estDerivs {rties}

Estimates first and second derivatives of an oberved state variable

Description

This function makes use of 2 functions written by Steven Boker, "gllaWMatrix" and "gllaEmbed" which are available on his website, http://people.virginia.edu/~smb3u/. It fits a coupled oscillator model for each dyad at different combinations of the input parameters (tau, embeds) and returns the input values and period of oscillation that maximize the R^2 for each dyad. It also estimates first and second derivatives of the observed state variable for each person at the input values that maximize the R^2 for that dyad and returns a dataframe that contains them.

Usage

estDerivs(prepData, taus, embeds, delta, idConvention)

Arguments

prepData

A dataframe that was produced with the "dataPrep" function.

taus

A vector containing the values of tau to use. Tau indicates the number of time points to lag in the lagged data matrix (see Boker, S.M., Deboeck, P.R., Edler, C., & Keel, P.K. (2010). Generalized local linear approximation of derivatives from time series. In S.M. Chow & E. Ferrer (Eds.), Statistical Methods for Modeling Human Dynamics: An Interdisciplinary Dialogue (pp. 161-178). New York, NY: Taylor & Francis Group). The first derivative is estimated as the mean of the two adjacent slopes across that number of lags, e.g., if tau = 2 then the estimate of the first derivative at time = t is based on the mean of the slopes left and right of time t across 2 observations each. The second derivative is the difference in the two slopes with respect to time. Tau = 1 is sensitive to noise and increasing its value acts as smoothing.

embeds

A vector containing the values of embeds to use. Embeds indicates the number of columns in the lagged data matrix. The minimum = 3 for 2nd order derivatives and higher values increase smoothing.

delta

A value indicating the inter-observation interval. For example, if delta = 2, then every second observation is used in the estimation process.

idConvention

The value that was added to the dist1 ID number to get the dist2 ID number

Value

The function returns a list including: 1) "data" which is a dataframe containing first and second derivative estimates of an observed state variable, and 2) "fitTable" which shows the maximal R^2 achieved for each dyad for a coupled oscillator model, along with the associated tau, embed and estimated period of oscillation.

Examples

data <- rties_ExampleDataShort
newData <- dataPrep(basedata=data, dyadId="couple", personId="person", 
obs_name="dial", dist_name="female", time_name="time")
taus <-c(2,3)
embeds <- c(3,4)
delta <- 1
derivs <- estDerivs(prepData=newData, taus=taus, embeds=embeds, delta=delta, idConvention=500)
head(derivs$fitTable)
summary(derivs$fitTable[ ,4]) # summary of R-square
summary(derivs$fitTable[ ,5]) # summary of period of oscillation