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

## 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

 `1` ```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

 ``` 1 2 3 4 5 6 7 8 9 10``` ```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 ```

rties documentation built on July 2, 2020, 4:11 a.m.