We typically adopt some formative mathematical functions (usually called HDR functions or HRFs) to approximate the HDR based on the experimental data with the assumption of linearity and time-invariance (or stationarity) (Marrelec et al., 2003), and consider three common approaches to modeling the average HDR across trials. The first one presumes a fixed shape IRF (e.g., gamma variate or wave form in AFNI, Cohen, 1997; canonical IRF in SPM, FSL, and NIPY, Friston et al., 1998a). With this model-based or fixed-shape method (FSM), the regression coefficient or β associated with each condition in the individual subject analysis reflects the major HDR magnitude (e.g., percent signal change). The second approach makes no assumption about the IRF's shape and estimates it with a set of basis functions. The number of basis functions varies depending on the kernel set and the duration over which the response is being modeled. A common approach to this estimated-shape method (ESM) consists of using a set of equally-spaced TENT (piecewise linear) functions or linear splines, and each of the resulting regression coefficient represents an estimate of the response amplitude at some time after stimulus onset. Regardless of the kernel set, however, ESM generates the same number of regressors as the number of basis functions (e.g., m) per condition or task, resulting in m regression coefficients which need to be considered simultaneously at the group level. In addition to the aforementioned TENT basis set, options for ESM at the voxel level include cubic splines, Legendre polynomials, sines, or user-defined functions in AFNI, and finite impulse function (FIR) in SPM, FSL, and NIPY, inverse logit (Lindquist et al., 2009), and high-order B-splines (Degras and Lindquist, 2014). In addition, the python package PyHRF offers an ESM at the parcel level through the joint detection-estimation framework (Vincent et al., 2014). It is of note that one significant advantage of adopting basis functions such as TENT or cubic splines is the flexibility of creating regressors through piecewise interpolation when the stimulus onset times are not aligned with the TR grids (e.g., the acquisition time is shorter than TR if one wants to present “silent trials” as a control condition to speech or other auditory stimulus). The third approach lies between the two extremes of FSM and ESM, and uses a set of two or three basis functions (Friston et al., 1998b). In this adjusted-shape method (ASM), the first basis (canonical IRF) captures the major HDR shape, and the second basis, the time derivative of the canonical IRF, provides some flexibility in modeling the delay or time-to-peak, while the third basis, dispersion curve (derivative relative to the dispersion parameter in the canonical IRF), allows the peak duration to vary.