estDerivs: Estimates first and second derivatives of an oberved state...
In rties: Modeling Interpersonal Dynamics

Description Usage Arguments Value Examples

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.

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

`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

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.

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