Movatterモバイル変換

Recent changes to the fda package

Changes in fda version 6.0.5 (2022-07-02)

• Landmark registration using functionlandmarkreg can no longer be done by usingfunctionsmooth.basis instead of functionsmooth.morph. The warping function must be strictly monotonic, and we have found that usingsmooth.basis too often violates this monotonicity constraint. Functionsmooth.morph ensures monotonicity and in most in most applications takes negligible computer time to do so.

• FunctionpcaPACE carries out a functional PCA with regularization from the estimate of the covariance surface.FunctionscoresPACE estimates functional Principal Component scores through Conditional Expectation (PACE).

• Smooth.morph estimates a warping function when the target of the fit by registration is a functional data object. This function has been extended to work when the target for the fit and the fitted functions have different ranges or domains. The warping also maps each boundary into its target boundary. Similarlylandmarkreg uses a small number of discrete values to define the warping, and how has an extra argument,x0lim, that defines the range of the target domain. Since it defaults to the range of the warped domain, it continues to work if not used and the domains have the same range.

• This function works with multinomial data thatevolve over a continuum, such as the value of a latent variable in psychometrics. A multinomial observation consists of a set of probabilities that are in the open interval (0,1) and sum to one.The surprisal value S(P_m) corresponding to a probabity P_m is -log_M(P_m), where M is the number of probabities and is the base ofthe logarithm. The inverse function is P(S_m) = M^(-S_m).

  Surprisal is also known as "self-information" in the field of informationtheory. It has the characteristics of a true metric: Surprisals can be added, multiplied by positive numbers, and the difference between two surprisal values mean the same thing everywhere along the information.continuum. The unit of the metric is called the "M-bit", thegeneralization of the familiar "bit" or "2-bit" for binary data.The metric property is not possessed by so-called latent variables because they can be arbitrarily monotonically transformed.

  Smoothing surprisal data is much easier and faster than smoothingprobabilities since surprisal values are only constrained to be non-negative and are otherwise unbounded.

  The functionsmooth.surp estimates smooth curves which fit a set of surprisal values and which also satisfy the constraint that their probability versions sum to one.

• Many functions in the fda package optimize a fitting criterioniteratively. Functionsmooth.monotone is an example.The optimisation algorithm used was a rather early design,and many improvements have since been made. In most of ouroptimisations, we have switched to the algorithm to be foundin Press, Teukolsky, Vetterling and Flannery Numerical Recipesvolumes. We have noticed a bit improvement in speed, are in the process of upgrading all of our optimisers using this approach.