1. 
betaRestrictions 
An integer vector of length 
omegaRestrictions 
An integer vector of length 
maxiter 
Maximum number of iterations for the backfitting algorithm. By default, it is set at

stopFunction 
Function to check the convergence criterion for the backfitting algorithm (see Details). 
lengthAlphaGrid 
Precision of the grid of alpha in the search of the best model. If it is increased, more possible values of alpha will be considered, resulting in an increasing in the computation time too. By default, it is established at 48 possible values of alpha, equally spaced between 0 and 2*pi. 
lengthOmegaGrid 
Precision of the grid of omega in the search of the best model. If it is increased, more possible values of omega will be considered, resulting in an increasing in the computation time too. By default it is established at 24 possible values of omega, equally spaced between 0 and 1 in a logarithmic way. 
numReps 
Number of times that the fitting is repeated. Each repetition starts with a brute force approximation, followed by an optimization method. This argument establishes the number of times that this pair of teps are performed. By default, it is established at 3 times. Note that each step is focused on around the previous parameters. 
showProgress 

showTime 

parallelize 

Data will be collected over nPeriods
periods. When nPeriods > 1
the fitting is carried out by averaging the data collected at each time point across all considered periods. The model is fitting to summarized data.
timePoints
is a n
length numeric vector where n
is the number of different time points per period.
Two functions are allowed as stopFunction
argument:
alwaysFalse()
, its default value, which returns FALSE
to force maxiter
iterations; and
R2(vData,pred,prevPred,difMax = 0.001)
, a function that computes the difference between the
explained variability in two consecutive iterations returning TRUE
when the convergence criterion is
reached. To calculate the explained variability difference, the data and the fitted values from the current
and previous iteration are passed as arguments vData
, pred
and prevPred
, respectively.
The convergence criterion is fulfilled when the explained variability difference is less than the argument
difMax
(by default 0.001).
An S4 object of class 'FMM'
with information about the fitted model. The object contains the following slots:
@timePoints 
The time points as specified by the input argument. It is a numeric vector containing the time points at which each data of one single period is observed. 
@data 
The data as specified by the input argument. It is a numeric vector containing the data to be fitted a FMM model. Data could be collected over multiple periods. 
@summarizedData 
When the data has more than one period, a numeric vector containing 
@nPeriods 
A numeric value containing the number of periods in data as specified by the input argument. 
@fittedValues 
A numeric vector of the fitted values by the FMM model. 
@M 
A numeric value of the estimated intercept parameter M. 
@A 
A numeric value or vector of the estimated FMM wave amplitude parameter(s) A. 
@alpha 
A numeric value or vector of the estimated FMM wave phase translation parameter(s) α. 
@beta 
A numeric value or vector of the estimated FMM wave skewness parameter(s) β. 
@omega 
A numeric value or vector of the estimated FMM wave kurtosis parameter(s) ω. 
@SSE 
A numeric value of the sum of the residual squares values. 
@R2 
A numeric vector specifying the explained variance by each of the fitted FMM components. 
@nIter 
A numeric value specifying the number of iterations of the fitting algorithm. 
Rueda C, Larriba Y, Peddada SD (2019). Frequency Modulated Moebius Model Accurately Predicts Rhythmic Signals in Biological and Physical Sciences. Scientific reports, 9 (1), 18701. https://www.nature.com/articles/s41598019545691
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28  # A monocomponent FMM model is fitted.
FMM_data < generateFMM(2,3,1.5,2.3,0.1,
from = 0, to = 2*pi, length.out = 100,
outvalues = TRUE,sigmaNoise = 0.3, plot=FALSE)
fit < fitFMM(FMM_data$y, lengthAlphaGrid=10,lengthOmegaGrid=10)
summary(fit)
# To see the differences between number of repetitions.
FMM_data < generateFMM(2,1,1.5,1.1,0.14,outvalues = TRUE, sigmaNoise = 0.15, plot=TRUE)
fit1 < fitFMM(FMM_data$y,lengthAlphaGrid=6,lengthOmegaGrid=3,numReps=1)
fit2 < fitFMM(FMM_data$y,lengthAlphaGrid=6,lengthOmegaGrid=3,numReps=6,
showProgress = FALSE) # suppress progress messages
getSSE(fit1)
getSSE(fit2)
# Finer resolution grid.
fit3 < fitFMM(FMM_data$y,lengthAlphaGrid=10,lengthOmegaGrid=5,numReps=1)
getSSE(fit3)
# Two component FMM model with beta and omega restricted
restFMM2w_data < generateFMM(M = 3, A = c(7,4),
alpha = c(0.5,5), beta = c(rep(3, 2)), omega = rep(0.05, 2),
from = 0, to = 2*pi, length.out = 100,
sigmaNoise = 0.3, plot = FALSE)
fit2w.rest < fitFMM(restFMM2w_data$y, nback = 2, maxiter = 1, numReps = 1,
lengthAlphaGrid = 15,lengthOmegaGrid = 10,
betaRestrictions = c(1,1), omegaRestrictions=c(1,1))
plotFMM(fit2w.rest, components = TRUE)

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