TEglm: Generalized linear model with nonlinear time predictor

In akcochrane/TEfits: Time-evolving model fits

Generalized linear model with nonlinear time predictor

Description

Fit a generalized linear model with time as a covariate, while estimating the shape of the nonlinear interpolation between starting and ending time. First resamples data with replacement 200 times, and each time estimates the best-shaped curve to interpolate between initial time-related offset and asymptotic time (i.e., rate at which effect of time saturates at zero). Then uses the mean estimated rate to transform the timeVar predictor into an exponentially decaying variable interpolating between initial time (time offset magnitude of 1) and arbitrarily large time values (time offset magnitude 0). Last uses this transformed time variable in a glm model (i.e., attempts to answer the question "how different was the start than the end?").

Usage

TEglm(
  formIn,
  dat,
  timeVar,
  family = gaussian,
  startingOffset = T,
  fixRate = NA
)

Arguments

formIn	model formula, as in glm()
dat	model data, as in glm()
timeVar	String. Indicates which model predictor is time (i.e., should be transformed)
family	passed to glm()
startingOffset	By default (if T) time is coded to start at 1 and saturate to 0. If startingOffset is F, time starts at 0 and saturates to 1. May assist in interpreting interactions with other variables, etc.
fixRate	If numeric, use this as a rate parameter [binary-log of 50 percent time constant] rather than estimating it (e.g., to improve reproducibility)

Details

Rate is parameterized as a time constant, or the amount of time it takes for half of change to occur. The value of rate has a lower bound of the .0333 quantile of the time variable (i.e., 87.5% of change happens in the first 10% of time) and an upper bound of the .333 quantile of the time variable (i.e., 87.5% of change takes 100% of the time to happen). These bounds provide some robustness in estimates of asympototic effects (i.e., "controlling for time") as well as initial effects (i.e., "time-related starting offset").

Mean estimated rate is calculated after trimming the upper 25% and lower 25% of bootstrapped rate estimates, for robustness to extremes in resampling.

Note

Although the time variable is transformed to exponentially decay toward zero, this does not necessarily mean that the model prediction involves an exponential change with time. The nonlinear change in time relates to the time-associated model coefficients.

The TEglm approach to including a nonlinear time function in regression is quite different than the TEfit approach. TEglm utilizes a point estimate for the rate parameter in order to coerce the model into a generalized linear format; TEfit simultaneously finds the best combination of rate, start, and asympote parameters. In effect, TEglm treats magnitude of change as being of theoretical interest, while TEfit treats the starting value, rate, and the asymptotic value as each being of theoretical interest.

See Also

TEglmem for mixed-effects extension of TEglm; TElm for a linear model version of TEglm

Examples

dat <- data.frame(trialNum = 1:200, resp = rbinom(200,1,log(11:210)/log(300)))
m_glm <- TEglm(resp ~ trialNum,dat,'trialNum',family=binomial)
summary(m_glm)
m_glm$rate # estimated half-of-change time constant
summary(m_glm$bootRate) # bootstrapped parameter distributions
cor(m_glm$bootRate) # bootstrapped parameter correlations

akcochrane/TEfits documentation built on June 12, 2025, 11:10 a.m.